Carbon dioxide transport across membranes

Abstract

Carbon dioxide (CO₂) movement across cellular membranes is passive and governed by Fick's law of diffusion. Until recently, we believed that gases cross biological membranes exclusively by dissolving in and then diffusing through membrane lipid. However, the observation that some membranes are CO₂ impermeable led to the discovery of a gas molecule moving through a channel; namely, CO₂ diffusion through aquaporin-1 (AQP1). Later work demonstrated CO₂ diffusion through rhesus (Rh) proteins and NH₃ diffusion through both AQPs and Rh proteins. The tetrameric AQPs exhibit differential selectivity for CO₂ versus NH₃ versus H₂O, reflecting physico-chemical differences among the small molecules as well as among the hydrophilic monomeric pores and hydrophobic central pores of various AQPs. Preliminary work suggests that NH₃ moves through the monomeric pores of AQP1, whereas CO₂ moves through both monomeric and central pores. Initial work on AQP5 indicates that it is possible to create a metal-binding site on the central pore's extracellular face, thereby blocking CO₂ movement. The trimeric Rh proteins have monomers with hydrophilic pores surrounding a hydrophobic central pore. Preliminary work on the bacterial Rh homologue AmtB suggests that gas can diffuse through the central pore and three sets of interfacial clefts between monomers. Finally, initial work indicates that CO₂ diffuses through the electrogenic Na/HCO₃ cotransporter NBCe1. At least in some cells, CO₂-permeable proteins could provide important pathways for transmembrane CO₂ movements. Such pathways could be amenable to cellular regulation and could become valuable drug targets.

1. Introduction

The movement of gases across cell membranes is fundamental to life as we know it. As oxygen—or dioxygen (O₂) as chemists often call it—makes the journey in mammals from atmospheric air to mitochondria, the O₂ must pass through numerous biological membranes. The same is true for carbon dioxide (CO₂) in reverse. CO₂ traffic is critical for plants performing photosynthesis. In certain bacteria, plants in symbiotic relationships with such bacteria and in certain cyanobacteria, the traffic of nitrogen (or dinitrogen, N₂) and ammonia (NH₃) is likewise crucial for nitrogen fixation. In humans, abnormal gas movement across biological membranes is also important in a wide range of pathological settings that include heart failure, pulmonary disease (including SARS-CoV-2), vascular disease, hypoperfusion, carbon monoxide (CO) poisoning and a group of conditions associated with diving and/or high altitude, including decompression illness, oxygen toxicity, nitrogen narcosis and CO₂ narcosis.

For about a century, physiologists, at least, adhered to a paradigm—today we would more properly term it ‘solubility theory’—that they traced to the work of Overton [1]. He tested the membrane permeability of many substances by placing plant cells into a hypertonic solution containing the test substance and quantifying the resulting plasmolysis (see [2]). Overton recognized an association between the lipid solubility of substances and their increased ability to cross the membrane, which led him to suspect that the cell membrane—poorly understood at the time—has a lipid component [3]. He even explicitly suggested that this is cholesterol, or cholesteryl esters [3–5]. His was a monumental contribution to cell physiology. However, today Overton is mainly remembered for what others have termed the Overton lipoid theory (see [6]) or Overton's rule (see [7]), according to which the diffusion of solutes through the membrane depends on the oil–water partition coefficient of the solute, which approximates the solubility of the solute in the lipid phase of the membrane. A corollary of Overton's rule is that all gases cross all membranes by dissolving in the lipid phase of the membrane. However, we can identify six shortcomings of Overton's rule.

• (i)Overton did not develop solubility theory. A not-so-well-known American named John Kearsley Mitchell [8,9] developed the concept of solubility theory around 1830—roughly seven decades before Overton's work—at a time when the USA was still a relative backwater of scientific research.
• (ii)Thomas Graham in 1854 published his work on ‘solubility–diffusion theory’, which supplanted solubility theory [10]. In 1866, Graham specifically extended his treatment to gases, recognizing that, after partitioning into an artificial (rubber) membrane, the gas must diffuse through it. This diffusion represents a substantial impediment to the transfer across a membrane [11]. In 1879, Sigmund Wroblewski developed the modern mathematical expression that describes solubility–diffusion theory for gases [12]. Overton, in his classic 1895 paper, did cite Graham, but not Mitchell or Wroblewski.
• (iii)Work on artificial membranes of various lipid compositions [13–15] has shown that the diffusion constant for CO₂ can have as much as 500-fold more impact than its solubility in determining the rate of CO₂ movement across membranes (discussed in [16]). Thus, in applying solubility–diffusion theory to CO₂, one should be thinking primarily about the diffusion constant.
• (iv)In 1994, the Boron group showed that specific cell membranes have no measurable permeability to CO₂ [17]. Thus, not all membranes are permeable to all gases—Overton's rule is not always true.
• (v)It was the discovery of the first membranes with no measurable gas permeability that led to the discovery of the first membrane protein permeable to a dissolved gas, namely aquaporin-1 (AQP1), which is permeable to CO₂ [18,19]. Later work showed that rhesus (Rh) proteins also conduct CO₂ [20,21]. Thus, the very existence of such ‘gas channels’ is further evidence that Overton's rule is not always true.
• (vi)In 2014, Kai & Kaldenhoff [22] made the opposite observation: a membrane protein that does not conduct CO₂ can reduce the apparent CO₂ permeability of an artificial membrane—yet another example showing that Overton's rule is not always true.

The purpose of this review is to examine the historical background leading to the discovery of gas channels, to summarize the early and more recently published experiments on such channels and to introduce preliminary data that bear on the molecular mechanism of how gases like CO₂ move through membrane channels. We will also address questions raised by others [23] regarding gas channels.

Previous reviews on the gas permeability of membrane proteins include discussions of the earliest experiments [24,25]; commentaries on the history and theory of transmembrane CO₂ fluxes and summaries of early gas-channel work [16,26,27]; mathematical modelling of CO₂ transport [28], including the role of carbonic anhydrases (CAs) [29]; and the role of channels and the effects of cholesterol [30]. Also, the papers in this theme issue all deal with aspects of CO₂ [31–40], including the sensing and potential movement of CO₂ through connexons [41,42].

2. Background and classical view (before the discovery of gas channels)

2.1. How do we know that carbon dioxide crosses membranes?

In 1798, Davy demonstrated the presence of CO₂ and O₂ in red blood cells (RBCs) [43–45]. In 1871, Pflüger proposed a mechanism for blood-gas exchange. He invented an aerotonometer, a device to determine partial pressures of gases in liquids, which led to his theory that gases cross the RBC membrane according to Fick's law of diffusion [46,47]. In their classic 1904 paper, Bohr, Hasselbalch and Krogh demonstrated that increased blood levels of CO₂ (which had to cross the RBC membrane to enter the cell) leads to a right-shift in the HbO₂ dissociation curve known as the Bohr effect [48]. See [49] for a review of this early work.

Another approach that led to the demonstration that CO₂ can cross cell membranes involves measuring pH changes. In 1920, Jacobs showed that exposure to a solution equilibrated with a highly acidic 100% CO₂ causes the colour of flower petals to shift from blue to red [50], indicating a fall in pH as CO₂ arriving near the flower-petal pigment undergoes the reaction $\mathrm{C}{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}\to \mathrm{HC}{\mathrm{O}}_3^{-}+{\mathrm{H}}^{+}$. Nearly 40 years later, Caldwell used a pH-sensitive microelectrode to measure the intracellular pH (pH_i) of a crab muscle fibre or squid giant axon and found that exposure to 100% CO₂ causes pH_i to fall rapidly by greater than 0.5 [51]. More sophisticated pH-sensitive microelectrodes allowed Thomas to monitor pH_i changes in snail neurons as he introduced $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ into (or removed CO₂ from) the extracellular solution [52]. In their experiments on squid giant axons, Boron and De Weer confirmed that exposure to $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ causes pH_i to fall rapidly and also showed that, if the exposure is maintained, pH_i slowly increases from the intracellular acid load—the first evidence for active regulation of pH_i [53]. Nowadays, one can use the absorbance [54] or fluorescence [55–57] of pH-sensitive dyes to monitor pH_i changes produced by transmembrane CO₂ fluxes in mammalian cells.

A third experimental approach that confirms the entry of CO₂ across a cell membrane exploits the presence of CA within RBCs [58–60]. If one exposes RBCs to a solution containing ¹⁸O-labelled $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$, the C¹⁸O₂ will enter the cell and undergo the CA-catalysed reaction $\mathrm{C}{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}\to \mathrm{HC}{\mathrm{O}}_3^{-}+{\mathrm{H}}^{+}$, so that the ¹⁸O label now becomes part of $\mathrm{HC}{\mathrm{O}}_3^{-}$. However, the ¹⁸O-labelled $\mathrm{HC}{\mathrm{O}}_3^{-}$ can now undergo the reverse reaction, $\mathrm{HC}{\mathrm{O}}_3^{-}+{\mathrm{H}}^{+}\to \mathrm{C}{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}$, in which the ¹⁸O has only two chances in three in becoming part of a CO₂ molecule. Thus, each time the CA-catalysed reaction converts the carbon back and forth between CO₂ and $\mathrm{HC}{\mathrm{O}}_3^{-}$, one-third of the ¹⁸O label is lost to an infinite sink of H₂O [58]. If one uses mass spectrometry to monitor the time course of [C¹⁸O₂] and [HC¹⁸${\mathrm{O}}_3^{-}$], one can determine the CA activity of the RBC. Because virtually all of the CA activity of an RBC suspension is inside the RBCs, and if one takes into account possible shifts in CA activity between samples, one can also use this ¹⁸O approach to measure the permeability of RBC membranes to CO₂, as first done by Forster et al. [61].

2.2. The physical chemistry of gas diffusion across membranes

Having reviewed the history that established that CO₂ moves across biological membranes, let us now address this movement's mechanism.

2.2.1. Solubility theory

In the early 1770s, Priestley placed hydrogen gas (H₂) in a bladder and observed, over time, its replacement by common air [8,62]. In 1829, Graham performed similar experiments with ‘carbonic acid’ (i.e. the term used at that time for CO₂) [63]. However, Mitchell was the first to investigate the mechanism of gas movement across a barrier. He studied gas escape (i.e. H₂) from rubber balloons, which descended from some height in his lecture room as H₂ permeated through the rubber membrane [8]. In separate experiments, he used an inverted syphon filled with mercury, where its short limb was covered by animal tissue or a rubber membrane and trapped under a bell full of gas to be tested. As gas entered through the membrane into the short limb, the mercury in the long limb ascended, allowing him to calculate the velocity and quantity of influx of tested gas. In a systematic study of 10 gases, Mitchell found that their penetration rates varied by two orders of magnitude, deducing that the penetration rate depended on the amount of gas absorbed by the barrier [8]. This early statement of ‘solubility theory’ anticipates by more than six decades the oft-quoted works of Overton [1], who in 1895 established that the permeability of certain biological membranes increases with the lipophilic nature of the permeating molecules.

2.2.2. Fick's law of diffusion

In 1855, Fick published his theory of the diffusion to explain the passive movement of salts both within liquids and across collodion film and animal membranes¹ [64,65]. As Fick pointed out, his work is a logical extension of the ground-breaking work by Fourier, who developed the theory of heat diffusion [66,67], which had already inspired Ohm to develop his theory of electric-current flow [68]. Fick might also have noted that the successes of Fourier and Ohm had already inspired the Hagen–Poiseuille theory of fluid flow [69,70]. Fick proposed that the movement of salt from one ‘stratum’ to another is

$$\mathrm{Quantity}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\mathrm{salt}=-A\cdot k\cdot \left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)\cdot \mathrm{d}t\hspace{0.17em},$$ 2.1

where A is the area² (e.g. cm²) separating the two strata, k is the diffusion constant (e.g. cm² s⁻¹), y is the salt concentration (e.g. mol cm⁻³) and dt is an infinitesimal time increment (e.g. s). Rearranging, we obtain a modern expression of Fick's first law,

$$\frac{\mathrm{Quantity}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\mathrm{salt}}{A\cdot \mathrm{d}t}=J=-k\cdot \left(\frac{\mathrm{d}y}{\mathrm{d}x}\right),$$ 2.2

where J is the flux (e.g. mol cm⁻² s⁻¹) between the two strata.

2.2.3. Solubility–diffusion theory

Whereas Mitchell established the importance of solubility in the movement of gases, and Fick established the generalized importance of the diffusion of solutes, it was Graham in 1866—nearly 40 years after his first paper in this field—who explicitly showed that the rate of movement of gases across rubber membranes depends on both solubility and diffusion [11,71]. It fell to Wroblewski, 13 years later, to assemble Henry's law and Mitchell and Graham's thoughts into a single equation. Henry's law states that the concentration of dissolved gas X in an aqueous solution is proportional to the partial pressure of that gas (p_X) in the gas phase,

$$[\mathrm{X}]={\mathrm{s}}_{\mathrm{X}}\cdot {\mathrm{p}}_{\mathrm{X}},$$ 2.3

where s_X (i.e. the solubility coefficient) is that proportionality factor. The use of Henry's law is an important step because it recognizes that it is the concentration gradient of X in the aqueous solution—not the partial pressure gradient per se—that drives diffusion. Wroblewski's final equation is

$$\dot{Q}=K_{\mathrm{X}}\cdot D_{\mathrm{X}}\cdot p_{\mathrm{X}},$$ 2.4

where $\dot{\mathit{Q}}$ is the quantity of gas moving across a membrane (of standard area and thickness³) per unit time, K_X is the coefficient of absorption in the rubber membrane (i.e. analogous to s_X in Henry's law), D_X is the diffusion constant through the membrane and p_X is the partial pressure of X (which is present on only one side of the membrane). As implied above, Wroblewski assumed that all measurements would be made at equal membrane thickness (a). Modern versions of Wroblewski's equation often explicitly include membrane thickness, recognizing that effective membrane permeability is inversely proportional to membrane thickness,

$$J_{\mathrm{X}}=\frac{s_{\mathrm{X}}\cdot D_{\mathrm{X}}}{a}\cdot p_{\mathrm{X}},$$ 2.5

where J_X is the unidirectional flux (mol cm⁻² s⁻¹) from the side of the membrane where X is present to the side where X is absent. Modern versions of the equation also would recognize that the gas can be present on both sides of the membrane, and that the net flux from side 1 to side 2 of the membrane is proportional to the p_X difference on the two sides,

$$J_{\mathrm{X}}=s_{\mathrm{X}}\cdot D_{\mathrm{X}}\cdot \frac{(\hspace{0.17em}{p}_{\mathrm{X},1}-p_{\mathrm{X},2})}{a}.$$ 2.6

The model in figure 1a is called a two-compartment model because we assume perfect mixing in compartments 1 and 2. That is, X is uniform throughout compartment 1 and throughout compartment 2. (We will introduce unconvected layers in the next section.) In this modern form of the solubility–diffusion equation, the s_X is inspired by Mitchell, the D_X is inspired by Graham, the overall form of the equation comes from Fick and the implicit inclusion of Henry's law comes from Wroblewski. The term s_X(p_X,1–p_X,2)/a is analogous to the dy/dx in equations (2.1) and (2.2), and describes the gradient—expressed in terms of partial pressures—that drives diffusion. Finally, we note that one of Graham's important contributions (i.e. Graham's law [72]) was the recognition that the diffusion constant D_X is inversely proportional to a molecular weight of X,

$$D_{\mathrm{X}}\hspace{0.17em}\propto \hspace{0.17em}\frac{1}{\sqrt{MW}}.$$ 2.7

Thus, we see that the early history of the solubility–diffusion theory for the movement of gases is based on some of the earliest principles of physical chemistry, applied to a barrier consisting of artificial materials (e.g. rubber) or animal tissue.

Figure 1.

Simple model of CO₂ diffusion across a membrane. (a) Two-compartment model in which a synthetic membrane separates two solutions, 1 and 2. These solutions are so well mixed that [CO₂] is uniform throughout each compartment. Moreover, CO₂ is in equilibrium between air and each aqueous solution, with its concentration corresponding to Henry's law as indicated. Because [CO₂]₁ > [CO₂]₂, CO₂ diffuses from side 1 to side 2, and J_CO2 is positive. (b) A two-compartment model with a synthetic membrane separating two solutions, each with an unconvected fluid layer (UF₁ and UF₂) indicated in brown. Because [CO₂] at the membrane surface on side 1 exceeds [CO₂] at the membrane surface on side 2 (i.e. ([CO₂]_S1 > [CO₂]_S2), CO₂ diffuses from side 1 to side 2, and J_CO2 is positive, as in (a). This flux lowers [CO₂] throughout UF₁ and sets up a gradient for CO₂ to diffuse from the bulk fluid on side 1 (bF₁) through UF₁ and to the membrane surface on side 1. The transmembrane CO₂ flux also raises [CO₂]_S2, establishing a gradient for CO₂ to diffuse through UF₂ and into bF₂. s_CO2, CO₂ solubility; p_CO2, partial pressure of CO₂.

2.3. Carbon dioxide movement through lipid bilayers/lipid phase of biological membranes

2.3.1. Carbon dioxide diffusion across a hypothetical membrane

Let us now consider the diffusion of solute X, which will be CO₂ in this example, across a membrane bordered on both sides by aqueous solutions. To illustrate better the presence of Henry's law in equation (2.6), we rewrite this equation explicitly in terms of concentrations, recognizing from Henry's law in equation (2.3) that the product of s_CO2 and p_CO2 is [CO₂],

$$J_{\mathrm{C}{\mathrm{O}}_2}=D_{\mathrm{M},\mathrm{C}{\mathrm{O}}_2}\cdot \frac{({[\mathrm{C}{\mathrm{O}}_2]}_1-{[\mathrm{C}{\mathrm{O}}_2]}_2)}{a}\hspace{0.17em}.$$ 2.8

This equation still pertains to the two-compartment model, now shown for CO₂ in figure 1a, where the only relevant diffusion constant is that through the membrane (D_M,CO2). In addition, we can replace the ratio D_M,CO2/a with the empirical term permeability, which we will specify as membrane CO₂ permeability (P_M,CO2),

$$J_{\mathrm{C}{\mathrm{O}}_2}=P_{\mathrm{M},\mathrm{C}{\mathrm{O}}_2}\cdot ({[\mathrm{C}{\mathrm{O}}_2]}_1-{[\mathrm{C}{\mathrm{O}}_2]}_2)\hspace{0.17em}\hspace{0.17em}.$$ 2.9

If [CO₂]₁ is greater than [CO₂]₂, as shown in figure 1a, CO₂ diffuses from side 1 to side 2, and J_CO2 is a positive number.

In real life, unlike the two-compartment model in figure 1a, solutions are not perfectly mixed. Instead, as shown in figure 1b, [CO₂] in the unconvected fluid (UF) near the membrane is lower than [CO₂] in the bulk fluid (bF) on side 1 ([CO₂]_bF1). Moreover, on side 1, [CO₂] is the lowest of all at the membrane surface ([CO₂]_S1). This CO₂ gradient on side 1, from the bF to the membrane, is the consequence of the flux of CO₂ across the membrane, from side 1 to side 2. Conversely, [CO₂] at the membrane surface on side 2 ([CO₂]_S2) exceeds [CO₂] in the bF on side 2 ([CO₂]_bF2), again the consequence of the flux of CO₂ across the membrane. In a steady state, the fluxes of CO₂ at each of the three steps is the same: (i) from the BF to the membrane surface on side 1,

$$J_{\mathrm{C}{\mathrm{O}}_2}=D_{\mathrm{U}{\mathrm{F}}_1,\mathrm{C}{\mathrm{O}}_2}\cdot \frac{({[\mathrm{C}{\mathrm{O}}_2]}_{\mathrm{b}{\mathrm{F}}_1}-{[\mathrm{C}{\mathrm{O}}_2]}_{{\mathrm{S}}_1})}{{\ell }_1}\hspace{0.17em},$$ 2.10

where D_UF1,CO2 is the CO₂ diffusion constant in the bulk saline and ℓ₁ is the thickness of the unconvected fluid layer between the bF and the membrane; (ii) across the membrane,

$$J_{\mathrm{C}{\mathrm{O}}_2}=D_{\mathrm{M},\mathrm{C}{\mathrm{O}}_2}\cdot \frac{({[\mathrm{C}{\mathrm{O}}_2]}_{{\mathrm{S}}_1}-{[\mathrm{C}{\mathrm{O}}_2]}_{{\mathrm{S}}_2})}{a}\hspace{0.17em};$$ 2.11

and finally (iii) from the membrane surface to the bF on side 2,

$$J_{\mathrm{C}{\mathrm{O}}_2}=D_{\mathrm{U}{\mathrm{F}}_2,\mathrm{C}{\mathrm{O}}_2}\cdot \frac{({[\mathrm{C}{\mathrm{O}}_2]}_{{\mathrm{S}}_2}-{[\mathrm{C}{\mathrm{O}}_2]}_{\mathrm{b}{\mathrm{F}}_2})}{{\ell }_2}\hspace{0.17em},$$ 2.12

where ℓ₂ is the thickness of the unconvected fluid layer on side 2.

2.3.2. Two major routes by which cells can control transmembrane carbon dioxide diffusion

Focusing on the diffusion of CO₂ across the membrane per se in equation (2.11), we see that a cell can influence J_CO2 in two major ways. First, it can modulate the effective diffusion constant D_M,CO2 of the membrane. Second, the cell can use CAs to modify the CO₂ gradient ([CO₂]_S1 – [CO₂]_S2). We will address these two points of control in the next two sections.

2.3.2.1. Control of D_M,CO2

The cell can control membrane permeability by several mechanisms. First, it can alter the composition of membrane lipid. Artificial planar lipid bilayers inevitably contain a high concentration (up to 30%) of an organic solvent like n-decane and often comprise loosely packed phospholipids with unsaturated medium-chain fatty acids. Such membranes are highly fluid and highly permeable to CO₂ [73]. Biological membranes, of course, contain no n-decane and have a complex composition of lipids that can be tightly packed. Mammalian membranes typically contain 20% or more cholesterol, with some having greater than 70% cholesterol. Cholesterol and sphingomyelins tighten membranes. For example, in one study, raising cholesterol content from 0% to 20% reduced the CO₂ permeability of an artificial bilayer by 10-fold [74], and increasing the cholesterol to 70% reduced P_M,CO2 by another 10-fold [22,74].

Another potential tactic is for the cell to alter the abundance of membrane proteins that do not conduct CO₂—proteins that we term ‘blocking proteins’. An example is the CO₂-impermeable plant aquaporin NtPIP2;1. Kai & Kaldenhoff [22] found that introducing NtPIP2;1 into artificial bilayers reduced P_M,CO2.

A third consideration is proteins that obstruct access to (or egress from) the lipid bilayer. In his review, Engelman [75] noted that the ectodomains of membrane proteins could be sufficiently large to create steric restrictions in the access of solutes to the membrane lipid [76–78]. In a tour de force study of the protein composition of membrane vesicles, Takamori et al. [79] concluded that the exomembranous portions of various proteins are arranged so densely that they almost completely obstruct one's hypothetical view of the membrane lipid. Besides the exomembranous portions of integral membrane proteins, loosely attached proteins also represent obstructions. Boron coined the term access/egress efficiency [16] to describe how such an obstruction reduces the availability of the membrane lipid for diffusion events. The somewhat tongue-in-cheek term ‘solubility–diffusion–access/egress theory’ describes the macroscopic factors controlling gas permeability through the lipid phase of a biological membrane.

Clearly, even if we consider only the diffusion of CO₂ through its lipid component, a biological membrane—with a complex lipid composition that can cause marked stiffening, blocking proteins and limited access/egress by exomembranous protein domains—may be radically different from a planar lipid bilayer (figure 2). The fourth difference between planar lipid bilayers and at least some biological membranes is the presence of conductive pathways for dissolved gases, which we will address below in §3.

Figure 2.

Factors affecting D_M,CO2. The cell can control J_CO2 (red arrows) in two ways, by modifying the CO₂ diffusion constant (D_M,CO2) and by modifying the CO₂ gradient via CAs. In this figure, we focus on factors influencing D_M,CO2. The lipid membrane may contain a substantial amount of cholesterol and sphingolipids that reduce membrane fluidity and, therefore, the CO₂ diffusion constant through the lipid phase. Most integral transmembrane proteins (pink and dark purple) do not conduct CO₂ and thus reduce the surface area of lipid that is able to conduct CO₂. The exomembranous portions of some membrane proteins, which may be far more extensive on both sides of the membrane than shown here [79], may also hinder access of CO₂ to, or the egress of CO₂ from, the membrane, and thereby increase tortuosity and thus lower D_M,CO2 even further. On the other hand, some proteins in the membrane facilitate the movement of CO₂. These include AQP1, AQP4, AQP5, AQP6 and AQP9 (shown in the figure as AQP), RhAG, RhBG, RhCG and AmtB (shown in the figure as Rh) and potentially the electrogenic Na/HCO₃ cotransporter NBCe1. Modified from [26].

2.3.2.2. Control of the carbon dioxide gradient

In 1977, Gutknecht et al. [14] reported an elegant series of experiments in which they demonstrated, using planar lipid bilayers, the importance of CA in facilitating the diffusion of ¹⁴C-labelled CO₂ through the unstirred layers—for reasons described in [80], we prefer to use the term ‘unconvected layer’—near the membrane surface. In 2014, Musa-Aziz, Occhipinti and Boron extended these insights in a series of three papers [81–83] in which they used microelectrode measurements of intracellular pH and surface pH (pH_S) to explore transmembrane CO₂ diffusion in intact Xenopus oocytes, augmented by extensive mathematical simulations based on a three-dimensional reaction–diffusion mathematical model.

Figure 3 (in which the CA II and/or CA IV may be either absent or present) illustrates the fundamental principles provided by the above studies. The two key elements are (i) the unconvected layers on either side of the membrane and (ii) the presence of CAs. Figure 4 shows the arrangement of the microelectrodes in and around the oocyte, and figure 5 shows typical experiments for both a control oocyte without added CA II (Tris) and another oocyte previously injected with recombinant human CA II. We will now follow actual experiments as we alternately focus on figures 3 and 5. Imagine that the control cell initially contains no CO₂. We now introduce CO₂ into the bulk extracellular fluid (bECF), which by definition is well stirred. The CO₂ diffuses from the bECF, through the extracellular unconvected fluid (EUF), towards the cell membrane, through the cell membrane (here we make no assumption about whether the CO₂ diffuses through the membrane lipid or channels) and then through the intracellular fluid (ICF) towards the centre of the cell. We will assume that the ICF is entirely unconvected.

Figure 3.

Role of CAs in controlling the CO₂ gradient. The cell can control J_CO2 in two ways, by controlling the diffusion constant (D_M,CO2) and by modifying the CO₂ gradient via CAs. CAs can enhance the CO₂ gradient that facilitates CO₂ diffusion as follows. CO₂ diffuses from the bulk extracellular fluid (bECF), through the extracellular unconvected fluid (EUF), to the outer surface of the membrane (S_o). The diffusion of CO₂ through the membrane and into the cell diminishes [CO₂]_So. Extracellular CA IV, attached to the cell surface, facilitates the conversion of $\mathrm{HC}{\mathrm{O}}_3^{-}$ and H⁺ to CO₂ and H₂O, thereby replenishing the CO₂ and raising [CO₂]_So and tending to enhance the gradient driving CO₂ diffusion across the membrane. Once inside the cell, the newly arriving CO₂ raises [CO₂] on the inner surface of the membrane (S_i), which tends to slow the transmembrane CO₂ flux. The action of intracellular CA II lowers [CO₂]_Si and thereby enhances the gradient for the transmembrane flux of CO₂.

Figure 4.

Experimental arrangement of electrodes in oocyte experiments. (a) Side view, showing bulk extracellular fluid (bECF) flowing from left to right. (b) Top view, showing bECF flowing from the top of the panel to the bottom. The V_m and pH_i electrodes impale the cell. The pH_S electrode pushes up against the membrane, creating a dimple. See [84,85] for a description of the electronics. Modified from [81].

Figure 5.

Experiments showing the effects of recombinant human CA II injected into an oocyte. (a) Oocytes injected with Tris buffer. (b) Oocytes injected with recombinant human CA II dissolved in Tris buffer. In both ‘CA II’ or ‘Tris’ oocytes, the pH_i is represented by the red record and pH_S by the green record. The vertical blue bands represent periods during which the pH_S electrode was withdrawn to the bulk extracellular fluid (bECF) for calibration. The longer blue, dashed vertical lines represent the times of the initiation of a change of solutions. The shorter blue, dashed vertical lines indicate the times when pH_i began to change. The time shift between the longer and shorter lines indicates the delay for the CO₂ to reach the pH_i electrode. The downward vertical arrows near the pH_i records represent the CO₂-induced changes in steady state pH_i. The upward and downward arrows near the pH_S records represent maximal changes in pH_S (i.e. ΔpH_S). The pH_S spike is substantially higher in the oocyte with injected human recombinant CA II. The increased ΔpH_S reflects a greater CO₂ influx. Modified from [81].

As the extracellular CO₂ reaches the cell surface and enters the cell, [CO₂] near the outer surface (S_o) of the cell membrane falls, creating a gradient for CO₂ to diffuse from the bECF to the cell surface and thereby partially replenish the CO₂ (figure 3). The fall in [CO₂]_So also initiates the net conversion of $\mathrm{HC}{\mathrm{O}}_3^{-}$ and H⁺ near the cell surface to H₂O and CO₂, thereby further contributing to the CO₂ replenishment. The consumption of H⁺ leads to a rapid rise in pH_S (figure 5a), the peak magnitude (ΔpH_S) of which ceteris paribus depends on [CO₂]_So, which in turn depends on the rate of CO₂ entry. As CO₂ gradually equilibrates across the membrane, the cell surface reaction slows and pH_S returns to its initial value. In parallel with the pH_S transients, though with a slight delay because the pH_i electrode tip is perhaps 50 µm deep into the cell, pH_i falls monotonically and eventually reaches a stable value (figure 5a). With the removal of extracellular $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$, all of the reactions (figure 3) and pH transients reverse (figure 5a).

The three limiting factors for CO₂ diffusion are D_M,CO2 (or its empirical analogue, P_M,CO2, discussed above) and the diffusion of CO₂ through the EUF and ICF (figure 3). Facilitating the CO₂ diffusion through the EUF is the diffusion of $\mathrm{HC}{\mathrm{O}}_3^{-}$ from the bECF to the EUF and its subsequent conversion to CO₂ at the membrane surface. Similarly facilitating the CO₂ diffusion through the ICF is the conversion of the incoming CO₂ to $\mathrm{HC}{\mathrm{O}}_3^{-}$ at the inner surface of the membrane, and the subsequent diffusion of $\mathrm{HC}{\mathrm{O}}_3^{-}$ towards the centre of the cell. Nevertheless, the interconversion of CO₂ and $\mathrm{HC}{\mathrm{O}}_3^{-}$ is so slow that this facilitation of CO₂ diffusion is unremarkable at typical pH values in the absence of CAs.

The role of CAs, at either side of the membrane, is to maximize the CO₂ gradient across the membrane. Figure 5b is similar to figure 5a except for the presence of human CA II in the cytosol. Here, we see that the pH_S spike is substantially higher than before. An important principle is the concept of a trans-side effect [81–83]: if we make the pH measurement on the side of the membrane opposite the altered CA activity, a change in the pH signal reflects an altered transmembrane CO₂ flux. In this case, the increased ΔpH_S reflects a greater CO₂ influx owing to the addition of CA II to the cytosol.

Nearly every cell expresses CA II in the cytosol. In our example (figure 5), we injected this soluble enzyme, which catalyses the conversion of newly arriving CO₂ to $\mathrm{HC}{\mathrm{O}}_3^{-}$, thereby depleting CO₂ at the inner membrane surface (S_i). This lower [CO₂]_Si accentuates the inward CO₂ gradient across the membrane, and—like the rise in [CO₂]_So discussed in the previous paragraph—enhances the CO₂ influx. Note that the injected CA II also increases the maximal rate of CO₂-induced pH_i descent, which we reported as the signed value of (dpH_i/dt)_max. Because pH_i is falling, (dpH_i/dt)_max is a negative number, and CA II causes it to shift in this case from –0.0009 to –0.0021. This acceleration of acidification is due to both an increased CO₂ influx and an increased rate of conversion of newly arriving CO₂ (and H₂O) to $\mathrm{HC}{\mathrm{O}}_3^{-}+{\mathrm{H}}^{+}$ . Thus, a greater magnitude of (dpH_i/dt)_max does not tell us in any simple way whether the CA II has enhanced CO₂ influx (figure 3). This important principle is an example of a cis-side effect: if we make the pH measurement on the same side of the membrane as the altered CA activity, a change in the pH signal provides no intuitive information about the change in transmembrane CO₂ flux. Note: one can use reaction–diffusion mathematical modelling to predict the extent to which a change in (dpH_i/dt)_max depends on altered CO₂ flux versus an altered rate of $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ interconversion.

Although we are not showing an experimental example here, our laboratory has also investigated the effects of CA IV, which is coupled to the outer surface of the cell via a glycosylphosphatidylinositol (GPI) linkage. As illustrated in figure 3, during CO₂ influx, CA IV converts $\mathrm{HC}{\mathrm{O}}_3^{-}$ near the outer surface of the cell membrane to CO₂, thereby replenishing some of the lost CO₂. This higher [CO₂]_So accentuates the inward CO₂ gradient across the membrane and enhances the CO₂ influx [82,83].

Cytosolic and extracellular CAs enhance the passive flux of CO₂ not by increasing membrane permeability, but by increasing the CO₂ gradient that drives diffusion. A surprising observation in the studies by Musa-Aziz, Occhipinti and Boron was that the effects of introducing CA IV and CA II are supra-additive. As it happened, this prediction emerged from the mathematical simulations in this trio of papers [81–83], and subsequent physiological experiments then confirmed the prediction. This example illustrates one aspect of the power of mathematical simulations. The reason for the supra-additivity is that the addition of CA to only one side of the membrane ‘can only get you so far’. If CA is present only on the outer face of the cell, then the initial rapid influx of CO₂ eventually leads to a build-up of CO₂ near the inner surface of the membrane, and reduces the transmembrane gradient. The introduction of just a tiny amount of intracellular CA—not enough to have much effect by itself—now disposes of the rapidly entering CO₂, increases the gradient and greatly accentuates the CO₂ influx.

An important theoretical point is that, according to the Henderson–Hasselbalch equation, the ratio ${[{\text{HCO}}_3^{-}]}_{{\text{S}}_{\text{i}}}/{[{\text{CO}}_2]}_{{\text{S}}_{\text{i}}}={10}^{\text{pH-pK}}$ . If the pK of the $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ equilibrium is 6.1 and the pH near the inner surface of the membrane is 7.1, then the CA II keeps the ratio ${[{\text{HCO}}_3^{-}]}_{{\text{S}}_{\text{i}}}/{[{\text{CO}}_2]}_{{\text{S}}_{\text{i}}}$ near 10:1. Thus, for every 11 CO₂ molecules that enter the cell, CA II converts approximately 10 to $\mathrm{HC}{\mathrm{O}}_3^{-}$. This reaction not only lowers [CO₂]_Si but also transfers the carbon atom from low-concentration CO₂ to the high-concentration $\mathrm{HC}{\mathrm{O}}_3^{-}$. This is important because the concentration gradient for $\mathrm{HC}{\mathrm{O}}_3^{-}$ (from the inner membrane surface towards the cell centre) is about 10-fold greater than the gradient for CO₂. Because the diffusion constants for $\mathrm{HC}{\mathrm{O}}_3^{-}$ and CO₂ are similar, the conversion from CO₂ to $\mathrm{HC}{\mathrm{O}}_3^{-}$ greatly accentuates the disposal of the incoming carbon.

An important corollary to the above argument is that if the incoming carbon is in the form of $\mathrm{HC}{\mathrm{O}}_3^{-}$ or $\mathrm{C}{\mathrm{O}}_3^{=}$, the conversion to CO₂ would be of negative help—a theoretical argument against the $\mathrm{HC}{\mathrm{O}}_3^{-}$-transporter/CA-metabolon hypothesis [86].

3. Channels

3.1. Carbon dioxide-impermeable membranes

Until relatively recently, Overton's rule—essentially a restatement of solubility theory—was the universally accepted paradigm for understanding how small neutral molecules and dissolved gases like CO₂ cross cell membranes. This rule left little to the imagination: gases cross biological membranes to the extent that they have a high oil–water partition coefficient. However, in 1989, Kikeri et al. [87] found that introducing $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$ on the luminal side of a nephron segment called the medullary thick ascending limb (mTAL) produces a paradoxical decrease in the pH_i of these epithelial cells. The cause of the intracellular acidification is the dominant entry of the acidic $\mathrm{N}{\mathrm{H}}_4^{+}$, which inside the cell dissociates to form NH₃ + H⁺. The authors reached the not unreasonable conclusion that the apical membranes (i.e. those facing the tubule lumen) of mTAL cells—already known to have a low H₂O permeability—are also impermeable to NH₃. This is the first apparent challenge to Overton's rule, and they attributed it to an unusual lipid composition. However, the authors did consider other possibilities; for example, that the massive influx of $\mathrm{N}{\mathrm{H}}_4^{+}$, mediated by K⁺ channels and the Na/K/Cl cotransporter-2, merely overwhelmed a reasonable influx of NH₃. Thus, we really cannot be sure that these cell membranes are NH₃ impermeable.

In 1994, Waisbren and colleagues set out to use digital imaging of a pH-sensitive fluorescent dye to study pH_i regulation in isolated, perfused rabbit gastric glands. In an attempt to acid load the cells by the ammonium-prepulse technique [53,88,89], they exposed the lumen of the glands to 20 mM $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$ at pH 7.40 and were startled to observed no change in pH_i [17]. Even when they raised luminal pH to 8.0 or raised the total $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$ concentration to 135 mM, the result was the same: no change in pH_i. Thus, there could be little doubt but that the apical membranes of both parietal and chief cells have a negligible permeability to both NH₃ and $\mathrm{N}{\mathrm{H}}_4^{+}$. In the same series of experiments, the authors introduced into the lumen 5% CO₂/22 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$, 20% CO₂/22 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$ or even 100% CO₂/22 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$ (essentially a carbonated drink)—they observed no change in pH_i. These experiments show that the apical membranes of parietal and chief cells have a negligible permeability to both CO₂ and $\mathrm{HC}{\mathrm{O}}_3^{-}$. Thus, these experiments provided the first unequivocal evidence that Overton's rule can be broken.

In work published in 1995, Singh and colleagues [90] perfused the lumens of isolated rabbit colonic crypts with solutions containing $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$ up to concentrations of 100 mM $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$ at pH 8.0. They observed no change in pH_i, providing a second example of apical membranes with negligible permeability to both NH₃ and NH⁺₄. [90].

Below we will see that RBCs, although they have relatively high permeabilities to CO₂ and O₂, owe at least 90% of this gas permeability to various protein channels. Thus, without channels, RBCs would have CO₂ permeabilities only modestly higher than the apical membranes of gastric glands.

These various lines of research show that the function of certain biological membranes can be markedly different from that of typical planar lipid bilayers. Perhaps the observed impermeability to NH₃ and CO₂ is not so surprising, inasmuch as biological membranes are not simply phospholipid bilayers. As discussed above, biological membranes are complex mixtures of a wide range of lipids, integral and peripherally associated proteins and attached sugars. We propose that some combination of exotic lipid composition, blocking proteins, peripherally associated proteins, exomembranous protein domains and glycosylation or other modifications—on both sides of the membrane—produce low background permeability to dissolved gases like CO₂.

3.2. Aquaporins

It was while giving a seminar at the University of Pennsylvania that one of us (Boron) proposed to the audience that the explanation for the CO₂ impermeability of the apical membranes of gastric glands reflects an unusual lipid or protein composition. As they were exiting the seminar room, the host (Paul De Weer) suggested to Boron that he had it backwards: perhaps both the apical and basolateral membranes of gastric gland cells have the same fundamental protein–lipid composition, but the basolateral membranes have CO₂ channels. De Weer forgot the conversation but Boron could not, reasoning that if CO₂ channels existed, they would be found in a cell that does gas transport for a living (e.g. RBCs). Moreover, he reasoned that the hypothetical channels, if they existed, would be proteins present at great abundance, but that did not seem to belong there. AQP1 was an obvious candidate; RBCs carry gases for a living, not water. Peter Agre had already given the Boron lab the cDNA encoding human AQP1 [91,92], and it was straightforward for the group to express AQP1 in Xenopus oocytes and use rates of pH_i change as an assay for CO₂ influx.

3.2.1. Discovery and characterization of aquaporin-1

While purifying 32 kDa Rh polypeptides from RBCs in 1988, Denker et al. [91] noted a 28 kDa protein that co-purified during several steps of the process. In 1991, Smith & Agre [93] recognized the protein as a multimeric protein, identified in 1994 on the basis of two-dimensional crystallization as a tetramer [94]. Meanwhile, in 1991, Preston & Agre [92] cloned the cDNA encoding this protein from the human fetal liver. A year later, in experiments on Xenopus oocytes, Preston et al. [95] showed that the heterologous expression of the protein causes the osmotic water permeability (P_f) of oocytes to increase. Thus, they identified the 28 kDa protein as the water channel—now known as AQP1—long anticipated to be present in RBCs and to be susceptible to blockade by p-chloromercuribenzenesulfonate (pCMBS) [96]. Indeed, in 1993 Preston et al. [97] showed that, of the four cysteine residues present in AQP1, only the mutation of Cys-189 (e.g. to C189S), which is near the extracellular opening of the water pore, prevents mercury sensitivity.

In their cloning paper, Preston and Agre also provided evidence that the cDNA is the result of an ancient gene-duplication event that produced a tandem repeat, each module of which could encode three transmembrane segments (TMs), for a total of six [92]. Thus, TM1 from the first module would thread outwards through the membrane, whereas the homologous TM4 would thread inwards. In 1994, Jung et al. [98] produced the hourglass model in which they recognized that both the extracellular loop between TMs 2 and 3 (at the centre of which is a highly conserved asparagine--proline--alanine (NPA) motif), and the corresponding intracellular loop between TMs 5 and 6 (with its highly conserved NPA motif), actually dip into the plane of the membrane. Moreover, they recognized that the two inverted NPA motifs of each of the four monomers interact with one another in each water pore, in an hourglass arrangement. However, at this point—on the basis of a 6 Å structure [99]—their model showed that the NPA/NPA motifs of each monomer faced a central depression of the tetramer. In 2001, the 2.2 Å structure (figure 6) of Sui et al. [100] revealed that near the middle of each monomer is (progressing from the extra- to the intracellular side) an extracellular cytoplasmic vestibule, a highly conserved selectivity filter and the NPA/NPA. The four monomers surround a hydrophobic central pore that we now believe is a channel for CO₂ and O₂ [101].

Figure 6.

Extracellular view of the human AQP1 tetramer. Bovine AQP1 structure as determined by Sui et al. in 2001 [100]. The four AQP1 monomers form a functional tetramer, with four water pores and a central pore in the middle. The Cys-191 residue (highlighted in yellow) is on the extracellular half of the monomeric pores. Bovine Cys-191 is analogous to Cys-189 in human AQP1. In their 1998 study, Cooper & Boron [19] used Peter Agre's C189S mutant. Image created from PDB ID: 1J4N using PyMol v. 2.4.

3.2.2. Aquaglyceroporins

The mammalian genome includes 13 AQPs [102]. Based on sequence homology [103], we can classify them in three groups, the classical or orthodox AQPs (0, 1, 2, 4, 5, 6), whose monomeric pores exclude large molecules; the aquaglyceroporins (3, 7, 9, 10—the same as the numbers of cranial nerves that contain parasympathetic fibres); and the unorthodox AQPs (8, 11, 12).

A 2020 paper by Moss et al. [104] compared and contrasted the bacterial aquaglyceroporin GlpF with human AQP7 from the perspectives of structure, molecular dynamics (MD) and cellular physiology. They concluded that GlpF is a stiffer protein with a high occupancy of glycerol in the monomeric pores when expressed in Xenopus oocytes (and presumably other animal cells). Glycerol appears to move very slowly through GlpF monomeric pores, with the consequence that water permeability is extremely low. AQP7 is a far more flexible protein, glycerol appears to transit more rapidly through the monomeric pores and thus water permeability is relatively high. Thus, for the aquaglyceroporins, the glycerol occupancy of the monomeric pores—an issue easily overlooked in theoretical studies—can be a major determinant of function.

3.2.3. First evidence for the carbon dioxide permeability of aquaporin-1

In 1998, Nakhoul et al. [18] tested the hypothesis that human AQP1 is a CO₂ channel by injecting oocytes with either cRNA encoding AQP1 or water as control, using an approach similar to the one described in figure 4 (but without the pH_S electrode). In their first series of experiments (conducted without adding CA to the intracellular fluid), they found that introducing 1.5% CO₂/10 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$ to the bECF (i.e. bath) produced intracellular acidification that was slightly faster in AQP1 than in control oocytes, but the difference was not statistically significant. The authors reasoned that the intracellular reaction $\mathrm{C}{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}\to \mathrm{HC}{\mathrm{O}}_3^{-}+{\mathrm{H}}^{+}$, which disposes of the incoming CO₂ and also produces the H${\hspace{0.17em}}^{+}$ measured by the pH_i electrode, might be rate limiting (figure 3). Indeed, parallel experiments confirmed that oocytes have low endogenous CA activity [105]. Therefore, Nakhoul et al. performed a second set of experiments in which, after allowing AQP1 expression to proceed, they injected CA II protein. Now they observed that (dpH_i/dt)_max was 40% greater in AQP1 + CA II oocytes than in H₂O + CA II cells (figure 7). These experiments were the first indication that a gas may move through a channel [106]. However, this work did not rule out several alternative explanations [19]. (i) AQP1 expression could have enhanced the activity of the injected CA II. Furthermore, AQP1 expression in the presence of injected CA II could have (ii) altered the properties of the membrane lipids, thereby enhancing CO₂ diffusion through the lipids; (iii) increased the expression of native gas channel(s); or (iv) reduced the unconvected layer surrounding the oocyte. The studies in the next section addressed these concerns.

Figure 7.

Effect on expressing AQP1 on the CO₂ permeability of Xenopus oocytes, as judged by intracellular pH changes. Oocytes injected with water (blue background) or AQP1 (green background) were subsequently injected with CA. The oocytes were exposed to a short interval of 1.5% CO₂/10 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$ before (black trace) and after (red trace) adding ethoxzolamide (ETX), an inhibitor of CA. The arrow on the pH scale bar indicates that higher pH_i values are nearer the top. The negative numbers indicate maximal rates of pH_i decrease in pH units/s × 10^–4. Modified from [18].

3.2.4. Channel blockade

In their 1998 paper, Cooper & Boron [19] systematically addressed the aforementioned issues. To rule out the injection of CA II as a cause of the enhanced acidification, they carried out their experiments without added CA and found—in confirmation of the observations of Nakhoul et al. [18]—that the rate of acidification was very low. To unmask the effect of AQP1 on CO₂ permeability without added CA, Cooper and Boron removed the oocyte's vitelline membrane. Indeed, working with devitellinized oocytes, they found that in cells with a high level of AQP1 expression (judged by lysis time when dropped into deionized water), the CO₂-induced acidification rate was double that in H₂O-injected controls. They also noted an inverse linear relationship between (dpH_i/dt)_max and lysis time.

To assess whether the enhanced CO₂ permeability is due to simply overexpressing any channel, Cooper and Boron expressed the renal outer medullary potassium (ROMK) channel. However, they found no changes in CO₂ permeability, indicating some specificity to the AQP. This ROMK experiment may not have been the ideal control because they had no evidence that membrane levels of ROMK were similar to those of AQP1. We will see below that not all AQPs are CO₂ permeable, an observation that more directly addresses the issue of expressing a foreign protein.

As noted above, Agre's group showed that the mercury sensitivity of AQP1 is prevented by the mutation C189S [97]. Cooper and Boron showed that although pCMBS has little effect on (dpH_i/dt)_max in H₂O-injected control oocytes, the drug significantly slows CO₂-induced acidification in oocytes expressing AQP1. However, this result still leaves open the possibility that the pCMBS blocked a native CO₂ channel, or that the combination of AQP1 and pCMBS somehow alters the properties of the membrane lipid. To test these possibilities, Cooper examined the C189S mutant of AQP1, and found this mutant to support the same changes in pH_i as the wild-type (WT) protein, but without the sensitivity to pCMBS.⁴

These data ruled out idiosyncratic effects of injected CA II, effects on membrane lipids, the contribution of native CO₂ channels and altered unconvected layers—issues that we will examine in more detail in the last section of this review. Thus, this paper by Cooper and Boron, together with that by Nakhoul et al., provided the first evidence for gases crossing the membrane via channels, rather than through membrane lipids.

Endeward et al. [107] in 2006 published a study that included the effect of inhibitors on the CO₂ permeability of human RBCs, both from normal individuals and from those with a Colton-null mutation (i.e. lacking AQP1). Using the mass spectrometry approach outlined above, they found that either the Colton-null mutation or pCMBS treatment of normal cells reduces P_M,CO2 by approximately 60%. Treatment of normal RBCs with DIDS reduces P_M,CO2 by greater than 70%, and treatment of Colton-null cells with 4,4'-diisothiocyanatostilbene-2,2'-disulfonate (DIDS) reduces P_M,CO2 by approximately 90%. Thus, although pCMBS reduces P_M,CO2 by about half in normal RBCs, it is without effect in Colton-null cells. Taken at face value, this result is consistent with the idea that the only target of pCMBS is AQP1. A follow-up paper focused on human RBCs lacking the Rh complex and showed that simply the absence of Rh reduces P_M,CO2 by greater than 50%, and that the combination of the Rh deletion and DIDS reduces P_M,CO2 by greater than 80% [20].

The 2006 paper by Endeward et al. [107] also marked the introduction of pH_S experiments on oocytes (figures 5 and 8a(i)). In experiments in which they exposed oocytes to 5% CO₂/33 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$, the authors showed that although DIDS has no effect on ΔpH_S with H₂O-injected control oocytes, the DIDS reduces ΔpH_S substantially in AQP1-expressing oocytes, blocking about half of the AQP1-dependent component. DIDS also had no effect on P_f, either in H₂O-injected controls or in AQP1 oocytes. Thus, it is possible to reduce AQP-dependent CO₂ permeability with two small-molecule inhibitors.

Figure 8.

Effect of expressing AQP1 on the CO₂ permeability of Xenopus oocytes, as judged from surface pH changes. (a) Representative pH_S transients from an oocyte injected with H₂O (blue trace), an oocyte expressing AQP1 (green trace), an oocyte expressing Na/glucose cotransporter SGLT1 (red trace) and no oocyte (grey trace; pH_S electrode in the bulk extracellular fluid). All oocytes were exposed first to the $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ solution, and then (after removal of $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$) to $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$. (b,c) Summary of pH_S assay for CO₂ and NH₃ for control oocytes injected with H₂O or oocytes expressing either AQP1 or SGLT1. AQP1 but not SGLT enhanced both the CO₂-induced pH_S spike (b) and the NH₃-induced CO₂ spike (c). Although not shown, oocytes expressing the Na/K/Cl cotransporter NKCC2 or the H/oligopeptide cotransporter PepT1 yielded ΔpH_S values that were no different from controls, for both CO₂ and NH₃ exposures. Modified from [108].

3.2.5. Gas selectivity of aquaporins

In work that started with a 2009 study [108] and then extended markedly in 2013 [109], Musa-Aziz and her colleagues examined the CO₂, NH₃ and osmotic water permeability of each mammalian AQP from 0 to 9, as expressed in Xenopus oocytes. Figure 8a(i) (introduced above) shows the pH_S assay for CO₂. The authors defined (ΔpH_S*)_CO2 as the channel-dependent component of ΔpH_S (e.g. the green ΔpH_S – the blue ΔpH_S in figure 8a(i)). Figure 8a(ii) shows the pH_S assay for NH₃. The pH_S transient evoked by NH₃ influx is just the opposite to that for CO₂ influx: the influx of NH₃ leaves a deficit of NH₃ at the cell surface, some of which is replenished by NH₃ diffusion from the bulk extracellular solution. However, some surface NH₃ is replenished by the surface reaction $\mathrm{N}{\mathrm{H}}_4^{+}\to \mathrm{N}{\mathrm{H}}_3+{\mathrm{H}}^{+}$, which causes an abrupt fall in pH_S. As the NH₃ influx wanes, the [NH₃]_S rises towards its initial value, the reaction slows and pH_S rises towards its initial values. The maximal change in surface pH is an index of the NH₃ influx. The authors defined (ΔpH_S*)_NH3 as the channel-dependent component of ΔpH_S (e.g. the green ΔpH_S – the blue ΔpH_S in figure 8a(ii)). P_f* is the channel-dependent component of the osmotic water permeability. Figure 8b,c summarizes the results of a larger group of such experiments.

Musa-Aziz and colleagues found that each AQP has its own characteristic combination of permeabilities to CO₂, NH₃ and H₂O. Because it is difficult to measure the amounts of different AQPs in the plasma membrane, Musa-Aziz and colleagues computed oocyte by oocyte: (ΔpH_S*)_CO2/P_f*, (ΔpH_S*)_NH3/P_f* and ΔpH_S*)_CO2/(ΔpH_S*)_NH3. AQPs 1 and 9 are permeable to CO₂, NH₃ and H₂O. AQPs 0, 4 (starting translation at Met-23) and 5 are permeable to CO₂ and H₂O but not NH₃. AQPs 3, 7 and 8 are permeable to NH₃ and H₂O but not CO₂. AQP2 is permeable to H₂O but neither CO₂ nor NH₃. AQP6 is permeable to CO₂ and NH₃ but, as shown previously by Liu et al. [110], not permeable to H₂O. AQP5 has the highest (ΔpH_S*)_CO2/P_f*, except for AQP6, where the ratio is ∞ because P_f* = 0. We will see below that it is possible, with a single mutation, to convert AQP2 into a CO₂-conducting channel.

We note that Assentoft et al. [111] detected NH₃ permeability of AQP4 by measurements of either reflection coefficient or pH_i. The most straightforward explanation for the results of Assentoft and Musa-Aziz [108,109] is that the technique of Assentoft and colleagues is more sensitive than that of Musa-Aziz and colleagues. If this explanation is correct, then we could conclude that the AQPs that exhibited very high (ΔpH_S*)_NH3/P_f* ratios in the Musa-Aziz experiments (i.e. AQPs 3, 7, 8, 9) must have NH₃ permeabilities that are far higher than that of AQP4.

3.2.6. Molecular dynamics analyses

MD studies of Hub & de Groot [112] in 2006 show that it is feasible for CO₂ to diffuse through the four monomeric pores of human AQP1, although the absolute permeability is very low. Consistent with arguments of the Boron laboratory, Hub and de Groot concluded that AQP1 could be a useful CO₂ channel only if background membrane CO₂ permeability were extremely low. Later in their paper, they extended their MD analysis to the central pore of AQP1 and concluded that its CO₂ permeability is an order of magnitude greater than the four monomeric pores combined. Citing Cooper's observation that pCMBS (which targets the monomeric pores) significantly reduces the CO₂ permeability of AQP1 (see above), Hub and de Groot concluded that the central pore is probably blocked physiologically. Interestingly, preliminary work by Musa-Aziz, Geyer and Boron on Xenopus oocytes heterologously expressing AQP1 suggests that about half of the CO₂ moves through the pCMBS-sensitive monomeric pores and about half through an alternative DIDS-sensitive pathway that may be the central pore [101,113,114]. These physiological data are consistent with MD analyses of Wang et al. [115], who calculated that the energy barrier to permeation of CO₂ through the central pore of bovine AQP1 was only 3–4 kcal mol⁻¹, as opposed to the 5–6 kcal mol⁻¹ energy barrier exhibited by the monomeric water pores. These figures are similar to those obtained by Hub and de Groot, although Wang and colleagues concluded that the central pore is likely to be important—on the background of a membrane with low baseline gas conductance—for permeability to CO₂ and non-polar gases.

3.2.7. Role of carbonic anhydrases in augmenting carbon dioxide diffusion through aquaporin-5

In preliminary work from the Boron laboratory, Dengke Wang has monitored pH_S and pH_i in Xenopus oocytes expressing human AQP5 (or injected with H₂O rather than cRNA as a control), ± injection of purified CA II protein, ± presence of extracellular CA I/II [116]. Here, we will focus on the pH_S data in experiments for which Wang added no CA to the bECF. Wang injected oocytes with small amounts of CA II. Based on the above discussion of control of the CO₂ gradient, we might have expected the added cytosolic CA II to increase the ΔpH_S magnitude when he added or removed 1.5% CO₂/10 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$ to the bECF. However, he observed no effect of the very small amounts of injected CA II until he expressed an AQP, namely AQP5. Thus, P_M,CO2 must have been so low in the baseline condition that consuming incoming CO₂ in the cytosol (or regenerating departing CO₂ during CO₂ efflux) had minimal impact. With the CO₂-permeation pathway represented by AQP5, P_M,CO2 was no longer rate limiting, and the CA II had the anticipated effect.

In the above discussion on the importance of CO₂ gradients, we noted the conclusion of Musa-Aziz and Occhipinti [81–83] that the effects of CA II and CA IV on CO₂ diffusion are supra-additive because they mutually enhance each other's effects on magnifying transmembrane CO₂ gradients. Here we extend that principle: the effects of CA II (on the CO₂ gradient) and AQP5 (on CO₂ permeability) are also supra-additive. Note: if Wang had injected much larger amounts of CA II to achieve a much higher cytosolic CA activity, as in the experiments of Musa-Aziz and Occhipinti [81,83], then he would have observed an effect of cytosolic CA II even in the absence of exogenous AQP5.

3.2.8. Blockade of the central pore of aquaporin-5

In an extensive series of preliminary experiments, Xue Qin [117] generated all 19 possible mutations of threonine-41, which is at the end of an extracellular loop and overlooking the central pore of AQP5. Of these mutations, none affected P_f and only five affected (ΔpH_S*)_CO2. The three substitutions with aromatic side changes (T41F, T41W and T41Y) significantly reduced CO₂ permeability, and the mutations T41G and T41C increased CO₂ permeability. MD simulations and free-energy calculations by Hyea Hwang and Emad Tajkhorshid (unpublished data) confirm that, compared with WT AQP5, T41F has a substantially higher free-energy barrier opposing CO₂ diffusion through the central pore, whereas T41G has a substantially lower barrier.

In a follow-up study, Qin (unpublished data) recognized that the T41H mutation creates a possible interaction site with divalent transition metals at the extracellular mouth of the central pore. When she added either Ni²⁺ or Zn²⁺, (ΔpH_S*)_CO2 decreased substantially. These divalent cations had a much smaller effect on WT AQP5. Thus, it appears that, with the AQP5-T41H mutant, either Ni²⁺ or Zn²⁺ can act like a cork in a wine bottle and prevent CO₂ permeation through the central pore. To examine this possibility, Thomas Kowatz and Ardeschir Vahedi-Faridi (unpublished data) obtained the crystal structure of AQP5-T41H in the presence of Ni²⁺. Indeed, they found that Ni²⁺ is coordinating to the four histidine residues (T41H) of each monomer. MD simulations by Hwang (unpublished data) confirmed that binding of Ni²⁺ would indeed raise the free-energy barrier to extremely high levels, consistent with blockade of the central pore. These preliminary studies are the first to demonstrate directly the role of any central pore in any physiological process; in this case, CO₂ permeation.

3.2.9. Possible role of the C-terminus of aquaporin-2 in blocking carbon dioxide conductance

Recall from the above discussion that AQP2 appears to have permeability to neither CO₂ nor NH₃. Ardeschir Vahedi-Faridi (unpublished data) had obtained two structures of the AQP2-S256A (a dephosphomimetic mutation): the one from a three-dimensional crystal by X-ray diffraction and another from a two-dimensional array by electron diffraction. The two-dimensional structure includes a substantial portion of the carboxyl terminus (Ct) and shows the four Cts in a teepee-like conformation, thereby obstructing access to the central pore. The three-dimensional structure includes the most complete portion of the Ct of AQP2 to date and shows the four Ct segments oriented away from the central pore. Thus, the experimental structures are consistent with the notion that the Cts of the four AQP2-S256A monomers can exist in at least two confirmations, one obstructing the central pore and the other revealing it.

When Dengke Wang (unpublished data) expressed this AQP2-S256A in oocytes, he found that the mutant—unlike the WT, which he examined in parallel experiments—not only had a normal P_f, but conducted CO₂. At the suggestion of Vahedi-Faridi (2020, personal communication) Wang truncated the Ct of AQP2 just before teepee. That construct, too, conducts CO₂. Wang is now examining several phosphomimetic and dephosphomimetic mutation combinations in the Ct of AQP2 to establish the determinants of CO₂ permeability. These results are the first pointing to the possibility that cells could dynamically control access to the central pore—and thus gas permeability—by altering the phosphorylation pattern.

3.3. Rhesus proteins

3.3.1. Discovery and characterization of rhesus proteins

Rhesus proteins belong to the SLC42 family of transporters. A biological role for this family emerged in the early 1990s as microbiologists noted that Amt (‘ammonium transporter’ in Escherichia coli) and Mep (‘methylammonium permease’ in Saccharomyces cerevisiae) are necessary for growth when NH₄Cl or methylammonium is the only source of nitrogen [118,119]. It was Marini and colleagues who noted the similarity between the prokaryotic proteins and vertebrate Rh proteins [120] and then showed in 2000 that it is possible to complement the defect in Mep-deficient yeast by introducing either of two human Rh proteins [121].

Human RBCs express RhAG (which carries the RhA antigen; the ‘G’ stands for glycosylated) as well as RhCE (a non-glycosylated protein carrying both the RhC and RhE antigens) and RhD. Moreover, the RBC is virtually the only terminally differentiated cell that expresses any of these proteins. Some combination of the three forms of RBC Rh proteins form trimers called the ‘Rh complex’ in the RBC membrane. In oocytes, only RhAG is necessary for expression as well as NH₃ and CO₂ permeability [122]. By themselves, RhCE or RhD cannot support NH₃ or CO₂ transport. Moreover, the coexpression of RhCE and/or RhD with RhAG has no functional effect. Mice have only mRh, which is analogous to RhCE and RhD [123]. In mice, the knockout of the mRh gene eliminates the expression of RhAG in RBCs.

In mammals, the other two Rh family members, SLC42A2 (RhBG) and SLC42A3 (RhCG), are found in non-erythroid tissues like kidney, liver, brain and pancreas [124–131]. In the kidney, RhBG and RhCG play important roles in the medullary recycling (or short-circuiting) of $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$, a process that minimizes the return of $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$ to the blood in the renal cortex, and thereby maximizes the urinary excretion of $\mathrm{N}{\mathrm{H}}_3/\mathrm{N}{\mathrm{H}}_4^{+}$—a critical process in the response of the body to acid loads.

3.3.2. Carbon dioxide permeability of rhesus proteins

Working on normal and Rh-null human RBCs, Ripoche et al. [21] in 2006 and Endeward et al. [20] in 2008 developed evidence that the Rh complex acts as a CO₂ channel. Later, Musa-Aziz and colleagues heterologously expressed in Xenopus oocytes AmtB [108], RhAG [108,132], RhBG [132] or RhCG [132], and demonstrated using a pH_S-based assay (figure 8a) that all four are permeable to both NH₃ and CO₂. Unlike the AQPs, which demonstrate considerable variability in the ratio (ΔpH_S*)_CO2/(ΔpH_S*)_NH3, the Rh proteins are rather similar to one another in this regard.

3.3.3. Structure of rhesus proteins

In 2004, both Khademi et al. [133] and Zheng et al. [134] obtained high-resolution structures of the bacterial Rh homologue AmtB with NH₃ in the monomeric pores. These studies showed that AmtB is a homotrimer in which each monomer forms a channel permeable to NH₃. Moreover, the structures show that the monomers surround a hydrophobic central pore. Later Gruswitz et al. [135] obtained a high-resolution structure of RhCG that is, to date, the only example of a vertebrate Rh structure.

3.3.4. Pictures of xenon in putative gas pathways through the bacterial rhesus protein AmtB

In preliminary work Thomas Kowatz and Ardeschir Vahedi-Faridi (unpublished data) obtained high-resolution crystals of AmtB, and then introduced Xe gas under high pressure to probe potential binding sites and pathways for the gas species. The resulting structure shows Xe atoms both in the central pore and in three unanticipated interfacial crevices between monomers. This is the first example of visualizing a gas in a channel.

MD analyses of gas diffusion around the protein by Soumyo Sen, Eric Shinn and Emad Tajkhorshid (unpublished data) suggest, in addition to a central-pore pathway, that the three highly novel monomer–monomer interfacial pathways extend from the extracellular to the cytosolic side of the AmtB trimer. All four pathways are capable of conducting Xe and presumably smaller hydrophobic gases.

3.4. NBCe1

In preliminary electrophysiological experiments with out-of-equilibrium (OOE) $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ solutions [136], Jing Lu (unpublished data) made the expected observation that exposing control Xenopus oocytes (i.e. not expressing a heterologous protein) to ‘pure CO₂’ solutions (5% CO₂, pH 7.50, but virtually no $\mathrm{HC}{\mathrm{O}}_3^{-}$) causes pH_i to fall rapidly, exposing them to ‘pure $\mathrm{HC}{\mathrm{O}}_3^{-}$’ solutions (33 mM $\mathrm{HC}{\mathrm{O}}_3^{-}$, pH 7.50, but virtually no CO₂) causes little pH_i change and exposing them to an equilibrated (EQ) $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ solution causes a maximal rate of acidification—(dpH_i/dt)_max—that is virtually the sum of those produced by the pure-CO₂ and pure-$\mathrm{HC}{\mathrm{O}}_3^{-}$ solutions. However, in oocytes expressing NBCe1-A, Lu made a most unexpected set of observations. Because the pure-CO₂ solutions caused pH_i to fall rapidly and pure-$\mathrm{HC}{\mathrm{O}}_3^{-}$ solutions caused pH_i to rise moderately fast (owing to the uptake of $\mathrm{HC}{\mathrm{O}}_3^{-}$ equivalents), we expected that the EQ solutions would cause pH_i to fall at a rate intermediate between the two ‘pure’ solutions (i.e. pH_i would fall at a lower rate than in the pure-CO₂ solutions). Instead, with EQ solutions, pH_i fell as fast as with ‘pure CO₂’.

One might ask whether the expression of NBCe1-A enhances CA activity. However, in stopped-flow analyses in which we used an assay that we developed [137], we found no difference in CA activity between control and NBCe1-A oocytes.

Another potential explanation is that the presence of CO₂ unexpectedly inhibits NBCe1-A. However, two-electrode voltage-clamp experiments verify that NBCe1-A has similar slope conductances in both pure-$\mathrm{HC}{\mathrm{O}}_3^{-}$ and EQ solutions [138]. Thus, we can rule out this unlikely explanation.

The final explanation of which we are aware is that, in the presence but not in the absence of extracellular $\mathrm{HC}{\mathrm{O}}_3^{-}$, NBCe1-A conducts CO₂. A compartmental mathematical analysis by Boron and a reaction–diffusion analysis by Rossana Occhipinti confirm this as a potential explanation [139].

In additional preliminary experiments, Fraser Moss and Brian Zeise developed a neutral buoyancy assay (NBA) in which they injected an oocyte with a small bubble of N₂ gas, placed the oocyte into a pressure-resistant tube containing saline and an air–water interface and then applied sufficient pressure to the air phase to collapse the bubble enough to maintain the oocyte at a depth of 5 cm [140]. As N₂ exits the bubble and eventually crosses the plasma membrane to enter the extracellular fluid (ECF), the bubble shrinks, the oocyte sinks and a camera/computer combination detects the increase in depth and responds by decreasing the pressure in the air phase. Over time, the pressure falls more or less exponentially. Calibration exercises allow one to compute the time course of the number of gas molecules in the bubble, and thus the gas flux. This is the first assay for the transmembrane flux of an inert gas. In a twist on this assay, one can add CO₂ to the ECF. The result is an influx of CO₂ across the plasma membrane, an expansion of the bubble, followed by an increase in the computer-controlled air pressure to maintain neutral buoyancy. Using the CO₂ variant of this NBA assay, Moss and Zeise found that NBCe1-A (in the presence of $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$) enhances CO₂ influx.

In a final set of preliminary experiments, Dengke Wang monitored pH_S as he introduced $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ into the ECF, ± injected CA II [141]. He found that, in the presence of NBCe1-A, injected CA II leads to a transient increase in pH_S, indicative of enhanced CO₂ permeability.

Thus, the results of three fundamentally different assays are consistent with the hypothesis that NBCe1-A, in the presence of $\mathrm{HC}{\mathrm{O}}_3^{-}$, has a substantial CO₂ conductance. It is possible that the $\mathrm{HC}{\mathrm{O}}_3^{-}$ has an allosteric effect on NBCe1-A, thereby creating a CO₂ channel through the protein. Another explanation is that as NBCe1-A cycles through conformational changes during Na/HCO₃ cotransport, CO₂ moves through a transiently available CO₂ pathway.

Does it make teleological sense for NBCe1 to have an intrinsic CO₂ conductance? Boron & Boulpaep [142] have suggested, and preliminary data indicate [143], that NBCe1 actually transports $\mathrm{N}{\mathrm{a}}^{+}+\mathrm{C}{\mathrm{O}}_3^{=}$ or the $\mathrm{NaC}{\mathrm{O}}_3^{\text{–}}$ ion pair. In either case, two $\mathrm{HC}{\mathrm{O}}_3^{-}$ ions would approach the membrane, disproportionate into $\mathrm{C}{\mathrm{O}}_3^{=}$ and CO₂ and the NBCe1 would transport the $\mathrm{C}{\mathrm{O}}_3^{=}$. However, the CO₂ must also cross the membrane, through the membrane lipid, through a channel like AQP1 or through NBCe1 itself.

4. Carbon dioxide and dioxygen movement in biological systems

What are the potential physiological roles of CO₂ or other gases moving through channels? We will examine three groups of examples in the next three sections.

4.1. Plants

In 2003, Uehlein et al. [144] demonstrated that the tobacco plasma membrane aquaporin NtAQP1 has a CO₂ permeability comparable to that of human AQP1. Moreover, they found that NtAQP1 promotes photosynthesis and stomatal opening.

In 2016, Wang et al. [145] heterologously expressed the guard-cell S-type anion channel 1 (SLAC1) from Arabidopsis thaliana in Xenopus oocytes that co-expressed OST1, CPK6 or CPK23 protein kinases. They found that increased $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ levels enhance SLAC1 activity. Hu et al. [146] had previously identified that CAs βCA1 and βCA4 function in CO₂-induced stomatal closing. Wang and colleagues demonstrated that PIP2;1 (a plant aquaporin) is permeable to CO₂ and interacts with βCA4. A PIP2;1 mutation that blocks PIP2;1 CO₂ permeability in oocytes impairs abscisic acid-mediated/CO₂-induced stomatal closing in the plants.

4.2. Red blood cell membranes

In normal human RBCs as well as those lacking either AQP1 or RhAG, research exploiting the ¹⁸O-labelled $\mathrm{C}{\mathrm{O}}_2/\mathrm{HC}{\mathrm{O}}_3^{-}$ approach (see above) for assessing CO₂ permeability has revealed that AQP1 and the Rh complex each contribute about half of the total CO₂ permeability, for a total contribution of at least 90% [20,107].

More recent work on the O₂ permeability of murine RBCs is based on the use of stopped-flow absorbance spectroscopy to monitor the offloading of O₂ from oxyhaemoglobin (HbO₂) inside RBCs exposed to an O₂ scavenger [123]. Pan Zhao and her colleagues found that the knockout of both AQP1 and RhAG reduces the rate constant for O₂ offloading (k_HbO2) by about one-third. Because P_M,O2 is just one of several processes that offer ‘resistance’ to O₂ offloading—O₂ dissociation per se from HbO₂, diffusion through the cytosol, diffusion across the membrane and diffusion through the extracellular unconvected layer—this one-third decrease in k_HbO2 corresponds to an approximately 55% decrease in P_M,O2 according to mathematical simulations by Rossana Occhipinti [123]. Control studies show that changes in haematological parameters, RBC size and shape, membrane protein composition or membrane lipid composition cannot account for the data, leaving the explanation that O₂ moves through both AQP1 and the Rh complex.

The combination of the double knockout and inhibition by pCMBS reduces k_HbO2 by nearly 80%, which corresponds to an approximately 90% decrease in P_M,O2.

In summary, for the quintessential gas-transporting cell, at least 90% of CO₂ and O₂ appears to move through membrane channels.

4.3. Renal proximal tubule

One of the major tasks of the renal proximal tubule (PT) is to reabsorb from the tubule lumen approximately 80% of the $\mathrm{HC}{\mathrm{O}}_3^{-}$ filtered in the glomerulus. Although the PT apparently transports approximately 20% of this approximately 80% directly across the apical (i.e. lumen-facing) membrane as $\mathrm{HC}{\mathrm{O}}_3^{-}$ or $\mathrm{C}{\mathrm{O}}_3^{=}$, the PT titrates the vast majority of the luminal $\mathrm{HC}{\mathrm{O}}_3^{-}$ to CO₂, which then crosses the apical membrane to enter the PT cell. The PT apical membrane is one of the richest sources of AQP1, raising the possibility that AQP1 plays a role in $\mathrm{HC}{\mathrm{O}}_3^{-}$ reabsorption. In preliminary work on isolated perfused murine PTs, Yuehan Zhou found that the knockout of AQP1 reduces the $\mathrm{HC}{\mathrm{O}}_3^{-}$ reabsorption rate by up to 60% [147]. Moreover, he used basolateral OOE solutions to conclude that the AQP1 knockout reduces transepithelial CO₂ permeability by as much as 60%. Finally, work on intact mice with catheterized carotid arteries allowed Zhou and his collaborators to monitor arterial blood gases during an imposed chronic metabolic acidosis (MAc). They found that the AQP1-knockout mice have an impaired ability to stabilize arterial pH during MAc. Thus, AQP1 appears to play a crucial role in PT $\mathrm{HC}{\mathrm{O}}_3^{-}$ transport, with important consequences for whole-body pH regulation.

5. Concluding remarks

Some have argued that membrane channels could not possibly have a physiologically important role for the diffusion of dissolved gases because the lipid phases of cell membranes have such high background permeabilities to CO₂ and other gases [23,26,27]. The argument is that either the physiological measurements are somehow flawed to generate such unexpected results or that unconvected fluid layers somehow give rise to data that appear to support the contribution of channels.

One point on which all parties agree is that membrane channels can make a physiological contribution to the transport of gases (or any other substances) only if the background membrane permeability (i.e. in the absence of the channels) is relatively low [23]. It is important to note that the argument about the high background permeability of membranes is based on experiments on artificial planar lipid bilayers with especially high CO₂ permeabilities [73]. In fact, as we have already noted, at least some cell membranes—gastric gland apical membranes [17], RBC membranes [20,107,123], PT apical membranes [147] and oocyte membranes [80]—can have extremely low CO₂ or O₂ permeabilities.

It is worthwhile asking how it is possible that flawed measurements or unanticipated changes in extracellular unconvected layers could explain:

• (1)how simply expressing a channel in a Xenopus oocyte could affect pH_S and pH_i transients in a way consistent with increased P_M,CO2 (shorthand: pH_S/↑P_M,CO2)?
• (2)how knocking out AQP1 or RhAG in human or murine RBCs reduces apparent CO₂ and O₂ permeability as assessed by very different technologies (e.g. mass spectrometry vs stopped-flow absorbance spectroscopy)?
• (3)how blocking (with a small-molecule inhibitor) a natural or heterologously expressed channel could increase unconvected layers (although it is conceivable that such an inhibitor could affect the membrane lipid)?
• (4)how a point mutation to channel C189S (in the case of AQP1) could abrogate inhibition by a small-molecule blocker?
• (5)how a point mutation (T41H in the case of AQP5) could enable blockade by Ni²⁺ or Zn²⁺?
• (6)how a point mutation (several T41 mutations of AQP5) could either decrease or increase pH_S transients in a manner consistent with altered P_M,CO2?
• (7)why cytosolic CA II and AQP5 have supra-additive effects on pH_S/↑P_M,CO2?
• (8)how AQPs exhibit CO₂/NH₃ selectivity by various AQPs; for example, why do some AQPs appear to exhibit CO₂ permeability whereas others do not?
• (9)how a cytosolic phosphomimetic mutation (in the case of AQP2) produces pH_S/↑P_M,CO2?
• (10)how a cytosolic truncation (in the case of AQP2) produces pH_S/↑P_M,CO2?
• (11)why the apparent CO₂ permeability of NBCe1 depends on $\mathrm{HC}{\mathrm{O}}_3^{-}$?

• We also note that

• (12)MD analyses support the concept that various gases could diffuse through AQPs or Rh proteins.
• (13)The crystal structure and MD analyses of AmtB with Xe shows a gas molecule in a channel.

Although the above 13 points argue in favour of the view that channels can have an important impact on CO₂ permeability in at least certain cells, we do not suggest that channels are always the main pathway for dissolved gases to cross biological membranes. In some situations, background gas permeability could be sufficiently high to meet physiological demand with the limited impact of channels [26]. Thus, it is possible that biological membranes exhibit a continuum from the effectively CO₂-impermeable apical membranes of gastric glands, through RBC membranes with potent gas channels within membranes with low-background permeability, to as-yet-uncharacterized cells with fewer or lower-activity gas channels within membranes with higher background permeability.

Finally, how can one reconcile the observations of Overton (i.e. for small molecules, membrane permeability seems to track lipid solubility/lipophilicity) with more recent observations of CO₂-impermeable membranes and CO₂-permeable channels? One answer relates to the membrane continuum in the previous paragraph. At one extreme, Overton may have worked with biological membranes with relatively high background permeabilities to the lipophilic solutes that he studied, regardless of the presence of membrane protein pathways for lipophilic solutes. At another extreme of a continuum, Overton may have studied biological membranes more akin to those of RBCs, with relatively low background permeabilities to lipophilic solutes but with membrane protein pathways (e.g. AQP1 and Rh complex for CO₂ and O₂) for lipophilic molecules. A striking example is lactic acid, which moves across the RBC membrane via the transporter MCT1. In the case of gases, we note that the central pores of gas-permeable AQPs and Rh proteins (and interfacial crevices, at least in the case of AmtB) are lined with lipophilic amino acid residues. Thus, the movements of the volatile (i.e. lipophilic) solutes CO₂ and O₂ across the RBC membrane agree with Overton's general experimental observation that permeability rises in parallel with lipophilicity. However, we offer a very different interpretation: the reason that CO₂ and O₂ transit so well across the RBC membrane is not that these gases move predominantly through the lipid phase of the membrane, but that they diffuse through lipophilic pathways of specialized membrane proteins.

Data accessibility

All presented data are published and can be found in corresponding references. We do not show any new data.

Authors' contributions

M.M. and S.T. drafted the manuscript; W.F.B. edited the manuscript; the other co-authors provided data and contributed to the revision of the manuscript.

Competing interests

We declare we have no competing interests.

Funding

This work was supported by Office of Naval Research (ONR) grant nos. N00014-11-1-0889, N00014-14-1-0716 and N00014-15-1-2060; Multidisciplinary University Research Initiative (MURI) grant no. N00014-16-1-2535 from the DoD (to W.F.B., E.T., N.M. and A.V.-F.), NIH multi-scale modelling grant no. U01-GM111251 (to W.F.B. and E.T.). R.O. and the mathematical modelling were supported in part by NIH grant no. K01-DK107787. The MD simulation results were supported by NIH grant no. P41-GM104601 (to E.T.) and the MURI grant listed above. W.F.B. gratefully acknowledges the support of the Myers/Scarpa endowed chair.