Mechanism of pH-dependent activation of the sodium-proton antiporter NhaA

Escherichia coli NhaA is a prototype sodium-proton antiporter, which has been extensively characterized by X-ray crystallography, biochemical and biophysical experiments. However, the identities of proton carriers and details of pH-regulated mechanism remain controversial. Here we report constant pH molecular dynamics data, which reveal that NhaA activation involves a net charge switch of a pH sensor at the entrance of the cytoplasmic funnel and opening of a hydrophobic gate at the end of the funnel. The latter is triggered by charging of Asp164, the first proton carrier. The second proton carrier Lys300 forms a salt bridge with Asp163 in the inactive state, and releases a proton when a sodium ion binds Asp163. These data reconcile current models and illustrate the power of state-of-the-art molecular dynamics simulations in providing atomic details of proton-coupled transport across membrane which is challenging to elucidate by experimental techniques.

Distance from Lys300 (amine nitrogen) to Cys335 on TM XIc (backbone carbonyl oxygen) vs. the distance to Pro129 on TM IVp (backbone carbonyl oxygen) at different pH conditions. The condition of charged Lys300 is represented by pH 2, 4 and 8 corresponding to the conventional simulations S3, S1 and S2, respectively. The condition of neutralized Lys300 is represented by pH 11.5. The CpHMD simulation run 1 was used.    Histograms of the hydration number of deprotonated Asp163 when Lys300 is protonated (black) and deprotonated (magenta). The analysis is based on the CpHMD simulation run 1 using frames from the replicas at pH 5 and above. Data obtained from CpHMD simulation run 2 initiated from the previous crystal structure (PDB ID 1ZCD). The CpHMD simulations at pH 2.5, 4, 8, and 11.5 correspond to the conventional simulations S3, S1, S2 and S4 (see Table S1). S3: Asp163(0)/Asp164(0)/Lys300(+); S1: Asp163 ( Table S1). (b) Average Asp163-Lys300 distance from the conventional simulations. Error bars indicate one standard deviation of the data. (c) Distribution of the Asp163-Lys300 distance from CpHMD simulation run 1. Selected pH conditions roughly correspond to the conventional simulations S1-S4. (d) Average Asp163-Lys300 distance from CpHMD simulation run 1. Error bars indicate one standard deviation of the data. The Asp163-Lys300 distances in the two NhaA crystal structures with PDB ID 1ZCD and 4AU5 are 11.74 and 2.55Å, respectively.  ( a For simulation details see ref [2]. b These simulations were performed to verify if there is lipid dependence. It was found that sodium binding occurs in S2 and S4 but not in S1. Further, the binding sites are T132/D163/D164. Thus, the conclusions in the main text remain the same regardless whether POPC or a 4:1 POPE:POPG mixed membrane (which approximates the native E. coli inner membrane) is used, consistent with a recent review which found that, unlike ion channels, evidence of lipid dependence for transporters is scant [3].

Supplementary
Supplementary The model pK a values for Asp, Glu, His and Lys are 4.0, 4.4, 6.45 and 10.4, respectively [4]. The pK a of His225 could not be accurately calculated, as it extends into the bilayer and the membrane-GBSW model overestimates the desolvation free energy in such an environment, i.e. pK a of His225 is too low.

Supplementary Note 1 -Comparison to semi-macroscopic pK a calculations
Below we compare the calculated pK a 's of K300 and D163 in Ref. [5] and our results based on the same crystal structure (PDB ID 4AU5). In Ref. [5] the calculated pK a of K300 was 12.81, which is 2.81 units higher than our calculated value of 10.1 considering all configurations, with and without sodium binding to D163. However, if separating the sodium-bound and unbound configurations, the CpHMD predicted pK a 's are 8.9 and 11.6, respectively. The latter is higher than the model value of 10.4, in agreement with the value in Ref. [5](12.81). This is within expectation, since in the pK a calculation of Ref. [5], sodium binding was not taken into account (according to our reading of the paper). Now we compare the calculated pK a 's of D163. In Ref. [5], the calculation using implicit charge (assuming neutral background) gave 7.28 with D164(-) and 4.66 with D164(0); the calculation assuming D133(-1)/K300(+) gave 8.4 with D164(-) and 6.5 with D164(0). In our work, the calculated pK a of D163 was 2.4. This value is not affected by sodium binding, because the latter occurs at a much higher pH (above 6) than the titration range of D163. Since our calculated pK a 's of D133 and D164 were 4.5 and 5.0, both groups were neutral in the titration range of D163. Thus, our calculated pK a of D163 really corresponds to the result in Ref. [5] considering D164(0) and K300(+). Given that Ref. [5] gave 4.66 for the pK a of D163 with D164(0)/K300(0), we anticipate the pK a of D163 with D164(0)/K300(+) to shift lower (due to electrostatic attraction of K300), bringing it closer to our value of 2.4. Thus, we think the microscopic pK a 's of K300 and D163 obtained by us and in Ref. [5] are in qualitative agreement.

Supplementary Note 2 -Agreement between CpHMD, conventional fixed-protonation-state simulations and new crystal structure
A major limitation of the current CpHMD implementation is the relatively short time scale (about ten nanoseconds per pH replica), which may result in the incomplete sampling of conformational states of protein and solvent despite the use of the pH replica-exchange enhanced sampling protocol. The conventional fixed-protonation-state simulations discussed here, on the other hand, were repeated for different combinations of protonation states up to three times for the total sampling time between 1 µs and 3 µs (Supplementary Table 1), thus providing perhaps more complete conformational sampling. In order to establish the degree of convergence of the CpHMD simulations we compare key quantities with the conventional simulations. The hydration levels for Asp133, Asp163, and Asp164 in each conventional simulation match the hydration levels in the CpHMD simulations at the corresponding pH conditions. Specifically, the conventional simulations with Asp163/Asp164/Lys300 protonated (named S3) correspond to about pH 2; the simulations with Asp163 deprotonated and Asp164/Lys300 protonated (S1) to pH 4; Asp163/Asp164 deprotonated and Lys300 protonated (S2) to pH 8; and Asp163/Asp164/Lys300 deprotonated (S4) to pH 11.5 ( Supplementary Fig. 15). The correspondence over the whole pH range is remarkable, because the two sets of simulations used different force fields and water models (CHARMM with TIP3P for CpHMD, OPLS-AA with TIP4P for the conventional MD). Thus, hydration levels appear to be converged in the CpHMD simulations and can serve as a robust quantity to compare the two simulation approaches with each other and to assign an effective pH to the conventional simulations.
The probability of sodium binding to Asp163, Asp164 and Thr132 is also similar when comparing conventional MD data ( Supplementary Fig. 16) with the corresponding pH windows in CpHMD (Fig. 5 in main text). The CpHMD simulations are clearly capable of capturing this key event in the proposed model. The opening of the cytoplasmic hydrophobic gate across the pH range ( Fig. 4 in main text) is also qualitatively recapitulated in the conventional MD ( Supplementary Fig. 17), with the long simulations showing larger openings than the shorter CpHMD. It is possible that longer time-scale rearrangements in the gate region are not fully captured in the CpHMD simulations but the gate is already seen to open sufficiently to provide water molecules and sodium ions full access to the binding site.
The Asp163-Lys300 salt bridge shows very similar behavior in the conventional MD and CpHMD simulations ( Supplementary Fig. 18). At high pH (>8) the salt bridge is predominantly broken because a sodium ion can bind to Asp163 and compete with the salt bridge and thus further stabilize the deprotonated (neutral) charge state of Lys300. At very low pH (<3), the salt bridge is also weakened and often found dissociated because Asp163 is protonated and therefore the electrostatic interaction to Lys300 is weakened. In the intermediate pH range, both Asp163 and Lys300 are charged and the strong Coulomb interaction favors the salt bridge with a well-defined distance of about 2.8Å. The new NhaA crystal structure was solved at pH 3.5 [2] and contains the salt bridge, as also seen in the S1 and S2 simulations. The CpHMD simulations now clearly explain this observation as a consequence of the very low pK a of Asp163. The consistency between low-pH crystal structure and both sets of simulations also corroborates the hypothesis that Asp163 is not one of the proton carriers because it remains charged at all physiologically accessible pH conditions.