A protein called the sodium-potassium pump resides in the membrane that surrounds living cells. The role of this protein is to 'pump' sodium and potassium ions across the membrane to help restore their concentration inside and outside of the cell. About 25% of the body's energy is used to keep the pump going, rising to nearly 70% in the brain. Problems that affect the pump have been linked to several disorders, including heart, kidney and metabolic diseases, as well as severe neurological conditions.

The sodium-potassium pump must be able to effectively pick out the correct ions to transport from a mixture of many different types of ions. However, it was not clear how the pump succeeds in doing this efficiently. Rui et al. have now used a computational method called molecular dynamics simulations to model how the sodium-potassium pump transports the desired ions across the cell membrane.

The pump works via a so-called 'alternating-access' mechanism, repeatedly transitioning between inward-facing and outward-facing conformations. In each cycle, it binds three sodium ions from the cell’s interior and exports them to the outside. Then, the pump binds to two potassium ions from outside the cell and imports them inside. Although the bound sodium and potassium ions interact with similar binding sites in the pump, the pump sometimes preferentially binds sodium, and sometimes potassium. The study performed by Rui et al. shows that this preference is driven by how protons (hydrogen ions) bind to the amino acids that make up the binding site.

The simulations also suggest that the pump uses a ‘self-correcting’ mechanism to prevent the pump from transporting the wrong types of ions. When incorrect ions are present at the binding sites, the pump cycle pauses temporarily until the ions detach from the pump. Only when the correct ions are bound will the pump cycle continue again.

In the future, Rui et al. hope to use long time-scale molecular dynamics simulations to show the conformational transition in action. In addition, the 'self-correcting' mechanism will be directly tested by letting the wrong and correct ions compete for the binding sites to see whether the pump will transport only the correct ions.

The Na⁺/K⁺-pump is a primary active membrane transporter present in nearly all animal cells. It belongs to the P-type ATPase family, which utilizes the energy released from ATP hydrolysis to move ions against their concentration gradients across a membrane barrier. The ion species transported by the pump under physiological conditions are Na⁺ and K⁺. Like many other membrane transporters, the Na⁺/K⁺-pump works according to an 'alternating-access' ion transport mechanism, with the bound ions accessible from only one side of the membrane at a time. The consensus scheme of the pump cycle is known as the 'Albers-Post' cycle (Albers, 1967; Post et al., 1969). It involves two major conformations, E₁ and E₂, with inward- and outward-facing ion binding sites, respectively. In each cycle, the E₁ conformation binds three Na⁺ from the cytosol and exports them using the energy from ATP hydrolysis. After external release of Na⁺, binding of extracellular K⁺ promotes the structural transition to the occluded E₂ state, which finally imports two K⁺ as binding of ATP returns the pump to the E₁ conformation. E₁/E₂ conformational change and the accompanied electrogenic active transport are facilitated by the phosphorylation and dephosphorylation of an aspartate residue in the cytoplasmic domain, which is a hallmark of the P-type ATPase family (Axelsen et al., 1998).

The presence of the Na⁺/K⁺-pump is essential for excitability and secondary active transport. More than 40% of the energy produced in mammals is consumed by the Na⁺/K⁺-pump (Milligan et al., 1985). Although it is a machine designed for such a precise and important function, it has been shown that many cations, including congeners of K⁺ and some organic cations, can bind to the same sites used by the pump to bind and transport K⁺ ions (Mahmmoud et al., 2015; Ratheal et al., 2010). Competitive binding between Na⁺ and other cations at the cytoplasmic side of the membrane has also been observed (Schneeberger et al., 2001). An unsolved puzzle, therefore, is how the Na⁺/K⁺-pump is able to recognize and accept two K⁺ from the extracellular matrix, where Na⁺ concentration is much higher, and how it selectively binds Na⁺ from the cytoplasm to keep the pump cycle running forward.

Structural studies have provided tremendous insights into the function of the Na⁺/K⁺-pump, which consists of two obligatory subunits, α (catalytic) and β (auxiliary), and sometimes a tissue specific regulatory subunit from the FXYD protein family (Geering, 2006; Mercer et al., 1993). The transmembrane region of the α-subunit contains the ion binding sites within its 10 helices (called M1-M10). Recent crystal structures of the pump in its E₁ and E₂ states reveal the locations of the three Na⁺ binding sites in E₁ and the two K⁺ binding sites in E₂ (Kanai et al., 2013; Laursen et al., 2013; Morth et al., 2007; Shinoda et al., 2009). From structural alignments based on the heavy atom positions in the binding sites, it becomes clear that the binding pocket harboring sites I and II in E₁ overlaps with those in E₂ (Figure 1). Site III is only formed in E₁. It is located between the transmembrane helices M5, M6, and M8 and is thought to exclusively bind Na⁺ but appears to catalyze H⁺ transport (Poulsen et al., 2010; Ratheal et al., 2010) in a manner that presents a complex dependence on the concentrations of Na⁺, K⁺, and H⁺ (Mitchell et al., 2014). Previous studies have indicated that protonation at the ion binding pocket may play a role in the selectivity of these sites for K⁺ when the pump is in its E₂ state (Yu et al., 2011). Biochemical assays on the mutant D926N, which is often used as a surrogate for protonated D926, also show that it induces distinct effects on Na⁺ and K⁺ binding (Einholm et al., 2010; Jewell-Motz et al., 1993), suggesting a potential change in its protonation state upon the E₁/E₂ transition. Taken together, the evidence, although indirect, suggests the possibility of an E₁ specific protonation state that favors Na⁺ binding to the pump. The nature of this protonation state is, however, unclear.

Figure 1

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In the present study, we started with the recently published crystal structure of the Na⁺/K⁺-pump in a partially occluded Na₃·E₁(ADP·Pi) state and used molecular dynamics (MD) simulations to show that there is a correlation between the binding pocket protonation and the Na⁺ selectivity in E₁. The binding sites in Na₃·E₁(ADP·Pi) were tested one by one by 'alchemically transforming' the bound Na⁺ into a K⁺ while keeping the other two sites occupied by Na⁺. A similar approach was previously used to study the selectivity in other conformational states of the pump (Yu et al., 2011) (see also Materials and methods section). The results show that the Na⁺ selectivity at all three sites is realized only when a specific set of binding pocket residues are protonated. This set of residues is, by comparison, different from that in the K⁺ selective E₂ state. The implication is that the protonation state and the selectivity of the pump are tightly coupled; when the pump undergoes a transition between E₁ and E₂, a protonation state switch occurs. The present findings also show that the effective selectivity of the pump is reinforced by a self-correcting mechanism, which prevents the occlusion step on either side of the membrane if the wrong type of ions were loaded into the binding sites. This mechanism ensures that counterproductive transport cycles do not occur.

The results from the MD simulations support the notion that the protonation state of the binding pocket and its selectivity are closely related. Because the binding pocket in the Na⁺/K⁺-pump displays considerable flexibility, it is worth pausing to reflect on the possible mechanism that underlies this relation. While the selectivity of a very rigid binding site is first and foremost predetermined by its atomic geometry, the selectivity of a flexible binding site is strongly affected by local ion-ligand and ligand-ligand interactions. In such flexible systems, selectivity is controlled by the both number and the physicochemical properties of ion-coordinating ligands (Yu et al., 2010). For example, high-field ligands, such as deprotonated acidic side chains tend to favor Na⁺ binding and protonation revert those to low-field ligands, which tend to favor K⁺. Hence, in the Na⁺/K⁺-pump protonation is exploited to modulate selectivity by altering the electrostatic properties of several of residues in the binding pocket. This is also consistent with the results from our previous study on the ion selectivity in E₂(K₂), which concluded that changes in the electrostatic properties of the protonatable residues was the likely mechanism responsible for the K⁺ selectivity in the E₂ state of the pump (Yu et al., 2011). Even though the local structural rearrangements at the binding sites are small upon the change in protonation state, it is enough to change the physical properties of the coordinating ligand, thus giving rise to discernable differences in the ion selectivity. The crystal structures of the Na⁺/K⁺-pump in its Na₃.E₁·(ADP·Pi) and E₂(K₂) states show similarity in their binding pocket configurations (Figure 1), including the coordination patterns of the bound ions at sites I and II (Table 1). The heavy atom RMSD between the binding pocket residues is 2.5 Å and the structural difference remains after hundreds of ns of simulations. Empirical pKa and FEP calculations based on the MD simulation equilibrated structures indicate that the binding pocket glutamates (i.e., E327, E779, and E954) are likely protonated in both Na₃.E₁·(ADP·Pi) and E₂(K₂), although previous mutagenesis experiments showed that charge-neutralizing mutation E327Q affects pump function, possibly by altering ion-pump interactions and the kinetics of the occlusion/deocclusion reactions along the pump cycle (Jorgensen et al., 2001; Kuntzweiler et al., 1995; Li et al., 2006; Nielsen et al., 1998). The calculations also suggest that the protonation states of D804, D808, and D926 are different in Na₃·E₁·(ADP·Pi) and E₂(K₂). Among the three aspartates only D804 is protonated in order for all three sites to stay Na⁺ selective in Na₃·E₁·(ADP·Pi). The E₁ binding pocket devoid of ions carries a net charge of -2, consistent with that deduced from previous fluorescence studies (Schneeberger et al., 1999). Mutagenesis experiments are also consistent with the unlikely protonation of D808 and D926 when the pump is in E₁ trying to bind cytoplasmic Na⁺ (Jewell-Motz et al., 1993; Pedersen et al., 1997). The protonation states of these three residues are reversed in E₂(K₂) with D804 deprotonated and the other two protonated, a result that is supported by a previous computational study (Yu et al., 2011). The different protonation states for E₁ and E₂ also agree well with the 'four-site' model proposed by Skou and Esmann more than 30 years ago with the K⁺-bound E₂ state carrying two sidechain protons (H₂EK₂) and the Na⁺-bound E₁ state carrying only one (HENa₃) (Skou et al., 1980).

It is worth pointing out that the second proton (i.e., the proton on D926) in the K⁺ bound E₂ state must come from and return to the same side of the membrane during the pump cycle so that the net charge moved per cycle by the pump is one. It seems unlikely that this proton could come from the extracellular side because altering extracellular pH would then protonate or deprotonate D926, causing major changes in Na⁺ binding affinity and the maximum pumping turnover rate. This is not observed over an external pH range 9.6 to 5.6 (Mitchell et al., 2014; Vasilyev et al., 2004; Yu et al., 2011). Therefore, it is more likely that the D926 proton comes from the cytoplasmic side. This is supported by MD simulations of the P-E₂·Na₂ and Na₂·E₁·(ADP·Pi) revealing the existence of aqueous pathways connecting the cytoplasm and D926 (Figure 6). One of the water pathways is located between the helices M5, M7, and M8 (Figure 6B), similar to the C-terminal proton pathway previously proposed (Poulsen et al., 2010). A proton could enter through this pathway to protonate D926 and then leave through the same pathway during the E₂ to E₁ transition, or through an alternative path passing the main binding pocket along with the dissociating ions as seen in the Na₂·E₁·(ADP·Pi) simulation (Figure 6A).

Figure 6

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Under physiological conditions, the challenge faced by the Na⁺/K⁺-pump is to effectively pick out the correct ion species from a solution much more concentrated with other types of ions. Even when the binding affinity of the ion species being transported is a few orders of magnitude higher than that of the other ion (${\displaystyle \mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{d}}}$ = 1 to 3 kcal/mol), the advantage in binding is undermined by the higher concentration of the competing ion. The pump overcomes this problem by raising the free energy barrier for the occlusion step in the presence of incorrect ions in the binding pocket, thus preventing the faulty transport (Figure 5 and Table 5). This self-correcting mechanism makes sure that the intracellular and the extracellular gates do not close (i.e., occlude), which is required for the pump cycle to go forward, unless the correct ion configuration is present at the binding pocket. Therefore, this is an inherent part of the ping-pong mechanism the pump uses to transport ions with high selectivity. Although other energetic barriers, like pathways the ions use to travel to the binding site, could contribute to the ion binding specificity, it is not likely the case here as both Na⁺ and K⁺ can access the binding pocket in the simulations of the E₁ and P-E₂ states without ions bound.

The concept of a self-correcting pumping mechanism sheds new light on a number of puzzling functional observations. For instance, it explains why E₁ displays a strong apparent affinity for K⁺ in competitive binding assays (Schneeberger et al., 2001), even though the pump still binds and occludes Na⁺ from the cytoplasmic side. The calculations show that all the sites in the Na₃·E₁·(ADP·Pi) state are selective for Na⁺, likely because this is a partially occluded state. A wrong combination of binding site ions would not have been occluded and reached such a state. In a fully inward-open conformation, the selectivity of the sites ought to be fairly weak. The high affinity for K⁺ observed in E₁ in these experiments is due to the backward occlusion leading to the K⁺-bound state E₂(K₂). The proposed self-correcting mechanism parallels the suggestion based on experiments that the phosphorylation and occlusion of E₁ requires 3 Na⁺ bound, and this increases the apparent affinity for Na⁺ in the normal pump cycle (Schneeberger et al., 2001). The self-correcting mechanism can also account for the different effects of Na⁺ and K⁺ congeners on the release rate of the occluded ⁸⁶Rb⁺ (a K⁺ congener) to the extracellular side upon the “backdoor” phosphorylation in the presence of Pi reported by Forbush (Forbush, 1987). This backward deocclusion is accelerated in the presence of Na⁺, and it follows a single phase, while a much slower deocclusion process with a second slow phase is observed in the presence of K⁺ or Rb⁺. According to the self-correcting mechanism, it is likely that upon the replacement of one of the two occluded ⁴²K⁺ or ⁸⁶Rb⁺ by cold K⁺ at one site, the pump succeeded to occlude again, resulting in the second slow phase. These explanations are sensible, in turn lending support to the proposed self-correcting mechanism. Given that the selectivity in the outward/inward facing states is after all not as strong as previously thought, such a mechanism must be in place.

This analysis suggests that an important component of the overall selectivity emerges from the increased free energy barrier associated with the occlusion process while the wrong type of ion is bound to a site. Although the pump would be kinetically more efficient by preventing the wrong ions from reaching the binding sites to begin with, the free energy calculations do not support the notion of highly selective binding sites for the open-access states. While such mechanism may seem inefficient because the pump must try to figure out that there is an issue with selectivity only after binding of several ions of the wrong type, it is important to realize that the Na⁺/K⁺-pump is not a particular fast molecular machine. The estimated turnover rate is less than 100 per second and decreases even further as the transmembrane voltage becomes more negative (Heyse et al., 1994). The implication is that the system has plenty of time, at the molecular level, to function near thermodynamic equilibrium. In other words, the pump has not been evolutionarily optimized to be a particularly fast molecular machine, but an energetically efficient one. Thus, even though the idea of a self-correcting ion selectivity mechanism seems counterintuitive and inefficient, it is consistent with the physical conditions under which the pump has to operate.

In summary, the present study highlights the tight coupling between the Na⁺/K⁺ selectivity of the binding sites, the protonation state of the coordinating residues, and the conformational state of the pump. The important functional consequence of such tight coupling is the necessity to have the correct type and number of ions in the binding pocket for the pumping cycle to proceed forward toward the occlusion step. Because the ion binding selectivity is strongly dependent upon the protein conformation, a self-correcting mechanism counteracting the effect of the ion concentration in the environment ensures an efficient function of the pump.

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Thank you for submitting your article "Binding site protonation and self-correcting occlusion control the Na+/K⁺-pump selectivity" for consideration by eLife. Your article has been reviewed by three peer reviewers, including Erik Lindahl (Reviewer #3) and Nir Ben-Tal (Reviewer #1), who is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Richard Aldrich as the Senior Editor.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

The study examines the physicochemical determinants of binding site selectivity in the Na+/K⁺-ATPase using molecular dynamics simulations. Various conformation of the ATPase, corresponding to different states along the pump cycle are examined, including the crystal structures of its two main conformations, as well as several models of intermediate states based on the Ca²⁺ SERCA pump, and models derived from interpolating between well-defined states. Various protonation states of titratable residues in the pump's binding sites are energetically examined using molecular dynamic simulations as different resolutions. The results suggest that the protonation states of three aspartate residues in the binding sites (D804, D808 and D926) alter upon switching between conformations. The results indicate that the different selectivity of the binding sites emerges from the change in the protonation states. Using reduced structural models of the binding sites, this hypothesis is supported by calculating the difference in free energy between the pump bound to Na⁺ vs. K⁺ ions along the transport cycle. The authors conclude that initially the binding sites are only weakly selective for either Na⁺ or K⁺, and selectivity emerges as collective effect due to the (indirect) interaction of new ions with the ones that are already bound (a knock-on effect); the pump shifts towards K⁺ selectivity in the outward open state, and towards Na⁺ selectivity in the inward open state. Binding of the wrong type of ion increases the free energy barrier towards occlusion, preventing the transport cycle to proceed, thereby preventing the pump from operating in the opposite (wrong) direction.

The manuscript addresses an interesting and important question. It proposes a simple mechanism that dictates the shift in the selective properties of the Na+/K⁺-pump binding sites. However, based on the current draft of the manuscript it is difficult to decide whether the work is novel and solid enough to justify publication in eLife. The summary reflects a long discussion among the reviewers in an effort to resolve this. The author should submit a revised draft only if they are certain that they can address all the issues raised.

Essential revisions:

1) It is difficult to figure out which structures the various steps in Figure 5 are based on. Perhaps:

State 1 and 9 correspond to 3B9B (open SERCA);

State 2 calculated transition to;

State 3 corresponds to 1WPG (occluded SERCA) – but why not 2ZXE (occluded NKA)?

State 4 calculated transition to;

State 5, unclear: called K₂E₁. Maybe 1VFP with different protonation pattern and K instead of Na?

State 6 corresponds to 1VFP (Ca occluded SERCA) – but with K rather than Na?

State 7 corresponds to 3WGV (occluded NKA);

State 8 calculated transition to 9;

The authors should make perfectly clear which structures are used for which states.

2) The pump cycle should be based on all the relevant structures. Structures have been published of SERCA in E₂ (3W5C) and the open ready-to-bind Ca (4H1W) in 2013. These important steps are missing here, or guesses are attempted based on the Ca-occluded 1VFP structure, but that did not predict the structure for H and Ca exchange. The structures are not mentioned. (A nice and recent overview of P-type structures can be found here http://www.ncbi.nlm.nih.gov/pubmed/26695058).

Also, it would be preferable to use 4HYT (ouabain-bound NKA, mentioned as recent but it is from 2013) rather than 3B9B. At least the authors could show an overlay of the ion binding sites from 4HYT and their model.

3) Standard errors estimates should be added to the energy values, and conclusions that have been based on energy values with too large 'error bars' should be reconsidered.

4) If the calculations correctly describe the binding free energy of the pump cycle, they would also need to explain the ion release on the opposite side. Can they show this?

5) The simulations and free energy calculations assume a starting point in which all the pump's binding sites are occupied by a certain set of ions. The authors explicitly claim that selectivity emerges from the increased free energy barrier associate with binding of the wrong ion to a site. However, from a biological point of view to argue that selectivity is governed solely by such mechanism is puzzling, for it is inefficient. The mechanism proposed here beautifully explains the different selective properties of the pump's binding sites in its two conformations, and it is possibly a "last resort mechanism", designed, as the authors claim, to prevent the transport of the wrong kind of ion if it reaches the binding site. However one would expect that for the most part, under physiological conditions, the pump will prevent the wrong ions from reaching the binding site to begin with. The anticipation is that a fast machine, such as this pump, should follow a particularly efficient mechanism, rather than the one proposed here, which figures out that there is issue with selectivity only after binding of several ions of the wrong type. The manuscript does not account for the ions transition into the binding sites and other possible energetic barriers they might encounter on the way. This issue should, at the very least, be discussed.

6) In view of item 5, the authors should revise the title to reflect the fact that selectivity is presumably determined primarily by other mechanisms, and the suggested mechanism here is only a 'safe guard'.

Essential revisions:

1) It is difficult to figure out which structures the various steps in Figure 5 are based on. Perhaps: State 1 and 9 correspond to 3B9B (open SERCA); State 2 calculated transition to; State 3 corresponds to 1WPG (occluded SERCA) – but why not 2ZXE (occluded NKA)? State 4 calculated transition to; State 5, unclear: called K2E1. Maybe 1VFP with different protonation pattern and K instead of Na? State 6 corresponds to 1VFP (Ca occluded SERCA) – but with K rather than Na? State 7 corresponds to 3WGV (occluded NKA); State 8 calculated transition to 9; The authors should make perfectly clear which structures are used for which states.

We modified the “Selectivity calculations along the pump cycle” section in Materials and methods to introduce the structures used for the calculations of ΔΔG along the pump cycle. The updated text reads as follows:

“The structures used for them are: 1) the generated P-E₂.K₂ model, 3) the equilibrated crystal structure 2ZXE, the equilibrated crystal structure 3WGV with 7) bound Na⁺ and with 5) bound Na⁺ replaced by K⁺ at sites I and II, and 9) the generated P-E₂.Na₃ model. […] All the states included in the selectivity calculations and their relative placement along the pump cycle can be seen in Figure 5.”

2) The pump cycle should be based on all the relevant structures. Structures have been published of SERCA in E₂ (3W5C) and the open ready-to-bind Ca (4H1W) in 2013. These important steps are missing here, or guesses are attempted based on the Ca-occluded 1VFP structure, but that did not predict the structure for H and Ca exchange. The structures are not mentioned. (A nice and recent overview of P-type structures can be found here http://www.ncbi.nlm.nih.gov/pubmed/26695058)

Also, it would be preferable to use 4HYT (ouabain-bound NKA, mentioned as recent but it is from 2013) rather than 3B9B. At least the authors could show an overlay of the ion binding sites from 4HYT and their model.

First of all, we apologize for the confusion. Detailed descriptions on how the transition pathways are generated based on the Ca²⁺ SERCA pump structures are not included. We felt that it was not necessary because the complete protocol was described in our previous publication (Castillo et al., 2015). We hope that adding the sentences below in the manuscript could clarify some of the reviewers’ concerns:

“Since both the Na⁺/K⁺-pump and the Ca²⁺ SERCA pump are P-type ATPases, it is reasonable to assume that they have similar pumping mechanisms and they share the same set of states along the pump cycle. […] The two SERCA pump structures representing states Na₃.E₁ATP (3WGV) and E₂(K₂) (2ZXE) are 1VFP and 1WPG, respectively.”

We are aware of the 4HYT structure, but did not use it in the free energy calculations because it is in a P-E₂-like state with ouabain bound blocking the extracellular access rather than a true outward open state. The generated P-E₂ models and the crystal structure 4HYT show similarity, especially in the transmembrane region, where the backbone RMSD is 2.7 Å (see the Extended Data Figure 5 in our previous publication on the pump (Castillo et al., 2015)). This is mentioned in the main text of the manuscript in the Result section titled “Ion selectivity along the pump cycle”.

“The models appear sensible as they are structurally comparable to the recently published P-E₂ like structures of the Na⁺/K⁺-pump (Gregersen et al., 2016; Laursen et al., 2013) and the vanadate-Inhibited, P-E₂ mimic of the Ca²⁺ SERCA pump (Clausen et al., 2016).”

The K⁺-loaded P-E₂ model also reproduces the experimentally measured gating charge. Therefore, we think the current P-E₂ models are reasonable and can be used compute the free energy difference of Na⁺ and K⁺ binding.

3) Standard errors estimates should be added to the energy values, and conclusions that have been based on energy values with too large 'error bars' should be reconsidered (see comment 1 by Reviewer 3).

We updated the relevant figures and tables.

4) If the calculations correctly describe the binding free energy of the pump cycle, they would also need to explain the ion release on the opposite side. Can they show this?

Yes. The free energy values can be used to explain cytoplasmic release of the K⁺ as well. Once the pump opens to the cytoplasmic side, protonation states of the binding site aspartates change and the binding sites go from highly K⁺ selective in the occluded state to relatively non-discriminating. Even though rebinding of the two K⁺ is possible given the much higher K⁺ concentration in the cytoplasm, the rate of the backward transition to the occluded state is slow. At the same time, the binding of K⁺ to the site III is unlikely. Because occupancy of this site is the prerequisite of phosphorylation and occlusion of E₁, the pump cycle cannot go forward. All the factors favor the cytoplasmic release of K⁺ and binding of Na⁺, which keep pump cycle forward. To emphasize the point, we add the following sentences in the main text:

“When the pump is in this state, site I is Na⁺ selective and site II is only weakly K⁺ selective. Together, the E₂ to E₁ structural transition and the protonation state change promote the release of K⁺ to the cytoplasmic side.”

5) The simulations and free energy calculations assume a starting point in which all the pump's binding sites are occupied by a certain set of ions. The authors explicitly claim that selectivity emerges from the increased free energy barrier associate with binding of the wrong ion to a site. However, from a biological point of view to argue that selectivity is governed solely by such mechanism is puzzling, for it is inefficient. The mechanism proposed here beautifully explains the different selective properties of the pump's binding sites in its two conformations, and it is possibly a "last resort mechanism", designed, as the authors claim, to prevent the transport of the wrong kind of ion if it reaches the binding site. However one would expect that for the most part, under physiological conditions, the pump will prevent the wrong ions from reaching the binding site to begin with. The anticipation is that a fast machine, such as this pump, should follow a particularly efficient mechanism, rather than the one proposed here, which figures out that there is issue with selectivity only after binding of several ions of the wrong type. The manuscript does not account for the ions transition into the binding sites and other possible energetic barriers they might encounter on the way. This issue should, at the very least, be discussed.

First, we need to clarify that the selectivity of the pump is not solely governed by the “self-correcting” mechanism. The occluded states are indeed highly selective while the states that are open to the extracellular and cytoplasmic sides are less so. The “self-correcting” mechanism is one way for the pump to achieve this selectivity difference between the states.

The pump is prone to error when it tries to bind ions from the extracellular and cytoplasmic solutions. Take the extracellular ion binding for example – in order for K⁺ to have an advantage at binding in the presence of a Na⁺ concentration that is N times higher ${\displaystyle (\frac{[{\mathrm{K}}^{+}{]}_{\mathrm{o}}}{[\mathrm{N}{\mathrm{a}}^{+}{]}_{\mathrm{o}}}=\frac{1}{N})}$, there needs to be at least N fold difference in K_D to guarantee a 1:1 ratio between [ENa] and [EK]:

If the pump were to only pick out K⁺ from the extracellular media, the K_D,K binding should be much smaller than K_D,Na. Experimentally measured K_D,K at the extracellular side is on the order of 1 mM in mammalian cell Na⁺/K⁺-pump in the presence of Na⁺, while that of K_D,Na is on the order of 100 mM (Nakao and Gadsby, 1989; De Weer et al. 2001). Given that the extracellular [Na⁺] is about 25 times that of [K⁺], for every 5 ion-loaded pumps, 1 would have the wrong configuration at the binding pocket. The “self-correcting” mechanism is a strategy evolved in the pump to cope with the problem that comes with the not-quite-specific external and cytoplasmic binding.

From an evolution point of view, it is not surprising that the outward and inward open states of the pump are less selective than the occluded states. When the pump is in an inward or outward open state, the binding pocket is more voluminous and hydrated than it is in the occluded state. Because of the spatial restriction in the occluded state-binding site, the bound ions would feel the impact from mutations more strongly than when they are bound in a larger pocket. During the evolution process, it would be easier to create a tightly packed, ion specific pocket than to make a large aqueous compartment selective towards ions of similar size and charge.

The Na⁺/K⁺-pump is not a fast molecular machine. The estimated turnover rate is less than 100 per second and decreases even further as the transmembrane voltage becomes more negative. This is perhaps because the pump spends time wait for the correct ion configuration to be achieved at the binding site, even though the idea of a self-correcting ion selectivity mechanism seems counterintuitive and it is more natural to think of a pump that follows a particularly efficient mechanism where it prevents the wrong ions from reaching the binding site under physiological conditions. The truth could be that the pump has not been evolutionarily optimized to be a fast machine, but an energetically efficient one.

We agree with the reviewers that other possible energy barriers encountered by the ions when they move in and out of the binding should be discussed. Although not shown in the manuscript, we observed ions, both K⁺ and Na⁺, can access the binding pocket within tens of ns in MD simulations of the pump in its inward and outward open states. As a result, this is not likely to contribute to the observed binding affinity difference substantially. This is added to the updated Discussion session:

“Other energetic barriers, like pathways the ions use to travel to the binding site, could contribute to the ion binding specificity, it is not likely the case here as both Na⁺ and K⁺ can access the binding pocket in the simulations of the E₁ and P-E₂ states without ions bound.”

6) In view of item 5, the authors should revise the title to reflect the fact that selectivity is presumably determined primarily by other mechanisms, and the suggested mechanism here is only a 'safe guard'.

As mentioned above, we do think that the “self-correcting” mechanism is an essential element of the primary mechanism the pump uses to transport ions. To highlight this point, we changed the title to “The selectivity of the Na+/K⁺-pump is controlled by binding site protonation and self-correcting occlusion”.

Author details

1. Huan Rui

   Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, United States

   Contribution

   HR, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0002-6459-9871

2. Pablo Artigas

   Department of Cell Physiology and Molecular Biophysics, Texas Tech University Health Sciences Center, Lubbock, United States

   Contribution

   PA, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

3. Benoît Roux

   Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, United States

   Contribution

   BR, Conception and design, Drafting or revising the article

   For correspondence

   roux@uchicago.edu

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0002-5254-2712

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Article citation count generated by polling the highest count across the following sources: Crossref, Scopus, PubMed Central.