Christian Bohr. Discoverer of Homotropic and Heterotopic Allostery

ABSTRACT

This essay recounts and revisits the scientific contributions of Christian Bohr, highlighting his pivotal role in discovering allostery about 120 years ago. Bohr's meticulous experimentation led to identifying two distinct forms of allostery: homotropic (single‐ligand) and heterotropic (multi‐ligand), the latter widely recognized as the Bohr Effect. His insights into oxygen binding to hemoglobin, as also modulated by carbon dioxide presence, laid the foundation for part of modern pharmacological advancements. Today, allosteric principles drive drug development, improving specificity and potentially minimizing adverse effects, with numerous allosteric modulators emerging in pharmaceutical pipelines. The treatise spans 13 chapters and an appendix with definitions on allosteric terms. It begins with Bohr's background, laboratory environment, and pivotal experiments in 1903 that demonstrated allosteric mechanisms. It traces Bohr's scientific journey—from medical training to his professorship in Copenhagen—and his collaborative research with Karl Hasselbalch and August Krogh. The work situates Bohr within the broader historical context, examining influence of earlier, 19th‐century, and later physicochemical and physiological thoughts on his discoveries. Further chapters discuss dose‐response relationships, including Hüfner's hyperbolic equation and Henri's enzyme kinetics, parallel to Bohr's findings. Bohr's S‐shaped oxygen‐hemoglobin binding curve, analyzed in 1904, marked a critical advancement in understanding homotropic allostery. Subsequent developments, such as Hill's equation and the Monod‐Wyman‐Changeux model, settled both types of allostery description. My study concludes with Bohr's abandonment in 1910 of his secretion theory and his legacy. Despite his early death in 1911, Bohr's contributions remain fundamental, warranting revitalized recognition for his discovery of allostery.

To understand Nature, Karl J Niklas in the introduction to his book “Plant Physiology” wrote: “… if nothing in biology makes any sense except in the light of evolution, then nothing in evolutionary biology makes sense if not illuminated by studying plant biology… This is a blue planet, but it is a green world.” (Niklas 2016, p. vii) [1]

Long ago, Francis Crick is supposed to have remarked: “Hemoglobin has a ‘bore’ effect.” (Cui & Karplus 2008, p. 1304) [2]

1. Introduction

The main aim of this paper was to recount and rewrite the story and scientific life of Christian Bohr and document that it was Bohr, in particular, who 120 years ago discovered the important bioregulatory phenomenon we call allostery today. In fact, Bohr discovered both one form of homotropic—single‐type ligand—allostery and one form of heterotropic—multi‐type ligand—allostery. The latter is also known as the Bohr Effect. Bohr's early discoveries of allostery came about with his meticulous experimentation and reflections on oxygen binding to hemoglobin and that this binding was lowered in the presence of carbon dioxide. Presently, the allosteric principle is a major driver in developing new drugs as “test‐target allosters” and medicine for more selective treatments and reduced adverse effects. There is a steady stream and rise of potential allosteric pills in the pharmaceutical pipelines, such as positive allosteric modulators, PAMs, and negative allosteric modulators, NAMs. A definition of allostery, along with some of its derivative concepts, is provided in an appendix.

My story is divided into 13 chapters with sections and some with subsections. The first chapter is this Introduction which summarizes the content of the other chapters. Chapter 2 covers Bohr's background and laboratory facilities to set the stage for Bohr's cumulated wishes for additional investigations after 1900. Then a jump forward in time in Chapter 3 relaying the implementation of Bohr's wish for additional studies on gas binding to hemoglobin and performed by crucial experiments in 1903 with involvement and help from colleagues. Bohr requested the experiments, analyzed the results, and arranged for their publication, documenting the two mentioned aspects of allostery in 1904. After that, Chapter 4 describes Bohr's family and youth over the period from 1883 till 1903, divided into three periods. The first period describes Bohr's scientific life with medical training and becoming a Doctor of Science in Copenhagen. Next period covers visits to Ludwig's Leipzig institution in Germany, Neue Physiologische Anstalt, and the third period outlines his settlement as professor of physiology in Copenhagen, and his growing experience and insight obtained from further studies with oxygen and carbon dioxide binding to hemoglobin until the turn of the 19th century. This accumulated knowledge was part of the prerequisites for Bohr's wish to have the crucial experiments done, for his exchanges and collaborations with younger colleagues, especially Karl Hasselbalch and August Krogh, and for his teachings. There is as well a mention of Bohr's scientific view on physiology in his last publication shortly before his early death in 1911.

Starting some four generations before Bohr, the next, Chapter 5, is on the early natural sciences and some of the physiology scientists in Europe, surrounded by ideas of enlightenment and moods of natural philosophy in the German romanticism and its vitalist views about life's expression as influenced and challenged by a quest after empirical physicochemical experimentation and insight. This led up to Bohr's time, on how the zeitgeist affected him, and beyond. Thus, Bohr was deeply engaged in his predecessors' vitalist ideas but certainly not a vitalist.

A major part follows with three chapters related to discoveries of hyperbolic dose‐responses. First a description in Chapter 6's Section 6.2 of Gustav Hüfner's discovery of a mathematical hyperbolic relation for the chemical binding of gases to hemoglobin already in 1890s as based on the law of mass action. ¹ In the following years, Hüfner's discovery yielded a protracted acceptance, partly due to his wrong analysis of experimental results by the hyperbolic relation. For comparison, this is followed in Section 6.3 with the development of the simple hyperbolic relationship for enzyme function initiated by Adrian Brown and Victor Henri, approximately a decade later. Here Henri conjured the well‐known hyperbolic Michaelis–Menten expression and formulated an equation for the observed negative interference with the enzyme's activity by its own yielded product, “product inhibition.” This was one early form of a possible negative heterotropic allostery other than the Bohr Effect. Chapter 7 describes more details on the development and reception of Hüfner's rectangular hyperbola equation and the lives of Victor Henri, Maude Menten, and Leonor Michaelis. Chapter 8, describes Bohr's experimental finding in 1885 of a pharmacodynamic hyperbolic dose–response for oxygen binding to hemoglobin. This is the first clear experimental documentation in natural sciences of this fundamental process for ligand‐acceptor binding in general. Next, Chapter 9 is a switch to allostery with Bohr's discovery in 1904 of an S‐formed oxygen‐hemoglobin binding, positive cooperativity, and his analyses of the phenomenon, later aka positive homotropic allostery. ² More detailed, Chapter 9 describes Bohr's attempt on a formulation of homotropic allostery and additionally a description of Bohr's unfortunate aversion against using Hüfner's hyperbolic theory as a starting point for his own theoretical development. Due to causes relayed, Bohr sadly refrained from a hyperbolic description of the observed hyperbolic binding and rather invented his own non‐hyperbolic formulation for homotropic allostery. In Chapter 10, 6 years after Bohr's discovery of allostery, a more useful description of one‐type ligand (homotropic) binding took off with Hill's 1910 hyperbolic and multi‐binding equation. The Hill equation was a reasonable try for an allosteric model with its included generalized exponentiation of the concentration for a single type of ligand, namely oxygen. Fifty‐five years later, this equation resulted in the famous Monod–Wyman–Changeux allosteric model (MWC model) describing both homotropic and heterotropic allostery. Chapter 10 ends with a brief mention of the modern day simple homotropic and heterotropic allosteric two‐state models as well as other much more complex models. The history and definitions of homotropic and heterotropic allostery can be found in Appendix B.2, B.3, B.4, B.5, B.5.1, B.5.2, B.6 and B.8.

Bohr's other major discovery of allostery, the Bohr Effect, is presented in Chapter 11. It is a type of negative heterotropic cooperativity, analyzed by Bohr based on two distant binding sites, and therefore later recognized as “heterotropic allostery.” ³ Heterotropic allostery is when two different ligands interfere with each other's binding or function from a remote or non‐overlapping binding site. There has been some debate about who should be recognized as the discoverer of this type of bioregulation. Based on a repository of relevant literature and a referred letter from Krogh to his mother Mimi on January 3, 1904, it is revealed that Christian Bohr indeed was the pioneer of both homotropic and heterotropic allostery. Simultaneously, Adrian Brown demonstrated, and Victor Henri equated product inhibition as a form of heterotropic cooperativity. Eighty years later in 1983, part of their product inhibition turned out to be caused by heterotropic allostery. By ensuing analysis of molecular structure and simulation of function in remote or partially overlapping allosteric pockets, researchers are now‐a‐days capable of constructing conceivable both potentially positive and negative allosteric modulator drugs—“targeted test allosters.” Based on Bohr as the first to discover both types of allostery, it seems justified to name an auditorium in Denmark after him.

A final part begins with Chapter 12, which covers the story about how Bohr reached his “secretion theory,” and the cause of events that led to a fierce debate between several respiratory physiologists. In this debate Bohr and John Scott Haldane maintained that part of the gas exchange in lungs was achieved by an “active principle” or “spezifiche Tätigkeit,” whereas many others, including Pflüger, Hüfner, the Kroghs, and Barcroft favored pure diffusion. In the end, it turned out that both August Krogh and Bohr were wrong and right about a specific, cellular activity for additional oxygen uptake in lungs.

The last chapter, Chapter 13, in the final part of the story contains a view on the aftermath of Bohr's “spezifiche Tätigkeit” in form of capillary dilation, where Krogh gets a well‐deserved Nobel Prize for his discovery of the recruitment of capillaries in solving the necessary altered conditions during work. This was predicted but missed in its correct interpretation by Bohr. I argued that, had Bohr stayed alive he might also have obtained a Nobel Prize. Failures by scientists are discussed as agreeable, but Bohr, due to pride, seems to have crossed a red line into unacceptable behavior between scientists. No matter what, in the author's view, Christian Bohr's discovery of allostery is more than just a milestone.

Chapter 13 concludes with a summary of Bohr's legacy and death, followed by final conclusions. Bohr's early death led to a notable number of obituaries, proving Bohr's importance as a researcher and mentor at the time. Nevertheless, today Bohr's mistakes seem to dominate judgment by senses that steers the knowledge of his significant efforts and allosteric discoveries toward oblivion. The treatise tries to tilt this trend.

2. Bohr, a Leading Physiologist, His Lab Work, and Panum's Institute

2.1. Bohr on Centerstage for the Discovery of Allostery

For a historical view on how the allosteric behavior of oxygen binding to hemoglobin was discovered and who discovered the allosteric effects, this paper contains time periods leading up to the discovery and several aspects on persons related to the issue, with a focus centered on Christian Bohr's contributions and followed by later events.

2.2. Christian Bohr, a Leading Respiratory Physiologist

No doubt, Christian Bohr was both an eminent experimentalist and mathematician, as well as a capable instrument maker and theorist with the ability to set up suggestive hypotheses and equations to analytically simulate observed physiological phenomena in relation to lung function and gas exchange. In Chapter 2, I present events closely connected with discovery of the first examples of both homotropic and heterotropic allostery in 1903, along with the subsequent sequence of related papers published during 1904 by Christian Bohr, some together with colleagues. To set the stage, I start with some selected information on Bohr's lab work in Panum's Physiological Institution in Copenhagen.

2.3. Brief on Bohr's Lab Work

Through visits in Leipzig and work in Copenhagen, from 1883 until the turn of the century, Bohr accumulated substantial experiences and insights about O₂ and CO₂ binding to hemoglobin, both in crystal form and in whole blood, and as well on phenomena related to respiration in general. Thus, Bohr was a leading figure in European respiratory physiology circles just before the turn of the 19th century (Bohr 1885, 1887, 1891, 1892b, 1898; Perkins 1964; Astrup and Severinghaus 1985, 1986) [3, 4, 5, 6, 7, 8, 9, 10, 11].

2.4. Panum's Physiological Institution

Back in 1867, the Physiological Institution hosting Bohr's scientific projects in Copenhagen from 1886 until 1911 was built and laboratories installed on the request and guidance by Bohr's mentor, Peter Ludvig Panum (1820–1885). The Institution was located centrally in Copenhagen behind the College of Surgeons' building in Bredgade 62, named Norgesgade 46 before 1869 (Panum 1874; Pais 1991, p. 46; Christensen 2020, Ch. 11) [12, 13, 14]. The College of Surgeons' building, designed by architect Peter Meyn and facing Bredgade, was built in 1785 and served as home for Panum from about 1865 till his death in 1885 and then for the Bohr family from 1886 until 1911, Figure 1a,c (Moe 1988; Pais 1991; Christensen 2020) [13, 14, 15].

FIGURE 1.

(a) The Royal Surgical Academy building in Copenhagen, seen from the back. The “little yellow house” in front was raised in 1792 for small‐pox inoculation and from the 1830s served as a laundry for “Fødselsesstiftelsen” (The Maternity Hospital), which was positioned behind the viewer. In front, to the left, are drying racks. Painting by Wilhelm Bendz, 1830, belongs to and is presently in storage at Copenhagen Museum. Photo by author from Moe 1988, p. 10 [15]. Reproduced with permission. (b) Titkensgård, building in the middle, Bredgade 60. Entrances through the gateways for the Royal Surgical Academy building at the left, and the Fredericiagade 18 building to the right, with its gateway entrance shown at the far right, refer also to panel 1c. Picture by author. (c) Diagram of buildings surrounding the yard of the former Royal Surgical Academy right after acquisition of Titkensgård, Bredgade 60, and Fredericiagade 18 by Copenhagen's University in 1897, with the Physiological Institute erected in 1867. From 2004 buildings house Medical Museion. The diagram is produced shortly after 1897, still documenting the “light house” (Maskinhus 1888), in which direct current was generated especially for microscopy work. The “Maskinhus” and corner house indicated by “Toiletter,” “Høns,” “Brænde & Redskaber,” and “Duer” does not exist anymore. Copy from Moe 1988 [15], fig. 2.76. (d) Panum's Physiological Institute. In function from 1867, during Bohr's time, and on till about 1928. Until recently, the building functioned as a depository. The building still belongs to Museion and funding has now been obtained for its renovation, to be refurbished with facilities, and connected to the rest of Museion. Their physical relation is shown in panel 1c. Copy from SA Gammeltoft, BfL 1951 [16].

With Bohr's organizing talent, he arranged an early installment of electricity (1888), replacing the normal dim gas lightning for microscopic work, and an expansion of the institution with additional building facilities from 1897, Titkens Gaard and Fredericiagade 18, Figure 1b,c. Together with his engagement in teaching medical students, this provided for a major lift of physiological sciences in Copenhagen. Until 1897, the public entrance to the laboratories was through a gateway facing the street and afterward it was around the corner from Fredericiagade 18, Figure 1c, Moe 1988 [15]. ⁴

Among many collaborators, two 25‐year‐old assistants joined Bohr's physiological laboratories and teaching facilities in Copenhagen: Karl Albert Hasselbalch (1874–1962) in 1898 and Schack August Steenberg Krogh (1874–1949) in 1899. Hasselbalch obtained his Ph.D.s in 1899 and Krogh his in 1903 at Bohr's laboratory [17, 18]. Krogh's Danish thesis was translated and published in English half a year later [19].

3. How and Who Discovered Allostery

3.1. It Was the Physiologist Christan Bohr

One may ask: who was the first to discover and to try to disentangle and describe homotropic and heterotropic allostery? The short answer: it was the physiologist Christan Bohr. Father to Jenny, Niels, and Harald, Christian Bohr together with two gifted assistants, Karl Hasselbalch and August Krogh, performed experiments in 1903 creating a surface plot of oxygen binding to hemoglobin in whole blood. By systematically cross‐varying the pressures of both O₂ and CO₂, and by Bohr's analyses of the results based on theories with two different binding sites for both gases, they simultaneously discovered and documented allosteric homotropic effects for oxygen binding to hemoglobin and allosteric heterotropic effects by carbon dioxide interfering with the binding of oxygen (Bohr 1904a, b; Bohr et al. 1904a, b) [20, 21, 22, 23].

3.2. Challenging Experiments

The experiments and their observed effects in 1903 challenged both Gustav von Hüfner results and Bohr's own earlier observations and interpretations of O₂/CO₂ binding to hemoglobin. For one, due to Hüfner's massaging of Bohr's data as well as to fit his own data to his hyperbolic theory, repeated in 1901 [24, 25], and second, due to Hüfner's critique on the validity of Bohr's O₂ binding data from 1888 and 1892, Bohr felt uneasy with Hüfner's postulates of oxygen binding following a simple hyperbolic relationship, which he suspected not to be correct as based on his own findings [3, 5, 7, 8, 26]. With experiments in 1903, Bohr decisively proved Hüfner wrong [23]. Additionally, Bohr was provoked by a supposedly wrong interpretation by Werigo of Bohr's data on how O₂ in the lungs might increase evacuation of CO₂ in a reciprocal manner between the two gases [27]. Although Werigo turned out to be right on the supposed reciprocal effects between O₂ and CO₂ on binding to hemoglobin [28], based on earlier experiments by Bohr, Bohr and colleagues were unable to find a significant effect of O₂ on CO₂ binding and therefore refuted such a reciprocal effect [22].

3.3. Experiments Requested by Bohr

In late 1902 or early 1903, in order to solve challenges with results from earlier gas binding experiments and their interpretations, Christian Bohr asked his two assistants Krogh and Hasselbalch to conduct new studies both on binding of oxygen to hemoglobin and on his earlier observed interaction between O₂ and CO₂ at their mutual binding to hemoglobin in blood while the pressures of both gases were altered systematically. Bohr's wish for new experiments was based on his understanding prior to 1903 of a complex binding of oxygen, most likely to four different forms of hemoglobin [7, 29] and through his preliminary insight with interactions between O₂ and CO₂ on binding to hemoglobin [7, 8, 30]. Bohr's motivation, as mentioned, was probably triggered by Hüfner's claims as well by Werigo's mistaken interpretation of Bohr's data. Hence, from March 10th until May 29th, 1903, Krogh performed nine experiments with blood samples and gas analyses on dog blood, and a few additional experiments on horse blood with help from Hasselbalch. The results turned out to be the first firm discovery of direct homotropic and heterotropic allostery. “Direct” indicates that the complex binding was elicited between neighboring sites in a single binding macromolecule, here hemoglobin, or as suggested, by different forms of the hemoglobin molecule in solution.

3.4. Krogh's Involvement in the Bohr Effect

In a letter to his mother Mimi from February 1903, Krogh describes how he is preparing for additional experiments on gas binding. Sentences from that letter appear as a smoking gun in solving a long‐standing controversy about who discovered the “Bohr Effect.” The “smoking gun” is further detailed below in Subsections 11.7.1 till 11.7.3, with Subsection 11.7.1 entitled: “A triple‐barrel smoking gun.”

3.5. 1903. Krogh Is Busy

Shortly after collecting data in 1903, Krogh received confirmation of acceptance for his dissertation for a Ph.D. degree and was busy with different chores including preparation for his thesis defense, which he successfully undertook on Saturday, October 10, 1903 [18]. One of the chores that summer was a bike trip to Funen, where Krogh learned an important lesson about high nitrogen–low oxygen gas content leaving well walls during atmospheric low‐pressure periods as a cause of death among well workers (Schmidt‐Nielsen 1995, pp. 56–57, 1997, pp. 76–77) [31, 32]. Also, some of that summer was spent with the Bohr family at their vacation residence Nærumgaard, Figure 2a, including sailing trips at Furesø lake with water samples for analysis of their CO₂ content. In late autumn, he started handling data for two papers on results from a Greenland trip in 1902 and including results from the Furesø excursions (Schmidt‐Nielsen 1995, p. 58 and pp. 261–262) [32]. After the dissertation defense, Krogh was also busy translating his thesis into a 90‐page document in English [33].

FIGURE 2.

(a) Summer house for the Adler family, ‘Nærumgaard’. Lead as an orphanage by Jenny Adler, Christian Bohr's mother‐in‐law, and summer refuge for the Christian Bohr family. After Jenny's death in 1902, donated to Copenhagen municipality and continuously run by Ellen's elder sister Hanna Adler as an orphanage and a summer refuge for the family. From 1906 it became an orphanage (https://kbhbilleder.dk/kbh‐museum/49503). Picture by Peter Elfelt ca. 1905. Insert: The premise consisted of 30 acres, ca 4.5 ha farm country and 7 ha park, forest and bogs, less than 20 km north of Copenhagen. See H Trier in “Historiske Meddelelser om København” 1919. (b) Portrait of Jenny Raphael Adler with her daughters Ellen, Hanna and Emma. Jenny's three sons and husband are in paintings on the back wall. Arrow pointing at Ellen. By Johan Julius Exner (1825–1910), date 1868. At the Hirschsprung Collection, Copenhagen from 2019. Reproduced with permission. (c) Busts of Adler daughters Ellen (6 years, left) and Hanna (8 years, right). Plaster by HW Bissen. Date 1866. At National Gallery of Denmark (SMK). (d) Ellen Adler ca. 1881 (left) and Ellen and Christian Bohr, newlywed 1881 (right). N Bohr Archive. (e) Left. Ellen Bohr with kids, Jenny (left), Harald (on lab) and Niels (at right). Photo ca 1888–1889. Right. Christian Bohr (at right) with sons Niels and Harald, 1903. In the year 1903 Christian Bohr was co‐founder of a soccer club, “Akademisk Boldklub,” at which he often joined with his son. N Bohr Archive. (f) Ellen Adler Bohr and her son Niels Bohr (1902). N. Bohr archive, courtesy AIP Emilio Segrè Visual Archives.

3.6. More Letters to Mimi

In a letter of November 1903 (date uncertain) to his mother Mimi, Krogh tells about his recurring and debilitating stress symptoms also appearing during late autumn of that year (Schmidt‐Nielsen 1995, p. 59, 1997, p. 79) [31, 32]. In a third letter by Krogh to his mother on December 17,1903, despite Krogh's “stress,” Bohr had asked Krogh to write up a report on data from the 1903 spring experiments and initiate a first draft of the results, that is, the experiments that demonstrated an increased displacement of O₂ bound to hemoglobin by rising pressures of CO₂. In this December letter to his mother, Krogh also writes that during the stay in Copenhagen over X‐mas he would undertake writing the draft “with pleasure” (Schmidt‐Nielsen 1995, p. 59, 1997, p. 79) [31, 32]. ⁵ In a fourth letter to his mother, January 3, 1904, a single sentence appears as the ultimate smoking gun, revealing that Krogh in no way was involved in describing heterotropic allostery; referred more detailed below in Section 11.7.

3.7. Details on Publication of Two Allosteric Effects

Experimental results from the spring of 1903 resulted in seven papers published in 1904. Three of the papers had Bohr as sole author, two papers were coauthored by Bohr and collaborators, and two were authored by Krogh alone. Dates for these publications are in Table D1 in Appendix D. Two other unrelated publications by Krogh were prepared and their formulation initiated and completed during January till March 1904. They dealt with the carbonic acid content in seawater, including data from his 1902 Greenland expedition and the 1903 summer trips to the Bohrs (Krogh 1904c, e; Schmidt‐Nielsen 1995, p. 261, 1997 p. 311) [31, 32, 34, 35]. In the following, I comment on the publication of the two allosteric effects, homotropic and heterotropic. These terms are defined in an Appendix B.

3.7.1. Homotropy for O₂ Binding

Two of the papers, by Bohr alone, analyzed and described for the first time an observed S‐shaped binding of O₂ to hemoglobin as a clear demonstration of a “positive homotropic effects of allostery” for O₂ binding to hemoglobin in dog blood samples (Bohr 1904a, b) [20, 23]. The first of these two papers described a possible model for O₂ allostery by an equation and its fit to data, and the second displayed the obtained O₂ data employed for fit of parameters in the mathematical model, Figure 3b. In Bohr's third paper published a week later, a similar model was used and with a fit of parameters for binding of CO₂ to hemoglobin, employing earlier data, see Table D2 in the Appendix D [37].

FIGURE 3.

(a) Full and fractional (only positive values) hyperbolic curves (blue), r = R _max/(1 + (S/K _d )). From Bindslev 2008, Ch. 1, fig. 1.3 [36]. (b) Positive homotropic allostery. Insert demonstrates a Hill coefficient (n_H) of 2.2 for the oxygen binding to dog blood, curve I. Bohr 1904b [23]. (c) Negative heterotropic allostery by CO₂. Bohr, Hasselbalch, and Krogh, 1904a [21].

3.7.2. Heterotropy for O₂ Binding

Two other papers by Bohr, Hasselbalch and Krogh were both on the effects of CO₂ on binding of O₂ to hemoglobin in dog blood. These papers cover a first clear demonstration of a negative interaction between two different gas ligands, O₂ and CO₂, on binding to two different sites on hemoglobin—“negative heterotropic allostery.” The first of these two reports was also the paper first published of all seven papers, Figure 3c (Bohr et al. 1904a) [21]. The second paper that year, with authors Bohr, Hasselbalch, and Krogh (BHK #2), further suggested as an explanation for the lack of an effect of O₂ on CO₂ binding to hemoglobin, that it was due to a probable binding of CO₂ to globin moieties instead of heme in the hemoglobin molecule. The conclusion about lack of reciprocal effects was based on earlier studies by Bohr and Torup with binding of CO₂ per se at a fixed oxygen tension, but not on new experiments in 1903. Moreover, the 1904‐paper had a rebuttal of a claim by Werigo, that from Bohr's data one could deduce that an increased O₂ pressure would increase CO₂ release in the lungs (Werigo 1898) [8, 22, 30, 38]. This second Bohr et al. paper also included Krogh's oxygen binding data to horse blood at a single CO₂ pressure of 40 mmHg (Krogh 1904) but with no further important deductions or conclusions [22]. This paper remains the most cited of all seven papers on O₂, CO₂, and hemoglobin from 1904, the “Bohr Effect” paper.

3.7.3. CO₂ Binding

Bohr's third paper in 1904 had data on CO₂ binding to hemoglobin taken from earlier experiments by Bohr in the presence of only one O₂ pressure, 100 mmHg? [37, 39]. There is no record of measured CO₂ binding to hemoglobin in the 1903 experiments, lest with varying O₂ pressure (for a possible Haldane effect). Thus, the third paper by Bohr only reiterates earlier findings by Bohr and Sophus Torup. Bohr transforms the homotropy model to a heterotropic scheme with an understanding of two separate binding sites for the analysis of the measured bicarbonate binding lacking a variation in the oxygen pressure (Bohr 1892a, 1904c; Bohr and Torup 1892) [29, 37, 38]. Bohr believed too much in his own data from 1892 with lack of CO₂ displacement by O₂ and rashly refuted what later became the “Haldane Effect.”

3.7.4. Analysis of CO₂ Binding in 1904 and Later

In Bohr's third paper on CO₂ binding, as mentioned, with the use of a non‐substantiated theoretical model for CO₂ binding at increasing pressures of CO₂ from 6 to 189 mmHg, the binding followed a slightly homotropic allostery binding of CO₂ to hemoglobin from which Bohr was able to derive parameter values. When I analyze Bohr's data from 1904 on CO₂ binding to hemoglobin, a Hill plot yields a slightly negative homotropic allostery (negative co‐operativity) with values of maximal CO₂ binding: R _max = 5.22 ± 0.11 ccm/g hgb, half‐saturation: EC₅₀ = 44.3± 3.6 mmHg CO₂, and a Hill coefficient: n_H = 0.587 ± 0.013. It might be added that Bohr the year after also presented data where he measured the CO₂ binding over a pressure range from 0.6 to 82 mmHg CO₂ as nearly hyperbolic, see figure on p. 106 in Bohr 1905 [40]. Bohr also compared data values from experiments on binding of CO₂ to hemoglobin in dog and horse blood while now the oxygen tensions were simultaneously varied by a factor of 2 to nearly 8, and he could therefore rightly conclude that as the P_O2 rose it was without a clear decrease in the CO₂ binding (Bohr 1905, pp. 106–107) [40]. These latter experiments justified Bohr's earlier claim, that there was no reciprocal effect of O₂ on the CO₂ binding to hemoglobin. Ten years afterward, a publication came demonstrating that, yes, increasing O₂ pressure can reciprocally influence and lower the binding of CO₂ to hemoglobin [41, 42]. ⁶

3.7.5. Krogh's Papers on Gas Binding to Dog and Horse Blood

The first paper in 1904 by Krogh as sole author is just a short note on a gas sampling method, Table D1 in Appendix D.1. Krogh's second paper covered sampling methods and an improved Bohr‐tonometer used for the spring experiments (Krogh 1904b). A table, Table D2, in the Appendix D.2 has some of the used tonometers. Experiments especially for Krogh's 1904 paper (Krogh 1904) used horse blood for measuring O₂ binding to hemoglobin at varying O₂ pressures and at a constant CO₂ pressure of 40 mmHg. As mentioned, these data were also simultaneously included in the second paper by Bohr and co‐workers [22]. For other publications in 1904 by Krogh, see Hill 1950 [45].

3.8. Impact of the Discoveries Published in 1904

The story of how to theoretically tackle the assumed homotropic O₂ multi‐ligand binding to hemoglobin, observed by Bohr as the cause of S‐formed dissociation curves for hemoglobin‐oxygen binding, is somewhat instructive and profoundly important. Bohr's discovery of an unquestionable S‐shaped dose–response for oxygen's binding to hemoglobin, as also affected by CO₂, started a search for a molecular explanation and an algebraic formulation with two or more separate binding sites for homotropic and heterotropic cooperativity (allostery); a model exploration initiated by Bohr himself as detailed below in Chapter 9.4. Here 120 years later in the pharmaceutical industry, biomolecular searches for allosteric interactions with heterotropic allosters, with attempts to avoid adverse effects, are still ongoing in a very active field involving drug design deduction and development of “test‐target allosters” for treatment with use of for instance positive and negative allosteric modulators, PAMs and NAMs [46, 47, 48], and later maybe even in multi‐modulatory drug combinations [49].

4. Bohr's Life, Academic Career, and Publications

4.1. Bohr's Family and Youth

Several sketches of Christian Bohr's character, family, and life may be found in works by Adler, Rozental, Pais, Favrholdt, his own notes and several of the memorial words referred in the cited literature and an obituary in Figure 12a,b. Bohr was born in 1855. His grandfather Peter Georg Bohr (1776–1847) was a highly respected school master at Bornholm (Moore 1967, pp. 6–7) [50] with a late title as professor in Copenhagen. ⁷ Bohr's father Henrik Georg Christian Bohr (1813–1880) was rector at the von Westen Institute, a private gymnasium in Copenhagen (1844–1873). His mother, Caroline Louise Augusta Rimestad (1817–1896), was sister to a well‐known conservative politician, Christian Rimestad, Christian Bohr's maternal uncle. Christian Bohr, being the youngest, had five older siblings, 5–11 years older, so he was brought up as a semi‐only child. A brother, Peter Georg Bohr (1845–1912) followed their father as rector at the von Westen Institute (1873–1978). Already before his teens, Christian Bohr had an inclination for the basics in sciences; expressed in a later note by him (Adler 1964, pp. 9–10, 1967, pp. 12–13) [51, 52]. In his teens, zoology was one of his favorite subjects.

FIGURE 12.

(a) Christian Bohr's death, February 3, 1911. Clip from newspaper Politiken. Politiken Saturday February 4, 1911, p. 5. (b) Section of panel a showing obituary text on Bohr in detail. Translated from Danish: “As late as Thursday night, he worked in his laboratory, from where he first returned at midnight. He complained about chest pains and his assistant was called in. But a moment later the pain was over and Bohr joked at the event and uttered some word about ‘that now he so far better stop smoking Tobacco’. Few moments later he fell down and was dead.” (c) Death certificate for Christian Bohr, entered Saturday 4, 1911. The certificate is a bit ambiguous. It may indicate that Bohr's family doctor had treated him earlier for a heart disease but not at the time of death, or that Bohr died of an acute heart failure which the family doctor had not treated just before Bohr's death, or most likely the signing doctor is not Bohr's doctor at all but functions as a doctor on call, stating the death. Christian Bohr, according to the death certificate, suffered from a heart disease for “several years.” This statement is not recorded later. (d) Tomb statue for Christian Bohr, and for his sons Niels & Harald Bohr. Assistens Kirkegård in Copenhagen, by J.F. Willumsen 1912.

4.2. First Academic Period, 1872–1881

Student in 1872. Some of Bohr's early writings were notes on zoology and biological reproduction while following a course in his second year in medicine at the university, 1873 (original at Museion, Copenhagen). As medical student, Bohr performed experiments in Panum's physiology lab studying effects of salicylic acid on meat digestion and summarized in a monograph [53]. Bohr obtained his medical degree (cand. med.) in 1878, and 2 years later in 1880 became Doctor of Medical Science with a dissertation on lipoproteins in milch and their importance [54]. Bohr married Ellen Adler (1860–1930) in 1881, one of his pupils in a preparatory class for medical studies at Copenhagen University, Figure 2b–f. She came from a wealthy family as the youngest out of six. Both her mother, Jenny Raphael, Figure 2b, and her father, David Baruch Adler, were from banking families of Jewish decent. The Bohr and Adler families belonged to a liberal and open‐minded, leftist current, and to the better bourgeoisie in Copenhagen. Ellen gave birth to three children, the most well‐known is Niels, Figure 2e,f. Throughout the marriage Ellen was a great support for Christian. In this period Bohr also established several friendships, especially with two older colleagues, Carl Julius Salomonsen and Johan Henrik Chievitz, Figure 5c, as well with three non‐medic scientists, also in Figure 5b,d.

FIGURE 5.

(a) “A meeting in the Literary Club” (Bogstaveligheden). Author J.P. Jacobsen recites his short story “Pesten i Bergamo” (The Plague in Bergamo). Several of the Copenhagen intellectuals and artists are in the drawing: For example, Georg Brandes, Harald Høffding, Holger Drachmann, and Peter Severin Krøyer. Drawing by Erik Henningsen 1910. From “Den Store Danske,” with permission. (b) “A meeting in the Royal Danish Academy of Sciences and Letters.” Four discussion partners are marked with arrows: Harald Høffding, Christian Bohr, Christian Christiansen, and Vilhelm Thomsen. Two zoologists Steenstup, farther and son, are in the painting standing opposite each other and also opposed each other professionally. Father Japetus Steenstrup here, as chairman, died in the year the painting was finished. Frederik VIII of Denmark (1906–1912) was still Crown Prince when the painting was finished. Painted 1897 by Peder Severin Krøyer (1851–1909). The painting is a gift from the Carlsberg Foundation. Reproduced with permission. (c) Krogh's two mentors Wiliam Sørensen and Christian Bohr. Two of Christian Bohr's personal friends are also present, Carl Julius Salomonsen (1847–1924) and Johan Henrik Chievitz (1850–1901). Also in the figure: Japetus Steenstrup's son Johannes Christoffer Hagemann Reinhardt Steenstrup (1844–1935). Section of 5b. (d) The four “Fs” at an after‐meeting meeting in Bohr's home. The four “Fs” from left: Vilhelm Thomsen, philology, Harald Høffding, philosophy, Christian Bohr, physiology, and Christian Christiansen, physics. Drawing by artist Des Asmussen, year uncertain. It was a gift to Niels Bohr on his 70‐birthday in 1955 from Christiansen's daughter, Johanne Christiansen, a medical doctor. She cooperated with CG Douglas and JS Haldane on the Haldane effect. Johanne's father was Christian Bohr's good friend, the physicist Christian Christiansen. The drawing is in the Niels Bohr Archive. Reproduced with permission. https://www.carlsbergfondet.dk/da/Forskningsaktiviteter/Forskningsprojekter/Historiske‐forskningsprojekter/Niels‐Bohr‐og‐Carlsbergfondet.

4.3. Second Academic Period, 1881–1889

Bohr was research assistant 1881–1883 in Ludwig's lab in Leipzig. A special report about oxygen binding to hemoglobin in 1885, was dedicated to Carl Ludwig [3]. Herein, Bohr as the first ever demonstrated a near‐hyperbolic ligand binding! The treatise is an experimental milestone in ligand kinetics and pharmacodynamics, as it settled the hyperbolic behavior for ligands binding to macromolecules for the first time ever, see Figure 8a. In 1885, Bohr also obtained a silver medal from the Royal Danish Academy of Sciences and Letters for his study related to deviations from Boyle–Mariotte's law performed with his equipment for measuring the gas pressure against gas pressure‐volume product. The study was published as a journal article a year later [26]. In February 1886, through a lecture competition with several political obstacles [16], in which Bohr gave three public lectures on gas binding to hemoglobin, specifically addressed to colleague physicians, he became associate professor, see Sections 8.1, 8.3 below on Bohr's hyperbolae and teachings. Bohr issued yet another monograph in 1887, again dedicated to Ludwig at his 70th birthday, on carbonic acid binding to hemoglobin [4]. Content of this monograph was detailed further in a dissertation by Bohr's pupil, Sophus Torup [38]. In October 1888, Bohr published his first article indicating active secretion of gases (oxygen and carbon dioxide) across lung tissue in accordance with Ludwig's understanding of the process and of lungs, most likely as glands, see chapter 12.

FIGURE 8.

(a) Full hyperbolic O₂ dose‐binding curve, first ever, 1885. Left, front of Bohr's monograph from 1885. Right, the graph is in the back of the monograph. Employed pressures are from ca 2 to 470 mmHg. (A) thin salt solutions. (B) 0.2% and 4.2% hemoglobin solutions. Compare with Paul Bert's dose–response curves from 1878, Figure 4f. (b) Focus on O₂ binding to hemoglobin at low pressures. Bohr realized that there was something peculiar at the low range of O₂ tensions. Expanded section of 8a, Bohr 1885 [3]. (c) First hyperbolic binding of CO₂ to hemoglobin. Bohr suggested that the binding was maybe to the globin moiety. From “Beiträge zur Physiologie: Carl Ludwig zu seinem 70‐jahre Geburtstage.” Bohr 1887, pp. 164–172, Curve B, p. 171 [4]. (d) Repeated binding of CO₂ to hemoglobin and to methemoglobin. Bohr 1898 [8]. (e) Discussions about O₂ and CO₂ hyperbolic binding. Left: Bohr 1892a, pp. 139 and 142 [39]. Right: Bohr 1905, p. 106 [40]. In 1905, Bohr used Krogh's improved Bohr tonometer and gas analysis system to obtain the dose–response curve based on his own measurements at CO₂ pressures from 0.6 to 82 mmHg and data from Jaquet with CO₂ pressures from ca 20 to 125 mmHg.

4.4. Third Academic Period, 1890–1911

Bohr became a full professor in 1890. Three further publications on both O₂ and CO₂ binding to hemoglobin were issued in French 1890, and reissued in German in 1891 and 1892, supporting his secretion theory. For further developments about this theory, consult chapter 12 below on “Did Bohr sticks to his secretion theory?” In the period from 1892 until 1904, Bohr published some 17 papers on various subjects including handling of oxygen and carbon dioxide in different species. For references consult “Bohr's Publications” in section right after the Cited Literature page 55. Then, as mentioned, five papers in 1904 dealing with oxygen and carbon dioxide binding to hemoglobin while cross‐varying pressures of the two gases. All this knowledge was summarized in a 168 pages chapter in Nagel's handbook of Physiology 1905 [40]. A paper in 1906 provided Bohr's insight on the “Lung Vital Capacity” [57] and these insights were repeated in a German clinical journal in 1907, see section on page 55. Further, by use of Krogh's microtonomenter, Bohr published results the same year on expiration of carbon dioxide in dogs [58]. More details on the background for this paper is in Sindbæk (2022, pp. 156–158) [43]. In 1909, Bohr summarized his actual view on the secretion theory for lung passage of gases, also in German [59]. It is a key paper to understand Christian Bohr's thinking, much debated and by some designated as his testament. Then finally a monograph followed on the pathological outcomes due to reduced lung capacity, emphysema (Bohr 1910) [60]. This treatise starts with Bohr's view on physiology as a research field studying the organizing and self‐regulatory principles between organs and their organism. The monograph clearly, although tacitly, addresses the vitalism‐non‐vitalism debate and its hypostatic “purpose”; here reproduced in Appendix D.23 and to be discussed later.

Bohr's teachings are referred below with a focus specifically on hyperbolae and with a list over student's notes taken at Bohr's physiology lectures 1886–1910, see Chapter 8, Sections 2 and 3 “Bohr's hyperbolae and teachings.” Student notes are also listed at the end of Bohr's publication list and cover the years from 1886 till 1910, inserted on page 57.

5. Epoch of European ‘Naturphilosophie’. The Period 1740–1880. Bohr, His Time, and Beyond

5.1. Vitalism—An Early Start

Is bioregulation of life processes due to a form of vitalism, a life force beyond our cognition, or to a plain physicochemical causality? Vitalism was instigated by healers and nature philosophers, that is, in a sense by sages, early medics, and former forms of physiologists. Originally, the idea of vitalism imbued with death superstition analogies goes back in time to animation of nature by sapiens' forefathers, later in various forms by wise men in ancient China and Egypt, then moving to the early Greek enlightenment period with Hippocrates' writings, and effecting teaching at the Lyceum in Athens by Aristotle and Theophrastus. Later, transformed to and landing with Galen's visions of a life spirit being distributed in living organisms in the second century around 170 ad. With Galen's view of three spirits, vitalism wandered into the Arab golden age, 650–1150 ad, and then around 1200 ad to be reintroduced in medieval Europe, fore eventually during the Renaissance awakening in the late 14th century again to slowly shift into a more scientific approach with the European modernity and rationalism. An Nasin's description of the blood circuitry in 1050 AD in Damascus was reconfirmed 500 hundred years later nearly correctly by Jean Fernel (1542) and explicitly by Wiliam Harvey (1628). Even after this breakthrough, the belief was still that the circulation and function of blood and the inhaled air was to cool down heat produced in the heart and that a vital spirit located in the heart could thus be distributed to the various organs. This view was also supported by Paracelsus in 1527 with his life force, the ‘archeus’ [9, 10, 11]. Quantitative physiology emerged slowly with Italian Santorio Santori (1564–1636), with his measurements of human metabolism determined by early forms of calorimetry, and Deutch Herman Boerhaave (1668–1738) introducing thermometer measurements in the clinics. Vitalism and alchemy were still actual at the time of Robert Boyle (1627–1691), Antoni van Leeuwenhoek (1632–1723), Robert Hooke (1635–1703), and Isac Newton (1643–1727) from ca 1650 and on into late in the 19th century. L J Snyder issued a charming, engaging, and enlightening account on microscopic seeing by Johannes Vermeer (1632–1775), Leeuwenhoek, and Hooke in an over repetitious book from 2015 [61].

5.2. Idealism and Science. Vitalism Before Bohr, 1740 Until 1880

Part of the scientific milieu some four to three generations before Bohr's time was inspired by and going through major revisions and doubts about “vitalism,” known as the understanding of “principles of life” lacking physical causality and rather based on senses, feelings, and an idea of a mysterious life‐force, an “urkraft” (Sanskrit “prana,” Chinese “qi,” Egyptian “ka”). In the 18th century an organizing power was formulated by Boerhaave's pupil Albrecht von Haller (1708–1777), Figure 4a, and by his pupil the German physician and physiologist Johann Friedrich Blumenbach (1752–1840), Figure 4b. Blumenbach formulated the famous “Bildungstrieb” concept [64]. For natural philosophy's move unto natural sciences, specifically with a change in natural history, poetry, and physiology from 1740 until 1840, there are exquisite views on the romantic movement, including vitalism, in Gigante's essay delineating a shift away “from focus on form to the feel for force,” and for instance on gestation of physiology in Europe laid out and broadened with immense details in biographies by Zammito (Gigante 2009, pp. 1–48; Zammito 2018) [64, 65]. The romantic movement was explicitly initiated and driven by the so‐called Jena‐Set from around 1795 till 1803, a “Naturphilosophie” movement that took a decisive divergence from Descartes' mechanisms and from Kantian thinking in his “Critic of Judgement,” and which affected scientists in both Europe and The States from around the mid‐18th century till the mid‐19th century (Pinkard 2002; Jones 2005, pp. 54–79; Wulf 2022) [66, 67, 68]. The “Set” included Novalis, the brothers Friedrich and August Wilhelm Schlegel, and his wife Caroline Bøhmer‐Schlegel, besides Friedrich Schelling and to some extend the Ich‐philosopher Johan Gottlieb Fichte. Hegel, however, remained on the sidelines. While sustaining a vitalist view, Schelling was deeply influenced by the physiologist Blumenbach's teachings and by his textbook “Institutiones Physiologie” from 1787. With a historic backdrop and to mention just two of its events, Mozart's groundbreaking opera Idomeneo (1781) and the tranformative French revolution (1789), both influenced German poets as Johan Wolfgang Goethe and Friedrich Schiller. A bit later they wrote about and evolved the spirits of the German Romantic movement. In England the movement had its proponents in poets as Samuel Taylor Coleridge and William Wordsworth. In Denmark, Henrik Steffens (1773–1845) especially inspired by both Spinoza and Schelling presented the German Romantics in lectures between 1802 and 1804 at Elers' College in Copenhagen (Steffens 1803; Zammito 2018, Ch. 10) [64, 69]. In 1804 Steffens went to Halle with a title of professor in Philosophy, Mineralogy, Natural History and Physiology. Steffens' teachings were lofty, often unsubstantial, and wide‐ranging compared to for instance Blumenbach's balanced views on the organizing vital power, nisus formativus, in living creatures, see Blumenbach's “The Institutions of Physiology” filled with a strong sense of the Enlightenment's rationality (Zammito 2018, Chs. 7, 8, 9, 10, and 11) [64]. Even more so, this rationality was already in teachings and writings by Albrecht von Haller, a Swiss scientist by some known as “the father of physiology,” a concept for Haller coined by Bernard (Zammito 2018, Chs. 2 and 3) [64]. Ideas by Haller were developed and carried further by Johann Blumenbach, Carl Kielmeyer, and Johann Reil (Zammito 2018, Ch. 3 and throughout the text) [64]. ⁸ Haller's latin textbook “Elemanta Physiologiæ Corporis Humani” in 10 volumes from 1776 was also consulted by Bohr.

FIGURE 4.

(a–g) Some of Christian Bohr's physiologist predecessors. (a) Albrecht von Haller (1708–1777), ca. 1780, (b) Johann Friedrich Blumenbach (1752–1840), (c) Johannes Peter Müller (1801–1858), who was a German physiologist, comparative anatomist, ichthyologist, and herpetologist. The paramesonephric duct (Müllerian duct) is named in his honor, (d) Heinrich Gustav Magnus (1802–1870) and his blood pump (Ann Phys Chem 1837;40:583–606) [9], (e) Carl Ludwig (1816–1895) [62], (f) George Gabriel Stokes (math‐physics, 1819–1903), and (g) Paul Bert (1833–1886), French zoologist, physiologist and politician. Insert graph from Bert's book in 1878, fig. 32 [63].

5.2.1. Johannes Peter Müller (1801–1858)

In German scientific circles during the early 19th century, besides the Humboldt brothers—Wilhelm the philologist‐politician and Alexander the world‐traveler, nature scientist, and taxonomer—the German Romantic movement affected a physiologist as Johannes Müller, Figure 4c. In his early years Müller was taught and became somewhat a proponent of the vitalist movement for life's expression—speculative nature philosophy. Meanwhile, during the 30s of that century he forcefully turned to the empirical scientific approach by introducing the use of microscopes and chemistry teachings into medical research and learnings, while still attached to an idea of a “life‐soul, that could never be understood for part of the organic chemistry of life.” An account of Müller's dramatic life is in the Wayback Machine.mpiwg‐berlin.mpg.de, pp. 1–11, with shipwreck, depressions, lifelong stomach pains self‐treated with opium, and a possible suicide attempt.

5.2.2. Danish “Vitalism,” 1815–1870

“Christian vitalism” was represented by two significant Danes in the years 1840 till 1870. Kierkegaard (1813–1855), famous philosopher in Copenhagen, strongly opposed the scientific approach, criticizing the adherence to uses of telescopes and microscopes [70]. See for instance a note with one of Kierkegaard's infamous quotations on natural sciences, Appendix D.4. Simultaneously with Kierkegaard, Grundtvigianism, another strong Christian movement of realism and rationalism, but also encompassing transcendent thinking and nationalism, started in Denmark and is still in practice today across the globe through Grundtvig's views and establishment of Grundtvig's Cooperative Movement, “Andelsbevægelsen,” and the Folk High School movement. A dispute about faith and knowledge between Grundtvig (1783–1872) and Kierkegaard is well described. Grundtvig till his death in 1872 was split between a theological and a secular approach to natural sciences, an antimony, though clearly favoring a catholic and Christ oriented theologian's understanding [71]. Lately in English speaking communities, interest in Grundtvig's importance for culture, humanities, politics and learnings has surged significantly as also documented with a scholarly six volume thematic encyclopedia issued from Aarhus University, “N.F.S. Grundtvig. Works in English.” To grasp a man like Grundtvig is not easy. One may start by reading a mischievous and entertaining book in Danish with the title “Frederik,” wherein Grundtvig's and king Frederik VII's concurrent lives are entwined [72].

Kierkegaard's and Grundtvig's antagonistic opinions were quite strong, (Holm 2021, Afterword, vol. 5, pp. 383–396) [73] and both were in clear opposition to HC Ørsted's views about nature's laws in “The Soul in Nature.” For Ørsted (1777–1851), laws of nature were dictated by the deity of common sense. In 1850 Ørsted wrote “… the world is a revelation of the united power of Creation and Reason ‘in the Godhead’”; in Danish “i Altet” (Oersted 1852, p. 451, translated from German; Jensen 1971; Thulstrup 1971; Pedersen 2020) [70, 74, 75, 76].

5.2.3. Carl Friedrich Wilhelm Ludwig (1816–1895)

In the second half of the 19 century, Müller's views lead to a strong anti‐vitalist clan including his pupils such as Carl Ludwig, Emil Heinrich Du Bois‐Reymond (1818–1896), Ernst Wilhelm Brücke (1819–1892), and Hermann von Helmholtz (1821–1894). Brücke also being young Sigmund Freud's mentor.

This transition away from vitalism was instigated forcefully by leading physicochemists as Carl Ludwig, Figure 4e, in Leipzig and thinkers on teleomechanics as Herman Lotze (1817–1881) in Heidelberg. Ludwig was the most eager anti‐vitalist in the mid‐19th century and attacked several physiological questions accepting that life phenomena defying physicochemical principles still existed, though merely posing questions that were not yet resolved (Ludwig's “Physiology, 1856,” p. 331) [77]. From Fye 1986 [78]:

Ludwig explicitly outlined his formulation of physiology as a science based on the principles of physics and chemistry in his “Physiology.” Among Ludwig's most important contributions were his discoveries in the area of respiratory physiology. While still at Vienna, Ludwig and his Russian pupil Ivan Sechenov (1829 – 1905) invented a mercury blood pump that allowed them to separate the respiratory gases in blood in vivo. In an extensive series of experiments, Ludwig and his pupils elucidated the physiology of tissue oxygenation and respiratory gas exchange.

And further on with a hint to Bohr's work that followed later:

In the course of this work Ludwig first measured the oxygen tension in blood. His technique made it possible to measure the saturation of oxygen and carbon dioxide in the blood stream. The results of these experiments led Ludwig to conclude that the oxygen uptake of an organ was related to the work performed by that organ.

Now, blood pumps, tomometers, haemat‐aërometers and the like allowed the extraction of blood gases for chemical or photo‐optic determination and if inexplicable gradients resulted, in Ludwig's understanding the cell metabolism was the underlying power and when known in more detail on a physicochemical level would explain the “active” oxygen uptake. No mystery. In the journal Science there is a positive, very personal, and emphatic view on Ludwig's character by one of his research assistants [79].

5.2.4. Claude Bernard (1813–1878)

Another contemporary physiologist in Paris was Claude Bernard, claimed to be a somewhat hesitant anti‐vitalist with a concept of “physical vitalism” as an obscurant epistemological source of origin for life lingering in his head. In 1865, quoted by Normandin, Bernard wrote in his much‐acclaimed book “An Introduction to the Study of Experimental Medicine”:

This grouping takes place only according to the laws which govern the chemico‐physical properties of matter; but the guiding idea of the vital evolution is essentially the domain of life and belongs neither to chemistry nor to physics nor to anything else.

(Bernard 1865, p. 93) [80]. Thus, according to Normandin, Bernard, contrary to Carl Ludwig, had his doubt about that everything of life form in the end would turn out to be explained by physicochemical forces (Normandin 2007, p. 519) [81].

Meanwhile, when one reads Bernard's Section IX of Chapter 1 in Part 2 of his book, it is clear, that what troubles him is not vitalism, but the ability of man to pose question beginning with a “why?,” as such questions are equally unanswerable in a scientific manner for life processes as well as for inorganic processes (Bernard 1865, pp. 80–84) [80]. In his later life, according to Denis Noble, Bernard was more convinced of a physicochemical explanation of life's “source” and “grouping” [82]. Noble has interpreted the above statement and Bernard's understanding of life processes as basically physicochemical but with an overlaid complexity, governed by the “milieu intérieur,” to be solved in the future, parallel to Ludwig's understanding.

5.2.5. Louis Pasteur (1822–1895)

In 1885, with the help of Tyndall's knowledge from 1881 about bacterial spores and how to kill them, “Tyndallization” [83], Pasteur showed that sterilized broth kept out of contact with ambient air stayed constant and free of emerging organisms, indicating that without an input through ambient air, such a soup would not give rise to new life, thereby negating the idea of life rising spontaneously as suspected earlier. Hence Pasteur in a competition with peers confirmed Harvey's 1651 biogenesis “omen viva ex ovum,” and Redi's 1671‐ demonstration of how organisms as flies emerged through an egg‐larva‐pupa‐fly metamorphosis and not “out‐of‐nothing,” and at a cellular level in line with Remak's/Virchow's “omnis cellula e cellula” from 1852 to 1855. Shortly afterward the debate went from life's spontaneous generation, the abiogenesis meaning Life from non‐Life, a term coined by Thomas Henry Huxley (1825–1895), toward the origin of Life only from Life (“biogenesis”). Huxley's theory for life's was developed in his “Cell Theory,” published in a review of his lecture on the subject (Huxley 1853, http://www.biodiversitylibrary.org/item/50104#page/318/mode/1up, a damaged copy) [84]. In this connection there is a deep analysis of Huxley's view on embryology and life processes in Richmond (2000) [85]. Huxley also coined “agnosticism” (1868) and was known as “Darwin's bulldog.” James Strick gives a detailed description on the debates on spontaneous generation in the years 1860 till 1880 especially in England [86, 87]. Today the origin of the first life is still a mystery.

5.2.6. Eduard Buchner (1860–1917)

A bit later, Buchner proved that cell‐free solutions from grinded yeast cells could ferment sucrose (rohrzucher) to its end products, alcohol and CO₂, just as well as intact cells were able to do in solution [88]. Thus, biogenesis went from cells to enzymes. For his discovery of cell‐free fermentation Buchner received the Nobel Prize in 1907. On November 10th, 10 years later, he was wounded during WWI and died 10 days later. Slowly, all these experiments with mini‐creatures and cell extracts diminished the belief in a genuine vitalist understanding of living cells and organisms as equipped with a mysterious internal and organizing power. Presently, the ultimate modern form of vitalism is given by creationism, twisting and circumventing the arguments by for instance Harvey, Redi, Virchow, Huxley, Darwin, Ludwig, Bernard, Pasteur, and Buchner. ⁹

5.3. Europe After 1848 and The Modern Breakthrough, 1870–1890

Briefly, besides developments within the natural sciences, there was rolling revolts at the sociopolitical scene and shaky state formation in the mid‐19th century at Bohr's birth, with dramatic unrests and revolutionary turmoil leading to the emergence of new nations and unstable governments throughout Europe in 1848 and evoking the Communist Manifesto (Clark 2024, see especially index entries on Denmark) [89], and for Denmark in particular (Christensen 2020 chapter 6, Broadbridge and Iversen 2023, vol. 6, pp. 17–31) [14, 90]. Dramatic events that continued after 1948 brought Denmark to its knees in 1864 due to stupidity of national pride and phantasies of formidability, now to remain as a mini country, a Lilliputian state (Buk‐Swienty 2015; Christensen 2000, chapter 10; Broadbridge and Iversen 2023) [14, 90, 91]. Cited from Buk‐Swienty's book, pp. 385–386:

Christian Julius de Meza [dismissed Commander‐in‐chief, aged seventy‐two, when the war broke out, nb] was found dead in his apartment in Copenhagen one September day in 1865. [Christian Bohr is 10 and a half years old this September, nb]. On his desk was an unfinished handwritten manuscript with the title “My Last and Irrevocable Opinion about the Warfare and the State,” which he had been working on for weeks. The manuscript was one long defense of the withdrawal from the Dannevirke on 5 February 1864. In it, de Meza cuts the political leaders in Copenhagen down to size, describing them as dreamers with no understanding of the realities at the front. He accuses them of blindly following the will of the people and of being informed by a ridiculous romantic sentiment which held that the fortifications built by a legendary queen were impregnable.

Western philosophy, literature, arts, sciences, and social norms were affected by these upheavals, and of course influenced and changed the mindset of the working‐class and the bourgeoisie toward modernity and man's superiority and demands for freedom and self‐determination.

Between 1870 and 1890, there was a particular naturalist movement in Scandinavian literary circles inspired by Darwin with a proponent as JP Jacobsen (1847–1885), who after studying biology for 3 years translated Darwin's “Origin of Species” to Danish in 1872 from the 5th edition of the original which was issued in 1859. Jacobsen adopted the anti‐vitalistic view on biological evo‐devo and the naturalistic approach to culture, societal measures, and religion, which lead him to write a novel as “Niels Lyhne” (1880) with a clear atheistic and level‐headed understanding of life and death. Christian Bohr read the novel in its year of publication, see Appendix D.5. An example of JP's activities is depicted in Figure 5a in which he appears in the literary club “Bogstaveligheden” in 1882. Jacobsen's anti‐vitalist, atheist, and naturalist ideologies were very much in line with Bohr's whole approach to studies of physiology and regulatory principles in biology, although not explicit in his scientific writings.

5.4. Bohr and His Time

Bohr's mentor, the physiologist Peter Ludvig Panum, was trained in Bernard's Paris lab in 1852–1853 and Bohr himself in Ludwig's Leipzig lab during the years 1881–1882 (muscle physiology) and in 1883 (blood gases).

Bohr, an intellectual and a free thinker was engaged in all kinds of scientific discussions, exemplified in Figure 5b. Additionally, Bohr was a great admirer of the German romanticism, its literature and poetry. “Der Sänger” from Goethe's lyrics, with Schubert's accompanying music, was especially dear to him (Kalckar 1967, p. 237) [92].

However, was Christian Bohr in a sense also a vitalist? The theme on Bohr as a vitalist has been debated by several authors with most of them deriding that Bohr should have been any kind of vitalist. From an opposite corner, especially Barcroft accused both Bohr and John Scott Haldane (1860–1936) of belonging to the vitalism fraction of scientists due to maintaining their belief in a sort of an active process for secretion of gases in lung tissue. A conviction that was not a clear black‐or‐white ruling, as exemplified in the discussion of the “Secretion theory” by Sturdy (Sturdy 1987, pp. 216–242) [93]. Bohr's understanding of an active principle in nature was close to the understanding expounded in Ludwig's laboratory with an ultimate elucidation of physicochemical processes as underlying all vital processes—a more clarified belief than fickle views of Haller, Blumenbach, Kielmeyer, Reil, Müller, and others mentioned above. Despite this, Ludwig himself had shown the secretion of saliva from submandibular glands to be a kind of an active mechanism, since a simple push‐filtration process could be excluded as the pressure in the salivary duct was higher than in the blood stream. For Ludwig this process just represented a form of metabolically invested energy not yet discovered and interpreted, a viewpoint also confirmed and accepted currently [62].

5.5. Not That Kind of Vitalist

Bohr's understanding of the vitalism subject, as related to his physiology, came late in the introduction to his last treatise in Danish (Bohr 1910, pp. 5–6) [60], quoted full‐length in English by his son Niels Bohr (1885–1962) in his essay “On Atomic Physics and Life Experience” (Bohr 1958, pp. 95–96) [94], and likewise relayed by Favrholdt in his books on Niels Bohr (Favrholdt 1992, pp. 7–16, Favrholdt 2009, pp. 287–288 and further commented on pp. 312–313) [95, 96]. Bohr's view clearly demonstrates a sober, almost dry, and non‐philosophical approach on the vitalism‐versus‐causation question. Therefore, Christian Bohr with his open mind on the subject was far from a firm belief in vitalism as defined for instance in the opinion of Hans Driesch (1867–1941) in his “Der Vitalismus als Geschichte und als Lehre” from 1905 (Driesch 1914, English edition) [97] together with the Bergsonian “Élan vitale' in L'Évolution créatrice” from 1907, a life purpose‐power beyond mechanism and radical finalism (Bergson 1911, Ch. 1) [98]. Driesch's transition from conducting morphologic experiments in German embryology—involving “entwicklungsmechanik”—to developing a later vitalistic perspective is telling for the period [99]. A brief extract from Bohr's statement on the “purpose” of regulation of organ function for the overall integrated function of the organism is given here:

The a priori assumption of the purposiveness of vital manifestations is, on the other hand, a purely heuristic principle and can, since the conditions in the organism are extremely complicated and therefore difficult to survey, often be useful, even indispensable, for being able to pose the special research task and seek ways to answer it. But one thing is what can be used with utility in the preliminary research task, another what one is entitled to determine as a truly achieved result; such can, where it concerns the purposiveness of the individual function for the entire organism, as mentioned above, only be ensured by demonstrating step by step in detail, by which means the purpose is achieved (Bohr 1910; Edsall 1972) [60, 100]; see Appendix D.23.

Bohr's view was equal to John Scott Haldane's understanding of life's organicism, proven to be on par with causality according to Needham “the living and the lifeless are equal systems with different levels of complexity” (Needham 1928; Sturdy 1987; Favrholdt 1992, p. 287) [93, 95, 101]. Further, John West also wrote on a characterization of Christian Bohr as a scientist in 1975, Appendix D.6, as well as later [102]. We will return to West's view again below.

5.6. Hasselbalch's View on Bohr

Bohr's statement in 1910 seems to place him with an understanding of the active lung secretion as rather active lung function right between Ludwig's and Bernard's points of view. To get a good sense of Bohr's non‐vitalism and critical approach, a rather long extract from Karl Hasselbalch's obituary on Bohr is quoted in Appendix D.7. Here, Hasselbalch, who knew Bohr well from his collaboration with him, wrote the eulogy shortly after Bohr had passed away in 1911; including Bohr's clear statement and warning about the vitalism of the “Natural Philosophers.” Yet another typical view by Bohr is in a sentence of the quoted statement by Hasselbalch, “…, an observation that was collected without a plan and presented without an idea, bored or annoyed him.” The eulogy is a defense for Bohr's stubbornness about active gas secretion as also suggested in Sindbæk's marvelous and intriguing book on Marie and August Krogh's life and works (Sindbæk 2022, p. 205) [43], although with a view slightly deviating from mine on Bohr's character, as Bohr was somewhat justified in pinpointing an active element, “spezifische Tätigkeit” in the overall mechanisms of gas exchange across the alveolar epithelium. Bohr was persistent in maintaining his secretion theory in 1909, while correct in late 1910, when he altogether abandoned this theory. See below in Chapter 12 on the “Secretion Theory.”

The stubbornness was likewise a characteristic description later for John Scott Haldane, who as Bohr, stuck to the lung gas exchange as partly an active or special process, and a view that brought Haldane a lot of opposition (Sturdy 1987, pp. 216–242) [93].

In short: Bohr's endeavor with his instinct/drive was to explore physiological functions and their regulation bit by bit with the aim to understand nature in a physicochemical frame of Ludwig's logic and of Bernard's “how?” and not the “why?”

5.7. Vitalism After Bohr's Time

Discussing vitalism after 1911 was and still is a major subject in biology brought to the level of molecular biology in sciences of metabolism, reproduction, embryology, metamorphosis, and biosemiotics. Joseph Needham discussed the problem of life and organicism in his 1928 publication [101]. By a switch to the concept of “teleonomy,” in his book from 1970/1971, Jacques Monod with a more recent scientific approach, elegantly circumvented the conundrum of nature's purposiveness implied in “entelechy,” “unity‐multeity,” and “teleology” [103]. The “Teleonomy” concept, as a purposive but unintentional agency in biology, close to the Kantian “purposiveness without purpose,” was coined by the biologist Colin Stephenson Pittendrigh in 1958 [104] and invoked early on by Monod and Jacob [105]. Other speculations related to the vitalism puzzle can be found in for instance “semiotic causation” by Jesper Hoffmeyer [106]. On life and evo‐devo see also for instance in Corning [107], Denis Noble [108], papers by Cornish‐Bowden and Cardenas [109], and broadened further in “Extended Evolutionary Synthesis” [110], see Appendix D.8.

6. Hyperbolae by Hüfner, Henri, and Bohr. Bohr's Teachings and 1903 Insights

6.1. Early Equations. Hyperbolic Gas Binding and Enzymatic Activity

Chapter 6 starts a major part of the treatise with three consecutive chapters describing the prerequisites leading to Christian Bohrs attempt to algebraically describe homotropic and heterotropic allostery. The latter described in more detail in Chapter 11. Here I retell how the mass action laws, initially developed in the 1860s and revisited in 1877, set the stage for the late 19th and early 20th century experiments on adsorption–desorption processes and how to formulate the results in a theory of rectangular hyperbola, see Appendix A. These experiments and models significantly influenced the fields of physical chemistry, physiology, and enzymology. A rectangular hyperbolic algebraic expression appeared first in research on a single gas binding to hemoglobin by Hüfner in 1890 [24] and for hydrolysis of a single substrate by enzymes 13 years later by Victor Henri [111]. Lives of Gustav Hüfner and Victor Henri are described in Subsections 6.2.2 and 7.4.2. Meanwhile, it was not realized at that time, that an identical rectangular hyperbolic relation described both gas binding to hemoglobin and as well for enzymatic hydrolysis, while the latter also included product inhibition. Further, the situation around 1900 for chemical kinetics is compared and demonstrated to differ between inorganic and organic chemical kinetics although there are overlaps. A realization of more complex binding schemes, in form of non‐competitive cooperative activity, and attempts on an algebraic description of such non‐competitive cooperative (allosteric) binding appeared a year after Henri's discovery (Bohr 1904a, b) [20, 23] and is detailed in Chapters 8 and 9. On definitions of non‐competitive cooperativity and allostery see Table B1.

6.2. Gas Binding First

To grasp the transition from simple hyperbolic binding to a more complex allosteric behavior, it is advantageous to include experiments on both carbon monoxide binding to for instance hemoglobin, a hyperbolic and competitive binding, and binding of oxygen to hemoglobin, which is a non‐competitive allosteric binding and therefore deviates from a simple hyperbolic description.

6.2.1. Hüfner Discovers a Hyperbolic Relationship at Equilibrium

Cato Maximillian Guldberg (1836–1902) and Peter Waage (1833–1900), two Norwegian chemists, as the first, formulated their ground‐breaking law of mass action and further derived equations for the dynamic equilibrium dissociation constant [112, 113]. Formulation of their law of mass action was based on Wenzel and Berthollet's work [114]. ¹⁰ Independently, the law of mass action was rediscovered by Jacobus Henricus van't Hoff (1852–1911) 10 years later [115]. The formulations of the mass action law and the derived equilibrium constant was brought to the attention of a broader audience through a reissue of the G&W papers, translated from French and Danish into German [116]. Shortly after, Hüfner originally adapted his theory for data for mutual binding of carbon monoxide and oxygen to hemoglobin [55]. More details on this in Subsection 6.2.3. In 1885, by measurements with gas pressures as low as 2 mmHg, Christian Bohr could as the first ever publish an experimentally obtained near hyperbolic binding of oxygen to hemoglobin [3]; here reproduced in Figure 8a from a figure at the end of his treatise. Five years later, as we shall see below, Hüfner originally as the first derived a correct rectangular hyperbolic expression at equilibrium for the simple binding toward saturation of a single ligand, Figure 6bB, (Hüfner 1890) [24]. ¹¹ Jumping a bit ahead to enzymology, in fact, but almost forgotten, 30 years earlier the French mathematician and physicist Biot had derived an expression similar to Hüfner's and made semi‐hyperbolic plots of enzymatic activity (Biot 1860; Bindslev 2008, pp. 255 – 257 and Figure 10.2) [36, 118]. Meanwhile, regrettably for Hüfner and his works, he misused his algebraic insight by fitting oxygen binding data to his new and correct binding theory, rather than the other way around (Hüfner 1890, 1901) [24, 25]. Therefore, as binding of oxygen to hemoglobin shortly afterward in 1904 turned out not to follow a simple hyperbolic reaction scheme, that caused Hüfner's reputation to dwindle even further among peers and his algebraic insight to disappear into the land of lost lessons.

FIGURE 6.

(a) Gustav (von) Hüfner (1840–1908). Hüfner as the first derived the rectangular hyperbolic equation for single ligand binding in 1890 [24]. Professor at department of Physiological Chemistry in Tübingen University (1872). Figure from painting ca. 1875. (Portrait reproduced from Zeitschrift für physiologische Chemie, November 12, 1908). (b) Hyperbolic equations with different constants. (A) Ratio between two rate constants (Hüfner 1884, p. 212) [55]. (B) Equilibrium association constant for one ligand (Hüfner 1890, p. 11) [24]. (c) Hüfner's dose–response curve for CO binding to hemoglobin. Experimental data with a fixed O₂ and varying CO tensions are fitted to a hyperbolic theory, and therefore, not surprisingly, the plot is a nice hyperbolic curve. (Hüfner 1902, table p. 98, figure p. 99) [56]. (d) Hüfner's dose–response curves for O₂ binding to hemoglobin. Drawn with derived average association constants, based on both Bohr and own data, and with reversed pressure gradient at the x‐axis for oxygen values. Percent bound versus pressure in mmHg. Figure on p. 15, based on tables IX and XII on p. 14 in Hüfner 1890 [24]. (e) Hüfner dose–response curve for O₂ binding to hemoglobin, 1901. Results are still with data fitted incorrectly to his theory. Percent bound versus pressure in mmHg (Hüfner 1901, figure on p. 213 based on table p. 212) [25].

6.2.2. Hüfner's Time

Gustav von Hüfner (1842–1908) had a modest temper and from early on, with the help of his uncle Ernst Herger, enjoyed the German Romanticism and Idealism in literature, poetry, theater, music, and philosophy. The young Hüfner fancied protagonists as Goethe, Schiller, Schelling, and the Schlegel brothers with their longing for Mother Nature (Zynek 1909, pp. 1–10) [119]. Hüfner graduated in medicine from Leipzig University in 1865/1866 and from 1866 till 1872 joined several chemistry and physiology laboratories in Germany, Figure 6a. He settled in Tübingen as professor of chemical‐physiology, following Felix Hoppe‐Seyler from 1872, and kept contact with Ludwig's Leipzig laboratory until his death in 1908. In Tübingen he worked on gas binding, especially gas adsorption to crystals of isolated hemoglobin but also to hemoglobin in solutions and in blood samples. He determined the binding of 1.34 g oxygen to 1 g of hemoglobin, known as the Hüfner number, and he determined the weight of hemoglobin as 16 500 Da/M mass (von Zeynek 1909; Ronge 1972) [119, 123]. Unjustified, Hüfner is almost forgotten nowadays, mainly because he got a bad reputation in relation to Bohr's discoveries, including his misunderstood use of his own correct hyperbolic binding theory, where he as mentioned fitted data to the theory instead of the correct way around of fitting the theory parameters to follow obtained data (Barcroft 1914, pp. 20–22) [120].

6.2.3. Early Hyperbolae for CO Binding by Hüfner

Moreover, even less well‐known is Hüfner's understanding of the binding for carbon monoxide and his clear description of a theory following a rectangular semi‐hyperbolic relationship, initially studied for two gases simultaneously and written as x = Q v _c/(ιv _o  + v _c), in which x is percent bound CO, Q is max bound CO, v _o pressure of oxygen, v _c pressure of CO, and ι the ratio between the reaction rate constants for oxygen and CO, k/k′, given in an equilibrium expression: kv _o h _c = k′v _c h _o , where h _o and h _c are the partial total pressures of O₂ and CO, Figure 6bA [55]. Of note, Hüfner 18 years after the first publication of the semi‐hyperbolic binding of carbon oxide to hemoglobin, in the presence of oxygen, repeated the truly hyperbolic behavior for CO binding to hemoglobin again in 1902, demonstrating graphically that the hyperbolic behavior of CO‐binding to hemoglobin correctly followed his derived theory, although again with manipulated experimental data for a mean value of the equilibrium dissociation constant, Figure 6c [56]. This second article on CO deals with questions of concern about poisonous concentrations of CO in train tunnel air. It is a revealing paper on CO binding to hemoglobin and additionally interesting with its clinical implications, both in general as well as specifically for tunnel travelers through a nearly 1500 m long part of the Ronco train tunnel (total 8.291 m) completed in 1889 as part of the newly established dei Giovi Alps transit system (Secondo Valico) from Genua toward Turin. The paper as mentioned includes a constructed display of a CO‐binding curve at atmospheric pressure, with a fixed O₂ partial pressure and with a half saturation constant, EC₅₀, of 1.34 permille CO pressure, erroneously extractable for use when based on Hüfner's spurious data given in his table on p. 98. ¹² Hüfner's paper from 1902 demonstrates a factor of a little more than 1000 for the affinity of CO over oxygen. The modern mean value of this ratio is around 250 times. It is ironical, that a pupil of Christian Bohr, Johannes Bock, had already nicely described and correctly tabulated strong affinity of carbon monoxide to hemoglobin at pressures as low as 0.22 mmHg in his Danish dissertation. This was in a close collaboration with Bohr and in his lab, where Bock demonstrated a pure hyperbolic relationship in a table rather than as a curve plot [121], see Appendix Figure D1, p 65, and Appendix D.9.

6.2.4. Hüfner on Oxygen Binding

Unfortunately, Hüfner was so thrilled about his discovery of a hyperbolic description and so convinced about his insight of congruency between experimental data for CO binding and his own theory for gas binding already from 1890, Figure 6bB, that he also forced the binding between O₂ and hemoglobin to follow his theory of a simple hyperbolic binding relationship. By messaging actual O₂‐hemoglobin binding data as measured by Bohr in 1888 and by himself, he produced dissociation data sets and a dissociation curve for the oxygen binding to hemoglobin, Figure 6d (Hüfner 1890, p. 15) [24]. This oxygen binding curve, plotted by Hüfner in 1890, is a mirror‐image of our present‐day dose–response curves with a reversed concentration axis and just demonstrates that we are in the early days of displaying saturation binding.

Hüfner repeated this 11 years later in 1901, Figure 6e [25], including several of his own new data from 1894 [122]. With his three publications on oxygen binding to hemoglobin from 1890, 1894, and 1901, Hüfner firmly upheld the simple rectangular equation as a descriptive theory for O₂‐binding. ¹³

It is telling and quite contradictory concerning part of his research, that as a life motto for his students, Hüfner would use the saying by Robert von Mayer: “Truly I say unto you, a single number has more true and enduring value than a precious library full of hypotheses” (von Zeynek 1909, p. 33) [119].

6.3. Enzymatic Activity Next

6.3.1. From Oxygen Binding to Enzymatic Products

For an increased understanding of chemical binding and activity in general and in specifics for the details in an allosteric regulation, it is revealing to compare for instance the above displayed observations on O₂ binding to hemoglobin with the activity of converting substrates to products as performed by enzymatic entities, which is to follow immediately, and thereby hopefully yield a cognitive synthesis and revelation to a deeper comprehension of allostery.

6.3.2. Initial Hyperbolic Formulations for Enzyme Kinetics

In the very beginning of the 20th century a debate took place in circles of researchers on kinetics of enzyme activity, discussing how to formulate three lingering questions based on experimentally observed saturability and product inhibition, that is, (i) what saturability meant as it deviated from a simple linear physicochemical acid hydrolysis that followed the law of mass action, (ii) which molecular model to use for the saturability, and (iii) how to describe algebraically an observed product inhibition?

6.3.3. The Insight of Adrian John Brown (1852–1919)

Already in 1890, O'Sullivan and Tompson in a large review on enzyme activity had argued that enzymatic processes followed the simple kinetic scheme of mass action as described for acid hydrolysis of organic compounds [124]. However, these two researchers lacked proper experimentation at increasing substrate concentrations to elicit saturability as earlier documented by Biot in 1860 [118] and later demonstrated by Adrian Brown in 1902 [125]. Saturability of a kinetic process of enzymatic activity, as the supplement of substrate is increased, was not on face value an outcome of mass action. Also concerns about product inhibition as for instance observed and discussed by Duclaux, required additional insight and a mechanistic formulation as it also clearly deviated from a simple scheme of mass action [126]. Inspired by the three listed questions, Brown performed experiments with invertase, a plant enzyme and member together with sucrase of enzymes splitting saccharose (table sugar). (i) Brown could demonstrate a saturability of the enzymatic process as the substrate concentration was raised. (ii) Brown also formulated an explanation for the saturability assuming a protracted complexation between enzyme and substrate thus limiting the speed of enzymatic degradation by a prolonged binding of substrate compared to the speed of free diffusion. This argument is an early example of what has later been characterized as facilitated diffusion/transport when for instance passing mediated through cell membranes (Stein 1986, Ch. 4) [127]. Furthermore, (iii) Brown very convincingly demonstrated the specificity of product inhibition on invertase activity by showing that the product, invert sugar (D‐fructose and D‐glucose), but not the disaccharide lactose, could inhibit the invertase degradation of saccharose [125]. Meanwhile, Brown did not formulate an algebraic expression to explain his theory on saturability nor on the documented product inhibition. Another Brown (JH Brown) together with Glendinning confirmed Brown's observation of saturability but questioned the explanation of a protracted complexation as the explanation for saturability [128].

6.3.4. A Break‐Through by Victor Henri (1872–1940)

In the same year and a month after the two Browns publications appeared, Victor Henri, November 1902, came up with a hyperbolic expression that quantified and thereby explained the observed saturability as well as product inhibition [129]. A term for product inhibition and its right inclusion in a hyperbolic expression was inspired and developed through helpful discussions with Max Bodenstein, who in 1900 became a newly employed physical‐chemist and lecturer in Ostwald's laboratory in Leipzig until 1906, while Henri, overlapping Bodenstein, also worked part time as an assistant in the Ostwald laboratory in 1901 and in 1902 (Henri 1903, Introduction in his PhD; Nicolas 1994) [111, 130]. Bodenstein's help is relayed in the above‐mentioned November 1902 meeting contribution, in which Henri writes: “M. Bodenstein to whom I owe much valuable advice” [129]. Bodenstein later became renown as one of the founders of chemical kinetics. Thus, Bodenstein partly provided the equation for product inhibition, while Henri expanded the equation with a term for the non‐bound enzyme, to which Cornish‐Bowden adds:

According to Henri and a later paper by Bodenstein himself, [7] in 1901 or 1902, he [Bodenstein] suggested the enzyme‐kinetic rate law v = VS/(mS + nP), [in which v is hydrolysis rate, V maximal hydrolysis rate, m and n are equilibrium association constants]. Henri corrected this into v = VS/(1 + mS + nP), both written in modern notation; S for substrate concentration and P for product concentration. (Cornish‐Bowden et al. 2014, supplement) [131]. [The cited reference [7] is to Bodenstein's 1909 paper [132]. Note that “1” in the denominator represents the unbound concentration of enzyme]. ¹⁴

And then in his dissertation published 2 months later, January 1903, Henri got rid of the product term (nP) by deriving an initial rate equation, where nP is negligible, and reached at the famous rectangular hyperbolic rate equation for a single ligand ‘S’: v = VS/(1 + mS), Figure 7a,b. Compare this expression with Hüfner's hyperbolic equilibration equation in Figure 6bB (Hüfner 1890; Henri 1903). Ten years later Henri's formulation was scrutinized further by Leonor Michaelis in collaboration with Maud Menten, and ‘the rest is history’ (Haldane 1930; Bindslev 2008; Cornish‐Bowden 2013; Michaelis and Menten 2013 (1913); Cornish‐Bowden et al. 2014) [36, 131, 133, 134, 135].

FIGURE 7.

(a) Victor Henri (1872–1940) and front page of his dissertation from 1903. The author obtained Victor Henri's dissertation with great efforts in 2006 from a French library. The dissertation is now (2014) translated with helpful annotations into English by Athel Cornish‐Bowden, and accessible at the www‐net [131]. (b) Victor Henri, father of an equation for negative heterotropic allostery fin enzyme kinetics. Painting by Laure Binet around 1900 at the time when Henri discovered the Henri–Michaelis–Menten relationship and product inhibition equations. A slightly cropped version of the painting. Permission to reproduce is given by owner Mrs. Christine L Henri, widow of Victor Henri's son Victor Philippe Henri (1923–2014), and her daughters Ms. Janine J. Henri and Marianne J Henri, California.

7. Hyperbolae in Inorganic and Organic Chemistry

7.1. Inorganic Chemistry, Hyperbolae Ignored by Ostwald

Simultaneously, in a period from 1870s to 1910, it was a general standard in chemistry and physiology laboratories in Europe to prove an obedience for experimental kinetic data to the laws of mass action by use of a set of equations of the type: K = (1/t) × ln(S ₀/S _t ) in which K is the equilibrium association constant, and S ₀ and S _t , the amount of free ligand at time 0 and t, or free substrate at time 0 and t. By many, this understanding was based on a theory of a first‐order kinetics as the theoretical law for self‐limited chemical hydrolysis (Ostwald 1920, Chapter 11) [136], developed originally by Ludwig Ferdinand Wilhelmy (1812–1864) it included substrate‐limit and product‐inhibition in the chemical hydrolysis of for instance “rohrzucker” [117, 137] and furthered by van't Hoff [138], https://carnotcycle.wordpress.com/2019/09/01/ludwig‐wilhelmy‐and‐the‐birth‐of‐chemical‐kinetics/.

7.2. Hüfner “On Ice” by Ostwald?

Hüfner's theoretical insight with the rectangular relationship for ligand binding in nature from its start in 1884 and continued in 1890 was most likely interchanged, circulated, and debated between the neighboring Leipzig‐located laboratories of Walter Ostwald and Carl Ludwig, to both of whom Hüfner in Tübingen kept a close contact until Ludwig's death in 1894 and his own in 1908. But Hüfner's hyperbolae, although likely recognized and questioned, remained undescribed by the Leipzig laboratories and as well was missed in Henri's work and dissertation in Paris. In Bodenstein's opus magnum from Berlin there is a reference to Henri but not to Hüfner [132]. In spite Ostwald was one of the leading figures, especially on catalytic processes, astonishingly, there is no explicit mention of hyperbolic models by either Hüfner, Henri, or Bodenstein in Oswald's classical textbook on catalytic chemistry. This omission of Hüfner's and Henri's algebra is both in the 3rd edition from 1899 and in the last 6th edition of Ostwald's “Grundriss der allgemeinen Chemie” (Ostwald 1920, p. 331) [139]. Even in his Nobel prize lecture in 1909, he merely refers once to enzymatic activity in a work by Liebig and Wöhler [136]. ¹⁵ Was Ostwald really not aware of Henri's dissertation work 17 years earlier and the result of Bodenstein's collaboration with Henri?

7.3. General Chemistry Without Hyperbolic Models

It is surprising, that there is no explicit use of Hüfner's or Henri's hyperbolic models in kinetics of inorganic and organic chemistry in the early 20th century. Even in Partington's 3140‐page textbook “A History of Chemistry,” there are no hyperbolae. Partington's Volume 1 was first finalized in 1970, while the 4th volume came already in 1964 [140]. The latter is a 1007‐page volume covering the period from 1800 until 1964, without a single mention of the hyperbolic model for binding or activity in enzymatic processes or let alone for a comparison of enzymes activity to inorganic catalysis with limited reactants or its inhibition by catalysts and hydrolytic products as described much earlier already in 1884 [138].

7.4. Victor Henri, Maud Menten, Leonor Michaelis

7.4.1. ‘Henri–Michaelis–Menten Equation’

Actually, since first explicitly expressed in enzymology with a hyperbolic initial rate formulations by Henri (Henri 1903; Cornish‐Bowden et al. 2014) [111, 131] and only after being immortalized by Michaelis–Menten (Haldane 1930; Michaelis and Menten 2013 (1913)) [133, 134], the well‐known term “Michaelis–Menten equation” for initial rate enzymatic activity, arguably is now suggested to be signified as the “Henri–Michaelis–Menten equation,” HMM equation (Segel 1975, p. 19; Bindslev 2008, p. 257; Cornish‐Bowden et al. 2014, p. 165) [36, 131, 141]. Therefore, this spiral story on how the HMM steady‐state rate equation, like Hüfner's equilibrium expression, came about, is amusingly awesome with its initial dependence on product inhibition and then shortly afterward finalized by all together omitting product inhibition. Product inhibition was reinstated in the algebra by for instance Monod, Jeffries Wyman (1901–1995), and Jean‐Pierre Changeux (1936–present). These three authors referred to the Henri–Michaelis–Menten equation as the “Michaelis law” [142] or “Henri–Michaelis law” [143]; no mention of “Menten.” An understanding of the postponed implementation of the HMM equation for cooperativity is in Cárdenas 2013 [144].

7.4.2. Lives of Victor Henri, Maud Menten, and Leonor Michaelis

For readers interested in Henri's scientific career, it is beautifully laid out by Nicolas [130], by Deichmann and Schuster in Part 1 of a “triple part paper,” and in particular Henri's equation by Mazat [145], in Part 3 of the triple part paper [146]. Meanwhile, shortly after Cornish‐Bowden followed up with a biography on Henri, a revealing and thorough account of Henri's admirable, spectacular, astonishing, and adventurous private and scientific life in an introduction to Cornish‐Bowden's translation into English of Henri's dissertation, Figure 7a (Cornish‐Bowden et al. 2014, supplement, pp. 5–8, 1‐s2.0‐S0300908414002673‐mmc1.pdf at DOI: 10.1016/j.biochi.2014.09.018) [147] in (Cornish‐Bowden et al. 2014) [131]. Maud Leonora Menten's life (1879–1960) has been documented [148, 149], together with Michaela Ludwig's article in British Columbia Magazine (February 7, 2024), and as well the life from 1875 till 1949 of Leonor Michaelis (Deichmann et al. 2014, Part 1) [146].

7.5. Bohr's Insight in 1903

Did Bohr know about Hüfner's and Henri's hyperbolic expressions? Almost at the same time as Henri published his initial hyperbolic rate theory in 1903, exactly a year later, Bohr presented the first attempt ever to explain the observed positive cooperative binding for oxygen to hemoglobin, later known as “homotropic allostery,” ¹⁶ with a double‐ligand binding of one‐type ligand (oxygen) in an algebraic expression [20]. In this connection, Bohr most likely had no knowledge about Henri's initial rate formulation with a hyperbolic equation and the negative cooperativity for enzyme activity due to product inhibition. Meanwhile, Bohr certainly knew about Hüfner's suggested simple hyperbolic descriptions for oxygen binding to hemoglobin but intentionally abstained from use of it [20]. An unfortunate, although maybe excusable omission by Bohr which is unfolded below.

8. Bohr's Findings From 1883 and Until 1903

8.1. Bohr Finds Hyperbolic Binding

Bohr's discovery and attempt on a formulation of the allosteric binding of oxygen to hemoglobin in 1904 is no doubt based on a drive elicited by previous experiments, observations, challenges by peers about the binding of oxygen to hemoglobin, and also on earlier results in the presence of carbon dioxide and its binding to hemoglobin.

Let's initially, a bit more detailed, follow Bohr's experimental results on O₂‐ and CO₂‐binding to hemoglobin commencing in 1883 in Leipzig and lasting until 1903. Christian Bohr worked as a research assistant in 1881–82 on muscle physiology and again in 1883 on blood gases in Ludwig's laboratory. Back in Copenhagen, using a Bessel Hagen pump to create low pressure for gas extraction, ¹⁷ Bohr published a docent treatise with ‘hyperbolic’ O₂‐binding, Figure 8a,b, and 2 years later a monograph on “hyperbolic” CO₂ binding to hemoglobin, Figure 8c, both based on experimental data obtained in Leipzig and Copenhagen. And, both works were dedicated to Carl Ludwig [3, 4]. Bohr repeated the binding of CO₂ to hemoglobin at increasing CO₂ pressures in 1898, 1904, and again in 1905, Figure 8d,eB. The oxygen binding curve at increasing oxygen pressure and the same for CO₂ at increasing CO₂ pressures, Figure 8, are major improvements compared to similar data obtained by Paul Bert (1833–1886) a few years earlier, Figure 4g (Bert 1878, fig 32) [63]. Here with a refined technique, Bohr's curve for O₂ binding to hemoglobin, is the first clear demonstration of hyperbolic‐like saturability in a physicochemical process. Due to details in the binding curve for O₂ at low O₂ pressures, Bohr already in 1885 had his doubts about a simple hyperbolic binding, Figure 8b, partly due to the variability of the binding curve at higher pressures (P), and partly due to his observation of deviations from the Boyle‐Mariotte law, P × V = constant at low pressures, V stands for volume [26]. For his account on the deviation, Bohr was honored in 1986 by a silver medal from the University of Copenhagen.

8.2. Bohr's Teaching and Hyperbolae

Late 1885 and into January 1886, Bohr wrote three essays on respiratory physiology held as lectures in Copenhagen for physicians during a competition for an associate professorship which he won in early 1886, see Appendix D.10 with Figure D2. In neither of these lectures are there any indications of hyperbolic gas binding or use of hyperbolic formulations related to the gas binding to hemoglobin. ¹⁸ Meanwhile, notes were taken during Bohr's physiology lectures for medical students. For the four semesters: autumn 1886, spring and autumn 1887, and spring 1888, Simon Paulli ¹⁹ was the first student to note down the spoken words in three volumes and with inserted comments by Bohr himself. ²⁰ In these notes there are just four occasions on which there appear sketch‐drawings of semi‐hyperbolic saturation curves for dose‐binding, but no hint of an equation describing rectangular hyperbolic dose–responses. ²¹ Thus, already a year after their discovery and publication, simple hyperbolic‐like curves were implemented in Bohr's teachings and discussed thoroughly. A bit later, Bohr associated the semi‐hyperbolic behavior of oxygen binding to his observation of at least four different forms of a disaggregated hemoglobin [7, 8, 150]. Again later, notes from Bohr's physiology lectures were taken down by two other medical students, Frederik Hansen in 1890 and 1891 and Peter Hinkbøl Petersen in 1899 and 1900, ²² in which the same simple semi‐hyperbolic graphs for gas binding were repeated and discussed, without algebraic formulations or indications of “S‐forms.” I have noted, that as late as 1892 in evaluations of oxygen saturation of hemoglobin in salt containing solutions, Bohr still drew simple hyperbolic‐like curves for the oxygen‐hemoglobin binding to different forms of the hemoglobin molecule, properly partially imagined as dissociated protomers, Figure 8e (Bohr 1892b). Due to harsh handling of the hemoglobin, such possible dissociation could have destroyed an allosteric behavior. Discovery and documentation of an S‐formed non‐hyperbolic binding relation between oxygen and hemoglobin still had to wait for 12 years. Handwritten lecture notes by medical student Hagbard Vestergaard on oxygen binding to hemoglobin, as late as 1910, still had no indication of a deviation from a simple hyperbolic relationship, see Endnote 22.

8.3. Bohr Discovers Homotropic Allostery

Around 1900, based on Hüfner's two papers on oxygen binding (op. cit.) and his own insight from 1885 and later (Bohr 1885, 1886, 1892, 1898) [3, 8, 26, 29], Bohr dimly doubted a simple hyperbolic binding scheme for oxygen binding to hemoglobin, a hunch that culminated with and was confirmed by experiments in Bohr's lab in 1903. Bohr looked at an S‐shaped O₂‐Hgb binding, Figure 3b (Bohr 1904b) [23] and sought to theoretically treat it algebraically in an immediately preceding publication [20]. ²³ Hence, 14 years after Hüfner first suggested an algebraic simple hyperbolic binding of oxygen to hemoglobin [24], and reconfirmed it in 1901 [25], Bohr demonstrated a clear deviation from Hüfner's hyperbolic theory for O₂ binding in full blood [20, 23].

This was also touched on in later publications [40, 59]. Now well‐known, several decades later, this non‐hyperbolic behavior was mechanically explained at a molecular resolution, that is, oxygen binding followed a bit more complex binding scheme than for CO due to an O₂‐elicited allosteric change in intact hemoglobin upon simultaneous binding of more than one molecule of O₂, Perutz 1960 [151, 152, 153]. In the article from 1960, Max Perutz (1914–2002) and coworkers merely speculated that the conformational change eliciting the allostery upon binding of oxygen molecules, was due to an interrelated reconfiguration of the four hemoglobin subunits, only to be confirmed later, Perutz 1970 [154].

8.4. Bohr Rejects Hüfner's Hyperbolic Theory

Understandably, due to Hüfner's somewhat unjustified criticism of Bohr's findings and Hüfner's own mistaken method for analyzing O₂‐binding data, Bohr became a stern opponent to Hüfner's interpretations. Bohr never used Hüfner's hyperbolic equation for dose‐binding relations. Evidence for this is clear from different writings by Bohr and lecture notes as mentioned above, and explicitly in statements by Bohr [20] with reference to Hüfner's approach in both 1890 and 1901 [24, 25]. Thus, Hüfner's erroneous assumption that O₂ binding to hemoglobin followed a simple rectangular hyperbola, repeated as late as 1901, was also vividly described a decade later by Joseph Barcroft [120], where he pinpointed how Hüfner's method for O₂ binding to hemoglobin was wrong and how Bohr was right. Barcroft wrote:

You can have any number of rectangular hyperbola all of which pass through the point A [origo 0,0] and approximate to OX [i.e., 100 %, as shown in Barcroft's fig. 10]. The difference between them lies in the value of K. [K is the association constant for the binding process]. Now Hüfner assumed the correctness of the equation and set out to find the value of K. This can be done from one point. He used a number of samples of hemoglobin prepared in different ways, determined a point for each, found the value of K, averaged these values and produced a curve. [Comments in square brackets inserted by me.]

Barcroft here refers to a figure in Hüfner's 1890 publication and he continues arguing that Bohr took the right approach:

But a nemesis awaited Hüfner. His speculations fell into the hands of a physiologist of a diametrically opposite school. Bohr had inherited a tradition from the great laboratory of Ludwig which, though it may carry its holders to excessive lengths, at least forms a useful corrective to unjustifiable generalizations. Bohr's motto was that every experiment had a value, nothing which was obtained as the result of a test in the laboratory was set aside on the ground of its inherent unlikelihood, of its failure to fit general principles. Bohr therefore determined to map out the curve relating the pressure of oxygen to the relative quantities of oxy‐ and reduced hemoglobin point by point, irrespective of laws, and to find out experimentally what the curve was like. The actual curve determined point by point differs fundamentally from Hüfner's hyperbola [(Bohr 1904 b; Hüfner 1890, fig., p. 15)] [23, 24]. Barcroft (1914, pp. 21–22) [120]. The square bracket above is a comment by me.

8.5. Bohr Invents a CO Method for Lung Diffusion Capacity

As a matter of destiny, Bohr himself never got around to perform experiments and publish results for carbon monoxide (CO) absorption to hemoglobin in blood or salt solutions, although referring to such data by Winkler [155]. Johannes Bock mentioned above, a close associate of and guided by Bohr, did CO‐hemoglobin binding experiments with tabulated values of CO‐saturation versus CO‐pressure, and Bohr surveyed these experiments closely [121]. With modern software it is easy to show a nice hyperbolic relationship for these data, see Figure D1. Late in life, Bohr provided a detailed method to study gas diffusion capacity in lung tissue by reference to and based on CO inhalation experiments performed by N. Gréhant on dogs and by JS Haldane on mice. ²⁴ Bohr used their data with recalculated integral mean arterial pressure gradients for CO and employed those for determining the mean alveolar‐arterial O₂ pressure gradients and lung diffusion capacity (Bohr 1909) [59], a method also mentioned by the Kroghs in 1910 and later described in detail by Marie Krogh (1874–1943) in her 1914‐accepted dissertation, also published in English in 1915 [156].

9. Homotropic Allostery. Hemoglobin Binding and Enzyme Activity

9.1. Christian Bohr's Analysis of Saturation for Oxygen Binding to Hemoglobin

Of the two homotropy papers by Bohr published February 1904, the “first” was a theoretical evaluation aiming at a new set of equations to describe the peculiar non‐hyperbolic and S‐formed dose–response for oxygen binding to hemoglobin [20], while the “second” paper presented data and details on the obtained results with a presentation of a dose–response curve at rising O₂ concentrations [23], clearly deviating from Hüfner's suggested hyperbolic relationship for O₂ saturation binding at equilibrium (Hüfner 1890, 1901) [24, 25]. On the concepts “first” and “second” here, see Endnote no. 23.

9.2. Bohr Misses Hyperbolic CO‐Binding

During the years from 1898 to 1909, Bohr was totally concentrated on the binding of O₂ and CO₂ to hemoglobin and likely therefore came to ignore dissociation curves for CO‐hemoglobin and somewhat reject the hyperbolic relationship in equations for CO‐hemoglobin binding as employed by his adversary and critic, viz. Gustav von Hüfner. An unanswerable question: if Bohr had himself done experiments on CO‐hemoglobin dissociation, instead of his associate Johannes Bock, would he have realized the principal difference between CO and O₂ binding to hemoglobin and possibly accepted, rather than abhorred, Hüfner's hyperbolae as a starting point for equating the hyperbola‐deviating binding of oxygen to hemoglobin?

On Hüfner's hyperbolic theory and his handling of data, Bohr simply discarded the theory and only referred to the relative binding constant for O₂ as equated by Hüfner [20]. Looking back, Bohr should have developed the theory. Now, how Bohr, with an alternative algebraic analysis, abandoned Hüfner's hyperbolic theory and went wrong is detailed in the next Sections 9.3, 9.5.

9.3. Bohr's Refusal of Hüfner's Approach

In the first half of Bohr's first paper from 1904 [20] there is a thorough examination of Hüfner's theory for oxygen binding which Bohr rightfully rejects based on his own experimentally obtained data provided by August Krogh [23]. But Bohr simultaneously also ignored Hüfner's formulated hyperbolic relation at the end of both Hüfner's two papers on the issue, in which Hüfner forced oxygen binding data, according to his hyperbolic theory from 1890, onto predetermined parameters values for the constant K and assumptions about maximal saturation. As it turned out later, Hüfner's theory is correct for carbon monoxide, CO, ²⁵ where each of four protomers per unit of hemoglobin can bind one molecule CO, but without an induction of allosteric behavior. Unfortunately, with Hüfner's insistence on describing oxygen binding to hemoglobin in blood with a simple hyperbolic relation, as mentioned, it raised an aversion and resistance in Bohr to Hüfner's endeavor and seems to have blinded Bohr from using Hüfner's hyperbolic expression in his own development of a formulation for the binding of two molecules of oxygen simultaneously at two distant binding sites. This is one of Bohr's unfortunate but explicable misjudgements.

9.4. Bohr's Initial Algebraic Models of Allosteric Homotropy

A critical look with details is given here on Christian Bohr's paper describing the sigmoid O₂‐binding curve, Figure 3b, and formulating a theory for oxygen binding to hemoglobin, Figure 9a, Bohr 1904a [20]. In the second half of this paper, Bohr starts on a theory of his own for the sigmoid binding curve by listing reaction schemes based on the known law of mass action at equilibrium and a reaction scheme assuming two O₂ molecules binding simultaneously without possible intermediate complexes, where only one molecule of oxygen is bound. Also, in accordance with the mass action law, Bohr's formulation of the theory involved an expression in which oxygen pressure appears squared when there is binding with up to two identical ligands (2 × molecular oxygen, 2 × O₂) simultaneously as written in reaction scheme 2, Figure 9a. Meanwhile, there is a mistake in the further development by Bohr of his theory. Bohr gave two reaction schemes, 1 and 2, and two pertinent equilibrium equations, 1 and 2, but with a parameter F defined differently between reaction scheme 1 and equation 1. F is equal to all non‐globin bound heme in reaction scheme 1 and to just non‐oxygen‐bound, non‐globin bound heme in Equation 1, Figure 9a. Definitions for F in Equation 2 is as in reaction scheme 1, but not as in Equation 1. Nonetheless, Bohr completed a derivation by inserting Equation 2 with squared pressure terms for oxygen into Equation 1, thus accepting a mismatch between defined terms, that is, F in Equation 1 and Equation 2 being differently defined. Bohr's derived squared terms for both occupancy (y) and ligand pressure (x), as equated in the middle of page 686, and repeated here in Figure 9a. Onward, a fitting is done by Bohr yielding parameter values, some of which are assigned with astonishing accuracy, cf., k = K ₂ (760²/α²) = 26, K = k/(K ₁ B) = 40.37, and B equals actual maximal bound oxygen over heme bound oxygen → (y)/(z) = 1.29, Figure 9b, while cΧ K ₁ and K ₂ are equilibrium association constants in Equations 1 and 2 and α is an absorption coefficient. There is no indication in the paper of how one can specifically arrive at these values. Christian Bohr was known as a skilled mathematician solving undetermined gradients by using integrals, interpolation, and planimetry. He may have extracted the values for his three parameters by planimetry. We just do not know. Based on the presented experimental data and on equations at hand, specifically the last equation on Page 686, Figure 9b, it can be shown with modern nonlinear fitting techniques that there is a broad range of values for the first two parameters that will satisfy a reasonable fit to the obtained binding data of oxygen to hemoglobin.

FIGURE 9.

(a) Bohr's mismatch of model entities. Bohr writes a reaction scheme (1), where H is equal to non‐dissociated hemoglobin, F is total iron containing heme, and G dissociated globin. For the further derivation, iron containing free heme (F) is defined as partially oxygen bound (z or F _o) and partially not bound to oxygen (u or F) as written in reaction scheme (2). In Reaction scheme (2) G is equal to the sum of oxygen‐ and non‐oxygen bound heme (u + z), or (F _o + F), but F is different from F in reaction scheme (1). The pertaining mass action expressions are then derived by Bohr as Equations (1) and (2). K ₁ and K ₂ = association equilibrium constants, C = concentration of hemoglobin and heme, x = oxygen pressure, y = cm³ oxygen bound in one gram hemoglobin, B = maximal cm³ oxygen bound to a gram of hemoglobin, k = u ≅ x ²/z or K ₂ ≅ (760/Χ ≅ α)², K = k ≅ B/K ₁, in which α is an absorption coefficient. From Bohr 1904 [20]. (b) From Bohr's paper with a homotropic allostery model 1904. Marked with blueish weils are two differently defined Fs in model derived equations and evaluated parameter values. From Bohr 1904a, submitted 27 January [20]. (c) A summary of dose–response plots by Bohr and Hüfner from 1885 till 1904. Ligands are CO, O₂, and CO₂.

9.5. Present Algebraic Models for Homotropy

When starting up with a new approach in unknown territory, Bohr's theoretical evaluation and tests are somewhat justified. No doubt, Bohr began the theoretical game of analysis of homotropic allostery data, long before the adjective “homotropic allosteric” had its final definition settled in 1965, with binding of more than one ligand of the same type and at the same time (Bindslev 2008, Ch. 10; Stefan M and Le Novère N 2013a; Stefan and Le Novère 2013b) [36, 157, 158]. Nowadays also more generally referred to as “non‐competitive cooperativity,” see Appendix B.8, With the clarity of hindsight, Bohr should have accepted Hüfner's hyperbolic scheme as a starting point. A summary slide of the binding plots by Hüfner and Bohr for hyperbolic and homotropic CO₂, CO, and O₂ are in Figure 9c.

10. Hyperbolic Formulations of Homotropy After Bohr

Six years after Bohr's attempt to formulate a homotropic allostery, a new effort was made with a second attempt to develop a theory explaining the sigmoidal binding of oxygen to hemoglobin. It came with Hill's proposal in 1910 for an exponentiation of terms, similar to Bohr's two‐component hypothesis, but now with a hyperbolic relationship tacitly following Hüfner's derived equilibrium kinetics. Archibald Vivian Hill (1888–1977) was a young 22‐year‐old researcher in Scott Haldane's lab. A photo of Hill is in Figure 10a.

FIGURE 10.

(a) Scientists involved in developing equations for homotropic allostery. Starts with the eldest scientist in upper left—turning clockwise and ends with youngest at lower left. Bronislav Werigo was born in the Vitebsk Province, Belarus. He did not participate in allosteric model developments. “Changeux” picture published with his permission. (b) Two “young” scientists, Christian Bohr and August Krogh, before their break in 1907. Bohr to the left around 1890, age ca 35 (Medical Museion, Copenhagen). Krogh to the right, age 30, taken right after Krogh's courtship of Marie Jørgensen (photograph by Frederik Riise 1904, Royal Danish Library) [32].

10.1. Hill's Theory for Homotropic Allostery, 1910

Without mentioning Hüfner's principle of hyperbolic rectangular regime for single ligand binding to hemoglobin nor for that matter pointing to Bohr's algebra or to Henri's hyperbolic scheme for activity in enzymatic catalysis, Hill as the first adapted the hyperbolic formulation in his approach to simulate a simultaneous binding to hemoglobin of several (‘n’) one‐type ligands as molecular oxygen, O₂ [159]. Parameter “n” later became the Hill number or coefficient.

To address a second order or higher order relationship between occupancy and ligand (oxygen) concentration at equilibrium, Hill first suggested a sum of hyperbolic rectangular expressions going from one to increasing numbers of bound oxygen molecules, that is, from 1 to n (Hill AV 1910, equation A) [159]. By selecting parameter values somewhat at random for his equation and tedious calculations, Hill could obtain a rather acceptable fit to literature values for oxygen binding to hemoglobin in various salt solutions. The employed data were taken mostly from results published by Barcroft and Camis [160]. Thus, AV Hill was the first to give a hyperbolic expression for cooperative behavior, although the included parameters, dissociation constant, K, number of binding sites n (Hill's coefficient), and maximal binding constant, L _max, had no physical meaning; as also noted by Hill (Hill 1910; Bindslev 2008, Ch. 10; Stefan M and Le Novère N 2013a; Stefan and Le Novère 2013b) [36, 157, 158, 159].

As Bohr had good contact with John Scott Haldane in London, he may have known about the derived equation by AV Hill in Haldane's laboratory in early 1910 describing mathematically the S‐formed binding behavior for more than one oxygen molecule binding to hemoglobin, “Hill's aggregation theory.” My guess is that Bohr, had he lived long enough, could most likely have participated in developing Hill's ideas.

10.2. Hill Type Cooperativity. Models After 1910

In the following years several model researchers took up the challenge of how to understand and describe the O₂ binding to hemoglobin, before knowing the details about the hemoglobin structure and dynamic conformations behind the allostery, first documented 60 years after Hill's equation (Perutz 1970) [154]. Hill's approach was carried further by several authors ending with a generalized and elaborated set of equations for multi‐ligand binding [161, 162, 163] followed by Wyman, Monod, and Changeux and ending in 1966 with a fully developed theory by Koshland, Némethy, and Filmer, the KNF‐model [164], more than 60 years after Bohr's first try. Details on this development are given in several texts, for example [36, 157, 158, 165], with some of the participants depicted in Figure 10a.

Together with positive cooperative binding of oxygen binding to hemoglobin, a form of positive homotropic allostery, additionally enzymatic substrate inhibition, a form of negative homotropic allostery, was also described, that is, multiple binding of a single‐type ligand with self‐inhibition for instance of enzymatic activity or receptor activation also termed “negative cooperativity” [134, 165, 166].

10.3. Introduction of the “Allosteric” Concept

The origin and history of the term “allosteric” is detailed in Appendix B.2. The term “allosteric” was coined by François Jacob (1920–2013) and Monod in 1961 [105], and later in 1965 supplied with terms as “homotropic” and “heterotropic” effects. A reference to Christian Bohr 1904 [20] was included as well as text references to Leonor Michaelis and Victor Henri [143]. In the paper from 1965, based on his broad knowledge especially about positive cooperative regulation of hemoglobin entities, Wyman had a decisive impact on the formulations and aspects of defining allostery [167, 168, 169], while Monod was the expert on transcription factors [105] and Changeux the expert on product inhibition for enzymes (Changeux 1961, 1964) [142, 170], thus enclosing several of the issues on homotropic and heterotropic cooperativity. In Fact, Changeux already in 1961 operated with a non‐overlapping (allosteric) binding site for an end‐product. There is an interesting account of the interaction between Wyman and Monod about their collaboration leading to the MWC model [171]. Changeux kindly forwarded me a copy of his dissertation, in which there are early references to both Wyman, 1948 and 1963, and to Bohr's first 1904 paper. The combined insight resulted in one of the most fruitful, simple, although limited models for an allosteric description, and shortly afterward was surpassed by the more comprehensive KNF models as well as other models [36, 164, 172].

10.4. Present Simple Two‐State Allosteric Models

10.4.1. A Simple Homotropic Two‐State Model

The two homotropic papers with Bohr as sole author in 1904 demonstrated the S‐formed dissociation curve (cooperativity) and the O₂‐binding was analyzed by Bohr with two distant binding sites on a monomer or on different entities at increasing oxygen pressure and keeping the CO₂ pressure fixed. Due to separate binding sites, Bohr's non‐competitive cooperative binding later became known as positive homotropic allostery. The following models were developed for a tetramer of four entities, protomers (Adair 1924; Svedberg and Fåhraeus 1926) [173, 174] with four binding sites, each at a separate subunit, and with their interactions eliciting allostery as structurally confirmed in 1970 [154]. Returning to Bohr's two‐site model and to the two‐state model by Monod, Wyman and Changeux, but not to describe a four‐site model of O₂ binding to hemoglobin, which is the simplest model for allosteric binding? It is the homotropic allosteric two‐state model (HoATM or HOTSM) with only two binding sites for an allosteric binding behavior. That model with only two binding sites came 104 years after Bohr's attempt. As indicated this model includes spontaneous activity with only two binding sites per protomer, or two protomers each with a single site, including possible positive and negative non‐competitive cooperativity and tacitly with linked functions and energy cycles (Bindslev 2008, HOTSM Ch. 7, 2013) [36, 175]. A ligand eliciting either positive or negative homotropic allostery may be designated as either a positive homotropic alloster, PHoA, or a negetive homotropic alloster, NHoA [175].

10.4.2. A Simple Heterotropic Two‐State Model

Further, in 1904 two triple‐authored papers with Bohr, Hasselbalch, and Krogh documented and discussed the diminishing effect of CO₂ on O₂‐binding, so‐called negative “cooperativity,” and soon after known as the “Bohr Effect” [21, 22]. Due to Bohr's understanding of the CO₂‐effect as elicited from a distant secondary binding site, the effect was also later known as a negative heterotropic allostery [100], with CO₂ as a negative heterotropic alloster, NHeA. Brown's and Henri's product inhibition for enzymes did not initially discriminate between a competitive or non‐competitive mechanism [111, 125]. ²⁶ Therefore, the Bohr Effect was the first demonstration of one type of a negative heterotrophic allostery. Again, not to describe O₂ and CO₂ binding to hemoglobin, but rather to analyze the simplest noncompetitive heterotropic allosteric two‐state model, HeATM or ATSM, with spontaneous activity and only two binding sites, such a model appeared at the turn of the millennium 2000 (Hall 2000, Bindslev 2008, ATSM in Ch. 7, Bindslev 2013) [36, 175, 176]. Recently, a model was derived similar to the Hall model but based on a full set of equilibrium dissociation constants, see Ehlert 2015 and 2016 [177, 178]. For definitions and more details on terminology on cooperative product inhibition as either competitive or non‐competitive (allosteric) consult Appendix B.8 and Table B1. Heterotropic allostery, in form of the Bohr effect, is discussed in detail in Chapter 11. Thus, CO₂ in modern terminology is a negative allosteric modulator (NAM), or more to the point, a “negative heterotropic alloster” (NHeA).

Indeed, the four Bohr papers in 1904 are the sources referred to in this paper's title as the first demonstration by Bohr of what 60 years later was signified as homotropic (homotrope) and heterotropic (heterotrope) allostery (Changeux 1964, p. 84; Monod et al. 1965; Wyman 1965; Edsall 1980; Bindslev 2008, Ch. 7) [36, 100, 142, 143, 179].

10.5. Complex Cooperativity Models

It should be mentioned that today, beyond the simple two‐state models presented in the preceding Subsections 10.4.1 and 10.4.2, there is a huge literature on more complex models and folding of protein molecules as well as a host of intricate experimentation to reveal the mechanisms in systems questioning these complex systems as either single state, multistate, energy landscape dependent, including linked functions and other types of cooperativity also encompassing allostery. To just mention a few references with studies of direct relevance for hemoglobin and enzymes including states and energy cycles, see for instance those by Ackers & Johnson and McCullagh and coworkers [180, 181] and further on present and new ideas, terms and methods on cooperativity and allostery, see Appendix C. For a resolution on the questions about induced fit versus conformational selection see Appendix B.7.

11. Heterotropic Allostery, Including the Bohr Effect. Activity and Lack of Reciprocity

11.1. Introducing Cooperativity and Allostery With a Related Example

Before I start on Bohr's discovery of his “Bohr effect” in Chapter 11, we need to get some terminology about bioregulatory phenomena in place for signifiers as “cooperativity” and “allostery.” A regulatory phenomenon in biology is often observed when one ligand is able to augment or diminish the binding or effect of another ligand. That is, a primary ligand as a hormone may have its binding or effect increased or lowered by a different endogenous ligand binding nearby or at a common binding site. For instance, without considering reversibility in a lowered binding or of an effect, part of such a regulation is covered by the term “negative cooperativity,” which includes both competitive and non‐competitive mechanisms, see Table B1. In case cooperativity is effectuated by binding to a non‐common binding site, it is a non‐competitive regulation and equal to allostery. A negative allosteric effect is caused by a non‐competitive “negative cooperative ligand” or more distinct a “negative allosteric modulator,” NAM. If caused by two different ligands, there is a more specific term for the negative allosteric modulator, namely it is a “negative heterotropic alloster,” NHeA, see Appendix B.5 and B.6. Such a regulatory interaction may also take part mutually between two different ligands where both are in fact considered as equally primary ligands. In this connection with different but equally primary ligands it is relevant for Bohr's discovery of the interaction between the two gases, O₂ and CO₂, and for the Bohr Effect as well as for the Haldane effect. As both the Bohr and Haldane Effects are examples of highly reversible and negative non‐competitive cooperativity, we may designate the two gases as RNHeAs.

11.2. The “Bohr Effect”. One Type of Heterotropic Allostery

There were early proponents of a mutual and opposite exchange between O₂ and CO₂ content in arterial and venous blood and also more directly of a reciprocal interaction between the two gases on binding to hemoglobin. With his improved gas measuring apparatus, Heinrich Gustav Magnus, Figure 4d, showed a shift in gas content between arterial and venous blood samples from people, who were paid for their blood donation, and from horses. On Magnus around 1837 and his equipment there are exquisite sources [9]. Later Stokes, Figure 4f, by direct observation and photometry, found that CO₂ could displace O₂ in dilute blood solutions squeezed between two glass slides, explaining a diminished binding of O₂ to “purple cruorine” (i.e., reduced hemoglobin) in lungs [182], Appendix D.11.

11.3. Bohr Discovers the “Bohr Effect,” Heterotropic Allostery

As mentioned, Bohr and coworkers paper from January 30, 1904, covers one of the first demonstrations of an allosteric interaction between two different ligands, O₂ and CO₂, Figure 3c [21]. The conclusion was that CO₂ had a clear impact on the O₂ binding, whereas there did not seem to be a reciprocal interaction of O₂ interfering with binding of CO₂. And then in another paper of that year, it was again stated that there was a lack of reciprocity for an effect of O₂ on CO₂ binding. This observation was reasoned by a suggested binding of CO₂ to globin rather than to heme in hemoglobin. Except for a reference to the Werigo proposal mentioned below in Section 11.5, this second paper additionally included data on oxygen binding to horse full blood, and with no further information of importance [22]. Another early example of negative heterotropic cooperativity is Adrian Brown's demonstration of invertase inactivation by its own products, invert sugar in form of D‐glucose and D‐fructose, also discussed by Victor Henri [125, 129].

11.3.1. On the Lack of a Heterotropic Reciprocal Effect

From a physiochemical point of view, the suggested separate binding of two gases, oxygen to heme and carbon dioxide to globin, is not a valid physical argument as an explanation for the lack of an obtained reciprocal effect (Bohr et al. 1904a, b) [21, 22]. Therefore, as it later turned out, by employing several data sets and improved sensitive measurements, it was demonstrated that there is a reciprocal interaction of O₂ on CO₂ binding to hemoglobin—the so‐called “Haldane effect” already mentioned in Subsection 3.7.3 [41]. Lack of reciprocal interaction was debated by scientists in the early 20th century engaged in the problem of reciprocal effects for O₂‐CO₂ binding to hemoglobin. Nonetheless, the discussion of a reciprocal effect was first clearly recognized by Henderson in 1928 as an effect that had to be there for O₂ on the CO₂ binding to hemoglobin [183, 184]. Presently it is well‐known that, a major part of the CO₂ effect on O₂ binding is a pH effect (Ferry and Green 1929; Wyman 1948; Antonini et al. 1963; Imai and Yonetani 1975) [167, 169, 185, 186].

11.4. Another Form of Heterotropic Cooperativity—Henri's Enzymatic Product Inhibition

A year before Bohr et al. published their results on the effect of CO₂ on O₂ binding to hemoglobin, the Bohr Effect, Bown and Henri had described and formulated product inhibition in enzymatic catalysis, also an important process in the present‐day category of negative heterotropic cooperativity (Brown 1902; Henri 1903) [111, 125]. As neither Brown nor Henri differentiated between a competitive or non‐competitive (allosteric) cooperative action for product inhibition, the discovery of a heterotropic cooperative phenomenon considered by Bohr to take place from two distinct binding sites qualify him as the discoverer of heterotropic allostery in 1904. As mentioned for a reciprocal effect in the process, oxygen affecting the binding of CO₂ to hemoglobin, was first documented 10 years later by Christiansen and coworkers in 1914. Part of Brown's product inhibition was later found to be partially non‐competitive, i.e., allosteric, for D‐glucose and only competitive for D‐fructose when interacting with the invertase enzyme [187].

Product inhibition was equated with an algebra for chemical dissociation relations (Henri 1903; Yates and Pardee 1956; Changeux 1964) [111, 142, 188] and its description culminated with possible math models for both homo‐ and heterotropic binding, activation, and inhibition [143]. In a general view, this paper by Monod and coworkers is often considered the start of what relates to the modern understanding and development of positive and negative allosteric drugs with designators as PAMs and NAMs. The math for hemoglobin allostery with states and tacit linked function was treated and analyzed in detail by Ackers and coworkers [180, 189].

11.5. The Bohr‐Werigo Controversy

11.5.1. Werigo's Deduction

Although there was an inkling that O₂ should influence the binding of CO₂ to hemoglobin, Bohr was unable with experiments to demonstrate a significant effect of O₂ on the CO₂ binding to hemoglobin, both in 1892 and 1898 [7, 8]. With no further experimentation, this conclusion was repeated in 1904 together with Hasselbalch and Krogh [22]. An exchange between CO₂ and O₂, bound reversibly to hemoglobin as blood circulated between the periphery and lungs, was also explored and discussed by researchers in the last part of the 19th century ending with a prophetic statement by Werigo in a French journal, cited by Bohr in 1898 and again with collaborators Hasselbalch and Krogh in 1904 [8, 22, 27, 28]. Werigo writes (1898, p. 611) [27]:

Si I'oxygène pent ainsi chasser I'acide carbonique de sa combinaison avec I'hémoglobine, il est tres probable que I'acide carbonique doit aussi chasser I'oxygène de cette combinaison, c'est‐a‐dire que I'influence expulsive de ces deux gas est réciproque. En me fondant stir cette conception, j'ai émis une hypothése qui devait expliquer la régulation des échanges gazeux dans la profondeur des tissus et notamment le fait que la quantite d'oxygène que recoit chaque tissue est en relation directe avec I'activité de ce tissu.

[In English: Thus, if oxygen can displace carbon dioxide from its combination with hemoglobin, it is most likely that carbon dioxide must also displace oxygen from this combination, that is to say, that the expulsive influence of these two gases is reciprocal. Based on this conception, I have made a hypothesis that should explain the regulation of gas exchange in the depth of tissues and especially the fact that the amount of oxygen that each tissue receives is in direct relation to the activity of this tissue.]

Bronislav Werigo, Figure 10a, had earlier found a kind of Haldane Effect, that is, an interaction of O₂ pressure lowering CO₂ binding to hemoglobin [190] but had not looked at the reverse process, the Bohr Effect. Relying on his own experiments with an influence of O₂ on the CO₂ binding, Werigo made the logical physiochemical conclusion that in a reciprocal fashion CO₂ pressure had to influence the binding to and regulated release of O₂ from hemoglobin (Werigo 1898, p. 611) [27]. Thus, referring to Bohr's work, Werigo argued for the reciprocal effect with no experimental evidence for a Bohr Effect, in spite Bohr's paper on CO₂ binding clearly described no effect by an imposed O₂ pressure [39].

11.5.2. Bohr's Refusal of Werigo

Hence, repeatedly not being able to show a “Haldane effect” as late as 1904 (and 1905, see subsection 3.7.4), in his paper coauthored with Hasselbalch and Krogh, Bohr felt justified to brusquely refute Werigo's argumentation, and zealously to brush aside Werigo's reference to his own work from 1892 [22].

Bohr et al. 1904 [22] writes the following (translated from German):

Werigo assumed in Archiv der Physiologie (5) X. 3. S. 610 [reference to Werigo 1898 [27], nb], without conducting experiments on it, that carbon dioxide and oxygen mutually displace each other from their combination with hemoglobin. This assumption, which cannot be derived, as Werigo claimed, from the existence of a CO₂‐hemoglobin compound demonstrated by Bohr, is incorrect (see this Archiv, 1891, vol. 111, p. 64). [The publication year of this referred Bohr article is now 1892 [39], nb].

And they continue with the following:

Aus den obenstehenden Versuchen geht hervor: dass die Menge der an das Hämoglobin gebundenen Kohlensäure von gleichzeitig vorhandenem Sauerstoff nicht beeinflusst wird, indem die Absorption überall bei entsprechen dem Drucke und entsprechender Temperatur auf dieselbe Weise wie in reiner Kohlensäure vor sich gegangen ist [22].

[The above experiments show: that the amount of carbonic acid bound to hemoglobin is not influenced by simultaneously present oxygen, in that the absorption has taken place everywhere at corresponding pressure and corresponding temperature in the same way as in pure carbon dioxide.].

To obtain verification of truth and reality, the only means are repeated experimentation, improved resolution, critical analyses, and proper formulation, although results may always be shakable and falsifiable. Thus, as time passed Bohr was proven wrong and Werigo was right about the reciprocity including a real effect [27]; however, first later as the Haldane effect. Conclusion: Werigo presupposed the Bohr effect, while Bohr demonstrated it. On the other hand, Bohr missed its companion, a reciprocal interaction documented as the Haldane effect [41].

11.6. Another Bohr Effect Controversy. Rumors and Misinterpretation

As mentioned, the literature has several times dealt with who rightfully discovered the heterotropic allostery effect in form of the Bohr effect—was it Bohr, or was it Krogh? Hence physiologists including John Edsall, Figure 10a, Knut Schmidth‐Nielsen and John West in America have questioned who should be given credit for the discovery of the “Bohr effect”—with suggestions that the effect should rightly be assigned to August Krogh as the “Krogh effect” [102, 184, 191]. Edsall, who had a detailed insight into the subject, gave full credit to Bohr's mastery as a physiologist with an overwhelming positive and detailed account of Bohr's importance for respiratory physiology and his many achievements [184]. Meanwhile, Edsall concludes that the Bohr Effect should be termed the Krogh Effect based on Krogh's construction of a more accurate and sensitive tonometer, elegant sampling equipment, performing the experiments, and a rumor by Roughton conveyed to Edsall, that Krogh in 1948 had “stated unequivocally” that he was the rightful discoverer of the observed CO₂ effect on O₂ binding. ²⁷ Those were the reasons why Edsall meant that the “Bohr effect” rather be called the “Krogh effect.” Nearly 20 years later, Knut Schmidt‐Nielsen repeated and supported this view (Schmidt‐Nielsen 1991) [191]. Meanwhile, Dr. Albert Gjedde eloquently rebutted and with great insight defended that the “Bohr effect” term should indeed be accredited to Christian Bohr, while pointing to failures on both sides in the controversy on the “Bohr effect” as well as on the debate between Bohr and Krogh on Bohr's “Secretion Theory” (detailed below). The secretion theory concerns the movement of O₂ across lung tissue as either active or passive, secretion or diffusion, since there seemed to be an active element in the process during forced work or high altitude climbing with an increased number of open capillaries, thus increasing the diffusion capacity actively (Gjedde 1992, 2010) [192, 193].

11.7. Facts for the Bohr–Krogh Effect Controversy

During 1902 and early 1903, Bohr asked Krogh and Hasselbalch to look for reciprocal interactions between O₂ and CO₂ on binding to hemoglobin in blood samples, referred in a letter of February 1903 by Krogh to his mother Mimi, see below. Therefore, Krogh in collaboration with Karl Hasselbalch prepared and upgraded the equipment in Bohr's laboratory, including the available tonometer and other appliances for measurements of gas content, now sufficiently handling small 5 mL samples with an augmented surface ratio, Table D2, and thereby improved (shorter) equilibration time for gases. Krogh had no special interest or deep insight with the background for these types of experiments, see the following Subsections 11.7.1, 11.7.3. Note that the experiments in the spring of 1903 were not carried out with Krogh's microtonometer, as relayed later by several authors. The used tonometer was an improved Bohr‐tonometer. Krogh's microtonometer was first constructed during the year of 1906 and used for “the seven little devils” experiments carried out between1906 and 1909 [194, 195, 196]. ²⁸ In the 1903 experiments, pressures not lower than 7 mmHg for O₂ were employed. Observe though, that O₂ pressures in Bohr's elegant experiments from 1885 ran down to about 2 mmHg! As Bohr knew that the measurement at these low pressures could be unreliable [26], it is most likely the reason why Krogh in all measurements of 1903 only went down to an oxygen partial pressure around 7 mmHg O₂.

11.7.1. A Triple‐Barrel Smoking Gun. First Barrel

My understanding about the propriety to the “Bohr Effect” includes a triple‐barrel smoking gun. First barrel: In 1995 Krogh's daughter, physiology professor Bodil Schmidt‐Nielsen (1918–2015), published a thrilling and detailed book about her father and mother (Schmidt‐Nielsen 1995) [32]. In Chapter 6 of this book there is a balanced view on the “Bohr‐Krogh effect” controversy. Here you can read an extract from a referenced letter from August Krogh to his mother Mimi, dated Feb 1903, mentioned above, in which he writes:

I have had the satisfaction that my constructions seem to be highly successful.

(Schmidt‐Nielsen 1995, p. 54) [32]. This is a straight translation of the sentence in Krogh's letter in Danish where he writes “Jeg har haft den tilfredsstillelse at mine konstruktioner synes at være særdeles vellykkede.” However, in a Danish version of the same book from 1997, there is a bit longer excerpt from the letter, here translated to English:

In the laboratory, I am working with Dr. Hasselbalch on setting up some new instruments that I have planned and constructed for a series of experiments that Prof. Bohr wanted to have carried out. I have had the satisfaction that my constructions seem to be highly successful. [The underlining is by me.]

The 1997 book is a translation of the English version to Danish by Gitte Lyngs, slightly rearranged, modified and with additions, like the one above from the February 1903 letter.

11.7.2. Second Barrel

On appliances and methods used in the spring of 1903, including a newly reconstructed Bohr‐tonometer, and with results obtained on horse blood, August Krogh began his own paper with the following statement [198]:

Die in vorliegender Abhandlung beschriebenen Apparate und Methoden habe ich einer Aufforderung des Herrn Professor Bohr zu Folge construirt und ausgerabeitet, und sie wurden u. A. zu der Untersuchugsreihe angewandt, die den Gegenstand des folgenden Aufsatzes bildet.

[The apparatuses and methods described in the present paper were constructed and developed at the request of Professor Bohr, and they were applied, among other things, to the series of investigations that form the subject of the paper.]. Emphasises by me.

This citation which lends to Krogh's honesty, is not mentioned in either of the two books by his daughter. The mentioned equipment was used for all experiments in spring 1903 and as mentioned published in several of the seven articles from 1904, Appendix D.1. As also already mentioned, in December 1903 Bohr had suggested to Krogh to draft a paper on the results of varying CO₂ pressures on binding of O₂ to hemoglobin, referred to in a letter, Schmidt‐Nielsen 1995, p. 59, and 1997, p. 79 [31, 32]. Meanwhile, as clearly evidenced by the ensuing third barrel, Subsection 11.7.3, although Krogh is honored by Bohr's gesture to write the draft, it is without great enthusiasm that he intends to sit down to write an outline of a first draft for papers that later became known as a description of the Bohr effect.

11.7.3. The Third Barrel of a Smoking Gun

On January 3, 1904, Krogh wrote a letter to his mother Mimi in which he regrets he stayed in Copenhagen during Christmas holidays, although during the stay he enjoyed several visits to the Bohr's home in Bredgade 62—including the New Year's celebration with champagne and as the sole guest. This was the second time in Krogh's life that he was not home for X‐mas in Grenå. Krogh continues to write that after Christmas he has been very diligent, still has a big workload, and is struggling with uncle “Bill's Supplement,” see Endnote 5. Krogh is turned on in January 1904, ready to take action and finish writing two papers, his actual subject of real joy, for the journal “Meddelelser om Grønland” on carbonic acid content in sea water, in air, and in other matters as molluscan shells as well as its deposit by chemical reaction with basaltic rock; a total of more than 100 pages in English (Krogh 1904c, d) [33, 36]. Together with Svante Arrhenius, this was a start on the exploration of atmospheric CO₂ gas as cause of a greenhouse effect. English is now a language which Krogh feels comfortable with after writing his dissertation in English. In the letter, August also mentions that, with a suggestion from Prof. Bohr, Dr. Hasselbalch has agreed to draft the paper on the 1903 O₂‐CO₂ binding experiments instead of Krogh himself!

Krogh writes “/To this end, it helps a lot that Prof. Bohr has managed Dr. Hasselbalch to write the treatise on carbonic acid in the blood which he had intended for me/”.

The letter is mentioned in Schmidt‐Nielsen's books about her parents (Schmidt‐Nielsen 1995, 1997, pp. 59/79) [31, 32], with reference to the mentioned New Years celebration, but does not refer or comment on the decision by Bohr to help out. ²⁹ Why this is, I do not know. The complete letter is translated to English and cited in Appendix D.12. Thus, relieved and undisturbed, Krogh was happy to finish his two extensive “Greenland” papers on carbonic acid under natural conditions, as well as write up a lab protocol for his teachings in physiological lab exercises during May 1904. The resulting paper that Krogh should have drafted came shortly afterward as the first of seven papers, published on January 30, 1904, see Table D1 [21]. In May 1904, during his instructions in physiology labs, August Krogh met the medical student Birthe Marie Jørgensen. After the course, in a letter of June 7, 1904, he invited her to his flat for an evaluation of his teachings and in September 1904 they were engaged, Chapter 7 in Schmidt‐Nielsen 1995 and 1997 [31, 32]. My conclusion is that Krogh did the Bohr effect experiment in the spring of 1903 for the famous July 1904 BHK‐paper on Bohr's request and specifications, but Krogh did not contribute significantly to the analyses, nor did he participate in writing the papers on heterotropic allostery, not the first one in January 1904 nor the second one published in July [21, 22]. Moreover, in the next Section 11.8 Hasselbalch's account provides further justification for the “Bohr effect” term.

11.8. Hasselbalch Confirms the “Bohr's Effect”

In 1904, Karl Albert Hasselbalch was the other “young,” 29‐year‐old participant in the discovery of the Bohr effect. In his eulogy about Chr. Bohr's scientific life from 1911, there is an account related to the Bohr effect, from which it is clear that Bohr had an overall decisive role, a motif, and drive for its discovery and description, Appendix D.13.

The following sentence from Hasselbalch's eulogy seems to distinctly disclose the motivation in Bohr to search for the Bohr effect through experiments conducted in 1903 (translated from Danish):

On a specific occasion, Bohr then found himself, half a dozen years later, forced to resume and expand the investigation with improved methods (Hasselbalch 1911) [150].

This statement is most likely a reference to Hüfner's paper from 1901 on the interaction of O₂ and CO₂ on binding to hemoglobin. Again, this background for Bohr's drive and wish to have the experiments done confirms Bohr's propriety to the “Bohr effect.” All factual evidence and events, including Hasselbach's account described here and Krogh's letter of January 3, 1904 justifies the term “Bohr effect,” and therefore it is unfortunate that recent statements in both Wikipedia and by John West on the “Bohr effect” leave the impression that Bohr should be stripped of his claim to fame and indicating instead that it should be a “Krogh effect” when naming the CO₂ effect on oxygen binding to hemoglobin.

11.9. Misinterpretations Related to Edsall's Rumor

Statements by Edsall and especially West leave an impression that Bohr had nothing to do with the discovery of the Bohr Effect, heterotropic allostery. Obviously, if it is true what Krogh is cited for to have said in his statement, see Endnote 27, there are at least two explanations. (1) Krogh is just confirming that he did the experiments, not Bohr, which is true, or (2) Krogh just a year before he died in 1949, may have forgotten how the situation was when he wrote to his mother in February 1903 and just after New Years day in 1904, 44 years earlier, clearly indicating that Bohr in the spring of 1903, not Krogh nor Hasselbalch, had the insight to require the experiment performed as documented above, and that Bohr was the driver of the studies carried out with the help of Krogh and Hasselbalch, and that Krogh was not involved in analyzing the results for or writing the Bohr effect papers. To me, it is unlikely that Krogh had forgotten the sense in his February 1903‐ and 3 of January 1904 letters or the statement in the introduction of his 1904 paper [198] and therefore is bragging about his propriety. Krogh is most likely just confirming Explanation 1. The wandering gossiped Roughton statement is misinterpreted due to prejudice. Without presented documentation rumors run readily and fast.

John West has written about Bohr's skills and claimed that Bohr most likely did not write the famous paper from July 1904 by Bohr, Hasselbalch and Krogh on the Bohr effect (BHK#2 1904) [22]. Readers are encouraged to form their own conclusions, as West [102] discusses the Bohr et al. paper from July 1904 on page L586:

The first thing that the reader notices is that this paper is authored by three people, and it may be recognized that two of them were arguably more eminent scientists than Bohr, whose name, nevertheless, comes first.

And further from West's 2019‐paper on page L587 about the BHK July‐1904 paper:

This paper is a delight to read, and the style of writing is so different from that of the previous paper (1) discussed here that one wonders who wrote it. Bohr has pride of place as first author, but, as pointed out above, the writing style is nothing like that of the preceding paper discussed here. It seems very likely that either Hasselbalch or Krogh must get the credit. [Comment by me: the reference in (1) is to Bohr's paper on Pulmonary Respiration from 1892 [7].]

With my arguments about a three‐barreled smoking gun I have documented that these statements are wrong. Although West's article is supposed to praise Bohr's achievements, statements like these are unfortunate [102, 199]. Contrary to West's view, Bohr was capable of writing in a short and pointed style, just look at his three papers from 1904 presenting, discussing, and analyzing homotropic allostery for O₂ binding to hemoglobin and for CO₂ binding to hemoglobin [20, 23, 37]. One may also cite August Krogh's introduction statement about Bohr in his 1904 paper (Krogh 1904b) [198], clearly demonstrating who had the insight to suggest and formulate the protocol for the crucial experiments in the spring of 1903.

11.10. Resumé of Propriety to the “Bohr effect”

The claim referred to Krogh, transformed to an understanding of him as the real discoverer of the “Bohr effect” in 1948 (Edsall 1972) [184], looks like a slight slip of accuracy, but also a destructive one. In my understanding of the “Bohr effect”‐dispute it is fine to credit Bohr for the “Bohr effect,” while a term as the “Bohr‐Hasselbalch‐Krogh effect” would certainly also be acceptable. Historically, it would be incorrect to quote the effects of CO₂ on O₂ binding to hemoglobin as the “Krogh effect,” as first suggested by Edsall and later again by the late Knut Schmidt‐Nielsen (1915–2007), while correctly refuted by Dr. Gjedde. It may be added, Krogh never returned to further study the allosteric issue after 1904. In closing the controversy on who discovered the “Bohr effect”—heterotropic allostery—relaying the points above in the article on the Bohr Effect in Wikipedia will need relevant corrections.

12. Secretion Theory and “Specific Activity” Against Simple Diffusion

12.1. Did Bohr Stick to His Secretion Theory?

The “secretion theory” was a term associated with the claim that gases as oxygen and carbon dioxide in lung tissue in some situations were exchanged by an active principle [200]. Despite variations in the retelling of the fate of the oxygen secretion theory, the account here in Chapter 12 provides context for a more detailed insight with Bohr's character, the milieu in which the discovery of allostery took place, and the simultaneous and subsequent debate on mechanisms of gas transport in lung tissue. It is documented that shortly before his death, Christian Bohr abandoned his secretion theory.

12.2. Oxygen Secretion Theory Over 70 Years

In a somewhat substantial narrative, I delve into a dispute on the secretion theory as it emerged and evolved between physiologists in Germany, Denmark, England, and France during nearly 70 years, 1850–1920, and in its late phase, after 1890, also involved antagonist and agonist researchers as Leon Fredericq, Hüfner, Bohr, Krogh, Haldane, and Barcroft. The theory held that at least part of the gas passage across the alveolar wall in lungs implicated an active process, not only pure diffusion.

12.2.1. Biot and Swim Bladders

The above‐mentioned French physicist, Jean‐Baptiste Biot (1774–1862), Figure 11a, in his early thirties made a study on fish swim bladders in his leisure time. He had noticed that fishermen in catches from the depths got fishes with their swim bladder protruding out of the mouth, Figure 11b. In the year 1807, Biot rationed that the fishes were victims of a buoyancy trauma, and even after 2 days' delay, he found a content of oxygen in these bladders way beyond the content in ambient air; for example, in Oriola with up to 87% oxygen. Collected bladder air could ignite and explode in his eudiometer. For the oxygen accumulation, Biot concluded that a secretory process was at work, not a mechanical one (Biot 1807). ³⁰ Associated with polysitic (closed) swim bladders, today we have an explanation for the high oxygen content which is based on a forceful release of oxygen from hemoglobin by a pH‐dependent lower hem‐oxygen affinity (Bohr Effect) and lower hem‐oxygen capacity (Root effect) due to an acidification of capillary blood and combined with a counter current vessel arrangement of the blood bed and epithelia in form of a gas gland [202, 203], thus providing up to nearly 90% oxygen of total gas pressure in closed swim bladders.

FIGURE 11.

(a) Jean‐Baptiste Biot, French physicist 1774–1862. Biot attacked the buoyancy–swim‐bladder‐blown‐up‐to‐blast conundrum in 1807. Left picture from the www‐net and right picture from: https://link.springer.com/referenceworkentry/10.1007/978‐1‐4419‐9917‐7_157. (b) Fish with barotrauma. Expanded swim bladder protruding out of its mouth. Figure taken from the www‐net: From the site: In today's highly regulated climate in the offshore waters off of Florida, many anglers will be faced with releasing unintentional catches of Grouper, Snapper and Sea Bass. Above, typical signs of barotrauma. (Image for Space Coast Daily). https://spacecoastdaily.com/2020/06/the‐importance‐of‐venting‐deep‐water‐fish/.

12.2.2. Ludwig and Salivary Secretion

In 1842, Carl Ludwig with coworkers found the saliva production to be formed at a pressure higher than blood pressure and concluded that saliva was actively secreted by a gland mechanism, and different from the kidney secretion that was due to a mechanical filtration process [62, 77, 204]. Biot's and Ludwig's observations inspired physiologists in Europe, including Bohr, to as well argue for an active gas exchange in lungs. While the secretory mechanism was still undetected in the mentioned two examples, equipped with experimental evidence and based on these two initial examples, both Ludwig and his pupil Bohr were convinced that part of the gas exchange across the lung tissue was also somehow an active gland process, as they repeatedly found oxygen pressures in the arterial blood to be higher than in the expired air, and vice versa for carbon dioxide.

12.3. Start of Bohr's Active Gas Exchange

A discussion and disagreement about passive or active gas exchange in lung tissue, between Pflüger in Bonn and Ludwig in Leipzig, had ceased in the 1860s. In October 1888, Bohr published his first article indicating active secretion of gases (oxygen and carbon dioxide) across lung tissue in accordance with Ludwig's understanding of the process. Based on seven experiments out of nine, which showed pressure gradients opposite to simple diffusion from air to blood for oxygen and the other way around for carbon dioxide, Bohr wrote the following:

…; es hat also das Lungengewebe in diesen Fällen eine active Rolle sowohl bei der Kohlensäureauscheidung, wie bei der Sauerstoffaufnahme gespielt [5]. ³¹

Though, two additional experiments pointed at a diffusional process, a fair comparison was made to the assumed active transport in fish swim bladder [5]. This presumed active oxygen transport was also shown to be vagally regulated [205].

12.3.1. Active Physiological Processes

The processes in swim bladder, salivary gland duct, and alveolar tissue seemed driven by a yet unknown metabolic activity, thus vindicating a non‐vitalist view. On releasing oxygen from the swollen swim bladders, fishermen, with a flame nearby, had observed that could cause a minor explosion. Bohr, during a visit to London in 1898, demonstrated such an explosion for Scott Haldane and Claude Douglas, who had also become convinced that gas breathing across the lung tissue could be caused by an energy requiring mechanism [206]. Their stands were and are referred to as “the secretion theory.” It led to many discussions within the respiratory physiologist's community. The debate had started around 1850s and ended around the 1920s between people as Carl Ludwig, Christian Bohr until 1911, John Scott Haldane, August Krogh, and Claude Douglas against Eduard Pflüger, Leon Fredericq, Gustav von Hüfner, and August Krogh from 1910 (1907), Joseph Barcroft, and with a plethora of other physiologists and physicians [200]. Later bystanders and commentators were, for instance, Poul Astrup, John Severinghaus, Steven Sturdy, and John West. As mentioned above, Hüfner was one early opponent to Bohr's secretion theory.

12.4. Hüfner and the “Secretion Theory”

Hüfner read Bohr's 1888‐paper on the active secretion for gas (oxygen) exchange across the wall of lung capillaries [24]. Although Bohr's “activity” was not an activity as in the zeitgeist's vitalism with a mysterious active force, a type of the “Geist in der Natur,” as later purported by Bergson, Driesch, and others, ³² Hüfner challenged Bohr on his proposed gas secretion involving an active physicochemical force rather than just simple diffusion (Hüfner 1890, p. 10) [24].

Hüfner writes in the “polite” fashion of the time that he explicitly doubts Bohr's measurement of O₂‐ and CO₂ pressures in exhaled air and blood, results of measurements which had led Bohr to suggest active export of CO₂ and active influx of O₂ across the lung tissue, see Appendix D.14.

12.5. Details on the Krogh‐Bohr Controversy

Visions and versions of this controversy have been offered several times earlier [31, 32, 192, 193]. Section 12.5 with Subsections 12.5.1, 12.5.9 is a rather detailed account on a delicate matter. I found it was necessary to expand on issues related to the Krogh‐Bohr controversy, at least for me to understand the differences in views, arguments, and personalities between Krogh and Bohr, that in 1907 lead to the start of their controversial break‐up, and how they tackled their mutual discrepancies afterward. Was Bohr completely wrong?

12.5.1. Bohr and Krogh on Active or Passive Lung O₂ Uptake

During the year 1907 there evolved a notable controversy between Christian Bohr and his assistant August Krogh about the uptake of oxygen through lung tissue. The conflict is best described by Krogh's daughter Bodil (Schmidt‐Nielsen 1995, 1997, Chs. 6 and 9) [31, 32] and Hanne Sindbæk [43]. With his hæmataërometer, Bohr had repeatedly measured that the O₂ content in arterial blood was often above that of lung air [5, 6] and therefore, in a related dispute among respiratory physiologists, Bohr held that the passage of O₂ could be active from alveoli to the bloodstream across lung tissue. This was also the understanding of other physiologists in the field in the early 1900s, and Krogh as well had supported this view together with Bohr (Bohr et al. 1904b; Schmidt‐Nielsen 1995, pp. 55–56, 1997, pp. 75–76) [22, 31, 32]. Bohr's findings of a gland‐like secretory process of gases triggered him to continue to study the problem, that is, “secretion or no secretion?” In April 1907, it was decided by an invitation from Krogh to Bohr to do experiments together to try to answer the question and finally settle the uncertainty.

12.5.2. The Break

But after the first experiments with Krogh's recently improved tonometers, his new microtonometer, Table D2, and newly developed gas microanalyses, a dispute erupted between Bohr and Krogh. The content and sentiment of the dissonance is uncertain. Facts are, in April 1907, their mutual understanding about lung secretion surceased. Bohr broke off all communication and experimentation with Krogh (Schmidt‐Nielsen 1995, pp. 79–81, 92–93, 1997, pp. 102 and 109) [31, 32]. Despite Krogh's insistence on trying to reach Bohr with a conviction of a pure diffusion process, Bohr ignored Krogh and still refused to completely accept the diffusion theory as sole explanation for lung gas exchange in all circumstances (Bohr 1909, submitted April 30, in German) [59]. It should also be recognized that already 2 years before, in august 1907, Bohr published a paper for which he used Krogh's microtonometer and by which he could show a possible active secretion of carbon dioxide (Bohr 1907, p. 368) [58]. With an initial understanding, Krogh was supposed to be a coauthor of this paper, but due to the controversy was excluded on agreement by both. Bohr's results with the microtonometer and subsequent gas analyses were criticized by Krogh 3 years later, on grounds of possible inaccuracies with the method [196].

12.5.3. “The Seven Little Devils”

The stalemate lasted till Krogh together with his wife, Marie Krogh, in some of seven simultaneously published papers proved that the passage of O₂ was driven by diffusion, and diffusion alone (“The seven little Devils”). ³³ As mentioned, the Kroghs employed improved tonometers and an elegant microtonometer developed by August Krogh; allowing both slow and fast equilibration times. As before, as well for the microtonometer mesurements, tips were inserted directly into circulating blood, observing a bobble of ca. 4 μL while gas analyses were performed on small samples of 10 μL, which together gave more accurate measurements of the content of dissolved gases and with greater ease, Table D2 [194, 195].

In the second paper of the seven little devils, submitted in November 1909, Krogh had also demonstrated that during the method's microanalyses, processing time did not cause metabolism of oxygen as suggested by Haldane and tacitly suspected by Bohr [207]. Therefore, in the last “Devil,” Krogh could conclude:

The absorption of oxygen and the elimination of carbon dioxide in the lungs takes place by diffusion and by diffusion alone. There is no trustworthy evidence of any regulation of this process on the part of the organism. [Received December 5, 1909 and published in January the following year [196].]

In this paper, Krogh also admitted he had given up after trying everything and failing to find the flaw in Haldane and Smith's method used to demonstrate active secretion in lung gas handling. As it turned out 10 years later, there was an active regulation “on the part of the organism.”

For the full picture of lung gas exchange, as pointed out by Gjedde, August Krogh did not explain the increase in diffusion capacity during work when he declared “that there is no other mechanism than diffusion for oxygen passing through the alveolar wall” and in the citation above “… no trustworthy evidence of any regulation of this process on the part of the organism.” The explanation came later, when Krogh demonstrated that capillary recruitment was involved during muscular work (Krogh 1921; Gjedde 2010, 2020) [192, 206, 216]. Capillary recruitment settled the debate between Bohr and Krogh, to Krogh's advantage, as respiratory physiologist in general accepted the pure diffusion over the secretion theory.

In the course of refuting all the arguments against a pure diffusional process for the gas exchange at rest, in all fairness, Krogh remembered to acknowledge his former mentor in the introduction of the last of “The seven little Devils” (Krogh 1910b, pp. 248–249) [196], Appendix D.15.

12.5.4. A Cause for the Break?

Why Bohr ended the collaboration with Krogh on testing the secretion theory is still an unanswered question [31, 32]. Together with Schmidt‐Nielsen's and Sindbæk's books, there exists a fairly engaged literature on this dispute and its causes, viz., that Krogh was right about his diffusion theory, and then maybe not completely, as the capillary recruitment story evolved [193]. Likely reasons are undocumented suggestive assumptions as loss of prestige for the master together with a vanishing chance of getting the Nobel prize for Bohr, a prize Bohr had been nominated for twice, and barely missed (Nielsen and Nielsen 2001, Ch. 11, pp. 373–388, and pp. 606–607) [208]. Lately, Gjedde has shown how Krogh's Nobel prize work on recruitment of capillaries during exercise is also partly a justification for Bohr's claim about an active principle, the “special (cell) activity,” “proving the Kroghs, August and Marie, wrong when they claimed that only diffusion for oxygen across the lung tissue was necessary” [193, 209], and “no trustworthy evidence of any regulation.” A terrible nagging discomfort and bad wipe between the two, bothered both Bohr and Krogh during the years from 1907 till 1910. Krogh was devastated during the fall of 1907, totally uneasy with work in the laboratory, leading to headaches, while Bohr kept telling friends of his great concerns and worries (Høffding 1928, p. 246; Schmidt‐Nielsen 1995, p. 82, 1997, p. 106; Sindbæk 2022, p. 163) [31, 32, 43, 210].

A late and long plausible explanation for the break is offered in Hanne Sindbæk's well‐written book on “August and Marie” (Sindbæk 2022, pp. 151–205) [43]. For Bohr with his pride, prestige, and a potentiality shattered image, I agree, the conditions seem to have blinded him from good judgments, which lasted till his death. Unluckily, two great scientists, Figure 10b, went wearily wrong of each other.

12.5.5. Is Lack of Sufficient Diffusion Capacity Equal Specific Activity?

As parameters as the diffusive capacity in lungs at rest could not account for the measured gas exchanges at work, Bohr kept his secretion theory alive in 1909 with a term as “specific activity” and maintained “secretion” for the additional absorption of O₂ and release of CO₂ needed at muscular work [59]. Of Note, in this paper Bohr accepted a possible pure diffusion process as explanation for gas exchange at rest. Moreover, in this “specific activity”‐paper (spezifische Tätigkeit), Bohr analyzed thoroughly the gas pressure gradient axially along the capillary employing his now famous integration equation. With that study, Bohr found part of a possible explanation but had to realize that an increase in the radial pressure gradients at increased blood flow still would not fully explain the demand for oxygen transport during exercise [59].

12.5.6. The Meaning of “Spezifische Tätigkeit” Shifts in 1910

Dr. Gjedde has divided the meaning of “specific activity” seen with regulated extra supply of oxygen and increased excretion of CO₂ during work into two, and elegantly documented that Bohr, eo ipso was partly right with his “specific activity” as a mean of this regulation, see Appendix D.16 and D.17.

And one may add that Bohr, as not deaf to new incoming facts related to gas exchange in lungs, acknowledged the results by Krogh's microtonometer and microanalyses but simultaneously noted that the measured CO₂ gradient with this setup sometimes indicated “specific activity” [58, 59]. Then finally on the 10 of November 1910, at least 5 years before an eureka moment for Krogh [60, 211, 212], Bohr discussed a dilation of capillaries during exercise as an explanation for the increased flow, implicitly implicating his calculated, although not sufficiently augmented, necessary diffusion capacity at work [45, 59, 60]. That is, just 3 months before Bohr died, he addressed regulated capillary distention as a parallel measure to an active increased diffusion capacity needed in lung gas exchange under different conditions, but without a clear overlap between the two arguments. So, therefore Bohr clearly misses the right explanation, but he was close to it. Translated from Danish, Bohr wrote:

At a greater muscular work, as is known, the respiratory metabolism increases, which in turn leads to both a greater exchange of oxygen and carbon dioxide in the lungs and an increase in blood circulation and thus heart work, often to a considerable degree. By increasing the average capacity, on the other hand, the respiratory surface becomes larger, thereby providing better conditions for the air exchange that takes place through it; but also, as the anatomical structure of the lungs is, the capillaries of the lungs are dilated; this causes a lowering of the flow resistance, which facilitates the passage of blood through the lungs and thus also the work of the heart (Bohr 1910) [60]. [Emphasized wordings by me.]

And Bohr continued to argue for similar measures in hypercapnic and hypoxic conditions and suggested a reflex regulation through the vagal nerve [60]. I have noted that there is no mention of “gas secretion” in lung tissue in this late statement from 1910 by Bohr.

12.5.7. Regulated Blood Bed Dilation and Capillary Recruitment

In relation to the dilation of the blood vessel bed as regulated by the vagus nerve, both Bohr and Krogh knew that already from Maar's studies in 1902–1904, also relayed by Wang in 1911 [213]. In November 1910, Bohr focused on capillary distention in his late description of pulmonary emphysema [60], while Krogh's emphasis was on a distinct description of vagal influence and anatomical structure of the lung vessel network in his VIIth‐little devil (Krogh 1910) [196]. Without a mention of increased blood flow during work in lungs, Krogh rejected a possible capillary wall structure as possessing an active mechanism for gas transport, Appendix D.18, and in this devil Krogh also corrected his clear statement of a regulated secretion process discussed in his 1903 dissertation, Appendix D.19. To specify, with his calculated insufficient gas gradients for diffusion at work in capillaries [59], Bohr is not directly linking the dilation of capillaries to a regulated increase in capillary diffusion capacity [60], that came with Krogh's discovery of capillary recruitment in 1919. About an increased diffusion capacity in a regulated, “active,” fashion, especially during exercise, August Krogh, after Bohr's early death, had to realize, that Bohr's “specific activity” could be part of the gas exchange across the capillary wall in lungs and other organs (Gjedde 2010, 2020) [193, 209].

12.5.8. “A last‐days debate between master and pupil”

In a way, Bohr just before he died inconspicuously reemphasized and pinpointed a gap in the solution of the seven little devils on how a needed work‐dependent increase in diffusion capacity was established. As mentioned, a gap that Krogh was also well aware of. Was Bohr's last gasp a hint which triggered Krogh to keep studying the problem and come up with a solution for regulated capillary perfusion and altered diffusion capacity, in form of capillary recruitment, albeit with an omission of a reference to lung tissue (Bohr 1910; Krogh 1920, 1950) [60, 211, 212]?

12.5.9. Semantics on “Pure Diffusion” Versus “Specific Activity”

In an exchange with Drs. Niels‐Henrik von Holstein‐Rathlou and Erik Hviid Larsen, when writing this Section 12.5 on the secretion‐diffusion debate, I realized that sure enough, when focusing specifically at the passage of gas across the aveolar‐capillary wall per se, no matter what, it is by “pure diffusion,” also held by August Krogh. Meanwhile, when looking at the overall regulatory process of gas exchange in the lungs, for instance going from rest to work, certainly there is an element of “specific activity” in form of an engaged complex of regulatory mechanisms involving several specific mechanisms. Thus, no wonder, presently we know of several additional adjustments to the “active” regulated capillary recruitment for gas exchange in lung [214], mechanisms that for unknown reasons are still left out by some [215]. As more results were obtained, the haze cleared from the battel field about the secretion‐diffusion theories for lung gas exchange. The opposing experimental results and their interpretation on gas exchange, as capillary recruitment thanks to Krogh, ended in a banality as science often does. First there is a mystery, then a scientific contemplation, a hypothesis and scrutiny, disagreements, followed by a squabble and debate about analyses, interpretations of methods, results and discussions, and finally the solution becomes a banality when everybody has grasped it.

12.6. Krogh's Nobel Prize and an Aftermath of the Secretion Theory

The explanation for work‐dependent increase in diffusion capacity in lungs first came with Krogh's insight, demonstration, and discussion of capillary recruitment in striated muscular tissue and other organs, although not explicitly discussed for lungs. On Krogh's discovery of regulated (active) capillary recruitment and thus increased passage area, diffusion capacity/coefficient, during exercise, he was swiftly awarded the Nobel Prize in 1920 as it seemed, all in all, to all, to be the answer as well to the conclusion of the lung secretion‐diffusion debate [216, 217, 218]. ³⁴

In his Nobel Banquet speech in 1920, Krogh did credit Bohr for his mentorship, Appendix D.20 [211]. Krogh for some unknown reason in his “Nobel work” did not mention the lungs at all. What Bohr conceived for lung function as “specific activity,” involving a nervous regulation of an increased diffusion capacity, came too late and was lost in the aftermath of the secretion‐diffusion debate. Although surprised, Krogh rightfully received the Nobel Prize. Another Nobel Prize might have been awarded to Bohr for his significant contributions to respiratory physiology and particularly for his pioneering work on allostery, had he not passed away prematurely.

12.6.1. Other Perspectives on the Secretion Theory Debate

A fight between head of the Nobel committee, Karl Mörner and Johan Erik Johansson, Bohr's nominator in 1907 and 1908, is also likely a cause of costing Bohr the imminent reception of the Nobel Prize (Nielsen and Nielsen 2001, pp. 385–388) [208]. In a special report on Bohr, Mörner (1908) asked for a delay in awarding the prize to Bohr until the secretion‐diffusion debate was solved. The Kroghs' publication of “The seven little Devils” in 1910 obviously, killed the possibility for a prize on the secretion theory anno 1910. Besides a look on the Krogh‐Bohr battle about the understanding of how lung tissue handles O₂ and CO₂ as presented in this essay, in Steven Sturdy's thesis there is an interesting and eminent overview, though with a rather different angle and approach to the lung secretion controversy when reading about the historical details on the life and works of John Scott Haldane. According to Sturdy, the secretion‐debate continued into the late 1920s before it died out, while Haldane kept it alive until his death in March 1936 (Sturdy 1987, Chapter 3) [93]. Sturdy leaves us with an open end and no definitive conclusion for the theory, based on a balanced view between “direct” and “indirect” methods used for the determination of the arterial content and tension of oxygen. Within a rather widespread literature on the issue, Sturdy's thesis from 1987 is interesting by arguing that most of the debate was predominantly on a disagreement on use of methods and their result's interpretation. He concludes that it is an issue that was never really settled. Contrary, John West like most other researchers in respiratory physiology firmly assume that the question about oxygen secretion in the lungs was settled once and for all with the Kroghs' and Barcroft's research results on the issue, clearly showing that at rest only diffusion is necessary and at work it is still a diffusional process [196, 199, 217, 219]. Haldane's “biological organicism” view on what physiology was about, also elicited concerns and refusals in scientific circles dealing with his paradoxical attitude to natural sciences. In my view, there is a cross‐link in Haldane's approach to the secretion debate when realizing that an active regulation was also necessary for a full understanding of the lung gas exchange. However, a deeper dig into this exciting aspect of the controversy on oxygen secretion in lungs is beyond the present paper's theme, Appendix D.21.

12.6.2. Aspects of Scientist's Mistakes

If the break‐up between Bohr and Krogh was caused by Bohr alone on personal grounds, it appears, on face value, as Bohr's “Greatest Mistake.” A decisive, fatal, incomprehensible, and unfortunate mistake by a beacon physiologist as Bohr, and an unforgivable attitude in science. Contrary, even if caused on insufficient methodology or semantics, great scientists are still bound to make mistakes. Others have sought to soften and defend Bohr's view on secretion of gases in lung tissue [220, 221]. The momentous domination and inspiration in respiratory physiology attributed to Bohr is also attested to by an excerpt from a review article on Krogh's life: “It should be clear from this brief account that even if Christian Bohr sided on active secretion, it must not distract from his indisputable colossal contribution to Scandinavian physiology” [222]. Meanwhile, as mentioned above respiration physiologist John Burnard West has recently characterized his predecessor, Christian Bohr, somewhat demeaning, see Section 11.9. West is right that Bohr's writing style often was verbose, a typical trend at Bohr's time in the 1890s, but Bohr was certainly not minor to either of his two assistants, Karl Emil Hasselbalch and August Krogh as claimed by West [102].

Bohr made several mistakes, some of which I have commented on above while just repeating that certainly great scientists make mistakes. Both Max Planck, Albert Einstein and Niels Bohr are examples, with Planck so much so, that it is said about him trying to solve the spectrum emanating from dark‐bodies in a single equation, that ‘he tried so many times and failed again and again till only the right solution was left for him to choose’ (Pais 1991, p. 83) [13], also see Appendix D.22. Bohr is known to have abhorred personal controversies. Rather, it just confirms that great minds can also be mistaken and misjudge each other's intentions and viewpoints; often especially when under great pressure.

Regrettably, a great scientist like West has also made a forgivable mistake in his judgment and characterization of Christian Bohr.

My take home message is: as a scientist you will make mistakes but stick to it until it is unattainable. AV Hill's wise words in relation to his wrong aggregation theory for oxygen binding to hemoglobin also apply here to Bohr's mistakes about gas exchange across alveolar tissue. “The whole story is a good example of a frequent phenomenon in the history of science: of how a theory, ultimately shown to be untenable, could nevertheless describe and co‐ordinate the facts for a time and provoke further research which led finally to a better (but more complicated) theory. Without the unexplained mystery of the rectangular hyperbolas of 1909 and 1910 the theory would probably never have been proposed, and the later research might have been delayed for years,” Hill 1965, pp. 101–102 [223].

13. Bohr's Credo, Death, Legacy, and Conclusions

13.1. Bohr's Credo About Physiology, Organicism, and Further on

Operating at a bioregulatory level, within an organism, and without a clear insight into Nature's mutational variance, Bohr with his view on physiology, landed at a level of cells and organs in a mutual interaction with a “purpose” for the organism as a whole, that is, “biological organicism.” This view is in his late publication from 1910 on emphysema, reproduced in a lengthy appendix note, Appendix D.23 [60]. I consider this text as Bohr's testament in which he also abandons his secretion theory from 1909 and merely states that something is missing for a full understanding of how gases are exchanged across lung tissue.

On biological organicism. Théophile de Bordeu (1722–1776), a vitalist and early organicist published a book on gland function in 1751. ³⁵ Later in 1775 he proposed a concept of a general “internal secretion” (Ishida 2018, pp. 23–25) [224]. Others considered as organicists, are the embryologist Wilhelm Roux (1850–1924) in the late 19th century and Bohr's ally Scott Haldane till his death in 1936 [93, 101]. Today the organicist view is broadened by insights from the Modern Synthesis and further into parts of the Extended Evolutionary Synthesis debate [108, 110]. In a brief account, the biological organicist view is included in Nature's affordances through its play (mutations) with effector molecules and Nature's selection of these molecules' phenotype (natural selection). The providence thereby has secured a steered energy expenditure, compartmentalization, and regulatory means as allosteric behavior with accumulated intricacies, multicellularity with subsequent “fitness for survival,” toppled with aesthetic and etic judgments, and evolving into a global human society, so far, the most complex system in the universe. Presently, this defines what “purpose” means for life's evo‐devo, see Appendix D.8. An insight of course only after Bohr's time.

13.2. Christian Bohr Dies February 3, 1911

On Christian Bohr's untimely death, the most trustworthy description of how he succumbed is told by Margrethe (Nørlund) Bohr, at the time Niels Bohr's fiancé, to my former formidable teacher Professor Christian Crone (Pais 1991, pp. 111–112) [13]. Her recapitulation is corroborated by an obituary in the newspaper Politiken on February 4th, 1911, Figure 12a,b. It describes the fatal illness late on Thursday the 2nd. Bohr's death certificate, issued on Friday the 3rd, outlines the likely cause of his mortality, Figure 12c. On the cause of death there are some discrepancies. For instance, according to Poul Astrup, Bohr had worked at the laboratory until 10 PM and had always felt healthy (Astrup and Severinhausen 1985, p. 135) [10, 11]. So, his death was unexpected. On the contrary, the doctor, not Bohr's personal doctor though, who filled out the death certificate about causes of preceding illnesses wrote: ‘heart disease’ (Hjertesygdom), and “several years of illness,” Figure 12c. Following a growing cultural trend, Christian Bohr was cremated on the 6th of February, and the interment of ashes took place at Assistens Cemetery in Copenhagen a week later, Figure 12d.

13.3. Christian Bohr's Legacy

13.3.1. My View on Christian Bohr

Christian Bohr is rightfully famous for several discoveries and explorations, including the experimental saturable hyperbolic relationship for ligand binding, the “Bohr effect,” Bohr's dead space, his integration equation for oxygen's mean pressure/binding in lung capillaries, and his insistence on and request for the crucial experiments demonstrating heterotropic allostery, as well as his persistence on “specific activity” for gas exchange, not to forget his discovery of homotropic allostery. The discovery of allostery by Bohr started a whole new field on regulatory means in biology and physiology, presently captured by the pharmaceutical industry.

Due to his tenacity and insistence on a “specific activity,” replacing his “secretion theory” in late 1910, Bohr managed to keep a debate open on how to explain a needed increased gas exchange. With his suggestion for a distension of the capillary bed and its nervous, “active,” regulation, to increase the lung diffusion capacity during work, Bohr kept the solution to the “secretion theory” open and ongoing without “secretion” [59, 60]. Due to concurrent events, the fact that Bohr revised his “secretion theory” in 1910 was missed and later overlooked. This has left a focus on the spurious secretion theory from 1909 and deemed a lasting mistake on Bohr's behalf [102, 184]. Christian Bohr was nominated twice and nearly received the Nobel Prize in 1908 for his leading role in respiratory physiology with a main focus on lung function and the regulated binding of oxygen to hemoglobin [208]. If Bohr had dreams of receiving the price, they died due to his adherence to a premature secretion theory over a diffusional process.

13.3.2. Obituaries for Christian Bohr

On the oxygen secretion issue, I will let Karl Hasselbalch start and finish with his balanced words. He of course knew what the impact of ‘the Seven Little Devils’ meant to Bohr (Sindbæk 2022, p. 205) [43]. In his eulogy on Chr. Bohr and Bohr's approach to the “vital force” and “secretory activity,” Hasselbalch wrote, translated from Danish (Hasselbalch 1911, pp. 3–4) [150]:

The future will be able to judge more impartially than I, whether Bohr in the development of respiratory physiology, which his secretion theory gave the impetus to, showed too much or too little resignation with regard to giving up his work theory as obsolete. For my part, I believe that precisely the tenacity with which he held onto it and modified it, according to the new facts that his own and others' work brought to light, worked highly promotional for this work. “Everything is so complicated” (Bohr statement). It pays to have high thoughts about the organism's self‐regulating subject, and it does not harm the work to have too high thoughts about it.

It is of significance how many eulogies, some lengthy, appeared in 1911 about Bohr's life and work. The list includes Robert Tigerstedt [225], Karl Hasselbalch [150], Johannes Bock [226], Valdemar Henriques [227], Vilhelm Thomsen (Thomsen 1911, Festskr Kbh Univ.), Carl Julius Salomonsen (Festskr. Kbh.s Univ. nov. 1911, p. 53), Frederik Tobiesen (Nord. Tidsskrift for terapi, 1911), and Harald Høffding, who held a funeral oration at the casket in 1911 and later in his memoirs recapitulated the qualities of his deceased friend and interlocutor [210]. Others, some also with a lengthy praise for Christiann Bohr's efforts, are for instance Louis Sigurd Fridericia [228, 229], John T Edsall [184], and latest Albert Gjedde [193]. Thus, many like Krogh praised Bohr as they had benefitted immensely from his insight and guidance.

13.4. Conclusions

The present paper tries to answer a profound question put forward several times: was it Bohr, his assistant August Krogh, or both of them, who discovered the two types of allostery, homotropic and heterotropic allostery? Some has recently suggested that on the discovery of the Bohr Effect, Bohr was at the periphery of its discovery and description. Meanwhile, what does support Bohr's engagement in finding the Bohr effect is evidence in the literature, the timing of events as documented in this paper, including track records for Bohr, Hasselbalch, and Krogh during the period from 1883 until July 1904, Barcroft's statements on Hüfner versus Bohr, Krogh's three letters sent to his mother in February, December 1903 and early January 1904 and Krogh's own introductory remark about Bohr's request for experiments to be done. All the evidence gives a clear indication that overall, it was Bohr's wish to scrutinize the subject of O₂/CO₂ binding to hemoglobin, based on his ideas, insights, experience, and earlier data analyses. Bohr drove and steered the experiments with results published in 1904 about the S‐formed binding of O₂ to hemoglobin, and the effect of CO₂ on the S‐formed O₂‐heme binding also published in 1904 together with Hasselbalch and Krogh. Four publications on what later became known as positive homotropic and negative heterotropic allostery.

Therefore, it is only fair to acknowledge Bohr for his pioneering discoveries of both homotropic and heterotropic allostery related to the pressure of O₂ against its binding to hemoglobin and the CO₂ effects on this binding, known as the “Bohr effect.” It is also documented that Christian Bohr replaced his secretion theory for a capillary dilation just before he died.

I advocate for greater recognition of Christian Bohr in his home country, proposing a well‐deserved and spectacular material memorial to honor his groundbreaking work on allostery from 120 years ago, as well as his contributions to respiratory physiology in general.

Author Contributions

Niels Bindslev: writing – original draft, writing – review and editing, conceptualization, methodology, validation, project administration, data curation, funding acquisition.

Conflicts of Interest

Defraying cost for publication. Publication cost was partially covered by Cand. Pharm Povl M Assens Fond, Biofarma A/S. Naverland 22. 2600 Glostrup, for which I am most grateful. Response to applications for additional publication expenses are pending. Otherwise, the author is not paid by any external sources.

Bohr's Publications

Annotated publication list for Christian Bohr. Most of the list is taken from Tigerstedt's Nachruf 1911 (Tigerstedt 1911). The roman‐arabic numbers refer to page and number of citations on the page.

Physiology lecture notes by four medical students are referred to at the end.

• –Chr B(ohr) Zool(ogi). Own lecture notes during autumn semester 1973 at Copenhagen University, 1873. Notebook given to Medical Museion by Hans Bohr on behalf of the Bohr family.

v‐1 Om salicylsyrens Indflydelse paa Kjødfordøjelsen hos Hunde. Hospitalstidende, 2. Raekke. Vol. III. 129–138, 1876. Bohr becomes medical doctor in 1878.

vi‐1 Studier over mælk med særligt hensyn til de i samme suspenderede fedtkugler. Kopenhagen. 91 pages 1880. Doctoral thesis. Bohr is gift in 1881.

vi‐2 Über den Einfluss der tetanisierenden Irriamente auf Form und Grösse der Tetanuskurve. Arch. f. (Anat. u.) Physiol. 233–234. 1882.

viii‐2 Experimentale Untersuchungen über die Sauerstoffaufnahme des Blutes. Kopenhagen. 1885. Bohr's w/dedications to C. Ludwig. O.C. Kopenhagen. Olsen & Co's Buchdruckerei. A hyperboic relationship measured experimentally for the first time ever!

• –Om Blodfarvestoffet og dets Betydning for Respirationen. 1886. Associate professorship competition lectures given to medical doctors in Danish. L 1, 1–102 ; L 2, 1–102; L 3, 1–70. Handwritten. (reside with author)

vii‐1 Om en Anvendelse af Momentanfotografien ved muskelfysiologiske Undersøgelser. Kopenhagen. 39 pages, 1886.

x‐1 Über die Verbindung des Hämoglobins mit Kohlensäure. Festschrift f. Ludwig. Leipzig. 164–172. 1887 (also listed as 1886).

vii‐3 Ueber die Abweichung des Sauerstoffs von dem Boyle‐Mariotteschen Gesetz bei niedrigen Drucken. Ann. d. Phys. u. Chem. N. F. Vol. XXVII. 459–479, 1886. Silver medal treatise, also referred to by Henriques in his eulogy on Bohr, 1911.

• –Bohr, C. Ueber die Gaspannungen im Lebenden arteriellen Blute', Centralb. Physiol., 1887, 1, 293–99; Skand. Arch. Physiol., 1891, 2, 236–68; ibid., 1905, 17, 205–10. Here Bohr describes his haematometer and thanks Carl Ludwig.
• –Bohr, C. Ueber den Gasvechsel durch die Lunge. Zentralbl. f. Physiol. Vol. II. 437–440, 1888 – In this paper, Bohr for the first time refers to possible active transport of gases across lung tissue. Hüfner refers to this paper in 1890.

xi‐1 Über die Lungenatmung. Skand. Arch. f. Physiol. Vol. II. 236–268, 1890. (1890/91). O₂ binding and apparatus descriptions!

vii‐4 Bestimmung der Absorption einiger Gase in Wasser bei den Temperaturen zwischen 0 und l00^o. Ann. d. Phys. u. Chem. N. F. Vol. XLIV. 318–343, 1891.

Here follows 4 doubled issued publications, in French (1890) and German (1891–1892).

• –Etudes sur les combinaisons du sang avec l'acide carbonique. Bull Acad Royal Danoise Sci Lett 111: 278–309, 1890. Also referred to in Gjedde 2010. Roy Dan Acad Sci Lett, 1890, pp 171–99.
• –+ Torup. Sur la teneur en oxygène des cristaux d'oxyhémoglobine. Roy Dan Acad Sci Lett, 1890, pp 200–207.
• –Sur le combinasions de l'hémoglobine avec l'oxygène. 1890. Roy Dan Acad Sci Lett, 1890, pp 208–240.
• –Sur la teneur spécifique du sang en oxygène.1890. Roy Dan Acad Sci Lett, 1890, pp 241 – 294.

x‐2 Beiträge zur Lehre von den Kohlensäureverbindungen des Blutes. Skan. Ar. Physi. Vol. III. 47–68, 1892.

viii‐3 + Torup. Der Sauerstoffgehgalt der Oxyhämoglobinkristalle. Skand. Arch. f. Physiol. Vol. III. 69–75 1892.

viii‐4 Über die Verbindung des Hämoglobins mit Sauerstoff. Skand. Arch. f. Physiol. Vol. III. 76–100, 1892.

ix‐1 Über den spezifischen Sauerstoffgehalt des Blutes. Skand. Arch. f. Physiol. Vol. III. 101–144, 1892.

xiv‐2 Über den respiratorischen Stoffwechsel. Zentralbl. f. Physiol. Vol. VI. pp 22–227, 1892.

xiv‐1 The influence of section of the vagus nerve on the disengagement of gases in the air‐bladder of fishes. J. Physiol. Vol. XV. 494 – 500, 1894.

xv‐3 Über die Blutmenge, welche den Herzmuskel durchströmt. Skand. Archiv f. Physiol. Vol. V. 232–237, 1895.

vii‐5 Über die Absorption von Gasen in Flüssigkeiten bei verschiedenen Temperaturen. Ann. d. Phys. u. Chem. N. F. Vol. LXII. 644–651, 1897.

xv‐2 Recherches sur le lieu de la consommation de l'oxygène et de la formation de l'acide carbonique dans l'organisme. Archives de physiol. 459–474 1897.

xiv‐3 Recherches expérimentales sur la production de l'acide carbonique et la consommation d'oxygène dans le poumon. Archives de Physiol. 590–605, 1897.

xv‐1 Comparaison des quotients respiratoires determinés simultanément dans le sang et dans l'air expiré. Archives de physiol. 819–831, 1897.

xvi‐1 Bidrag til Svømmefuglenes Fysiologi. Roy Dan Acad Sci Lett, 207–234. 1897

x‐3 Über Verbindungen von Methaemoglobin mit Kohlensäure. Skand. Arch. f. Physiol. Vol. VIII. 363–366, 1898. Der Redaction am 16. September 1898 zugegangen. In this, there are references to 1) Bohr for the year 1891, the year now instead is 1892, and 2) Beiträge x. Physiologie, Ludwig gewidmet. 1887. S.164. Dieses Archiv, 1891. S. 47.

vii‐6 Definition und Methode zur Bestimmung der Invasions‐ und Evasionaköffizienten bei der Auflösung von Gasen in Flüssigkeiten. Werte der genannten Konstanten sowie der Absorptionsköffizienten der Kohlensäure bei Auflösung in Wasser und Chlornatriumlösungen. Ann. d. Phys. u. Chem. N. F. Vol. LXVIII. 500–525, 1899.

xvi‐2 Über die Haut und Lungenatmung der Frösche. Skand. Arch. f. Physiol. Vol. X. 74–90, 1899 (later 1900). This publication should have had August Krogh as coauthor, but he had asked Bohr not to include his name, since the paper was in German (Schmidt‐Nielsen 1997, p 66).

vii‐7 Löslichkeit der Kohlensäure in Alkohol zwischen – 67 und + 45⁰ C. In‐ und Evasionsköffizienten bei 0^o. Ann. d. Phys. u. Chem. Vierte Folge. Vol. I. 244–256, 1900.

xvi‐3 Hasselbalch not Bohr. Über die Kohlensäureproduktion des Hühnerembryos. Skand. Arch. f. Physiol. Vol. X. 149–173, 1900.

vi‐5 Der respiratorische Stoffwechsel des Säugetierembryo. Skand. Arch. f. Physiol. Vol. X. 413–424,1900.

xvi‐4 Über die Wärmeproduktion und den Stoffwechsel des Embryos. Skand. Arch. f. Physiol. Vol. XIV. 398–429, 1903. Together with Hasselbalch.

xvi‐6 Über den respiratorischen Stoffwechsel beim Embryo kaltblütiger Tiere. Skand. Arch. f. Physiol. Vol. XV. 23–34 1903 (later 1904).

xvi‐7 Über den Einfluss der Ozoneinatmung auf die Funktion der Lunge. Skand. Arch. f. Physiol. Vol. XVI. 41–66, 1904. With Maar.

• –Über den Einfluss der Kohlensäurespannung auf die Sauerstoffaufnahme im Blute. Zentralbl. f. Physiol. Vol. XVII. 661–664, 1904. With Hasselbalch and Krogh.

ix‐x‐4 Theoretische Behandlung der quantitativen Verhältnisse bei der Sauerstoffaufnahme des Hämoglobins. Zentralbl. f. Physiol. Vol. XVII. 682–688, 1904. (Should have been published in reverse order with the following publication (see Tigerstedt's listing in 1911).

ix‐3 Die Sauerstoffaufnahme des genuinen Blutfarbstoffes und des aus dem Blute dargestellten Hämoglobins. Zentralbl. f. Physiol. Vol. XVII. 688–691, 1904.

x‐4 Theoretische Behandlung der quantitativen Verhältnisse der Kohlensäurebindung des Hämoglobins. Zentralbl. f. Physiol. Vol. XVII. 713–715, 1904.

ix‐2 Über einen in biologischer Beziehung wichtigen Einfluss, den die Kohlensäurespannung des Blutes auf dessen Sauerstoffbindung hat. Skand. Arch. f. Physiol. Vol. XVI. 402–412, 1904. With Hasselbalch and Krogh

xvi‐10 Blutgase und respiratorischer Stoffwechsel. Nagels Handb. d. Physiol. Braunschweig. Vol. I. 54–220, 1905.

• –Absorptionscoëfficienten des blutes und des blut plasmas für gases. Skand. Arch. f. Physiol. Vol. XVII. 104–112, 1905
• –Lungens Vitale Middelstilling og dennes funktionelle middelstilling. Københavns Universitets Festskrift, Juni 1906. København. Forlaget af GEC Gads Universitetsboghandel, 1906.

xvi‐8 Die funktionellen Änderungen in der Mittellage und Vitalkapazität der Lungen. Deutsch. Arch. f. klin. Med. Vol. LXXXVIII. 385–434, 1907.

xii‐1 Über die Ausscheidung der Kohlensäure in den Lungen. Zentralbl. f Physiol. Vol. XXI. Pp 367–373, 1907.

xiii‐1 Über die spezifische Tätigkeit der Lungen bei der respiratorischen Gasaufnahme und ihr Verhalten zu der durch die Alveolarwand stattfindenden Gasdiffusion. Skand. Arch. f. Physiol. Vol. XXII. 221–280, 1909. (transl to English in J West, 1975)

xiii‐2 Experimentelle Bestimmungen der Gasdiffision durch die Lunge. Zentralbl. f. Physiol. Vol. XXIII. 243–248, 1909.

xiii‐2 Über die Bestimmung der Gasdiffusion durch die Lunge und ihre Grösse bei Ruhe und Arbeit. Zentrlbl f Physiol. Vol. XXIII. 374–379, 1909.

viii‐1 Über die Löslichkeit von Gasen in konzentrierter Schwefelsäure und in Mischungen von Schwefelsäure und Wasser. Zeitschr. f. Physik. Chemie. Vol. LXXI. 47–50, 1910.

xvi‐9 Om den pathologiske Lungeudvidning (Lungeemphysem). Copenhagen November 1910. Festskrift, Universitetes Aarsfest (in Dansih). Kopenhagen, Cph Uni. Press. 48 pages. 1910. (Begins with a statement about Bohr's physiology and what its method is about, pp 5–6).

xvi‐1 Die Gasarten des Blutes. Tigerstedts Handb. d. physiol. Methodik. Leipzig Vol. II (1). 1–47, 1910.

Student lecture notes. Docent lectures in 3 handwritten volumes from 1886. Is at Medical Museion, Copenhagen.

Four examples of medical student notes from Bohr's physiology lectures:

Paulli, Simon. Chr Bohrs Fysiologi. Notes during 3 semesters 1888 and 1889, 3 volumes. Medical Museion, Copenhagen.

Hansen, Frederik CC. Christian Bohr. Forelæsninger over Physiologi (sic). Vol I semesters 2 in 1890 and 1 (partly) in 1891, vol II rest of semester 1 in 1891, and vol III semester 2 in 1891. In vol I: Four forms for Hgb, pp 27–28, CO₂ likely binds to the globin, p 29, no color change with CO binding, pp 30 ‐31. All three volumes reside with professor Søren‐Peter Olesen.

Hinkbøl P. Fysiologi. 1899 and 1900. At the Royal Danish Library in 2 volumes. (vol 1 also resides at Medical Museion). Author's full name: Peder Clemmesen Hinkbøl.

Vestergaard, Hagbard, Med. Stud.: Bohr's Fysiologi, 1910, in a single volume with two parts. At the Royal Danish Library.

[Petersen, Ekkert: optegnelser from 1906 – 1908 (this is referred to by A. Gjedde in 'Peter Ludvig Panums videnskabelige indsats' 1971). Material could not be retrieved by me.]

Appendix A. Hyperbolic Rectangular Dose‐Binding or Dose‐Activation Relationships at Equilibrium

A.1.

The rectangular hyperbolic expression for simple dose–responses at equilibrium has the form: y = (Y _max ≅ C)/(C + K), where y stands for the actual saturation of ligand binding to or ligand activation of a macromolecule; Y _max is maximum for y; C the pressure or concentration of the ligand; and K the equilibrium dissociation constant for the description of dose‐response curves, Figure 3a (Bindslev 2008, Ch. 1 and fig. 1.3) [36]: As mentioned, the equation was formulated initially for gas binding by Gustav Hüfner as early as 1890 [24].

Appendix B. Allosteric Regulation, Modern Allosteric Concepts, and Notes

B.1. Allosteric Regulation

Allostery is regulation of site binding, site activity, or of a bioregulatory function elicited from a secondary non‐overlapping binding site, for instance in proteins. Thus, allostery per se is non‐competitive. In a popular saying: “allostery is a reversible, remote regulation of a bioregulation,” or in an analogous quote about quantum mechanics' entanglement: “spooky action at a distance,” Einstein in a letter to Max Born 1947 (The Born‐Einstein letters: correspondence between Albert Einstein and Max and Hedwig Born from 1916–1955, with commentaries by Max Born. Macmillan 1971, p. 158.)

FIGURE B1.

Simple heterotropic allostery regulation with reciprocal action. Figure by author.

For other more detailed definitions of allostery and cognate ligands see Bindslev 2013 and Christopoulos et al. 2014 [175, 230]. A decision about allosteric nomenclature may also involve terms as “reciprocity” and “reversibility” depending on the experimental conditions.

B.1.1. Some Introductory Remarks

Obviously, our detailed knowledge about the complexity of bioregulation has increased tremendously since the definition of allostery by Monod, Wyman and Changeux (1965) [143]. Therefore, as an example in different fields of bioregulation two terms as “cooperativity” and “allostery” presently appear as two rather generalizing concepts when used to characterize for instance non‐hyperbolic or other “more‐than‐hyperbolic” reaction schemes; often with no details required for their assignment. For many, cooperativity may be of use for a host of systems characterized as allosteric, while cooperativity has a wider world in which to define processes. Allostery is a non‐competitive process, albite depending on how to define the influence of an allosteric site on a primary binding site or on an active site when the allosteric site is in the pathway toward the active site as for instance in G protein‐coupled receptors, Figure B1 [231, 232, 233]. The literature has different definition on the differences between the two terms. For a start, in relation to the more general approach to the terms in this historic monograph, there may be deviations from the definitions of the terms as defined in Table B1 and their use in subject‐specific fields.

B.1.2. An Additional Introductory Remark

Initially, I would also like to emphasize that allosteric “acceptor‐actor entities” or allosteric “effectors” described below in Appendix B.2 are not to be confused with “allosteric ligands,” originally termed “allosteric effectors” or just “effectors” by Monod et al. 1965. In this essay, allosteric effectors are acceptor‐actor entities, typically protein macromolecules, possessing allosteric regulatory control. Due to originality in the definition of “allosteric,” the literature on allosteric actions of hemoglobin and enzymes still clings to a tradition for using the term “allosteric effector” or just “effector” for allosteric ligands binding to an allosteric macromolecule. Despite this, one of the originators of the term “allosteric effector” for allosteric ligands in 1965 [143] has now accepted the switch to using the term “allosteric modulator,” which is commonly used in other bioregulatory fields [230].

B.2. Introducing the Terms “Allosteric,” “Homotropic,” and “Heterotropic”

The terminology related to allosteric behavior was initially coined in 1961 by Monod and Jacob as equal to enzymatic “end‐product inhibition” from a site distant from the catalytic site (“allosteric inhibition”), and also for repressors/reactivators working in a unit of transcription [105]. Two years later the term ‘allosteric’ was redefined by Monod and co‐workers with a focus on substrate analogues, repressor molecules, substrates, and metabolites acting at a binding site distant from the primary binding site [234]. In 1965 the definition of “allosteric” was finally tighten and expanded further by clearly observing that both “homotropic” (identical to the primary ligand) and “heterotropic” (different from the primary ligand) allosteric ligands operated from a site distinct from a primary binding site or from yet another site of primary action as distributed between oligomers [143]. “Substrate inhibition,” a negative homotropic allosteric action from a distant binding site as described by JBS Haldane in his book “Enzymes [134],” is not dealt with in Monod et al.'s three mentioned publications. John Burdon Sanderson (JBS) Haldane (1892–1964) was son of John Scott Haldane. ³⁶ Additionally, cooperativity (“allosterism”) for homotropic ligands was only positive for Monod and coworkers in 1965. The co‐author Wyman had a decisive impact on the formulation and broad aspects of allostery drawn from his knowledge about physiological/thermodynamic regulation of the hemoglobin molecule, binding more than one oxygen molecule, that is, positive homotropic allostery [167], while Monod was expert on transcription and Changeux a newcomer expert on end‐product inhibition of enzymes, which is one aspect of heterotropic allostery when the product only acts from a distant secondary site and does not interact directly with the catalytic site (Jacob et al. 1960; Monod et al. 1963; Changeux 1963, 1964, dissertation) [142, 234, 235, 236]. Product inhibition is not necessarily allosteric but can be a negative cooperative effect if its inhibitory action takes place competitively in the active or the orthosteric binding site (Christopoulos et al. 2014, fig. 1) [230]. Below, Appendix B.8 more explicitly explains the differences between “cooperativity” and “allostery.”

B.3. Acceptor‐Actor Entities as Allosteric “Effectors”

In biology, macromolecular activity and its regulation are the base for most live processes, including adaptability due to mutations. The allosteric “entity” concept includes multi‐sited monomers, as well as multi‐sited and multimeric (oligomeric) macromolecule aggregates involved in a single chain of natural evo‐devo bioregulation. Types of regulated macromolecules are many and most often belong to the group of larger protein molecules. Examples are enzymes, receptors, transporters (pumps, channels, uni‐, co‐, and counter transporters), including ATP synthase, which is both an enzyme and a reverse proton pump. Others are membrane‐free transport carriers as hemoglobin and albumin, motor molecules as dynein/kinesin. Furthermore, also operating through allosteric means are a plethora of supportive, auxiliary molecules, receptor activity‐modifying proteins—RAMPs [237], and scaffolding entities [238], that take part in all types of regulated macromolecular function.

B.4. “Entity”. Separating Allosteric “Entities” From Bioregulatory Networks

I use the specifying term “entity” for molecular complexes designed by nature to typically elicit a single, allosteric function. The purpose of using this definition of “entity” is an attempt to exclude defining functions as “allosteric,” when the function relies on several pathways in an entwined network of actors [239, 240, 241, 242]. In fields of antigen–antibody complexation with more than one pair and in replication where the latter involves large complexes including ribozymes, different forms of RNA, DNA, and a lot of other nucleic acids, as well as cofactors and coenzymes, the adjective term “allosteric” may start to lose its meaning, although, I will argue that as long as the regulatory means can be characterized as happening in an “entity” that transmits signals in a single pathway for function, it is through an “allosteric” entity, while regulation through several ‘entities’ and spread out over multiple pathways is rather a “bioregulatory network.”

B.5. Primary Ligands and Secondary Ligands

B.5.1. Primary Ligands, Orthosters

Ligands with fitted binding to primary binding sites (orthosteric pockets) in functional macromolecules are “primary ligands” or “orthosters” and elicit the pertinent (prime) function of the macromolecule, the “effector,” Figure B1. The orthoster may be a substrate meant for transformation to a product by enzymes, typically a metabolite. Regulation of macromolecular function is induced by several means at ångstrøm/atomic and larger scales, for instance by ligand association and binding, either within cavities of the macromolecule or at its surface, or by spontaneous conformational changes. The binding can be by covalent or non‐covalent attachment to the architecture of these cavities. The cavities may be sporadically altered by evolutionary evasions determined by functional selections from a bobbling sea of mutated macromolecules and if successful for survival, sustained over long durations of development before eventually discarded due to the natural selection process.

B.5.2. Secondary Ligands, Allosteric Modulators, or Allosters

Other ligands may bind to the macromolecule at secondary sites, other than the primary binding and/or catalytic site. Secondary sites may be more or less distant and distinct from the primary binding sites. As mentioned, if binding of a secondary ligand alters the binding or activity at the primary site, the secondary ligand is an alloster or an allosteric modulator (see Figure B1). The allosteric binding may take place before or after the binding of other ligands, even orthosters, in functional or supporting organic macromolecules. Bioregulation via secondary ligands, allosters, is widespread, thus allostery is one fundamental regulatory principle in all of biology. Allosters may also behave as ordinary orthosteric ligand in their own right. Alloster examples are endogenous‐and bitopic ligands. Further allosteric examples are allo‐ago synergistic and allo‐ago‐ inverse‐synergistic allosters. For a more complete listing see [175].

B.6. Homotropic and Heterotropic Allostery. Positive or Negative Allosters

When, a ligand binds to secondary binding sites in a macromolecular “entity” and alter the configuration or energy distribution in the entity and thereby change the binding and/or activity elicited by another identical ligand binding at a primary or active site, such a regulation is termed “homotropic allostery,” whereas if an allosteric regulation is induced by non‐identical ligands, allosters different from orthosters, an elicited regulation is termed ‘heterotropic allostery’ [143].

Homotropic and heterotropic allostery may be positive or negative with designators “P” and “N” for their ligands. For future simplified segregated designation, positive homotropic and heterotropic allosters and negative homotropic and heterotropic allosters may be abbreviated as PHoA, PHeA, NHoA, and NHeA.

B.7. Resolution of the Dichotomy Between Induced‐Fit and Conformational‐Selection

The general discussion of state model(s) in the MWC‐model versus non‐state model(s) as in the KNF‐model [164] in relation to “cooperativty”‐versus‐“allostery” seems to have reached a mutual acceptance, for example, in Cornish‐Bowden 2014 [166]. Further, the corresponding and intensified discussion between conformational selection (CS) in MWC, as maintained by for instance Changeux in 1993 and 2013 [243, 244, 245] onward, and the induced‐fit (IF) in KNF have been settled in the physical world, besides there is still an ongoing debate [246]. Both the CS and the IF are likely events, it depends on the system and experimental conditions [247, 248, 249]. Therefore, as I see it, in the use of signifiers as “cooperativity” and “allostery” in allosteric systems, it is rather hard to discern them in relation to homotropy.

B.8. Cooperativity and Allostery

In biology, typically in protein molecules, “cooperativity” is observed with an interacting secondary ligand that changes a primary ligand's binding or its induced function at a primary site. The change may either be positive (enhancing) or negative (diminishing). If the interacting (cooperative) ligand operates at the primary binding site or in the primary active site, the process is “competitive.” Alternatively, if the cooperative ligand operates from a site different from the primary binding site, the process is non‐competitive. Cooperativity may also be qualified as homotropic if the cooperative ligand is identical to the primary ligand as for instance in substrate inhibition. Obviously homotropic cooperativity needs two separate binding sites and is only non‐competitive, unless there is a hysteresis process or time‐delay in the primary binding site that allows a second binding to the primary site under altered conditions. In case the cooperative ligand is different from the primary ligand, the cooperation is heterotropic and can be both competitive, displacing the primary ligand, or non‐competitive by operating from a distant site. Here a special case is product inhibition. This inhibition may be elicited by competitive binding of enzyme products or metabolites to the primary active site or be non‐competitive when binding is at remote binding site that elicits inhibition. To exemplify, cooperative systems and product inhibition may involve competitive, un‐competitive, mixed‐type, and non‐competitive kinetics (Segel 1975/1993) [141]. Product inhibition from a remote non‐primary binding site is non‐competitive and allosteric cooperativity. An “allosteric” process has the same characteristics as a “non‐competitive” process. Thus, in other words, allostery is a signifier that requires that the allosteric effect is elicited by ligand binding to a site distant from or not overlapping a primary activity or binding site. Table B1 shows the possible designations for cooperativity and allostery.

Two questions arise in connection with the signifier “allosteric.” For instance, with our expanding insight in transcription factor regulation, how many elements do we allow in the regulatory process and still signify it as “allosteric” [250]? And, if a network of two or many more functions or signaling pathways also involves allostery in some of the single pathways, is the network to be signified as an “allo‐network”? My answer would be: “allostery” is a designator for an “entity” with a single function. So, I add the term “entity” to the “allostery” definition, in an attempt not to blur the concept of allostery.

TABLE B1.

Cooperativity versus allostery.

“Cooperativity” as designator in processes that are	“Allostery” as designator in processes that are
Competitive or non‐competitive	Only non‐competitive
Positive or negative	Positive or negative
Homotropic or heterotropic	Homotropic or heterotropic
Displaying substrate and/or product inhibition	Only displaying non‐competitive Substrate and/or product inhibition
Also for “entities” in networks with several functions	Mostly for one “entity” with a single function

Note: An “entity” can encompass a complex of macromolecules and associated co‐factors serving a single regulatory function, potentially constituting an “allosteric pathway,” even including information or cargo/substrate transfer/channeling, while combinations of macromolecules and associated cofactors serving several regulatory functions, may be designated a “cooperative network” rather than an “allosteric network.”

Appendix C. Summary of Terms and Methods Related to “Allostery in Biology”

C.1. Basic Terms Referred to in the Article

Allostery is a form of bioregulation, and often it is a regulation of a regulatory function. Allostery is a regulation of regulation. An allosteric effector (or just effector) is an “allosteric entity” in form of a monomer or a macromolecular multimeric complex with a single function. When several entities combine for multiple functions, we have a regulatory network. A primary ligand or an orthoster is a molecule binding to a natural or endogenous site for primary action in an “entity.” The involved binding site is a primary or othosteric binding site. A hormone like insulin is an example of an othoster. An allosteric modulator or an alloster is a ligand, that from a distant site or from a non‐overlapping binding site in the path to the primary binding site, can affect the binding or function of the primary ligand. This distant or nearby but separate binding site is the secondary or allosteric binding site. Note that an alloster may bind before an orthoster. Allosters may be heterotropic, either negative or positive (NHeA/PHeA), or homotropic, either negative or positive (NHoA/PHoA). Examples of negative heterotropic allostery is non‐competitive product inhibition and substrate inhibition is by a negative homotropic ortho−/allo‐ster.

C.2. Examples of Additional Keywords Related to Cooperativity and Allostery

Just for reference, I list some keywords in a nonalphabetical order related to ideas, terms, concepts, and methods for cooperativity and allostery developed after Bohr. The contents of the keywords are easily retrieved at the web.

C.2.1. Energy Ensemble

Non‐conformational dynamics, thermodynamics, energy landscapes, allosteric model analysis/simulation, states versus energy cycles, and intrinsic disordered proteins (IDP).

C.2.2. Structure and Methods

Structure–activity‐relations, SARs, X‐ray methods, fluorescence resonance energy transfer (FRET), cryoelectron‐microscopy (cryo‐EM), deep learning (DL) for instance with AlphaFold 2 and 3, molecular dynamics (MD), software for molecular dynamics, gaussian accelerated molecular dynamics (GaMD), Markov‐state‐models, free energy Profiling Workflow (GLOW), quantum mechanics (QM), nuclear magnetic resonance (NMR), temperature‐dependent Isothermal Titration Calorimetry (ITC), Circular Dichroism (CD) spectroscopy, hydrogen exchange (HX), mass spectrometry (MS), and genetic manipulations with full‐protein alanine‐scanning mutagenesis.

C.2.3. Signaling

Equilibrium and steady‐state, pharmaco‐dynamics (PD), pharmacokinetics (PK), non‐steady‐state analyses, functional selectivity, probe‐dependence, trafficking, linked‐function, temporally sequential signaling, substrate channeling, antigen–antibody avidity, bitopic ligands, dualsteric ligands, biased signaling, binding assays, functional assays, bell‐shaped dose response curves, desensitization and inactivation.

Appendix D. Notes to the Main Text

D.1. Bohr and Krogh Papers in 1904 From Experiments Carried out in Early 1903

Table D1 includes specific dates for submission and publication of seven papers. This allows for a precise timeline of certain events mentioned in the text.

TABLE D1.

Timeline for papers in 1904, based on experiments in 1903.

	Date of submission	Date of publication
Zentralblatt f Physiologie 1904
Bohr et al. a—Band 17, nr 22	January 20	January 30
Bohr a—Band17, nr 23	January 27	February 13
Bohr b—Band 17, nr 23	January 27	February 13
Bohr c—Band 17, nr 24	January 27	February 20
Krogh a—Band 18, nr 3	April/May	May 7
Skand Arch f Physiologie 1904
Krogh b—Band 16 nr 5/6	July 19	July
Bohr et al. b—Band 16 nr 5/6	July 19	July

Note: From two journals: Zentralblatt f Physiologie 1904 and Skand Arch f Physiologie 1904.

D.2. Some of the Used Tonometers by Bohr and Krogh

Both Bohr and the physical‐chemist Gustav Hüfner were disciples of the famous physiologist Carl Ludwig when he had a laboratory in Leipzig. Here Bohr learned to measure gas content and its relation to gas pressure (concentration) rather efficiently. Bohr also designed his own apparatus to obtain blood samples and to get a better surface to volume ratio for his tonometres, thus, determining the gas content in the samples more efficiently than for instance Eduard Pflüger. The volume‐surface ratio was further improved later by Krogh for studies in 1903 [198] and again in 1906–1908 and as well with use of Krogh's famous microtonometer with a specific surface (surface to volume ratio) of 30, and analyses of gas content in samples of ca. 10 μL, without spurious loss of O₂ and neither accumulation of CO₂ [194, 195, 197].

TABLE D2.

Characteristics of tonometers for O₂ volume measurements.

Tonometers and measurements of blood gas content 1860–1909
Researcher year	Gas‐tonometer terminology	“Specific surface” open area/volume	Equilibration time (min)	Accuracy (vol‐%)
Setchenow‐Ludwig #	—	—	—	—
Pflüger 1866–68	Aëro‐tonometer	3.3	20–30?	0.05
Bohr 1888–92	Haemat‐aërometer	5.2	20–30?	0.005
Fredericq 1890s	Blood tonometer	3.7	20–30?	—
Krogh 1903–09	Blood tonometers*	20–33	10–20	0.005
Krogh 1906–09	Micro‐tonometer**	30	5–10	0.2–0.1

Note: Data are from Krogh 1908a [194]. see below where tables are listed. Accuracy for the CO₂ measurement: 0.2% in 1–2 mL samples—otherwise 0.005%.

^*Modified Pflüger tonometer, measurements in 1903 and onward—further improved 1906, described 1908 [194].

^**Used for measurements from 1906 and onward. Sample size down to 4–10 μL.

^# Setchenow‐Ludwig 1859–1866. The name Setchenow is also spelled Sechenov. For details see ‘The Development of Blood Gas Analysis’ by C. S. Breathnach. Med Hist. 1972;16(1):51–62. DOI: 10.1017/s0025727300017257.

D.3. On Christian Bohr's Scientific Drive in Childhood and Youth

Cited by Adler in 1967 [52]: Bohr himself in a handwritten note: “When I speak of the earliest which I can recollect then, like the whole of my later life, it was characterize to a very high degree by one single gift, if can call it such, which goes back as far as I can remember, and which was never out of my m0ind for a single week, I dare say hardly a single days. I owe it to this gift that my life has retained some coherence and that in no period, in spite of quite few less fortunate tendencies, did I ever depart from a serious unselfish striving. I refer here to the love for natural science, or more precisely certain aspects of the study of nature. I am quite sure that I had this love in my ninth year in essentially the same form as it still dominates my life today. If I had to describe it more closely, I think it would be best to say it is an instinct; certainly, with regard for my position in life or the like has not been involved in it; neither was it any definite purpose which obsessed me. It was not until much later in my life that I became grateful that this love made me work along a line—that of scientific research and the spreading of knowledge—which from the ethical point of view I place on the highest level. And I remember well that when this became clear to me I had the definite conception of what a misfortune it would have been for me if this instinctive urge had not been such, that what was necessary to my nature must lead to an aim that I could respect.

I began at an early age to collect objects of natural history and naturally my collection gradually grew to a considerable size. I collected all such objects, especially parts of skeleton, stuffed animals (I did not have many of these because they were so expensive) and specimens in spirit. It must have been my love of systematic scholarship which led me to collect; a passion for collecting as such is very foreign to my nature, and I do not think that I ever collected stamps or anything like that (or only for so short a time that I cannot remember it). Nonetheless I have no aptitude for natural history as such; I lack the ability to recognize the forms of plants and animals, and I have no interest in the determination of species, and later I even had difficulty in seeing its scientific importance” (Adler 1967, pp. 11–12) [52].

Danish version of Christian Bohr's impetus to become a natural scientist, cited by Adler: »Når jeg skal omtale den tid af min tidligste barndom, som jeg selv har nogen klar erindring om, så er den som hele mit følgende liv præget i højeste grad af en enkelt evne, om jeg tør kalde den sådan, der går tilbage så langt, jeg kan huske, der aldrig, tør jeg sige, nogen uge, ja knap nok nogen dag har været ude af mit sind, og som jeg skylder, at mit liv har bevaret nogen sammenhæng, og at jeg i ingen periode, trods ikke få mindre heldige anlæg, er kommet bort fra en alvorlig uselvisk stræben. Jeg sigter her til den lyst for naturvidenskab, eller rettere for visse sider af naturforskning. Jeg er ganske vis på, at jeg var. i besiddelse af denne lyst i mit 9. år under væsentlig samme form, som den endnu behersker mig. Når jeg skal nærmere beskrive den, tror jeg, det sker bedst ved at betegne 9 den som et instinkt; det har ganske vist ikke været hensynet til livsstilling eller sligt, der har haft nogen andel deri; ikke heller formålet, som har betaget mig. Det er først langt senere i mit liv, at jeg blev taknemmelig for, at denne lyst bragte mig til at virke i en retning—den videnskabelige forskning og oplysning—som jeg ethisk set sætter som en af de højeste. Og jeg erindrer godt, at jeg, da dette blev mig klart, havde den tydeligste forestilling om, hvilken ulykke det havde været for mig om en sådan instinktiv trang ikke havde været af den art, at den naturnødvendigt måtte lede til et formål, jeg kunne agte. Jeg begyndte tidlig at samle naturhistoriske genstande, og samlingen voksede naturligvis efterhånden til ikke at være så lille i omfang. Jeg samlede på alle naturhistoriske genstande, dog især skeletdele, udstoppede dyr (hvoraf jeg ikke havde mange på grund af deres kostbarhed) og spirituseksemplarer. Det må have været lysten til systematisk videnskabelighed, der førte mig til at samle; egentlig samlers lyst ligger mig meget fjernt, og jeg tror aldrig (eller i hvert fald så kort tid, at jeg ikke husker det) at jeg har samlet på frimærker eller noget sådant. Ikke desto mindre har jeg ingen anlæg for den egentlige naturhistorie; jeg savner evnen til at genkende dyrs og planters form, og jeg har ingen interesse for artsbestemmelse, ja har endog senere hen haft svært ved at se dens videnskabelige betydning.« (Adler 1964, pp. 9–10) [51]. A search for the original was in wain, seems to be missing according to the N.B. Archive.

D.4. Kierkegaard on Natural Sciences

“Absolutely no benefit can be derived from involving oneself with the natural sciences. One stands there defenseless, with no control over anything. The researcher immediately begins to distract one with his details: First off to Australia; then to the moon; then into an underground cave; then, by Satan, up the ass—to look for an intestinal worm; first the telescope must be used, then the microscope: Who the Devil can endure it!” Under: “The Prophet of Modernity”. Søren Kierkegaard Research Center, Copenhagen. Journalen NB source SKS.dk or Graff 2007, p. 468 [251].

D.5. Bohr Read Niels Lyhne During Christmas 1880

In a letter to his friend Salomonsen, Figure 5c, Bohr wrote about the book: “it is among the most interesting things I have ever read; I am completely moved by it; I do not want to write more, even though I have plenty more to say about it.” I express my gratitude to Anja Skaar Jacobsen for informing me of the existence and content of this letter.

D.6. On Bohr's Character

“In writing, Bohr certainly formulated himself in an entangled and thus unclear style. This was inherited by his son Niels [inserted by author: ‘regarding aunt Hanna and Jenny who help Niels and Harald to express themselves’] and it is a bit surprising that he so clearly does not respect or acknowledge the importance of the systematic species determination and thus taxonomy‐classification. Bohr wanted function and its regulation to understand nature. I interpret it as an early distinction of his own choices as being the right ones, a certain disrespect for other approaches to science. But in a way, Christian Bohr is just honest” [199].

D.7. Hasselbalch, Part of His Eulogy Translated From Danish

“Science has several kinds of lovers. The humble and modest cultivator gathers the fragments of knowledge together as material for the temple of science, which he will not erect, but a later one. Bohr was not humble in that sense. True enough, he knew and appreciated the difficulties his striving prepared. ‘Everything is so complicated’, he could exclaim with a voice in which one could hear both despair and defiance, both admiration for nature's fortifications and the firm will to climb them. He knew well that ‘Everything is complicated’, but he valued everything, including his own talent, so soundly that he could never have been content with just stating it. A fact that stood without connection to our insight into the organism's wonderful appropriateness; an observation that was collected without a plan and presented without an idea, bored or annoyed him. Science has another group of worshipers: the lyrical lovers, in casu the natural philosophers. ‘Beware of them,’ Bohr once said, ‘they are the worst of them all’. The natural philosopher poetizes about his subject; he presses his own mood or his ‘worldview’ into the phenomena. There is a piece of a natural philosopher hidden in every idea‐rich physiologist. Bohr knew this and valued the associated risk accordingly. If you want to know how consciously and sharply he himself kept himself free of natural philosophy you should read the introduction to the recently published treatise: ‘On pathological lung expansion,’ where he takes a position on ‘The Appropriateness of the Organism’ as an article of faith. ‘The a priori assumption of the purposefulness of life manifestations is as a mere heuristic principle natural enough and can, since conditions in the organism are so extraordinarily complicated and therefore difficult to oversee, often be useful even indispensable in order to be able to set the special research task and seek ways to its answer. But one thing is what can be usefully used in preliminary research, another what one is entitled to establish as a really achieved result.’ I have highlighted these two types of natural science worshipers, the Collector and the Natural Philosopher, not to show that Bohr's fine and rich talent assigned him a place between these two, with happy avoidance of the dangers that threaten either of them, but to claim that he represented a third type: The Conqueror. (1). Bohr was a lover and favorite of science. But he was also and especially a field marshal, led by an idea—The Appropriateness of Life Manifestations—chose his enemies: physiological problems, and with a kind of cold passion fought them according to a cunningly devised plan. That he did not underestimate the enemy has already been mentioned; he had all too often experienced that a defeated problem meant seven new ones to fight. Therefore, he could not sharpen his weapons enough between battles; his love for exact method was dictated both by his nature and by necessity. That Bohr's relationship to his science was like that of a skilled and purposeful field marshal to his task, I believe is an observation that will be accepted by those who knew him. When I now say what is true, that two of his most important campaigns brought him personal defeats, I will not be misunderstood when I add that those who suffer many such defeats conquer the world.” (Hasselbalch 1911) [150]. Translated to English and with three sentences bolded by me, the author.

D.8. Life's Enlightenment

A post‐Bohrian understanding of Vitalism and origin of life going from abiogenesis to biogenesis may be as follows under the spell of Darwin's views from 1859 and till his death in 1882, and with information gathered after 1911, including Hubble's expansion of the Universe 1923–1929, and a realization of genetic code mutations in the 1940s. Based on attraction and repulsive forces in quantum fields, by inorganic star‐dust elements formation, Jean‐Marie Lehn's 4% “as visible matter, our matter, the matter that matters” with constitutional dynamic chemistry onto biomolecule‐complexity with self‐replicating adaptive chemistry, “memory” has evolved over more than 8–9 billion years—and based on nature's perpetual large scale physicochemical experimentation with building blocks as nucleic acids and proteins. Information entities are created, they interact, they are constantly modified through mutations, equipped with self‐replicating power, and eventually adapt‐regulated by post‐modifications, thus combined into non‐parasitic live organisms with ever changing features of “forward” forming and fitting in with ambient conditions. After cells were formed, large jumps are taken through endosymbiotic morphosis mechanisms later displaying metamorphosis and punctuated equilibria. Simultaneously, living organisms at all levels are “furthered” by natural selection and “survival of the fittest” but parallel also through selections of aesthetic feeling movements, pattern‐preferences, and other means such as cooperation, cross‐species interactions and ethic rulings. This has resulted in live organisms, which to our wonder display entities as eyes, movement patterns, feelings, and evolved language and abstract communication with an underlying consciousness, now developed to the most complex “organism” in the universe in form the homo sapiens ' global community, with perpetual underlying synergistic and parasitic life forms exemplified by commensurable microbiota and virus‐initiated parasitic infections and cancers. The imprecise, personal language and lack of complete insight we have, when we observe, judge, and describe what we see, feel and phantasies about live organisms, are reasons why some employ explanatory concepts instead of “Purpose” as “Entelechy,” “Vitalism,” “Kraft,” “Geist,” “Bildungstrieb,” “Élan vitale,” “Ordering principle,” and others like “Teleonomy.” I think, as Bohr would have, had he lived long enough, that in the end it is all just based on physicochemical processes. Therefore, life products of evolution, that is, unfolded life with its ever‐increasing complexity as the speaking man and his AI and global society, is no mystery. Rather: The big mystery or question is when, where, and how it all started, how life came about—abiogenesis → biogenesis—out there with its memory‐mechanism for self‐replication before an RNA/DNA world. A question which immediately for some evokes the idea of an unheimlich life‐force in nature as God's will with a purpose. The universe is without a purpose, but man demands a purpose (nb).

D.9. CO‐Binding

The relationship of carbon monoxide binding to hemoglobin in solution is drawn in a figure by me based on three experiments in Bock's 1895‐dissertation with data that appear as fresh as if they were obtained yesterday [121]. Figure in this section, Figure D1 “Bock's Carbon monoxide binding to hgb.” As seen, there is a nice hyperbolic binding with an equilibrium dissociation constant P₅₀ of 0.53 mmHg for CO.

FIGURE D1.

Carbon monoxide binding to hemoglobin by J Bock, 1895, Dissertation [121].

D.10. Handwritten Lectures by Bohr 1886

First page of Bohr's handwritten Lecture 1, 1886. Can be obtained at Medical Museion in Copenhagen (Figure D2).

FIGURE D2.

First page of Bohr's handwritten Lecture 1, 1886. (Medical Museion, Copenhagen).

D.11. From Stokes, 1864

Start of Stokes paragraph 8: “We may infer from the facts above mentioned that the colouring matter of blood, like indigo, is capable of existing in two states of oxidation, distinguishable by a difference of colour and a fundamental difference in the action on the spectrum. It may be made to pass from the more to the less oxidized state by the action of suitable reducing agents (Stokes had shown CO₂ to function as a reducing agent on hemoglobin) and recovers its oxygen by absorption from the air.”

And Stokes continues at the end of his Paragraph 16: “Seeing then that the change of color from arterial to venous blood as far as it goes is in the direction of the change from scarlet to purple cruorine (hemoglobin), that scarlet cruorine is capable of reduction …, we have every reason to believe that a portion of the cruorine present in venous blood exists in the state of purple cruorine, and is reoxidized in passing through the lungs” [182].

D.12. Krogh's Letter to Mimi of January 3, 1904

“Kære Moder!/Tak for dine breve og for gaverne som jeg blev meget glad for. De kom allerede 1st Juledag om eftermiddagen da jeg just sad og sled med at gennemgaa onkel W's Supplement./Jeg har været meget flittig hele tiden og faaet ikke saa lidt udrettet saa at det nu ser noget mere rimeligt ud at jeg kan naa hvad der skal naaes i løbet af foraaret./Hertil hjælper det meget at prof Bohr har faaet Dr Hasselbalch til at skrive den afhandling om kulsyren i blodet som han havde tiltænkt mig./En anden ting der ogsaa vil hjælper er at jeg nu fra Nytaar opgiver al registreringsarbejde af videnskabelig literatur som jeg hidtil har haft. Det har kedet mig ubeskriveligt og taget ikke så lidt tid men jo ogsaa indbragt mig ca 200 kr om aaret. Dem mener jeg imidlertid at kunne undvære, især naar det bliver til noget med docenturen til sommer./Jeg har været to gange hos prof Bohr i Julen, først til et stort ‘ungt’ selskab 3^de Juledag og derefter ganske alene nytaarsaften. Det sidste satte jeg betydelig mere pris paa end det første. Jeg kom der til aften kl 10 og vi havde det yderst fornøjeligt til længe efter kl 12. Kl 12 præcis stillede vi os op og drak champagne og ønskede hinanden glædelig Nytaar./Nu i dag har jeg siddet herhjemme og ventet på at Johan skulde komme, (jeg har ikke set ham endnu siden han kom til byen) men det lader ikke til at han vil vise sig./Jeg medsender, foruden en bog til Frida en anden bog som der er gaaet meget ry af og som jeg ogsaa finder særdeles læseværdig. Jeg tænker at det vil interessere Dig og Frida at læse den. Det er snart gjort./Jeg vil bede dig sende saa snart det kan lade sig gøre” The Life of Mrs. Carlyle “da Fru Bohr har ønsket at læse den./Hermed stopper jeg foreløbig. Jeg haaber at se Johan inden jeg afsender pakken Mandag./Fra Johan er der ikke andet at melde end at han gerne igen vil læse Brevene som han ikke fik og at Du derfor ikke må beholde dem forlænge./Hilsen til alle./Din August.”

In the (Royal Danish Library. Arkiv: I. Breve. II. Personalia. III. Manuskripter. IV. Slægtninges papirer og optegnelser. V. Tryksager. Kps. 41: I.3. Breve til August og Marie Kroghs børn og slægtninge. Marie (Mimi) Krogh, 1900–1908).

Krogh's letter to Mimi, January 3, 1904, translated to English in the following paragraph:

“Dear Mother!/Thank you for your letters and for the gifts which I was very happy for. They arrived already on 1st Christmas Day in the afternoon when I just sat and struggled to go through Uncle W's Supplement./I have consistently been diligent and have made not that little progress, making it increasingly likely I will achieve my goals by spring./To this end, it helps a lot that Prof. Bohr has managed Dr. Hasselbalch to write the treatise on carbonic acid in the blood which he had intended for me./Another thing that will also help is that I now from New Year give up all registration work of scientific literature that I have had so far. It has bored me indescribably and taken not that little time but also brought me ca. 200 kr a year. However, I think I can do without them, especially when it comes to the readership in the summer./I have been twice at Prof. Bohr's during Christmas, first to a big ‘youth’ party on 3rd Christmas Day and then quite alone on New Year's Eve. I appreciated the latter much more than the former. I got there in the evening at 10 and we had it extremely enjoyable until long after 12. At 12 precisely we stood up and drank champagne and wished each other a Happy New Year./Now today I have sat at home and waited for Johan to come, (I have not seen him yet since he came to town) but it does not seem that he will show up./I enclose, besides a book for Frida another book which has gained a lot of reputation and which I also find very readable. I think it will interest You and Frida to read it. It is soon done./I'm asking you to send as soon as it can be done ‘The Life of Mrs Carlyle’ as Mrs. Bohr has wished to read it./Hereby I stop for now. I hope to see Johan before I send the package on Monday./From Johan there is nothing else to report than that he would like to read the Letters that he did not get and that you therefore must not keep them for long./Greetings to all./Yours, August.” There are no New Years Greetings in the letter. The two underlinings in the text above is by me. Reference to the text is placed with the Danish version.

D.13. Another Quote From Hasselbalch's Eulogy on Bohr

“The history of hemoglobin modifications is somewhat more accessible in its details and should therefore be briefly outlined. Bohr found that purified oxyhemoglobin occurred in 4 different modifications with respect to oxygen binding capacity; by certain simple interventions, oxyhemoglobin could be transferred from one modification to another. He now imagined that the blood pigment underwent the same state changes in the order that as the oxygen in the blood disappeared due to tissue respiration, influences from cells of unknown nature caused the hemoglobin's originally high specific oxygen content to be reduced. This would achieve a regulation of the oxygen tension in the plasma, so that it remained relatively constant throughout the entire circulation despite tissue oxygen consumption. Attempts to confirm this assumption, which looks extremely daring, almost fantastic, led—using the methods that were then the finest—to the desired result: The specific oxygen content of venous blood was found to be somewhat lower than that of arterial blood. These investigations aroused much attention and doubt among physiologists; they were confirmed by some, but still doubted by most. On a specific occasion, Bohr then found himself, half a dozen years later, forced to resume and expand the investigation with improved methods. [This is most likely a reference to Hüfner's paper from 1901 on the interaction of O₂ and CO₂ on binding to hemoglobin, with my bolding of the sentence]. In conjunction with two of his students, he now succeeded in clarifying the matter: there really is a regulation like the one assumed, whereby the oxygen tension in the plasma, in the well‐understood interest of the cells, is kept up despite the constant consumption of oxygen in oxyhemoglobin; but the regulation is of a completely different and less mysterious mechanism than previously assumed. As the carbon dioxide tension in the blood rises during passage through the capillaries, oxygen is expelled from oxyhemoglobin and thus becomes available to cells. Or, as one can also say it: The dissociation curve of oxyhemoglobin lies lower, the higher the present carbon dioxide tension is. It will be easy to see that by this arrangement, the organism achieves exactly the same as by a ‘hemoglobin modification’ with higher ‘specific oxygen content’ going over to one with lower.” Hasselbalch 1911 [150].

D.14. Hüfner's Original Text Criticizing Bohr, With a Translation to English Below

“Hinsichtlich der neueren Versuche des Hrn. Bohr, welche die gleiche Frage betreffen und welche im Centralblatt für Physiologie, 1888, S. 437—440, kurz veröffentlicht sind, muss ich leider bekennen, dass mir deren Ergebnisse so sehr sowohl mit dem Dissociationsgesetze, wie mit allen unseren Erfahrungen über Gasdiffusion im Widerspruch zu stehen scheinen, dass ich eher an einen Mangel des Bohr'schen Versuchsverfahrens als an die Richtigkeit der dort gezogenen Schlüsse zu glauben vermag. Anstatt mit Hrn. Bohr anzunehmen, dass bei allen seinen Versuchen im Blute die Kohlensäuretension niedriger, die Sauerstofftension höher als in der Exspirationsluft seien, und dass demnach dem Lungengewebe eine active Rolle sowohl bei der Kohlensäureausscheidung wie bei der Sauerstoffaufnahme zuzuschreiben sei, möchte ich vielmehr der Vermuthung Raum geben, dass eine so innige Berührung von Blut und Versuchsluft (in der Stromuhr), wie sie zur Herstellung des chemischen Gleichgewichtes zwischen beiden erforderlich ist, unter den durch Hrn. Bohr's Versuchsweise eingeführten Bedingungen niemals stattgefunden habe. Eine solche innige Berührung und mit ihr das gewünschte chemische Gleichgewicht wird nach nıeiner Erfahrung immer nur durch ein mehrere Minuten hindurch fortgesetztes sehr heftiges Durcheinanderschütteln von Blut und Gasgemisch zu Stande gebracht.” (Hüfner 1890, footnote, p. 10) [24].

[“Regarding Mr. Bohr's recent attempts, which concern the same question and which are briefly published in the Centralblatt für Physiologie, 1888, pp. 437–440, I must unfortunately confess that these results seem to me to be so much in contradiction with the law of dissociation, as well as with all our experiences about gas diffusion, that I am more inclined to believe in a deficiency of Bohr's experimental procedure than in the correctness of the conclusions drawn there. Instead of assuming with Mr. Bohr that in all his experiments in the blood the carbon dioxide tension is lower, the oxygen tension higher than in the exhaled air, and that therefore an active role should be attributed to the lung tissue both in carbon dioxide excretion and in oxygen uptake, I would rather give room to the assumption that such intimate contact between blood and experimental air (in the manometer) as is necessary for establishing chemical equilibrium between the two has never taken place under the conditions introduced by Mr. Bohr's experimental method. Such intimate contact and with it the desired chemical equilibrium is, according to my experience, always only brought about by a very vigorous shaking of blood and gas mixture for several minutes”.]

D.15. In 1910, Krogh Writes

“Taking as my basis the work of Bohr and being able to draw upon the rich experience gained by him and in his laboratory, I proposed in 1906 to utilize my new methods of gas‐tonometry for a series of investigations of the gas‐tensions in the blood leaving the lungs, by which I hoped to throw some further light upon the secretory processes and to study the influence which external conditions, varied in several ways, might exercise upon them. Failing to obtain evidence of any secretion of gases in the first series of experiments I tried in such other ways as seemed to be promising, but the results, which are given in detail in the preceding special papers, were entirely negative, and I was led, though very reluctantly, to give up the secretion‐theory altogether” [196].

D.16. Gjedde Writes

“… It was no longer possible to maintain the hypothesis of an active transport of oxygen in the lungs by reference to measurements of the tension difference between the lungs and the bloodstream. The reasoning now had to focus on the adequacy of the diffusion capacity. But the parties did not commuicate, and only later did Krogh elaborate on the realization that the dispute had two themes: when Krogh focused on the diffusion mechanism, Bohr in reality but unknowingly addressed the question of the mechanism responsible for the adjustment of diffusion capacity” [193].

D.17. Gjedde Continues

“In the last of the seven little devils, where the mechanisms of pulmonary gas exchange are recapitulated (Krogh 1910b), Krogh returns to his doctoral thesis where he had concluded that absorption of O₂ across the frog lung must have taken place by secretion, and correctly reinterprets the ability of frogs to alter pulmonary oxygen uptake as an indication of being able to increase perfusion.”

D.18. Krogh 1910a, p. 271

“I drew the conclusion that the absorption of oxygen, through the lungs must take place by secretion, though it is evident that no conceivable amount of secretion can increase the quantity of oxygen, in the blood bejond saturation of the hemoglobin. My results make, in fact, the existence of vasomotors for the pulmonary vessels in the frog extremely probable, even if they do not constitute an absolute proof” [196].

D.19. Krogh 1903

“The pulmonary respiration, predominantly at least, is effected by secretory processes in the epithelium and is regulated through the nervous system” [18].

D.20. Quote by Krogh

“I shall be obliged in the following pages to combat the views of my teacher Prof. Bohr on certain essential points and also to criticise a few of his experimental results. I wish here not only to acknowledge the debt of gratitude which I, personally, owe to him, but also to emphasize the fact, apparent to everybody, who is familiar with the problems here discussed, that the real progress, made during the last twenty years in the knowledge of the processes in the lungs, is mainly due to his labours and to that refinement of methods, which he has introduced. The theory of the lung as a gland has justified its existence and done excellent service in bringing forward facts, which will survive any theoretical construction, which has been put or shall hereafter be put upon them” [196].

D.21. Settlement of the Secretion Debate

Readers interested in the history about the oxygen secretion theory in general, how it evolved and ended, should delight themselves by carefully reading Chapter 3 in Sturdy's thesis [93]. It is a gold mine. Meanwhile, I am convinced by Milledge's arguments, that the debate was settled by Barcroft and colleague's explorations and that Haldane's tenacity of keeping the debate open until 1936 may partially have been caused by a methodological problem due to a variable CO/O₂ affinity ratio [221, 252]. Milledge ends with an acknowledgment of Haldane's insistence, which drove a scientific question to its solution and with this characterization of Haldane: “(…) found it more attractive to think of the delicate living membrane that separates air from blood in the lungs as having an active function, positively promoting the transport of life‐giving oxygen into the body, than merely as an inert membrane like an artificial sausage skin.” Interestingly, the alveolar epithelium, the endothelium, and also the tracheal epithelium are all three very active in ion transport [252, 253, 254].

D.22. All Researchers Make Mistakes, and Especially Great Scientists Make Great Mistakes

For me, recognizing three mistakes, or rather failures, by Bohr with his (1) formular derivation and parameter determination for homotropic allostery in 1904, (2) missing the Haldane Effect, although likely due to lack of equipment precision in 1891/1904, as well as (3) Bohr's continued belief in a “special cellular activity” for oxygen secretion to the blood phase in lungs as late as 1909. In the end it turned out to rather be a question of capillary recruitment and elicit a Nobel Prize to Krogh. Bohr's insistence does not diminish the admiration and respect I have for Christian Bohr's geniality and impressive work in respiratory physiology (Bohr 1904a, b; 1905, 1909, 1910; Bohr et al. 1904a, as listed in Bohr bibliograph below the cited literature), see also Edsall (1972) [184]. On Scientific mistakes, just a few other examples are for instance two other classical examples with Einstein's (a) “God does not play dice with the Universe” till his death not believing in the complementarity (Niels Bohr) and uncertainty (Heisenberg) principles of quantum mechanics, that is, the principle that we cannot know everything about the physics of the universe on a subatomic scale (Bodanis 2017, Ch. 17 “Arguing with a Dane,” pp. 191–203) [256] and (b) as well at a cosmological scale, that is, Einstein's cosmological constant—first being constant, then increasing—for the expansion of the universe (Weinberg 1994, Ch. 9, pp. 211–229) [257]. However, on face value, it is an unforgivable misjudgement by Bohr to cut off all communication with August Krogh if alone on personal grounds or scientific disagreements, but we do not have the full picture enabling us to firmly judge between the two and who essentially effected the break. On face value, it was Bohr (Schmidt‐Nielsen 1995, Ch. 9; Sindbæk 2022, pp. 151–168) [32, 43]. Bohr is known to have abhorred personal controversies. The propriety to scientific discoveries is an extremely sensitive issue and may just explain why great minds can also be mistaken, mean, and misjudge each other's intentions and viewpoints; often especially when under great stress.

D.23. Bohr's View on How He Understood “Appropriateness” (“Purpose”) in Physiology and His Own Work Method

Clearly, Bohr was influenced by Carl Ludwig, Claude Bernard and John Scott Haldane. Here I cite in full length, what I consider Bohr's testament:

“Notwithstanding differences in external” influences, and despite the internal metabolic processes occurring with varying intensity, the organism remains, over significant periods relative to its lifespan, remarkably unchanged as a cohesive whole; experientially, it forms a self‐regulating entity.

The primary task of physiology, insofar as the task characterizes physiology as a distinct branch of science, is to investigate the phenomena that are peculiar to the organism as a given object of experience. Through this investigation, it seeks to understand how the individual components of self‐regulation function, how they are harmonized with each other, and how they align with variations in external influences and internal processes. It is inherent in the nature of this task to consider the organism as a purpose, and the regulatory mechanisms that contribute to its maintenance as appropriate. In this sense, the term ‘appropriate’ will be used to describe an organic function in the following (underline added by author).

In order for the use of this concept in each specific case not to be empty or misleading, it must be demanded that a comprehensive investigation of the organic phenomenon being studied has always preceded it. This investigation should clarify, step by step, the specific way in which it contributes to the maintenance of the organism. This requirement is, of course, inherent, as it merely necessitates the scientific demonstration that the term ‘appropriate’ has been used in accordance with its definition in the given context. However, there may be occasions where it is particularly important to emphasize this.

The physiological examination has gradually brought forth such an infinity of unforeseen regulations of the utmost delicacy for the day that there can easily be a tendency to consider any observed vital expression as appropriate without simultaneously determining its mode of action experimentally. This can, in turn, lead to constructing the reality of the assumed vital expression's appropriateness based on a subjective judgment of the specific nature of appropriateness in the given case, using loose analogies that readily present themselves among the diversity of organic processes. However, it is evident how often, with such limited knowledge of the organism, such personal judgments may be erroneous, and there are ample examples of this. In such cases, the lack of experimental clarification of process details is to blame for the method leading to incorrect results.

The a priori assumption of the appropriateness of vital expressions, on the other hand, is merely a heuristic principle and, in itself, naturally, understandable. Given that the conditions within the organism are so profoundly complex and therefore difficult to comprehend, this assumption can often be useful, even indispensable, for formulating specific research questions and seeking ways to answer them. However, one thing is what utility can be applied during preliminary investigations; another is what one is entitled to assert as a truly achieved result. In cases where it concerns the individual functional appropriateness for the entire organism, as mentioned above, this assurance can only be secured by meticulously demonstrating, step by step, the pathways through which the purpose is achieved.

The most essential and challenging work, as is the case throughout science, lies in the detailed examination of the individual organs and the components of the cells that compose them—their structure, composition, and specific physical and chemical properties.

Bindslev N. Christian Bohr. Discoverer of Homotropic and Heterotopic Allostery. Acta Physiol. 2025;241(Suppl. 734):e70016. doi: 10.1111/apha.70016