Toward a Multipathway Perspective: pH-Dependent Kinetic Selection of Competing Pathways and the Role of the Internal Glutamate in Cl⁻/H⁺ Antiporters

Abstract

Canonical descriptions of multistep biomolecular transformations generally follow a single-pathway viewpoint, with a series of transitions through intermediates converting reactants to products or repeating a conformational cycle. However, mounting evidence suggests that more complexity and pathway heterogeneity are mechanistically relevant due to the statistical distribution of multiple interconnected rate processes. Making sense of such pathway complexity remains a significant challenge. To better understand the role and relevance of pathway heterogeneity, we herein probe the chemical reaction network of a Cl⁻/H⁺ antiporter, ClC-ec1, and analyze reaction pathways using multiscale kinetic modeling (MKM). This approach allows us to describe the nature of the competing pathways and how they change as a function of pH. We reveal that although pH-dependent Cl⁻/H⁺ transport rates are largely regulated by the charge state of amino acid E148, the charge state of E203 determines relative contributions from coexisting pathways and can shift the flux pH-dependence. The selection of pathways via E203 explains how ionizable mutations (D/H/K/R) would impact the ClC-ec1 bioactivity from a kinetic perspective and lends further support to the indispensability of an internal glutamate in ClC antiporters. Our results demonstrate how quantifying the kinetic selection of competing pathways under varying conditions leads to a deeper understanding of the Cl⁻/H⁺ exchange mechanism and can suggest new approaches for mechanistic control.

Graphical Abstract

1. INTRODUCTION

With the goal of understanding and ultimately influencing biomolecular transformations, there is an increasing need to move past the single-pathway perspective, to understand the role of stochasticity and the relevance of kinetic selection of multiple competing mechanistic pathways. Herein, we investigate how the flux through a reaction network varies with reaction conditions in an example system from the Chloride Channel (ClC) family of proteins, which are found in all branches of life and involved in diverse physiological functions (e.g., ion homeostasis, electrical excitation, transepithelial transport, and endocytosis).^1–2 Mutations in human ClC genes can cause pathologies, including osteopetrosis, kidney dysfunction, blindness, deafness, and neurodegeneration.^2–3

One unique feature of ClC proteins is that they can function as either Cl⁻ channels, which transport Cl⁻ across membranes down their concentration gradient, or secondary active Cl⁻/H⁺ antiporters, which couple the transport of H⁺ and Cl⁻ ions in opposite directions.⁴ Many have sought to understand the molecular mechanisms that enable nearly identical structures to carry out such different processes. We focus on a prototypical ClC antiporter, ClC-ec1 from Escherichia coli. A homodimer in vivo, though able to act as a monomer (when mutagenized) in vitro,⁵ ClC-ec1 exchanges ions in either direction^6–7 with a constant Cl⁻:H⁺ exchange ratio (2.2:1) over a wide range of pH and Cl⁻ gradients.^6,8–10 Three Cl⁻ binding sites have been identified from crystal structures (S_int, S_cen and S_out from the intra- to extracellular sides, Figure 1A).^11–12 E148 and E203, residing near the extra- and intracellular sides, respectively, were identified by mutagenesis to be involved in H⁺ transport.^{6–7,12–14} The replacement of E148 (e.g., E148A) can decouple Cl⁻/H⁺ transport by blocking H⁺ flux and making Cl⁻ flux pH-independent.¹⁵ Interestingly, E148A can regain H⁺ transfer activity if exogenous glutamate is present.¹⁶ These findings led to a prediction that was later demonstrated in simulations: that H⁺ transport requires E148 but is also facilitated by Cl⁻ in S_cen to overcome the barrier of up-rotation for H⁺ release.¹⁷

Figure 1. ClC-ec1 and multiscale kinetic modeling (MKM) representation.

(A) ClC-ec1 structure (PDB ID: 1OTS) showing two monomers (ribbon representation), essential residues E148 and E203 (sticks), crystallographic Cl⁻ ions (green spheres), and outer Cl⁻ binding site, S_out, which is not occupied in 1OTS (dashed circles). Ion pathways are indicated by dashed arrows (dark green for Cl⁻, red for H⁺). Only the biological orientation is depicted (E148 on the extracellular side, E203 on the intracellular side). (B) Six descriptors used by MKM to model Cl⁻/H⁺ exchange: Cl⁻ binding to S_int, S_cen, or S_out; charge states of E148 and E203; and side-chain orientation (“up” or “down”) of E148. Each descriptor can be “0” (Cl⁻ absent, Glu deprotonated, E148 down) or “1” (Cl⁻ present, Glu protonated, E148 up). Every system state can thus be described by a unique six-digit binary number. For example, state 100011 has a deprotonated up E148, a deprotonated E203, and two Cl⁻ ions bound to S_cen and S_int. (C) Schematic of a H⁺ influx pathway comprised of five system states. Each state is indexed by a unique decimal number (e.g., 35) converted from the corresponding binary number (e.g., 100011). Note that the pathway has no net Cl⁻ transfer.

Similar to most biomolecular transformations, the proposed ClC antiporter mechanisms to date have one pathway connected by serial transitions between intermediates, i.e., they follow the single-pathway model. While all models explain an approximate 2:1 stoichiometry and coupled ion exchange, they generally differ in the existence of a lower gate, the key intermediates involved, and the sequence of events.^{10,14,16,18–23} However, emerging evidence suggests that there exist multiple pathways in membrane channels/transporters and the choice of a specific pathway is stochastic.^24–25 For example, kinetic modeling using Metropolis Markov chain Monte Carlo was applied to a bacterial Na⁺/glucose symporter, revealing that slippage may be essential for substrate selectivity.^26–27 Similarly, kinetic modeling of the H⁺-coupled multidrug transporter EmrE revealed that perfect coupling requires the delicate tuning of various transporter models (i.e., antiporter, symporter, and uniporter), again underlining the importance of kinetic control in molecular processes.²⁸ Aligned with these studies, the nonintegral stoichiometry (2.2:1) in ClC transporters is indicative that multiple pathways must contribute to the ion exchange flux.

Multiscale simulations have been used to study Cl⁻/H⁺ exchange in ClC-ec1 by calculating barriers for each of the relevant elementary steps with free energy calculations.^17,29–35 While these results alone could not provide a complete mechanistic explanation, they did pave the way for studying the underlying chemical reaction network with kinetic modeling. Based on the rate coefficients (k’s) derived from these free energy simulations, Mayes et al. applied a novel multiscale kinetic modeling (MKM) approach based on Markov models to refine the calculated rate coefficients based on macroscopic restraints (experimental Cl⁻ transport rates and Cl⁻:H⁺ exchange ratios)^13,36 to generate physically meaningful solutions.³³ They found that the macroscopic observables indeed arise from an ensemble of microscopic pathways, lending support to the multiple-pathway model. The results explained how E148 couples ion exchange through protonation-dependent blockage of Cl⁻ transport and anion-dependent release of H⁺, as well as how kinetic selection of multiple pathways results in the nonintegral 2.2:1 Cl⁻:H⁺ exchange stoichiometry.

Despite these advances, it remains unclear how the flux through heterogeneous pathways shifts under different reaction conditions to collectively to yield the macroscopic pH-dependent ion exchange in ClC-ec1. The flux in the previous study was only examined at pH 4.5. It is also unclear which if any of the 10 proposed MKM solutions³³ is correct, which is consistent with a common challenge in kinetic modeling of narrowing the solution space given the large number of variable parameters (k’s) and a small number of known macroscopic observables. Herein, we further probe the mechanistic description via pH-dependent pathway analysis of the proposed kinetic solutions. Our aims are 4-fold: (1) to examine the pathway heterogeneity in wild-type (WT) ClC-ec1; (2) to investigate how microscopic pathway fluxes change with external conditions like pH; (3) to identify testable predictions that can help narrow the mechanistic solution space, and (4) to examine how ionization of E203 redistributes ion flux among pathways and shifts the net flux. We find that while the overall pH-dependent Cl⁻/H⁺ transport is mostly regulated by the charge state of the upper glutamic acid, E148, the relative contribution of microscopic pathways at different pH values is determined by the charge state of the lower glutamic acid, E203. Thus, dominant mechanistic pathways change as a function of pH and the net flux pH-dependence can be altered by increasing the pK_a of E203. This redistribution of H⁺ pathways upon E203 ionization is particularly interesting in the context of E203 (D/H/K/R) mutants, which retain activity and have been interpreted as obviating the role of E203 in H⁺ transport.¹³ Our results provide a kinetic explanation for how a range of residue pK_a values at the internal glutamate site retain coupling while still playing a crucial role in H⁺ transport in ClC antiporters.

2. METHODS

The current study specifically focuses on the mechanistic characterization of how a reaction network responds to external pH change based on the existing MKM solutions.³³ No new solution was generated. We give a brief overview of the MKM methodology by introducing key principles and explaining how the solutions were determined below. A more in-depth discussion can be found in Mayes et al.³³

2.1. MKM methodology.

Based on the idea that biomolecular processes rely on the kinetic selection of many microscopic stochastic steps collectively contributing to macroscopic observables,³⁷ MKM models a reaction network comprised of all possible system intermediates (or metastable states) connected by physically meaningful transitions.³³ To represent the major metastable states of ClC-ec1, previous computational studies^{17,31,33,38–41} have suggested that at least six system descriptors should be included: Cl⁻ occupancy at three binding sites (S_int, S_cen, and S_out), the protonation state of two residues (E148 and E203), and the orientation of the E148 side chain (“up” or “down”) (Figure 1B, left). Two options are allowed for each descriptor: 0 for S_int/S_cen/S_out unoccupied, E148/E203 deprotonated, and E148 in the down orientation; versus 1 for S_int/S_cen/S_out occupied, E148/E203 protonated, and E148 in the up orientation. As such, every system state is uniquely assigned a six-digit binary number (Figure 1B, right). Sixty-four (2⁶) possible system states yield a 64 ´ 64 (4096) transition matrix A, where each matrix element k_ij represents the rate coefficient of transition from state i to j. After removing unphysical transitions (e.g., direct Cl⁻ shuttling between S_int and S_out without transiting S_cen, H⁺ binding to S_int/S_cen/S_out), 68 allowed transitions remain in the transition matrix and define a reaction network consisting of many permissible permeation pathways (series of transitions through intermediates). The eigenvector and eigenvalues of A computed by matrix diagonalization determine the steady-state populations of all system states. With the knowledge of transition rate coefficients (k’s) and the bulk Cl⁻ and/or H⁺ concentrations, Cl⁻ and H⁺ transport rates (population-based rates) can be computed, which in turn give Cl⁻:H⁺ exchange ratio. The net number of Cl⁻ or H⁺ transferred (or flux, J) through any pathway (e.g., Figure 1C) can also be computed in the same fashion. Summing up the J’s from all possible pathways should give Cl⁻ or H⁺ transport rate (pathway-based rate) equal to the population-based rate. The foundation of the kinetic analysis of multistate systems can be found in refs 42–43. Starting from the rate coefficients derived from free energy calculations,^17,31,33 a particle swarm optimization^44–47 was used to refine the rate coefficients under restraints of experimentally measured macroscopic properties, (specifically the Cl⁻:H⁺ exchange ratio (2.2:1) and Cl⁻ transport rates at pH 4.5, 6.0, and 7.5).^13,36 In all MKM optimizations, there was no pH gradient, while the extra- and intracellular Cl⁻ concentrations were 300 and 1 mM, respectively. Since the antiporter cannot be oriented in in vitro assays, both the biological orientation (E148 and E203 face extra- and intracellular side, respectively, Figure 1A) and opposite orientation (E203 and E148 face extra- and intracellular side, respectively) are expected to contribute approximately equivalently. For each MKM optimization, a rate coefficient (k) was first randomly chosen from A and perturbed by a random amount within the allowed adjustment range. The Cl⁻:H⁺ exchange ratio and the Cl⁻ transport rates at pH 4.5, 6.0 and 7.5, were then computed and compared with the experimental values. The difference was scored to determine if current perturbation, i.e., the change made to the k, should be accepted using a Monte Carlo criterion.⁴⁸ The same procedure was repeated until the calculated macroscopic properties agreed with the experimental values (within the permitted uncertainty). The final “solutions” including optimized k’s can then be used to predict macroscopic properties such as the pH-dependent ion fluxes and the pK_a of E148. MKM program (version 0.11.1) was written in Python⁴⁹ 2.7 and requires libraries NumPy⁵⁰ (version 1.16.5) and DEAP⁵¹ (version 1.3.0). For more details of MKM theory and methodology, refer to ref 33.

Note that the kinetic solutions employed in this study³³ modeled the WT ClC-ec1 reaction network according to the experimental Cl⁻ transfer rate determined by Picollo et al.³⁶ These rates were measured using a ³⁶Cl⁻ uptake assay, which quantifies the electroneutral ³⁶Cl⁻/³⁵Cl⁻ exchange rate in the absence of pH gradient.^15,52–55 Referencing full turnover rates¹³ from a Cl⁻ efflux assay^56–58 was also tested, but not chosen due to a poor fit³³ and concern over ion leakage through liposomes above pH 5.5.³⁶ Future work will include calibration of the WT ClC-ec1 MKM model factoring in differences between these two experimental approaches.^13,36

2.2. Pathway Analysis.

Based on the 10 solution sets optimized by Mayes et al.,³³ we performed pathway analysis in three steps. First, we set up a pathway space by searching for pathways with a net ion transfer across the membrane at pH values ranging from 4.0 to 7.5 in 0.5 increments for each solution. During the search, no restriction on pathway length or complexity was applied and a plethora of permissible pathways of various lengths can be generated. Consistent with the previous pathway analysis at pH 4.5,³³ dominant pathways were identified by starting with ion release and tracing back through transitions with the largest flux. Once net ion transport was encountered, the flux through that pathway was assigned, and a subsequent search started. As new pathways were identified, the flux contributing to any previously identified pathway involving a common transition was subtracted to obtain the correct net flux. As the search continues and longer pathways are encountered, the contributing flux, J, decreases due to the inclusion of more slow transitions. The resulting pathway space complexity also grows. We, thus, limited the pathway space to include only “significant” pathways with a minimum J of 0.10 ions/ms and a maximum of up to 12 transitions. This approximated population-based net flux values calculated from steady-state populations to within 10%. Note the flow decomposition algorithm employed here does not necessarily model the expected cyclic flow decomposition, but for a given reaction network, it will always generate the same unique decomposition upon repeated application. Future efforts will explore the use of more rigorous cyclic flow decomposition which does not rely on the order in which pathways are encountered.⁵⁹ Other MKM settings followed the optimization procedure (e.g., no pH gradient, 300 mM extracellular, and 1 mM intracellular Cl⁻ concentration).³³ Then, we categorized the pathway space based on the dependence of pathway J on pH. Three patterns were found: single (one dominant pathway, e.g., Figure 3A,B), parallel (multiple pathways with the same pH-dependence in fluxes, e.g., Figure 3C,D), and competitive (multiple pathways with different pH-dependence in fluxes, e.g., Figure 3E,F). Finally, we compared these patterns by investigating features such as the rate-limiting step (RLS), the charge states of E148 and E203. Consequently, we were able to identify the microscopic determinants of pathway parallelization/competition and understand how they collectively generate the macroscopic pH-dependence in Cl⁻/H⁺ transfer. As both biological and opposite orientations contribute, ion transport in both directions was investigated separately.

Figure 3. Pathway heterogeneity for H⁺ transport in biological orientation.

Schematic representation and associated pH-dependent fluxes of single (AB), parallel (CD) and competing (EF) H⁺ transport pathways. The images and numbers display the ClC-ec1 states. The width of an arrow represents the transition rate with the RLS highlighted by an asterisk. Lines associated with fluxes are the best fit to eq 1 or a bell-shaped distribution. Note that there is no net Cl⁻ flux along H⁺ transfer pathways and although each transition is reversible only the flux-relevant directions are shown.

2.3. Macroscopic pK_a.

The pH-dependence of the Cl⁻ or H⁺ rate (or flux, ions/ms) J through ClC-ec1 can be described by a logistic function³⁶

$$J=\frac{A}{1+\frac{K_{\text{a}}}{\left[{\text{H}}^{+}\right]}}$$ (1)

where A is the maximal rate, K_a is the macroscopic H⁺ binding constant, and [H⁺] is the proton concentration.

2.4. Microscopic pK_a.

The pK_a’s for E148 and E203 were computed by fitting the pH-dependent unprotonated fraction (S^unprot) to the Hill equation⁶⁰

$$S^{\text{unprot }}=\frac{\sum p_{\text{deprot }}}{\sum p_{\text{deprot }}+\sum p_{\text{prot }}}=\frac{1}{1+{10}^{n\left(\text{p}{K}_{\text{a}}-\text{pH}\right)}}$$ (2)

where p_deprot and p_prot are steady-state populations for deprotonated and protonated states, respectively, and n is the Hill coefficient representing the slope of the transition region in the titration curve. p_deprot and p_prot were calculated with the MKM program (see section 2.1) by summing the population of all states with the relevant protonation state (e.g., $\sum p_{\text{deprot }}^{\text{E}148}$ for E148 deprotonated) regardless of the status of the other five state descriptors. Multiple S^unprot values were computed versus pH and fit to eq 2 to obtain a microscopic pK_a. Note that the term “microscopic” is used to describe the pK_a of a specific residue, while the “macroscopic” pK_a described above reflects the pH-dependence of ion exchange in ClC-ec1. Since the pH-dependent Cl⁻ flux is strongly coupled to the protonation of E148,¹⁷ the macroscopic pK_a should largely reflect the microscopic pK_a of E148 (Table S1). Microscopic pK_a of 203 impacts its ability of passing the H⁺ to E148, directly affecting the net H⁺ flux. E203 pK_a was used to understand the differences among the solution sets displaying competitive pathways (see Section 3.1).

2.5. Guidance on How to Read Pathway Diagrams.

All significant pathways (J ≥ 0.10 ions/ms) of a solution set are plotted in the corresponding pathway diagram. Each pathway diagram has a series of cartoon representations of ClC-ec1 intermediates (states) connected by arrows representing transitions. The depictions include:

1. ClC-ec1 represented by two empty rectangular boxes .

2. Cl⁻ represented by a closed dark green circle .

3. H⁺ indicated by different charge states of E148 and E203 .

4. E148 and E203 represented by sticks mimicking side chains with carboxylate oxygen and hydrogen atoms annotated. Black Glu is deprotonated. Orange Glu is protonated and thus has an “H” attached. Note the Glu up and down rotamers are always E148.

5. The orientation of ClC-ec1 has either the extracellular side on top and intracellular side on bottom (biological, e.g., Figures 1A and 2A) or vice versa (opposite).

6. Three dotted circles represent three Cl⁻ binding sites, either occupied by a Cl⁻ () or empty (). In biological orientation, the three circles sequentially stand for S_out, S_cen, and S_int from top to bottom (Figure 1A,B).

Figure 2. Illustration of a pathway diagram and the associated pH-dependent flux profiles.

(A) Cl⁻/H⁺ pathways from the MKM solution set #1 in biological orientation reported in ref 33. H⁺ pathway (left) is indicated by orange arrows while two Cl⁻ pathways (right) are indicated by dark green and blue arrow, respectively. The width of an arrow represents the transition rate with the RLS highlighted by an asterisk. Latin numerals mark the transitions along the H⁺ pathway. (B) pH-dependent fluxes for H⁺ pathway. (C) pH-dependent fluxes for Cl⁻ pathways. The associated lines are the best fit to either eq 1 or bell-shaped distribution. The colors of the flux profiles are consistent with the representing pathway arrows. Note that the H⁺ transfer pathway has no net Cl⁻ flux and vice versa.

Taking Figure 2 as an example, we explain how to read pathway diagrams and the associated flux plots. Figure 2 plots the pathways generated by MKM solution set #1 in biological orientation (E148 and E203 face extra- and intracellular side, respectively). Three “cycles” represent three ion transport pathways (orange for H⁺ transport from inside to outside; blue and green for Cl⁻ transport from outside to inside). The H⁺ pathway consisting of seven system states connected by seven transitions includes:

• step I: state 00 (E148: down, deprotonated; E203: deprotonated; no Cl⁻ bound) binds a Cl⁻ to S_out and generates state 04 (E148: down, deprotonated; E203: deprotonated; Cl⁻ binds S_out);

• step II: state 04 binds a H⁺ to E203 and generates state 12 (E148: down, deprotonated; E203: protonated; Cl⁻ binds S_out);

• step III: state 12 releases its H⁺ from E230 to E148 and generates state 20 (E148: down, protonated; E203: deprotonated; Cl⁻ binds S_out);

• step IV: state 20 releases the S_out Cl⁻ to extracellular bulk and generates state 16 (E148: down, protonated; E203: deprotonated; no Cl⁻ bound);

• step V: state 16 rotates the protonated E148 side chain up and generates state 48 (E148: up, protonated; E203: deprotonated; no Cl⁻ bound);

• step VI: state 48 releases the H⁺ from E148 into extracellular bulk and generates state 32 (E148: up, deprotonated; E203: deprotonated; no Cl⁻ bound); and

• step VII: state 32 rotates the deprotonated E148 side chain down and returns to state 00.

The whole cycle net transfers one H⁺ upward from intra- to extracellular bulk and has not Cl⁻ net transfer. Additional features of the pathway diagrams include: (1) the width of an arrow represents the flux of transition, (2) the RLS is highlighted by an asterisk (e.g., for the H⁺ pathway, E203 releasing its H⁺ to E148 (12 ➔ 20) is the RLS), (3) although simultaneous Cl⁻ and H⁺ transport is accessible via combinations of pathways (e.g. 20 ➔ 50 ➔ 17 ➔ 16 ➔ 48 ➔ 32 ➔ 00 ➔ 04 ➔ 12 ➔ 20 combining orange and green), we focus on “pure” pathways to avoid redundancy, and (4) although each transition is reversible, only the flux-relevant directions are shown in pathway diagrams (thus single rather than double arrows are displayed).

After identifying dominant pathways (Figure 2A), the flux through each individual pathway is computed and plotted as a function of pH for H⁺ (Figure 2B) and Cl⁻ (Figure 2C), respectively. Note that flux profiles use the same color code as the representing pathway. Flux through the sole H⁺ pathway displays a sigmoidal, specifically logistic, behavior (eq 1), i.e., H⁺ flux increases as pH decreases then plateaus at pH 4.5 and below. The two Cl⁻ pathways differ a lot in the pH-regulated fluxes. As pH decreases, flux through pathway I (dark green curve) shows a bell-shaped behavior and maximizes at pH 5. In contrast, flux through pathway II (blue curve) monotonically increases within the pH range investigated. However, the sum of the two pathway fluxes (black curve) is mostly logistic pH-dependence.

3. RESULTS AND DISCUSSION

3.1. Pathway Heterogeneity in H⁺ Transport in Biological Orientation.

We first discuss H⁺ pathways in the biological orientation (where E148 and E203 face the extra- and intracellular space, respectively), which demonstrate the most variation. Three patterns are apparent. In pattern 1, there is a single dominant H⁺ pathway, and the pH-dependent H⁺ rate can be described by a logistic, pK_a-dependent equation (eq 1) in which the flux saturates at low pH.³⁶ One such solution (#2) is shown in Figure 3A,B (see also solutions 1, 7, and 9 in the Supporting Information; Figures S1, S13, and S17). In contrast, patterns 2 and 3 have multiple H⁺ pathways. Pattern 2 harbors two coexisting pathways running in parallel (i.e., both with logistic pH-dependence), as found in solution #6 (Figures 3C,D and S11). By contrast, the coexisting pathways in pattern 3 are competitive with relative weights (or fluxes) changing with pH; one pathway (II) remains logistic, while the other (I) displays a bell-shaped pH-dependence in which H⁺ flux decreases with decreasing pH (solution #8, Figures 3E,F and S15). A notable difference in pathways I and II is that E203 is protonated while E148 is releasing its H⁺ to bulk in the logistic pathway II, but deprotonated in the bell-shaped pathway I.

Solutions 3, 5, 8, and 10 also fit this pattern (Figures S5, S9, S15, and S19). For each solution, E203 is deprotonated during H⁺ release to external bulk in the bell-shaped pathway(s), but protonated in the logistic pathway(s). The sum of H⁺ fluxes through the two pathways in solution 8 approximates that of a single logistic pathway in pattern 1, but this does not always have to be the case. As shown in solution 10 (Figure S19), the cumulative flux can shift to a bell-shaped pH-dependence. Further inspection of the net flux from all pathways revealed that the origin of net bell-shaped behavior is increased backflow at low pH values (Figure S21); as pH decreases, the H⁺ uptake rates to both E203 (Figure S21C,F, red lines) and E148 (Figure S21A,D, blue lines) increase, while the release rate from E148 to bulk plateaus (Figure S21A,D, red lines), meaning the population of protonated E148 must also plateau. Since uptake and release to and from E203 (Figure S21C,F) are significantly faster, the rate of H⁺ transfer from E148 to E203 to internal bulk increases (Figure S21B,C,E,F, blue lines), compensating for the increased protonation of E148 from external bulk. Concurrently, the population of deprotonated E203 decreases and the associated flux through any pathway involving deprotonated E203 during H⁺ release from E148 decreases. This flux shifts to logistic pathways in which E203 is protonated.

The solutions fitting pattern 3 (3, 5, 8, and 10) differ in the pH where the logistic pathway becomes dominant (i.e., the pH where logistic and bell-shaped flux curves cross-over), suggesting that the prevalence of deprotonated E203 is different. For example, the logistic pathways in solutions 10 and 8 become dominant when pH goes below around 5.5 (Figure S19) and 4.2 (Figure S15), respectively. To verify this, we calculated E203 pK_a from the steady-state populations (eq 2) and obtained pK_a values of 3.8, 4.5, 4.8, and 5.5 for solutions 8, 3, 5, and 10, respectively (Table S1), which are indeed consistent with the order of “cross-over” pH values (Figure S22). Interestingly, only solution 10, with the largest pK_a, shows a cumulative flux that is bell-shaped. As discussed above, this is consistent with the flux requirements for decreasing outward net flux with decreasing pH; as pH decreases and the H⁺ uptake rate from outside bulk to E148 increases, the reverse flow (E148 to internal bulk) must increase in order for the population of protonated E148, and thus the release rate from E148 to outside bulk, to decrease relative to higher pH values. The concurrent increased population of protonated E203 is consistent with the observed higher pK_a value of solution 10. Similarly, the increased pK_a value of E203 brings its relative free energy down, closer to that of E148 (pK_a ~ 6.2), consistent with the increased reverse flow. This in turn suggests that while all mutants that alter the pK_a of E203 will shift the distribution between pathways, those that increase it significantly could also shift the cumulative flux to a bell-shaped pH-dependence. Although multiple E203 mutants have been reported, the pH-dependence of their rates have not. Moreover, mutations in this region are complicated by the nearby E113 residue, which is coupled to the protonation of E203 via a competitive salt bridge with R28 from twin monomer and likely takes over in delivering a proton when residue 203 is not able to.

3.2. Pathway Heterogeneity in Cl⁻ Transport in Biological Orientation.

Cl⁻ pathways in biological orientation also have significantly more variation than those in the opposite orientation. As previously discussed, the RLS for Cl⁻ transfer is consistently movement past E148 and only happens when E148 is protonated. We found multiple Cl⁻ pathways in all solutions (see the Supporting Information). With the exception of solutions 6 and 7, all solutions involved a logistic pathway in which E203 is protonated during the rate-limiting Cl⁻ transfer from S_out to S_cen, and a bell-shaped pathway in which E203 is deprotonated. Consistent with the findings for H⁺ transport discussed above, the prevalence of deprotonated E203 decreases with decreasing pH and thus the flux through pathways involving deprotonated E203 decreases. The relative contribution of the logistic and bell-shaped pathways also reflects the pK_a of E203 (Table S1). As the pK_a of E203 increases, the prevalence of deprotonated E203 decreases and thus the contribution from bell-shaped pathway decreases. This is shown in Figure 4; the bell-shaped pathway dominates at low pH in solution #1 with a E203 pK_a of 3.6 (Figure 4B) but becomes minor in solution #9 with a E203 pK_a of 4.1 (Figure 4C). The Cl⁻ flux patterns in solutions #6 (Figure S11) and #7 (Figure S13) only involve pathways with E203 deprotonated, such that E203 stays charged in both the major and minor pathways. Although they show logistic pH-dependence for Cl⁻ flux above pH 4, bell-shaped dependence becomes apparent below pH 4. Correspondingly, the pK_a calculation for E203 from steady-state populations shows a very low pK_a (2.9 and 2.1 for solutions 6 and 7, respectively, Table S1).

Figure 4. Pathway heterogeneity in Cl⁻ transport in biological orientation.

(A) Schematic representation of major (I) and minor (II) Cl⁻ microscopic pathways. The images and numbers display the ClC-ec1 states. The width of an arrow represents the transition rate with the RLS highlighted by an asterisk. pH-dependent Cl⁻ fluxes through competitive pathways with a low (B) and high (C) E203 pK_a. Lines associated with fluxes are the best fit to eq 1 or a bell-shaped distribution. Note that there is no net H⁺ flux along Cl⁻ transfer pathways, and although each transition is reversible, only the flux-relevant directions are shown.

3.3. Cl⁻/H⁺ Pathways in Opposite Orientation.

There is considerably less pathway heterogeneity for ion flow in the opposite orientation (wherein E203 and E148 face extra- and intracellular side, respectively) relative to biological orientation (see the Supporting Information). The RLS in Cl⁻ pathways is consistently the Cl⁻ transfer from S_cen to S_out concurrent with down-rotation of a neutral E148. Although the RLS in H⁺ pathways has some variation, it is most often H⁺ transfer from E148 to E203 in the presence of Cl⁻ at S_cen, consistent with previous simulations.³¹ When multiple pathways coexist for Cl⁻ or H⁺ transfer, they differ in the Cl⁻ occupancy of S_int. In contrast to biological orientation, only parallel pathways were found in which the fluxes through each pathway as well as their sum show logistic behavior. Given that H⁺ uptake is through E148 in the opposite orientation and the barrier for E148 rotation is considerable,¹⁷ it is not surprising that the associated fluxes are logistic. Since the RLS for H⁺ flow in the opposite orientation is transferred from E148 to E203, the charge state of E203 is less influential on the population of protonated E148 or associated flux, explaining the absence of competing pathways. This also helps reduce the pathway complexity in the opposite orientation. Although not always appreciated, it is clear that the mechanism of ion exchange is significantly different in the two orientations.

3.4. E203 Mutations.

Although E203 is not strictly conserved like E148 in ClCs,^11,61 proper function of ClC-ec1 requires at least a protonatable residue near this position.^7,36 Mutation to nonprotonatable residues, such as valine (a common equivalence across the ClC family), can collapse H⁺ transfer and/or decouple Cl⁻/H⁺ exchange.¹³ However, replacement with D/H/K/R retained Cl⁻/H⁺ exchange activity,¹³ albeit to different degrees. While mutants E203D and E203H behave approximately like WT, mutations E203K and E203R significantly reduce H⁺ flux and the ClC-ec1 turnover rate.¹³ Given their intrinsic H⁺ affinities, the pK_a’s of E203, D203, and H203 could be perturbed to similar values in ClC-ec1 such that all are capable of shuttling H⁺ in a similar fashion. In contrast, K203 or R203 will have high barriers for H⁺ release to E148 given their higher intrinsic H⁺ affinity, as demonstrated by Lee et al.³¹

Our predicted E203 pK_a-regulated pathway patterns are consistent with those experimentally observed impact of E203 mutations on H⁺ flux and ClC-ec1 activity. As displayed in Figure S22, higher E203 pK_a suppresses the H⁺ flux through bell-shaped pathways in the biological orientation from pH 4 to 5, where those E203 mutants were studied.¹³ If the H⁺ flux through the corresponding logistic pathway with a deprotonated 203 is negligible, which is likely the case in mutants E203K and E203R, the expected observation would be significantly reduced H⁺ flux and ClC-ec1 activity (as long as the coupling via E148 is not severely affected). In contrast, mutants E203D and E203H should enable abundant flux through the logistic pathways, leaving the H⁺ flux and ClC-ec1 activity only marginally affected. Thus, we do not expect significant changes in the H⁺ transfer mechanism or pathway behaviors in mutants E203D and E203H. However, detailed studies of any of the D203/H203/K203/R203 mutants will require recalculation of free energy profiles, which may be the focus of future work. E203K and E203R, in particular, may require more computational work. In WT ClC-ec1, E203 is surrounded by several ionizable residues: E113, E202, and R28´ (from the twin monomer). Previous computational studies have demonstrated that E113 has an impact on the charge state of E203.^36,62 One study suggested that E113 and E203 are in close contact to share a proton, i.e., one is proton donor, the other is nucleophile,⁶³ while our work indicated a small H⁺ transfer free energy barrier between the two.³¹ Both residues are within ion-pairing distance of R28´. Though it is not clear if there exists any crucial interaction between E203 and conserved E202, E202 has been suggested to help create a water path connecting E203 and intracellular bulk.⁶⁴ Thus, replacing E203 by a basic residue (e.g., K or R) may substantially alter local electrostatics and the H⁺ shuttling mechanism. Consequently, the reaction network for these mutants may need to be redefined for further kinetic modeling.

3.5. Conformational Changes.

The role of conformational changes has long been debated in ClC exchangers. On one side, little difference in the backbone conformation of ClC structures⁶⁵ has supported the notion that only local rotameric movements of a single Glu side chain (E148 in ClC-ec1) is required for ion exchange coupling.^7,12,14,36 On the other, comparison to other antiporters suggested conformational changes should be essential.^20,23 Recently, Maduke and co-workers reported considerable backbone rearrangement at physiologically relevant low pH values,^20,23 and the crystal structure of mutant QQQ (E113Q/E148Q/E203Q; PDB ID: 6V2J) with a substantially altered backbone conformation. Although the authors argued that these findings support a conformational change-induced transporter mechanism,²³ our previous simulations found no support for a substantial conformational change.³³ Their work additionally included MD simulations of the QQQ mutant and reported a continuous water path connecting E148 with intracellular bulk, calling into question the role of E203 in direct H⁺ shuttling at all.²³ However, not only is it unclear if this triple mutant would be representative of the WT system, but the simulations also excluded an entire helix (helix A) from the twin monomer. This omission would increase solvation around the intracellular H⁺ entrance and artificially create a long water path up to E148. Thus, although future work will continue to explore the role of conformational rearrangements in Cl⁻/H⁺ exchange, the inclusion of such transitions is not warranted yet, and further will not alter the major conclusions of this study related to the kinetic selection of competing pathways.

4. CONCLUDING REMARKS

It is well understood that altering reaction conditions, such as the ion gradient in secondary active ion exchange, will influence reactive flux, e.g., the dissipation of that ion gradient as the system reestablishes equilibrium. It is less clear, however, how the mechanism (e.g., of ion exchange) might also change under varying conditions. By analyzing the pH-dependence of ion exchange in ClC-ec1, we have demonstrated herein how the dominance of competing pathways shifts as a function of reactant (H⁺ in this case) concentration. This provides another level of mechanistic understanding for how multiple pathways in WT ClC-ec1 work collectively to generate macroscopic observables.

The importance of the upper E148 in regulating Cl⁻/H⁺ exchange in ClC-ec1 is well established.^6,12,14,17 By competing with Cl⁻ for the central binding site, S_cen, deprotonated E148 effectively blocks Cl⁻ transport in either direction. In turn, the presence of Cl⁻ ions at S_cen and S_out facilitate H⁺ release from E148. Thus, the origin of the coupling is clear. Moreover, it is expected that the pK_a of E148 predominantly determines the maximal Cl⁻ flux (eq. 1) and that the steady-state populations are in good agreement with the macroscopic pK_a in eq 1 (Table S1). What is less clear is the role of the lower glutamic acid, E203, in pH-regulation and in maintaining the 2.2:1 Cl⁻:H⁺ stoichiometric ratio.

The results herein demonstrate how the charge state of E203 can play an influential role; with decreasing pH, pathways involving deprotonated E203 in both H⁺ (Figure 3) and Cl⁻ (Figure 4) transport fade out, resulting in a bell-shaped pH-dependence. In contrast, those involving protonated E203 retain a logistic pH-dependence. More importantly, the net flux depends on the relative uptake and release rates from the two sides of the membrane, and thus to both E148 and E203. In the absence of a lower glutamic acid residue, the maximal Cl⁻ flux would continue to increase with decreasing pH up to the limit of Cl⁻ transport (as if through a channel) and the coupling between ions would require a balanced efficiency of H⁺ release (i.e., matched barriers) to retain the 2.2:1 stoichiometry. By contrast, the existence of E203 introduces another control knob. The net flux retains logistic pH-dependence due to faster uptake and release through E203 compared to that through E148 (Figure S21). Thus, as pH decreases and uptake to E148 increases from the increasing external [H⁺], release from E148 is able to plateau only due to increased back flux through E203.

Importantly, the existence of multiple competing pathways consistently described herein should not be confused with the simultaneous presence of multiple kinetic solutions (or sets of rate constants). For a given set of external conditions (e.g., transmembrane potential), the actual system is characterized by just one “correct” set of rate constants. We cannot verify that we have exhausted the solution space or identified the correct model; this remains a central challenge in kinetic modeling. However, the 10 solutions analyzed in this study are the best fit to the calculated rate constants and physiological data as previously described,³³ and represent our best current estimates of the real network. In light of the significant pathway heterogeneity found in each of the studied solutions (Figures S1–S20) and the nonintegral Cl⁻/H⁺ exchange ratio (2.2:1), which cannot be explained by a single pathway, we anticipate that multiple competing pathways will remain a feature of any refined or correct solution. Moreover, the principles revealed herein, i.e., shifting flux and pathway dominance as a function of pH, will still apply in these solutions.

If the presented patterns of competing pathways are correct, mutations or alterations that significantly increase the pK_a of E203 will decrease the cumulative flux of both ions at low pH values, shifting their pH-dependence toward bell-shaped behavior. As intriguing as these predictions are, their validation awaits further in vitro experiments. For example, full turnover rates in the absence of ion leakage,^13,36 controlled protein orientation, and time-resolved data would be extremely valuable in refining our mechanistic understanding. Our future work will additionally focus on modeling specific mutants, integrating the role of transmembrane potential in liposome studies,³⁶ and improved methods for characterizing heterogeneous reaction networks including cyclic pathway flux quantification.⁵⁹ In the meantime, the major findings of the present work highlight the potential relevance of heterogeneous reaction networks for multistep biological processes, both in their mechanistic outcome and in their response to reactant conditions.

ABBREVIATIONS USED

MKM

multiscale kinetic modeling

ClC

chloride channel

WT

wild type

RLS

rate-limiting step