The Na⁺,K⁺-ATPase and its stoichiometric ratio: some thermodynamic speculations

Abstract

 Almost seventy years after its discovery, the sodium–potassium adenosine triphosphatase (the sodium pump) located in the cell plasma membrane remains a source of novel mechanistic and physiologic findings. A noteworthy feature of this enzyme/transporter is its robust stoichiometric ratio under physiological conditions: it sequentially counter-transports three sodium ions and two potassium ions against their electrochemical potential gradients per each hydrolyzed ATP molecule. Here we summarize some present knowledge about the sodium pump and its physiological roles, and speculate whether energetic constraints may have played a role in the evolutionary selection of its characteristic stoichiometric ratio.

Introduction 

Since its recognition, identification and initial characterization in the fifties and sixties (Ussing 1947; Hodgkin and Keynes 1955; Glynn 1956; Post and Jolly 1957; Skou 1957; Garrahan and Glynn 1967a,d), the Na⁺,K⁺-ATPase (NKA) or “sodium pump” located in the plasma membrane of almost all eukaryotic cells has been the subject of a myriad of studies concerning its biochemical, biophysical and physiological properties.

The NKA is the prototypical example of a primary active transporter: it extrudes sodium ions from the cell interior coupled to the entry of potassium ions, both against their electrochemical potential gradients, using the hydrolysis of ATP as energy source. Thus, the direct consequence of its activity is the creation and maintenance of opposing electrochemical gradients of sodium and potassium across the plasma membrane, characterized by high potassium and low sodium concentrations in the intracellular compartment. Many of the physiological roles of the enzyme are a consequence of these ion transport properties. The NKA is one of the most remarkable enzymes in the entire biological world, both from the point of view of its structural and functional characteristics as a complex molecular machine, and for its relevance to animal physiology and participation in several cell signaling processes. Among other notable features, the enzyme exhibits a robust stoichiometric ratio of three sodium and two potassium ions transported per hydrolyzed ATP, under physiological conditions in both excitable and non-excitable cells. The robustness of this stoichiometric ratio suggests that it became particularly relevant during the evolution of animal cells.

In this review, we first summarize some properties of the sodium pump, with an emphasis on several of its functional characteristics and physiological roles, and then consider the main thermodynamic aspects of its activity. We particularly speculate whether some energetic constraints could have played a role in the establishment of its stoichiometric ratio during the course of evolution. The many biochemical, biophysical, and physiological aspects of the NKA cannot be possibly accounted for or discussed within the contents of a single short review. There are many detailed reviews covering its diverse structural and functional features (Glynn 1985; Clausen et al. 2017; Apell 2018, 2019; Fedosova et al. 2021) and physiological roles (Iannello et al. 2007; Aperia et al. 2016; Shah et al. 2016; Yan and Shapiro 2016; Clausen et al. 2017; Apell 2018; Pivovarov et al. 2018; Kay and Blaustein 2019; Bejcek et al. 2021; Fedosova et al. 2021). Here we only introduce these topics, with an emphasis on aspects that may be related to the characteristic stoichiometric ratio of the NKA in modern animal cells.

Functional characteristics

The Na⁺,K⁺-ATPase belongs to the family of P-type ATPases (subfamily IIC, Palmgren and Axelsen 1998). This enzyme/transporter, which is present in almost all eukaryotes, enables the vectorial movement of Na and K ions against their electrochemical potential gradients by using energy derived from a coupled chemical reaction, the hydrolysis of ATP to ADP and inorganic phosphate.

General characteristics

The functional enzyme is a complex of two or three proteins: alpha, beta, and, depending on the cell type and tissue, FXYD subunits (Clausen et al. 2017). The ten-transmembrane-domain (TMD) alpha subunit, the so-called catalytic subunit, has four isoforms (α₁ to α₄, see Clausen et al. 2017, and references therein), and it is responsible for ATP hydrolysis, energy transduction, cardiac glycoside binding, and ion transport (Kyte 1971; Ruoho and Kyte 1974; Jørgensen and Andersen 1988; Clausen et al. 2017; Apell 2018). The single-TMD glycoprotein, beta subunit, includes three isoforms (β₁ to β₃) and, although it does not carry out any catalytic activity per se, its absence leads to a complete loss of enzymatic function (McDonough et al. 1990). The beta subunit has been described to be important for appropriate trafficking to and correct folding of the α subunit in the cell membrane, NKA maturation, trypsin resistance in the endoplasmic reticulum, and cell–cell adhesiveness (Geering 1990, 2008). Finally, the single-membrane-spanning small polypeptide, FXYD subunit, includes seven members (Sweadner and Rael 2000; Geering et al. 2003). These FXYD polypeptides interact with the α subunit by modulating ion-transport kinetics, thus allowing certain cell types to adapt to acute metabolic situations (Garty and Karlish 2006). The minimal protein array able to perform all NKA activities in vitro is the complex αβ; however, some experimental evidence is hard to reconcile with the presence of a single NKA heterodimer in the cell plasma membrane and, instead, it would be better explained by a (αβ)₂ complex (Peluffo et al. 1992, 1994; Pilotelle-Bunner et al. 2008).

Reaction scheme

The ion pumping process that takes place in the α subunit is achieved through a series of intermediate steps and cyclic conformational changes in the protein that are common to all P-type ATPases. In fact, these proteins are also known as E₁-E₂ ATPases, as a reference to the two major conformations adopted during the reaction cycle. Figure 1 shows a simplified Post-Albers model (Glynn 1985) describing ATP hydrolysis and ion transport reactions (for a more detailed reaction scheme, see Apell 2019). Basically, the left-side branch represents enzyme phosphorylation and Na⁺ outward transport, whereas the right-side half depicts K⁺ inward translocation and enzyme dephosphorylation. Under physiological conditions, owing to millimolar cytosolic ATP concentrations, the NKA likely resides in an ATP-bound E₁ conformation (intermediate “1” in the scheme of Fig. 1, but see Schneeberger and Apell 2001), a state characterized by inwardly-facing high-affinity binding sites for sodium and ATP (Hegyvary and Post 1971). Binding of the first Na⁺ to E₁ has been reported to occur with affinities that range from 0.7 to 8 mM, depending on the presence of Mg²⁺ (Heyse et al. 1994). Despite the presence of much higher intracellular K⁺ concentrations, fast, quasi-equilibrium distribution of ATP-bound intermediates (see Fig. 1) and selectivity for Na⁺ binding to at least one intracellularly-facing site (Rui et al. 2016) promote, by mass action, NKA forward running (clockwise direction in the scheme of Fig. 1, see Apell 2019). Once the complex Na₃E₁ATP is formed (intermediate “2”), the γ-phosphate of ATP is covalently transferred to a highly-conserved aspartyl residue in the protein (phosphoenzyme) and Na ions become occluded within the NKA (Hokin et al. 1965; Nagano et al. 1965; Matsui and Homareda 1982; Shull et al. 1985; Esmann and Skou 1985; Lutsenko and Kaplan 1995). This phosphorylation reaction has been identified as the rate limiting step for Na⁺ extrusion, with a rate constant of ~ 200 s^‒1 at pH 7.4 and 24 °C (Clarke et al. 1998; Ganea et al. 1999). It is worthwhile mentioning the recent results from Rossi’s lab (Faraj et al. 2023) that show spontaneous Na occlusion within non-phosphorylated E₁ intermediates, thus challenging the long-standing paradigm of Na ions only being occluded upon phosphoenzyme formation. The complex (Na₃)E₁ ~ P•ADP (intermediate “3”) contains a high-energy phosphate bond, i.e. the reaction is reversible as the phosphate group can be transferred back to ADP to resynthesize ATP (Kaplan and Hollis 1980; Cavieres 1983; Glynn 1985). Nonetheless, (Na₃)E₁ ~ P•ADP is a short-lived intermediate in the NKA reaction cycle (see Peluffo 2004, and references therein). After ADP is released (intermediate “4”), Na ions undergo deocclusion and release to the extracellular medium, a reaction that takes place simultaneously with or after the enzyme conformational change to E₂-P (intermediate “5”, see Apell 2019). The intermediate E₂-P shows low affinity for Na⁺ and relatively high affinity for K⁺, so that, under physiological conditions, E₂-P binds extracellular K⁺ despite the unfavorable concentration ratio (intermediate “6”). Potassium binding to E₂-P favors enzyme dephosphorylation as ions become occluded during inward transport (intermediate “7”, Forbush 1988). Under physiologically high intracellular ATP concentrations, the nucleotide binds to E₂(K₂) with low apparent affinity (intermediate “8”, Post et al. 1972), greatly accelerating K⁺ deocclusion and release. By symmetry with the E₁ ~ P to E₂-P transition, K⁺ deocclusion and release reactions are linked to the conformational change from E₂ to E₁, which reinitiates the cycle (Karlish and Yates 1978; Glynn and Richards 1982). High resolution crystal structures for most of these intermediates, with bound or occluded ions, nucleotides, P_i or ouabain, as well as the organization of the NKA isoforms within the cell plasma membrane, confirmed many of the features described here and shed new light on the enzyme/transporter molecular mechanisms (Shinoda et al. 2009; Laursen et al. 2013; Kanai et al. 2013, 2021; Nyblom et al. 2013; Clausen et al. 2017).

Fig. 1.

Simplified Post-Albers model (Glynn 1985) describing ATP hydrolysis and ion transport by the Na,K-ATPase. The enzyme is distributed in two conformations, E₁ and E₂. In its forward running (clockwise), the NKA binds intracellular Na⁺ and MgATP with high affinity to form the complex Na₃E₁ATP (Mg ions, not shown). The γ-phosphate of ATP is then transferred to the ATPase, and Na ions become occluded (occluded states are depicted by parentheses). The complex (Na₃)E₁ ~ P•ADP contains a high- energy phosphate bond, i.e. this reaction is reversible. After ADP release, Na ions are deoccluded and released to the extracellular medium along with or after the enzyme conformational change to E₂-P. Extracellular K⁺ binds to E₂-P, favoring P_i release from de NKA, as ions become occluded during their trip to the cytosol (protons, that are proposed to travel bound to the “third Na⁺ site” together with the two K ions, are not depicted). ATP, acting with low apparent affinity, greatly accelerates K⁺ deocclusion and intracellular release. The NKA then experiences a conformational transition from E₂ to E₁ to restart the reaction cycle 

Stoichiometry

A ratio of 3 Na⁺ moving outward for 2 K⁺ transported inward was first determined by Post and Jolly (1957), when measuring cardiac glycoside-sensitive ion fluxes, a proportion that remained unchanged at all tested concentrations of the transported ions. Few years later, Sen and Post (1964) and Whittam and Ager (1965) found that 3 Na ions were extruded per hydrolyzed ATP molecule under a great variety of Na gradients. Garrahan and Glynn (1967d), using radioisotopes ²⁴Na, ⁴² K and [γ-³²P]ATP on red blood cells and resealed ghosts, obtained an estimate for the NKA stoichiometry of 3 Na/2 K/1 ATP, although indirect, due to some difficulties measuring potassium influx in resealed ghosts. An excellent review by Glynn (1985) about all these experiments (and others) is recommended. Reconstituted vesicles were used as well to measure ²²Na uptake and ⁸⁶Rb extrusion, also yielding an approximate 3 Na⁺:2 Rb⁺ stoichiometric ratio (Anner et al. 1977; Rakowski et al. 1989). Rakowski et al. (1989) studied the stoichiometry and membrane-potential dependence (see Sect. 1e) of the NKA in internally dialyzed, voltage-clamped squid giant axons. Simultaneous measurements of ²²Na efflux and cardiac glycoside-sensitive membrane currents as a function of membrane potential showed that the 3 Na⁺: 2 K⁺ transport stoichiometry is independent of membrane potential and, instead, that the membrane electric field affects Na,K pump turnover rates. The 3:2 coupling ratio remained constant under different ionic and physicochemical conditions, probed with different approaches, and within a broad variety of cell types and tissues. Furthermore, an invariant stoichiometry appears to be a general feature of all P-type ATPases. It was later established that the first two Na ions compete with the two K ions for the same sites in the NKA (Goldshlegger et al. 1987; Schneeberger and Apell 1999, 2001), whereas the third Na ion binds with a much higher activation energy (Apell et al. 2017) to a unique site in the intracellularly-facing E₁ conformation (Heyse et al. 1994; Wuddel and Apell 1995; Pintschovius et al. 1999). More recently, high resolution crystal structures confirmed the presence of three Na⁺ binding sites and that two of them are shared by K ions (see Clausen et al. 2017, and references therein).

Non-canonical modes

Besides its physiologic (3:2) Na/K exchange per hydrolyzed ATP, the NKA can engage in several non-canonical flux modes, depending on ion, nucleotide and inorganic phosphate concentrations. These non-canonical modes are six: a) electroneutral (3:3) Na⁺/Na⁺ exchange with no net ATP consumption (Cavieres and Glynn 1979; Peluffo 2004); b) electroneutral (2:2) K⁺/K⁺ exchange with no net ATP consumption (Simons 1974; Peluffo and Berlin 1997); c) ATP-consuming uncoupled Na⁺ efflux (Garrahan and Glynn 1967b,c) or 3Na⁺/2H⁺ exchange (Apell et al. 2011); d) electrogenic, ATP-consuming 3Na⁺/2Na⁺ exchange (Lee and Blostein 1980; Forgac and Chin 1982; Apell et al. 1990; Peluffo et al. 2000); e) ATP-independent, uncoupled K⁺ efflux (Sachs 1986); f) NKA backward running, with ATP synthesis (Garrahan and Glynn 1967a; De Weer and Rakowski 1984). For a reaction scheme that accounts for all six flux modes as well as the physiologic forward running, see Apell (2019).

Electrogenicity

A crucial feature of the NKA, and with key consequences for physiology and pathology, is its electrogenicity (first measured by De Weer and Geduldig 1973, in axons). As a result of its 3:2 stoichiometry, one net positive charge leaves the cell per each hydrolyzed ATP molecule and, thus, the NKA steady-state functioning affects and is affected by the cell membrane potential (see Apell 2019). Furthermore, some partial reactions involving ion binding/occlusion/release generate transient, capacitive currents that are also voltage-dependent (Läuger and Apell 1988). These features opened the field of NKA electrophysiology and added the “voltage” dimension to the myriad of kinetic, thermodynamic, biochemical, and biophysical ongoing studies (see, for example, Rakowski et al. 1989; Nakao and Gadsby 1989; Hilgemann 1994; Sagar and Rakowski 1994; Peluffo and Berlin 1997; Holmgren et al. 2000; Peluffo 2004; Gadsby et al. 2012). Particularly, pre-steady-state charge movements allowed for the detailed description of ion binding/release reactions and the determination of rate constants for fast reactions that were out of reach by other techniques, as well as probing the high-field access channel hypothesis (see Apell 2019, for a thorough discussion) and the estimation of dielectric coefficients (Läuger and Apell 1986).

Specific inhibitors

Cardiac glycosides are a family of NKA specific inhibitors, from which the best known and most used is the relatively water-soluble ouabain (Schatzmann 1953; Gill et al. 1956; Glynn 1957). Several functional studies were aimed to reveal the mechanism of ouabain inhibition (see, for example, Palasis et al. 1996; Or et al. 1996; Lingrel et al. 1997). It was finally demonstrated that ouabain binds to extracellularly-facing sites in the E₂-P conformation, preventing K ions from reaching their sites, thus explaining earlier observations of ouabain and extracellular K⁺ competition. These findings were unequivocally confirmed by high-resolution NKA crystal structures obtained with bound ouabain or other cardiac glycosides (Ogawa et al. 2009; Kanai et al. 2021). Digitalis, a type of cardiac glycosides, are used to treat cardiac conditions such as atrial fibrillation and congestive heart failure. Although the NKA is the primary receptor for these digitalis effects, a decrease in heart rate due to vagal activation has also been invoked (Ziff and Kotecha 2016). In any case, it is well established that cardiac glycoside inhibition of the NKA is independent of the electric membrane potential (V_m). In this regard, organic quaternary amines, such as benzyl-triethylammonium (BTEA) chloride, were shown to block NKA currents in a V_m-dependent manner, with apparent affinities in the low millimolar range (Peluffo et al. 2004). These compounds proved to be useful tools to investigate the extracellular access channel for K⁺ and K⁺ binding/occlusion reaction kinetics (Peluffo et al. 2009), as well as charge movements associated to phosphoenzyme conformational transitions (Mares et al. 2014). Furthermore, a custom-synthesized para-nitro derivative of BTEA (pNBTEA) was reported to inhibit the NKA in a V_m-dependent fashion, with an apparent affinity in the low micromolar range (Peluffo and Berlin 2012). These features open the interesting possibility of developing further these compounds to replace available V_m-independent drugs that modulate this enzyme.

Physiological roles of the sodium pump

As mentioned above, the NKA plays many relevant roles in animal physiology, which can roughly be grouped into two categories, depending on whether they directly rest on the ion transport properties of this enzyme.

Cytosolic concentrations of sodium and potassium

The significance of the existence of different sodium and potassium concentrations in the interior of modern animal cells may be appropriately envisaged from an evolutionary perspective. Thus, the necessity to maintain low amounts of intracellular sodium could be a consequence of the evolution of organisms in sodium-rich media (e.g., in seawater, Stein 1995; 2002). Under this condition, in a unicellular organism this ion would tend to massively enter the cell across a sodium-permeable plasma membrane together with an accompanying diffusible anion, as imposed by the conservation of macroscopic electroneutrality. The consequence would be an osmotically-coupled water entry and, in turn, increase in the intracellular hydrostatic pressure. Bacteria and plant cells evolved by generating external walls that were resistant to this increase provoked by the natural tendency of cells to achieve a Gibbs-Donnan equilibrium (Byrne and Schultz 1988; Stein 2002; Kay 2017; Kay and Blaustein 2019) due to the presence of non-diffusible anionic species in the cell interior (e.g., nucleic acids and proteins). Animal cells, having distensible cell membranes and therefore prone to damage by hydrostatic pressure increases, developed owing to the appearance of active sodium extrusion systems, the modern version of which is the NKA. These active transport systems allowed animal cells to counterbalance the osmotic threat by driving out sodium salts. In general, the active extrusion of net positive charges under the functional mode of the 3Na⁺:2 K⁺ stoichiometric ratio is accompanied by chloride, the most abundant inorganic anion in animal systems. The movement of chloride ions against their electrochemical potential gradient across the plasma membrane takes place mostly by secondary active transport (Gagnon and Delpire 2020). The existence of primary active transport processes of chloride in animal cells remains an uncertain issue (Gerencser and Zhang 2003; Menzikov et al. 2021).

The significance of the high intracellular potassium concentrations found in most cells, from archaebacteria to eukaryote (Dibrova et al. 2015), is somewhat more controversial and closely related to the speculations about the circumstances surrounding the appearance of primitive forms of life. Many authors support the idea that life originated in environments rich in potassium, such as vapors of geothermal systems (Mulkidjanian et al. 2012; Dibrova et al. 2015) or muscovite mica (Hansma 2013; 2022). The gradual modification of ambient conditions toward sodium-rich environments may have acted as an evolutionary pressure factor to select cells with active transport systems capable of extruding sodium (see above), while conserving the primitive feature of high intracellular potassium (Dibrova et al. 2015). Other arguments in favor of selecting a potassium-rich cytoplasm invoke differential effects of this ion with respect to sodium on relevant biochemical reactions (Page and Di Cera 2006; Dubina et al. 2013; Campbell et al. 2018; Korolev 2021), a property that may have also contributed to its consolidation as the main intracellular cation during evolution (Dubina et al. 2013; Campbell et al. 2018; Danchin and Nikel 2019).

Resting plasma membrane potential

The electrochemical gradients of sodium and potassium, created and maintained by the NKA, play relevant physiological roles in animals. In most cells, both excitable and non-excitable, the resting membrane potential is mainly generated as a diffusion potential dominated by sodium, potassium, and chloride, and kept approximately in steady state at the expense of the ATP consumed by the NKA (Byrne and Schultz 1988). In the electrogenic mode (i.e., with the NKA functioning under the 3Na⁺:2 K⁺ ratio) the enzyme behaves as an electric current source and thus contributes directly to the electrical potential across the plasma membrane (Läuger 1991). In most animal cell types, characterized by a high potassium permeability of the plasma membrane, it was early recognized that the electrogenic contribution of the sodium pump is small (Abercrombie and de Weer 1978; de Weer and Geduldig 1978; Sjodin 1984, see also above). Some cells, however, are capable of generating the resting membrane potential in an almost purely electrogenic fashion (e.g., human neutrophils, Bashford and Pasternak 1985; 1986; murine T lymphocytes, Ishida and Chused 1993). For this to happen, the necessary conditions appear to be low potassium permeability and a high rate of electroneutral sodium–potassium exchange across the plasma membrane (Jacob et al. 1984; Hernandez and Chifflet 2000).

Fundamental roles of sodium and potassium electrochemical gradients

For most animal cell types, the sodium gradient constitutes the energy source for secondary active transport of diverse inorganic and organic species (Zhao and Noskov 2013; Gagnon and Delpire 2020). In excitable cells, the ionic gradients of sodium and potassium are a pre-requisite for the generation of action potentials. Diverse textbooks can be consulted that thoroughly describe the mechanisms of generation of action potentials (e.g., Greger and Windhorst 1996; Sperelakis 2012). In this type of cells, the NKA has more recently been described to be also involved in other functions (Forrest 2014; Pivovarov et al. 2018; Shao et al. 2021), for example in the relation between sodium removal and high-frequency spiking in neurons (Zang and Marder 2021).

Homeostasis of the cell volume

Why did the active exchange of sodium and potassium across the plasma membrane, mediated by the sodium pump, evolve to the present day’s 3Na⁺:2 K⁺ stoichiometric ratio? Again, speculations on this topic may require an evolutionary perspective. As mentioned above, the active extrusion of sodium could have constituted a powerful resource to fight against the osmotic threat during the evolution of cells with distensible plasma membranes in sodium-rich environments. Although protists do not express the NKA, diverse systems for active sodium extrusion have been identified in their plasma membranes, among them Na⁺-ATPases (Rodríguez-Navarro and Benito 2010; Dick et al. 2020). Metazoans evolved thanks to the appearance of the NKA, a critical evolutionary step that permitted the development of epithelial tissues (Stein 2002; Rossier et al. 2015; Lambropoulos et al. 2016; see also below). In modern metazoans, with tight control of the composition and osmolarity of the internal milieu, the sodium pump plays a pivotal role in cell volume homeostasis under isosmotic conditions (Hallows and Knauf 1994; Baumgarten and Feher 2001; Stein 2002). This was already recognized in the early days of investigation of the NKA and its physiological importance, where the “pump-leak” model was established as a robust strategy for animal cells to maintain their cell volume within a physiological range (Tosteson and Hoffman 1960). Many studies have supported the critical role of the NKA 3Na⁺:2 K⁺ stoichiometric ratio in the homeostasis of the cell volume (Jakobsson 1980; Hernandez and Cristina 1998; Stein 2002; Armstrong 2003; Fraser and Huang 2004; Kay and Blaustein 2019). The necessity for a tight regulation of the cell volume has been extensively discussed (Hallows and Knauf 1994; Lang et al. 1998; Baumgarten and Feher 2001). Several authors have suggested that the primary physiological purpose of maintaining the cell volume within a certain range is the conservation of intracellular protein concentration (Minton et al. 1992; Parker 1993; Lang et al. 1998).

Epithelial transport

The NKA plays a key role in several other cellular functions. In transport epithelia, the polarized distribution of the NKA between the apical and basolateral domains is crucial to determine the direction and magnitude of transcellular transport (Rodriguez-Boulan and Nelson 1989; Rajasekaran and Rajasekaran 2003; Cereijido et al. 2008; Pedersen et al. 2013). Evolutionary considerations suggest that differentiation of a homogeneous cellular conglomerate to generate an epithelial layer may have been among the first morphogenetic events in the path towards the existence of animal organisms (Salazar-Ciudad 2010; Leys and Riesgo 2012; Dickinson et al. 2012; Brunet and King 2017). Thus, the appearance of cellular mechanisms that determined a polarized distribution of active sodium transport systems may have played a crucial role in the origin and development of animals.

Thermogenesis

We make below further speculations on the establishment of the 3Na⁺:2 K⁺ stoichiometric ratio during the evolution of animal cells, based on thermodynamic considerations. We additionally comment there that the NKA has also been recognized as an important contributor to cell thermogenesis (Clarke et al. 2013).

Cell signaling

The physiological roles of the NKA considered so far depend, directly or indirectly, on the capacity of this enzyme to actively transport sodium and potassium ions across the plasma membrane. Nonetheless, the NKA has also been suggested to participate in various cell signaling processes. Since, as mentioned above, the main purpose of this short review is to discuss the significance of the NKA sodium/potassium stoichiometric ratio, we shall not refer here to the many roles in cell signaling proposed for this enzyme. The reader is encouraged to visit the abundant recent literature on this topic (e.g., Pavlovic et al. 2013; Aperia et al. 2016; Shah et al. 2016; Cui and Xie 2017; Pratt et al. 2018; Bartlett et al. 2018; Askari 2019).

Relevance in pathology

Single amino acid substitutions in sodium pump α-subunit isoforms (due to DNA mutations) have been related to specific diseases, such as migraine, Parkinsonism, and aldosteronism, among others (see Clausen et al. 2017; Apell 2019). In addition, considering its many physiological roles, the NKA represents a potential target for therapeutic strategies in several pathological conditions (Kaplan 2005; Terkildsen et al. 2007; Yan and Shapiro 2016; Clausen et al. 2017; Felippe Goncalves-de-Albuquerque et al. 2017; Apell 2019; Maxwell et al. 2021).

Energetics of active sodium and potassium transport

In the previous section we suggested that the need to fulfill some physiological requirements may have represented a pressure factor in the selection of the characteristic NKA stoichiometric ratio. In this section we speculate whether energetic constraints could have impeded the choice of a ratio with a larger number of transported ions while maintaining an electrogenic balance (e.g., 4Na⁺:3 K⁺ or 4Na⁺:2 K⁺).

The analysis of the thermodynamic aspects of electrogenic ion pumps has been thoroughly performed by Peter Läuger in his classic monograph (Läuger 1991), which we follow herein. The Na,K-ATPase equilibrium condition is:

$$\mathrm{\Delta }{G}_{\mathit{ATP}}=\nu \mathrm{\Delta }{\tilde{\mu }}_{\mathit{Na}}-\kappa \mathrm{\Delta }{\tilde{\mu }}_K$$ 1

where

$$\mathrm{\Delta }{\tilde{\mu }}_{\mathit{Na}}={\tilde{\mu }}_{{\mathit{Na}}_1}-{\tilde{\mu }}_{{\mathit{Na}}_2}=RTln\left(\frac{{[{\mathit{Na}}^{+}]}_1}{{[{\mathit{Na}}^{+}]}_2}\right)+zF\left({\mathrm{\Psi }}_1,-,{\mathrm{\Psi }}_2\right)$$ 2

$$\mathrm{\Delta }{\tilde{\mu }}_K={\tilde{\mu }}_{K_1}-{\tilde{\mu }}_{K_2}=RTln\left(\frac{{[K^{+}]}_1}{{[K^{+}]}_2}\right)+zF\left({\mathrm{\Psi }}_1,-,{\mathrm{\Psi }}_2\right)$$ 3

In Eqs. (2)-(3), subindexes 1 and 2 denote the cytosolic and extracellular compartments, respectively; V_m is the electrical potential difference across the plasma membrane, given by $V_m=\left({\mathrm{\Psi }}_1,-,{\mathrm{\Psi }}_2\right)$; and ν and κ are the stoichiometric coefficients for sodium and potassium transport by the NKA, respectively. The rest of the symbols have their usual meanings.

Based on Eq. (1), the transport work performed by the Na,K-ATPase (W_Na,K) is therefore given by:

$$W_{Na,K}=\nu RTln\left(\frac{{[{\mathit{Na}}^{+}]}_1}{{[{\mathit{Na}}^{+}]}_2}\right)+\nu zF{V}_m-\kappa RTln\left(\frac{{\left[K^{+}\right]}_1}{{\left[K^{+}\right]}_2}\right)-\kappa zF{V}_m$$

or

$$W_{Na,K}=RT\left(\nu ,l,n,\left(\frac{{[{\mathit{Na}}^{+}]}_1}{{[{\mathit{Na}}^{+}]}_2}\right),-,\kappa ,l,n,\left(\frac{{\left[K^{+}\right]}_1}{{\left[K^{+}\right]}_2}\right)\right)+\left(\nu ,-,\kappa \right)zF{V}_m$$ 4

In a W_Na,K vs V_m plot using Eq. (4), the slope (ν – κ) determines that Na⁺:K⁺ stoichiometries of 3:2 and 4:3 will produce parallel curves; accordingly, the slope will be doubled for a 4:2 stoichiometry and it will be zero for electroneutral transport 3:3 (like the behavior for electrically silent ATP hydrolysis). The difference for all stoichiometries with similar (ν – κ) values will reside in the ordinate, given by:

$$RT\left(\nu ,l,n,\left(\frac{{[{\mathit{Na}}^{+}]}_1}{{[{\mathit{Na}}^{+}]}_2}\right),-,\kappa ,l,n,\left(\frac{{\left[K^{+}\right]}_1}{{\left[K^{+}\right]}_2}\right)\right)$$

We performed numerical calculations for the dependence of W_Na,K on V_m, using Eq. (4) and data available in the literature. In their elegant studies, Clarke et al. (2013) utilized the following values for sodium and potassium concentrations:

$$[{\mathrm{Na}}^{+}{]}_1=15\mathrm{mM};[{\mathrm{Na}}^{+}{]}_2=140\mathrm{mM};[{\mathrm{K}}^{+}{]}_1=120\mathrm{mM};[{\mathrm{K}}^{+}{]}_2=4\mathrm{mM}$$

Using these values, we calculated the ordinates (Ord, expressed in kJ/mol) at T = 310.15 K for different Na⁺:K⁺ stoichiometric ratios.

$$3:2\mathrm{Ord}=-34.819;4:3\mathrm{Ord}=-49.349;4:2\mathrm{Ord}=-40.579;3:3\mathrm{Ord}=-43.589$$

Only Na⁺:K⁺ stoichiometries with a larger number of transported ions were considered (with respect to the canonical 3:2 stoichiometry), aiming for a more efficient use of the energy released by ATP hydrolysis. The results show that the work performed by transporting ions at V_m = 0 under those stoichiometries is significantly larger than that for the 3:2 case. Slightly different numerical values for intra and extracellular sodium and potassium concentrations have been reported in several other sources (e.g., Allen and Orchard 1987; Alberts 2002; Boron and Boulpaep 2016). Calculations performed with these alternative combinations of values did not yield significant differences compared to the ordinate values obtained above (not shown).

The energy requirements for the simultaneous active transport of sodium and potassium performed by the NKA must be compared with the free energy yielded by ATP hydrolysis under cellular conditions. Again, following Clarke et al. (2013), a value for the change in free energy of ATP hydrolysis (ΔG_ATP) can be calculated under physiological conditions at 37 °C as:

$$\mathrm{\Delta }\mathrm{G}\text{ATP}=RT\ln \left(\frac{\left[A,D,P\right][P_i]}{\left[A,T,P\right]K_h}\right)=-54.0kJ/mole$$

The ATP, ADP and P_i concentration values used here were 4.4, 0.5 and 1 mM, respectively. The value of ΔG⁰_ATP varies within the range -27.9 to -33.5 kJ/mol, depending on the ionic strength and Mg²⁺ concentration (-33.5 kJ/mol in the absence of Mg and zero ionic strength, -27.9 kJ/mol for [Mg²⁺] = 10 mM and ionic strength 0.1). The Mg²⁺ effect is due to stabilization of phosphate groups in the ATP molecule (Rosing and Slater 1972; Milo et al. 2010). Considering a standard free energy change of ΔG^0’_ATP = -30.5 kJ/mol, equivalent to -7.3 kcal/mol (Cooper 2000), a value of 1.4 × 10⁵ was obtained for the equilibrium constant (K_h) that describes the ATP hydrolysis reaction at 37 °C.

However, large variations in these quantities have been reported in the literature, depending on the cell type, metabolic conditions, and detection techniques. For example, ATP concentrations examined in a variety of cells/tissues/organs ranged from 2.7 to 7.5 mM, with an average value of 4.4 ± 2.9 (SD) mM (Greiner and Glonek 2021). ADP levels have been reported to be in the micromolar range, with ATP/ADP ratios going from 10 to 1000 (depending on cell energy status and adenylate kinase enzyme activity), which usually translate into intracellular ADP concentrations of 5–500 μM (Soboll et al. 1978; Wackerhage et al. 1998; Wu et al. 2008; Milo et al. 2010). Inorganic phosphate intracellular levels are reported to be in the low millimolar range (Wackerhage et al. 1998; Milo et al. 2010). Interestingly, models that incorporate measurements using ³¹Phosphate-magnetic resonance spectroscopy report a baseline concentration of 0.29 mM for free inorganic phosphate in canine cardiac myocytes, increasing to 2.3 mM at near maximal oxygen consumption, and further raising to approximately 3.1 mM during acute ischemia (Greiner and Glonek 2021).

The value of -54 kJ/mol (21k_BT) for ΔG_ATP at 37 °C obtained with our selected concentrations of ATP, ADP and P_i agrees well with the numbers reported by Clarke et al. (2013) and with the average of all values reported by Läuger (1991, -56 kJ/mol, Table 1, p. 47). Nonetheless, it is worth mentioning that the above-reported inorganic phosphate concentrations of 0.29, 2.3 and 3.1 mM would result in ΔG_ATP values of -57.2, -51.8 and -51.1 kJ/mol, respectively (keeping unchanged the concentrations used for ATP and ADP). In general, a tenfold change in any single concentration will result in a 6 kJ/mol change in ΔG_ATP.

Figures 2 and 3 show plots of the electrochemical work performed by the NKA as a function of the membrane potential, according to Eq. (4) and with the sodium and potassium concentrations described above, for 3:2, 4:3 and 4:2 Na⁺:K⁺ stoichiometric ratios. The plots also include the maximum free energy available for active ion transport by the NKA as a result of ATP hydrolysis (-54 kJ/mol, with the numerical values considered here), and the amount of work needed for electroneutral 3:3 Na⁺:K⁺ exchange. The plots show that, under physiological conditions, the enzyme would not have the “fuel” to pump ions against their electrochemical potential gradient beyond some negative value of the cell membrane potential (approximately –50 and –70 mV, for Na⁺:K⁺ ratios of 4:3 and 4:2, respectively). Therefore, under these conditions, an excitable cell with a resting membrane potential of –85 to –75 mV would not have a working sodium pump. On the contrary, for a 3:2 stoichiometry, the hydrolysis of ATP is capable to fulfill the NKA energetic requirements for all V_m values positive to –100 mV. These observations appear to point to a thermodynamic constraint for the NKA stoichiometric ratio, subjected to the natural imposition of the existence of an electronegative intracellular compartment and to the amount of energy available from ATP hydrolysis.

Fig. 2.

Plots of ion transport work performed by the NKA (W_Na,K) vs cell membrane potential (V_m), using Eq. (4) for three different Na⁺:K⁺ stoichiometric ratios (3:2, 3:3, and 4:3). The dashed line indicates the free energy value obtainable per mole from ATP hydrolysis within physiological conditions (see main text). Notice that the curves for Na⁺:K⁺ stoichiometric ratios 3:2 and 4:3 exhibit identical slopes but ~ 14 kJ/mol different ordinates. The intercept between the (4:3) curve and ΔG_ATP occurs at –48.2 mV

Fig. 3.

Plots of ion transport work performed by the NKA (W_Na,K) vs cell membrane potential (V_m), using Eq. (4) for Na⁺:K⁺ stoichiometric ratios of 3:2 and 4:2. Notice that the curve representing the 4:2 Na⁺:K⁺ stoichiometric ratio has a slope twice as large as the curve with a 3:2 stoichiometry, and a ~ 6 kJ/mol more negative ordinate. The intercept between the (4:2) curve and ΔG_ATP takes place at –69.5 mV

Another constraint could be related to the sodium pump contribution to cell thermogenesis. This role of the pump is indirect, since heat production is, in this case, achieved via passive dissipative processes mediated by sodium and potassium channels, ultimately a consequence of the maintenance of electrochemical gradients for these ions by the NKA (Clarke et al. 2013). Further energetic demand to actively transport additional sodium and/or potassium ions (e.g., at negative membrane potentials, see Fig. 3) could encompass a loss of pump’s capacity to support sodium and potassium physiological gradients and, consequently, the amount of their contribution to cell thermogenesis. Thus, the need for a NKA contribution to cellular thermogenesis could have also played a role in optimizing the enzyme activity, in particular its Na⁺:K⁺ transport stoichiometric ratio, in the course of animal cell evolution. The plots shown in Figs. 2 and 3 also reveal that, under the normal 3Na⁺:2 K⁺ ratio, the enzyme appears to be a highly efficient machine throughout the range of values considered for the plasma membrane potential. Thus, for instance, the ratio (energy utilized for sodium and potassium transport / energy available from ATP hydrolysis) can be calculated as 34,819/54,000 = 0.64 at zero mV and would increase to 39,627/54,000 = 0.73 at –50 mV. However, efficient ATP free energy utilization by ion transport at membrane potentials negative to –30 mV will be compromised by a decrease in Na,K-pump current levels in the presence of physiologically high extracellular Na⁺ concentrations (see, for example, Nakao and Gadsby 1989).

Concluding remarks

During evolution, the stoichiometric ratio of the NKA was selected as a robust 3Na⁺:2 K⁺ transported per hydrolyzed ATP molecule. In this review we have discussed that there may be, at least, two important constraints underlying this selection: 1) thermodynamic restrictions, which precluded the selection of a larger number of ions from being transported per reaction cycle, and 2) adaptation to physiological requirements, such as the need to develop systems capable to contribute to cell volume homeostasis. Evolution may thus have occurred with a progressive stabilization of Na⁺,K⁺-ATPase molecules with that stoichiometric ratio, capable to simultaneously optimize the conservation of stable electrochemical ion gradients, the contribution to cell volume homeostasis and the efficient utilization of available ATP. Nonetheless, whether sodium pump ancestors with a larger number of binding sites for Na⁺ and/or K⁺ indeed existed, remains an open question.

Authors contributions

Both authors contributed equally to the conceptual work, the writing of the manuscript, and the making of the figures.

Funding

No funding was obtained for this study.

Declarations

Ethical approval

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Conflict of interest

R.D. Peluffo and J.A. Hernández declare that they have neither financial nor non-financial conflict of interests.