Luminal Cl^- modifies the amplitude and kinetics of VGLUT1_PM Cl^- currents

VGLUTs require luminal acidification for glutamate transport and anion channel activity and are activated by luminal and cytoplasmic [Cl^-] [5]. Since only luminal [Cl^-] undergoes major modification during synaptic function [4,7], we restricted our analysis to regulation by luminal Cl^-. We first focused on measuring Cl^- currents in the absence of the transport substrate glutamate. In all experiments, we expressed a surface membrane insertion-optimized mutant of VGLUT1 (VGLUT1_PM) in HEK293T cells, followed by whole-cell patch clamping [4]. As the luminal side of surface membrane-optimized VGLUT1_PM faces the external solution, the luminal [Cl^-] can be varied by changing [Cl^-] outside the cell ([Cl^-]_o).

Fig 1A shows the current responses of HEK293T cells with heterologously expressed VGLUT1_PM to voltage steps between -160 mV and +60 mV at three external [Cl^-] (0, 40, and 140 mM) and an external pH of 5.5. In the complete absence of external Cl^-, currents are small but clearly above background. Increased [Cl^-]_o enhances current amplitudes and accelerates the time course of activation (Fig 1A). Fig 1B depicts a plot of normalized late current amplitudes versus external [Cl^-], which can be fitted with a Michaelis-Menten relationship providing an apparent K_M of 28.3 ± 0.7 mM (mean and 95% confidence interval, with bootstrapped global fit and sampling of 1000, n = 11). Under all test conditions, VGLUT1 currents are pH dependent, with zero current amplitude at neutral external pH. Fig 1C provides the pH dependence for two different [Cl^-]_o at -160 mV, with indistinguishable pK_M values of 5.3 ± 0.003 (n = 10, Hill coefficient = 1.2) at [Cl^-]_o = 0 mM and 5.4 ± 0.003 (n = 11, Hill coefficient = 1.1, p = 0.082) at [Cl^-]_o = 140 mM.

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Fig 1. WT VGLUT1_PM chloride currents are modulated by voltage, pH, and [Cl^-].

(A) Representative WT VGLUT1_PM Cl^- current responses to voltage steps between -160 mV and +60 mV at pH 5.0 and external [Cl^-] of 0, 40, and 140 mM. (B) Dose-response plots for VGLUT1_PM Cl^- currents at pH 5.0 and rising [Cl^-]_o (means ± confidence interval, n = 11 cells, fitted with Michaelis-Menten relationships for a K_M of 28.3 ± 0.7). (C) Dose-response plots for VGLUT1_PM Cl^- currents with rising pH at either [Cl^-]_o = 0 (black, means ± confidence interval, n = 10 cells, fitted with Hill relationships for a pK_M of 5.3 ± 0.003 and a Hill coefficient of 1.2) or 140 mM (green, means ± confidence interval, n = 11 cells, fitted with Hill relationships for a pK_M of 5.4 ± 0.003 and a Hill coefficient of 1.1; lines and shaded areas depict the mean and 95% confidence interval). (D-F) Normalized chloride current responses to pH jumps from pH 7.4 to 5.0 at [Cl^-]_o = 0 mM (D), from pH 7.4 to 5.5 at [Cl^-]_o = 140 mM (E), or [Cl^-] jumps from 0 mM to 140 mM and back at pH 5.5 (F). Currents were recorded at four continuous voltage levels and shown as 95% confidence interval (gray) from at least 11 experiments, with currents at the most negative voltage fitted with a single (purple line) and double (dashed orange line) exponential functions provided with F-test p-values for each solution change to indicate whether they are better described by biexponential fits, with asterisks marking those that are.

https://doi.org/10.1371/journal.pcbi.1013214.g001

Transporters undergo conformational changes upon ligand association or dissociation, and rates for these processes can be quantified via a kinetic description of transporter currents upon fast substrate application [14–23]. Fig 1D and 1E depict normalized current responses to pH changes from 7.4 to 5.0 or 5.5 and back to pH 7.4 when the external solution is either Cl^- free (Fig 1D) or has a [Cl^-]_o of 140 mM (Fig 1E). Fast external solution exchange was achieved by the piezo-driven movement of a perfusion pipette made from dual-channel theta glass tubing [24–27]. Non-transfected HEK293T exhibit only negligible background currents [4] (S1 Fig).

External Cl^- accelerates the time course of both processes. Whereas VGLUT1_PM Cl^- currents activate on monoexponential time courses and deactivate on biexponential time courses upon acidification with a Cl^--free external solution, the activation is biexponential and deactivation is monoexponential when the [Cl^-]_o = 140 mM. The application of external Cl^- results in biexponential increases and its removal in monoexponential current deactivation (Fig 1F). Time constants were only minimally voltage dependent and were comparable with and without external Cl^-. Activation and deactivation time constants were within the same order of magnitude and largely voltage independent (S2 Fig). For Cl^- channels, rapid changes in external [Cl^-] will affect the driving force and thus the unitary current amplitude. However, since our recordings are performed at voltages far away from the current reversal potential, fast, diffusion-limited changes were not observed. Current responses to fast Cl^- application are slow (Fig 1F), since they are based on conformational changes that modify the open probability of the channel.

A kinetic scheme to describe VGLUT1 anion channel function

VGLUT1_PM Cl^- currents activate and deactivate upon pH jumps between 5.0 and 7.4, with comparable time constants (S2 Fig). This result excludes the possibility of direct channel activation by H⁺ and indicates that protonated and unprotonated transporters can both open and close, but at distinct rates [28]. A four-state model (with one open and one closed state for each protonation state) predicts monoexponential activation and deactivation upon pH steps. Therefore, we added one doubly protonated open and one doubly protonated closed state to account for biexponential activation or deactivation in response to pH steps. To describe faster activation and deactivation in the presence of external Cl^-, we assumed that channels with bound Cl^- activate or deactivate at different rates and added Cl^--bound open and closed states for each protonated state, resulting in a 12-state model (Fig 2). Cl^- binding is expected to be diffusion limited, and we combined Cl^- binding and associated processes into single rate constants.

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Fig 2. Kinetic model to describe gating of VGLUT1 Cl^- channels.

Green arrows depict Cl^- binding to the black states in front, red arrows depict protonation, and ligand unbinding is shown in corresponding black arrows. The six states on top are apo and other closed states, and the channel opens via black downward arrows. Dashed arrows show rate-limited opening without protonation.

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This kinetic scheme accurately predicts VGLUT1_PM anion channel gating in the presence or absence of external Cl^-. Fig 3 depicts the simultaneous fits to normalized current responses from at least 10 HEK293T cells expressing wild-type (WT) VGLUT1_PM to voltage steps either from a holding potential of 0 mV (Fig 3A and 3D) or after a prepulse to a more negative voltage (Fig 3B and 3E), or to pH steps using piezo-driven pipette movements (Fig 3C and 3F).

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Fig 3. VGLUT1 Cl^- currents are well described by a kinetic scheme that assumes three protonation states, each with a closed and open anion channel conformation and all of which can bind Cl^-.

(A–I) Current responses and predictions from the kinetic scheme for voltage steps from 0 mV to negative potentials with [Cl^-]_o = 0 (A), voltage steps from -190 mV to less negative potentials with [Cl^-]_o = 0 (B), rapid pH steps to pH 5.5 at [Cl^-]_o = 0 (C), voltage steps from 0 mV to negative potentials with [Cl^-]_o = 140 mM (D), voltage steps from -160 mV to less negative potentials with [Cl^-]_o = 140 mM (E), rapid pH steps to pH 5.5 at [Cl^-]_o = 140 mM (F), rapid Cl^- steps to 140 mM at pH 5.0 (G), late current plots versus [Cl^-]_o (means ± 95% confidence interval; H), late current plots versus pH at [Cl^-]_o = 0 and 140 mM (I). (J) Kinetic schemes describing VGLUT1 Cl^- channel activation, with circle size giving occupancy of individual states and curved arrow thickness the rate amplitude for [Cl^-]_o = 0 (top) and [Cl^-]_o= 140 mM (bottom) at pH 5.5 and -160 mV. (K) Simulated residence probabilities for the indicated closed (top) and open (bottom) states for VGLUT1 anion channels with (green) or without (black) bound Cl^-. (L) Three most frequently occurring pathways for activation from apo (left) or deactivation from the most common two open states (oH and oClH₂) to an unprotonated closed state (apo or cCl, right). Experimental data are given as the 95% confidence interval of patch clamp data (gray) and the fitting results of 250 simulations generated through exploratory mutations (blue) under the same conditions.

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Experiments were performed in the absence of external Cl^- (Fig 3A–C) or at [Cl^-]_o = 140 mM (Fig 3D–F); Fig 3G shows the fits to current responses upon changes in [Cl^-]_o at an external pH of 5.5, and Fig 3H and 3I depict the [Cl^-] and the pH dependence of normalized late currents. To ensure global model optimization and to assess how well the individual parameters are defined by our experimental data, we randomly modified the fit parameters using an explorative genetic algorithm and collected parameter set values that impaired the goodness of fit by < 25% for each simulated experimental time course and metric (we denote parameter-specific simulation output that results in a calculated value, such as open probability, open time, transport rate, pK_a values, pH and [Cl^-] dependence as metrics). From these sets of parameters, model predictions from 250 fits are shown as blue lines, evenly spaced from ≥ 10,000 individuals with ≥ 3000 unique values for each variable to provide reliable statistical distinction. Kinetic modeling enables the calculation and visual tracking of overall fluxes through the states of the kinetic model and, thus, provides insight into activation and deactivation pathways. Fig 3J shows the kinetic model with the occupancy of individual states depicted as the circle size and rate amplitude as the thickness of curved arrows in the absence or presence of external Cl^-, and Fig 3K residence probabilities for the transporter states under both conditions. In the absence of Cl^-, VGLUT1_PM predominantly opens from the singly protonated closed state (as shown in Fig 3J) and remains singly protonated in the open state (Fig 3K).

Fig 3L depicts the three most frequent activation and deactivation pathways at pH 5.5, 140 mM Cl^-, and -160 mV, according to transition path theory-based reactive flux analysis. Under these conditions, VGLUT1_PM anion channels predominantly activate via initial Cl^- binding, followed by protonation and subsequent channel opening into a singly protonated conformation (oClH). Low-affinity Cl^- binding and rapid unbinding make the Cl^--free singly protonated state (oH) the most common open state (Fig 3K). There is a much lower likelihood of channels opening after additional protonation from the doubly protonated Cl^- bound open state (oClH₂). Kinetic modeling also assigns a small probability to WT VGLUT1 opening without protonation (apo-cCl-oCl); however, this open state is unstable, leading to negligible channel opening at neutral pH, in agreement with current at pH 7.4 being indistinguishable from background [4]. Channel deactivation proceeds primarily via three pathways with comparable probabilities: by closing in the singly protonated state, followed by deprotonation; after deprotonation in the open state; or from a doubly protonated Cl^--bound state (Fig 3L).

Fig 4A depicts the pK_as for each of the two protonation sites for both Cl^--free and Cl^--bound VGLUT1 at 0 mV, and at -160 mV; the parameter sets that collectively describe the experimental data in an adequate fit, in the following denoted as parameter variants, are shown as violin plot. The z and d parameters that describe the voltage dependence of all values in Fig 4 are given in S3 Fig, and an overview of all optimized parameters for WT VGLUT1_PM is provided in S1 Table. Negative voltages reduce the apo state pK_a from a median of 2.3 (for a total amplitude range of 2.1–2.4) to 1.1 (0.9–1.2) and after Cl^- binding from 4.3 (4.1–4.5) to 2.0 (1.7–2.1). For the second proton in the closed state, the voltage increases the pK_a by roughly 2 points, regardless of Cl^-. This rise, from 6.3 (6.0–6.5) to 8.3 (8.2–8.5) without and from 6.4 (6.1–6.7) to 8.4 (8.1–8.6) with Cl^- bound, combined with opening from a single protonated state, explains the relatively high occupancy of cClH₂ while VGLUT1 is closed (Fig 3K).

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Fig 4. Cl^- binding changes VGLUT1 protonation and opening/closing rates.

(A) Cl^--dependent changes in predicted pK_as of the first and second protonation sites of the closed (top) or open (bottom) channel at -160 mV (green, Cl^- bound; black, no Cl^-) or at 0 mV (purple or dashed lines). (B) Violin plots of the amplitude range generated by exploratory mutation. (C) Rates for channel opening and closing, depicted as normalized RSS representing goodness of fit for a range of amplitudes.

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Titratable amino acids exhibit pK_a values above 2.0 in solution. Although pK_a values can shift in proteins, such changes always result in higher and not in lower values. Kinetic modeling predicted several pK_a below 2.0, and these low values are likely due to minimization of the state number, which makes lumping several separate reactions into one state necessary. Apparent pK_as of such compound protonation reaction can deviate from the pK_a describing protonation of the amino acid side because of additional energy-consuming steps that changes the accessibility of the titratable side chain.

Fig 4B and 4C show opening and closing rates with and without external Cl^- at 0 mV or -160 mV. In addition to comparing the full range of parameters obtained in the exploratory fitting (Fig 4B), we also applied a statistical test to calculate the change in the quality of fit upon only varying the compared parameter (Fig 4C; [27]). In such a plot, a sharply defined and distinct parameter value is associated with instantly increasing RSS upon small changes in parameter values without overlap with parameter values obtained under other conditions. The two tests—RSS goodness of fit by parameter amplitude and amplitude distribution via exploratory mutation—demonstrate that—except for closure of the singly protonated channel—all opening and closing transitions are well defined by the fitting procedure and undergo a statistically significant change upon the application of Cl^-. At -160 mV, Cl^- increases opening rates from 4.6 × 10⁴ (3.3 × 10⁴–7.5 × 10⁴, median and parameter amplitude range) s^-1 to 1.5 × 10⁵ (9.0 × 10⁴–2.2 × 10⁵) s^-1 in the singly protonated state, but reduces it from 71 (46–97) s^-1 to 41 (18–75) s^-1 in the doubly protonated state. The membrane voltage seems to dictate the preference for opening singly protonated, with otherwise low opening rates of 157 (129–174) s^-1 and 361 (305–451) s^-1 without and with Cl^-, respectively. Membrane hyperpolarization decreases the opening rates for doubly protonated VGLUT1 in the absence, but not in the presence of Cl^- (Fig 4B and 4C). Cl^- reduces the closing rates for all protonation states: at -160 mV from 277 (228–319) s^-1 to 9.9 × 10^-4 (5.8 × 10^-4–1.5 × 10^-3) s^-1 without protonation, from 51 (40–64) s^-1 to 0.08 (0.05–0.11) s^-1 for the singly protonated state, and from 1.1 × 10⁴ (9.4 × 10³–1.3 × 10⁴) s^-1 to 1.1 × 10^-3 (4.7 × 10^-4–1.8 × 10^-3) s^-1 for the doubly protonated state. The membrane voltage has only minor effects on channel closure.

Cl^- binding and unbinding depend on the protonation state and differ for the open and closed conformations (Fig 5, corresponding z and d parameters are given in S4 Fig). Cl^- association with open channels is close to the limits of diffusion control (10⁹ M^-1 s^-1; [29]. Whereas closed unprotonated and doubly protonated channels bind Cl^- at very high rates, at -160 mV with concentration-normalized rates of 6.7 × 10⁸ (5.8 × 10⁸–7.2 × 10⁸) M^-1 s^-1 and 1.1 × 10⁷ (9.4 × 10⁶–1.3 × 10⁷) M^-1 s^-1, respectively, we observed much lower association rates for the singly protonated closed channel of 1.8 × 10³ (1.6 × 10³–2.1 × 10³) M^-1 s^-1. Such association rates may indicate that Cl^- binding requires conformational changes that make the binding site accessible in this protonation state.

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Fig 5. Changes in Cl^- association with WT VGLUT1_PM with protonation state.

(A) Secondary Cl^--binding rates to closed (top) or open (bottom) WT VGLUT1_PM anion channels in the unprotonated state or the singly or doubly protonated state (light→dark red indicates increasing protonation). Rates are depicted as violin plots (left) showing the amplitude range generated by exploratory mutation and normalized RSS (right) representing goodness of fit for a range of amplitudes. (B) Cl^- binding rates at constant K_D, where the unbinding constants were simultaneously altered to maintain the Cl^--binding affinity. All rates are shown at -160 mV.

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Since changes in the Cl^--binding rate will also affect the likelihood of binding-site occupation, it was necessary to distinguish whether protonation adjusts transporter function via altering the binding affinity or association rate for Cl^-. Therefore, we also assessed how modification of both the association and dissociation rates of Cl^- (when held at a fixed ratio to maintain the Cl^- dissociation constant, K_D) affect the goodness of fit (Fig 5B). The analysis demonstrated that only the rate of Cl^- association with the singly protonated closed channels determines the fit quality, while for other states such differences could not be demonstrated (Fig 5). Moreover, with constant K_D, only singly protonated Cl^- in the closed state is sharply defined, showing the individual association rates are more important here than for any of the other states. We conclude that during anion channel activation VGLUT1 transiently assumes conformational states that are inaccessible to anions in the external solution. Such conformations might be inward facing or occluded with the Cl^--binding site inaccessible from either membrane side.

H120A impairs Cl^- binding to VGLUT1

Substitution of histidine at position 120 by alanine changes the permeation and gating of VGLUT1_PM anion channels (Fig 6A; [4]). We found that the H120A mutation modifies the Cl^- dependence of late current amplitudes (H120A: K_M = 19.4 ± 0.2 mM, WT: K_M = 28.3 ± 0.7 mM, mean and 95% confidence interval, p = 0.047; Fig 6B) and changes the pK_M of acid activation from 5.3 ± 0.003 (WT, Hill coefficient = 1.2) to 5.0 ± 0.004 (H120A, Hill coefficient = 1.2, p = 2.2 × 10^-6) in the absence of Cl^-, but not in the presence of Cl^- (5.4 ± 0.003 and Hill coefficient = 1.3, compared to 5.4 ± 0.003 with a Hill coefficient = 1.1 for the WT; Fig 6C).

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Fig 6. H120A VGLUT1_PM chloride currents are modulated by voltage, external pH, and [Cl^-].

(A) Representative H120A VGLUT1_PM Cl^- current responses to voltage steps between -160 mV and +60 mV at pH 5.0 and external [Cl^-] of 0, 40, or 140 mM. (B) Dose-response plots for VGLUT1_PM Cl^- currents at rising [Cl^-]_o at pH 5.0 (means ± confidence interval, n = 11 cells, fitted with Michaelis-Menten relationships for a K_M of 19.4 ± 0.2. (C) Dose-response plots for VGLUT1_PM Cl^- currents for rising pH at [Cl^-]_o = 0 (black, means ± confidence interval, n = 11 cells, fitted with Hill relationships for a pK_M of 5.0 ± 0.004 and a Hill coefficient of 1.2 for H120A) or 140 mM (green, means ± confidence interval, n = 11 cells, lines and shaded areas depict the mean and 95% confidence interval, fitted with Hill relationships for a pK_M of 5.4 ± 0.003 and a Hill coefficient of 1.3 for H120A). (D-F) Normalized chloride current responses to pH jumps from pH 7.4 to 5.0 at [Cl^-]_o = 0 mM (D), or from pH 7.4 to 5.5 at [Cl^-]_o = 140 mM (E), or [Cl^-] jumps from 0 mM to 140 mM and back at pH 5.5 (F) held at four continuous voltage levels. Solution change time courses are shown as the 95% confidence interval (gray) from at least 11 experiments; those at the most negative voltage are fitted with a single (purple line) and double (dashed orange line) exponential function and are provided with F-test p-values to indicate whether they are better described by biexponential fits, with asterisks marking those that are.

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H120A decelerates VGLUT1_PM kinetics in voltage steps (Fig 6A), pH steps (Fig 6D and 6E), and Cl^- steps (Fig 6F). Unlike WT, H120A VGLUT1_PM Cl^- currents activate and deactivate over a monoexponential time course upon acidification with external Cl^-. In the absence of external Cl^-, the kinetics of WT and H120A VGLUT1_PM current activation/deactivation upon pH steps are comparable; at high external [Cl^-], H120A decelerates activation and deactivation (S5 Fig). Changes in the external [Cl^-] resulted in monoexponential increases and decreases in the H120A VGLUT1 current (Fig 6F) at time courses much slower than those of the WT (S5 Fig); for all conditions, time constants were only minimally voltage dependent.

We reevaluated the parameter amplitudes with the 12 state model developed for WT VGLUT1_PM, until H120A VGLUT1_PM Cl^- currents were described well (Fig 7A–I). Fig 7J depicts the overall flux through the states of the kinetic model, and Fig 7K the occupancy of individual states. In the absence of Cl^-, H120A VGLUT1_PM anion channels predominantly open in the singly protonated state, with higher probabilities than the WT; in the presence of Cl^-, occupation of oClH₂ was slightly higher for H120A than for WT (Fig 7K). The H120A mutation alters the activation and deactivation pathways of VGLUT1 channels (Fig 7L, paths numbered by WT preference). Mutant anion channels primarily open from the doubly protonated state (cClH₂, path 2), with a lower probability of opening from the singly protonated Cl^--bound state. Whereas the WT mainly closes from the oH state, either by direct deprotonation or by deprotonation of the closed state, H120A VGLUT1_PM mainly passes through Cl^- unbinding to oH₂ and then to cH₂, cClH₂, cClH, and, finally, to cCl (path 3).

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Fig 7. H120A VGLUT1 Cl^- currents are well described by a kinetic scheme that assumes three protonation states, each with a closed and open anion channel conformation and all of which can bind Cl^-.

(A–I) Current responses and predictions by the kinetic scheme for voltage steps from 0 mV to negative potentials at [Cl^-]_o = 0 mM (A), more negative to less negative potentials at [Cl^-]_o = 0 (B), pH steps from pH 7.4 to pH 5.5 at [Cl^-]_o = 0 (C), voltage steps from 0 mV to negative potentials at [Cl^-]_o = 140 mM (D), more negative to less negative potentials at [Cl^-]_o = 140 mM (E), pH steps from pH 7.4 to pH 5.5 at [Cl^-]_o = 140 mM (F) or upon changes in [Cl^-]_o from 0 to 140 mM at pH 5 (G), plots of late currents (means ± 95% confidence interval) versus [Cl^-]_o (H) or pH (I). (J) Kinetic schemes describing H120A VGLUT1 Cl^- channel activation for [Cl^-]_o = 0 mM (top) and [Cl^-]_o= 140 mM (bottom, with circle size giving occupancy of individual states and curved arrow thickness the rate amplitude. (K) Simulated residence probabilities for the indicated closed (top) and open (bottom) states for H120A VGLUT1 anion channels with (green) or without (black) bound Cl^-. (L) Three most frequently occurring activation (left) or deactivation (right) pathways upon a rapid pH change. Experimental data are given as the 95% confidence interval of patch clamp data (gray) and the fitting results of 250 simulations from parameter sets generated through exploratory mutations (blue) under the same conditions.

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An overview of all optimized parameters for H120A VGLUT1_PM is provided in S2 Table. Without Cl^-, H120A strongly increases the pK_a of the first protonation site of the closed channel from 1.1 (0.9–1.2), median and parameter amplitude range) to 3.7 (3.5–3.9; all values obtained at -160 mV; Fig 8A). Cl^- binding reduces this value back to 3.1 (2.8–3.2). H120A impairs protonation of the second site, without effect of Cl^-. For Cl^--bound open VGLUT1, H120A decreases the pK_a of the first protonation site from 5.0 (5.0–5.1) to 2.7 (2.6–3.0), with a smaller increase from 6.7 (6.5–6.9) to 7.8 (7.6–8.0) for the second protonation site. H120A decreases opening rates for singly protonated states, from 4.6 × 10⁴ (3.3 × 10⁴–7.5 × 10⁴) s^-1 to 74 (55–93) s^-1 without Cl^- and from 1.5 × 10⁵ (9.0 × 10⁴–2.2 × 10⁵) s^-1 to 1439 (1044–1807) s^-1 with Cl^- (Fig 8B). It increases closing rates in the presence of Cl^-: from 9.9 × 10^-4 (5.8 × 10^-4–1.5 × 10^-3) s^-1 to 0.026 (0.012–0.050) s^-1 when unprotonated, from 1.1 × 10^-3 (4.7 × 10^-4–1.8 × 10^-3) s^-1 to 1.0 (0.5–1.5) s^-1 when doubly protonated; with single protonation, the rates are not sharply defined. Moreover, for doubly protonated states, H120A has a lower opening rate than the WT in the absence of Cl^- with 4.2 (2.7–5.7) s^-1 versus 71 (46–97) s^-1, but a higher rate in its presence with 250 (85–532) s^-1 versus 41 (18–75) s^-1. This likely forms the basis for its preferential channel opening under double protonation only in the presence of Cl^-. H120A alters the preferred pathways of channel activation through changes in channel opening and closing, effectively switching its primary Cl^--activated opening state from single to double protonation. S6 Fig depicts the effects of the H120A mutation on the voltage dependence of protonation, opening/closing, and Cl^- association in the absence and presence of luminal/external Cl^-.

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Fig 8. H120A VGLUT1_PM affects protonation and opening/closing rates as well as Cl^- binding.

(A) Cl^--dependent changes in pK_a for the first and second protonation sites of the closed (top) or open (bottom) H120A VGLUT1_PM channels. (B) Opening and closing rates (no Cl^- in black, Cl^--bound in green, WT in blue or dashed lines) for different protonation states. (C) Cl^- association K_D at different protonation states (light→dark red indicates increasing protonation). (D) Cl^- binding and unbinding rates for closed and open H120A VGLUT1_PM channels at different protonation states. Rates are depicted as violin plots (left) showing the amplitude range generated by exploratory mutation and normalized RSS (right) representing goodness of fit for a range of amplitudes. All rates are shown at -160 mV.

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The H120A mutation has pronounced effects on Cl^- binding and unbinding (Fig 8C). Whereas H120A left Cl^- dissociation constants for the unprotonated open channel unaffected, it increased the K_D under all other conditions, in the open channel from 869 (641–1263) mM to 5.8 × 10⁵ (2.9 × 10⁵–8.3 × 10⁵) mM when singly protonated, and from 0.24 (0.15–0.36) mM to 3.1 (2.0–4.5) mM when doubly protonated. For the closed channel, dissociation constants increase from 0.12 (0.08–0.20) mM to 3.4 (2.2–5.8) mM when unprotonated, from 0.017 (0.013–0.019) mM to 16 [11–22] mM when singly protonated, and from 0.014 (0.012–0.017 mM to 38 (11–85) mM when doubly protonated. These changes correspond to altered Cl^- association rates (Fig 8C). However, by testing the variation in Cl^- binding to open or closed channel at a fixed affinity (S7 Fig), we demonstrate that H120A does not affect the accessibility but, rather, the affinity of the binding sites.

A kinetic scheme to describe VGLUT1 glutamate and aspartate transport

VGLUT1_PM glutamate or aspartate currents are much smaller than Cl^- currents, requiring complete substitution of intracellular Cl^- with these anions to record such transport currents [4]. Fig 9 depicts representative glutamate and aspartate currents, as well as the pH and [Cl^-] dependence of late currents at -160 mV, with S8 Fig showing the time constants of pH and [Cl^-] jumps. Aspartate currents differ from glutamate, with a slightly higher amplitude and a more negative current reversal potential (Fig 9A and 9B), reflecting the difference in transport stoichiometry [4]. Glutamate and aspartate currents are close to background in the absence of Cl^-; therefore, we only recorded current responses to pH steps at [Cl^-]_o = 40 mM (Fig 9C and 9D) or to [Cl^-] steps at acidic pH (Fig 9E and 9F). For glutamate and aspartate, pH jumps resulted in monoexponential activation or deactivation, with closely similar kinetics (Fig 9C and 9D). The pH dependence of late glutamate and aspartate currents can be fitted with the Hill equation, and the pK_M values for both are indistinguishable (glutamate: 5.5 ± 0.005 with a Hill coefficient of 1.3, aspartate: 5.5 ± 0.002 with a Hill coefficient of 1.4, p = 0.53, mean and 95% confidence interval; Fig 9G) and similar to the values obtained with Cl^- currents.

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Fig 9. VGLUT1_PM glutamate and aspartate current are modulated by voltage, external pH, and [Cl^-].

(A, B) Representative current responses of transfected cells dialyzed with glutamate-based (blue; A) or aspartate-based (yellow; B) solutions to voltage steps with [Cl^-]_o of 40 mM and the pH of 5.5, (C - f) Current responses to pH steps from pH 7.4 to pH 5.0 with glutamate (C) or aspartate (D), or to concentration steps from [Cl^-]_o = 0 mM to 40 mM with glutamate (E) or aspartate (F). (G) pH dependence of normalized steady-state current amplitudes at [Cl^-]_o = 140 mM and a membrane potential of -160 mV bootstrapped using a Hill relationship with glutamate (pK_M = 5.5 ± 0.005, Hill coefficient = 1.3) and aspartate (pK_M = 5.5 ± 0.002, Hill coefficient = 1.4, [Cl^-]_o = 40 mM), (H) [Cl^-] dependence of steady-state current means at pH 5.0 and -160 mV fitted to a Michaelis-Menten relationship with glutamate (K_M = 8.1 ± 2.0 mM) and aspartate (K_M = 9.9 ± 2.2 mM; pH 5.5, -140 mV). Currents (gray) and error bars represent the 95% confidence interval from ≥ 10 measurements; currents at the most negative voltage are fitted with a single (purple line) and double (dashed orange line) exponential function along with F-test p-values to indicate whether they are better described by biexponential fits, with asterisks marking those that are..

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Cl^- concentration jumps elicited very different responses for the glutamate and aspartate currents. Rapid increases in [Cl^-]_o from 0 to 40 mM resulted in monoexponential increases of glutamate currents with time constants of around 10 ms, and the currents decayed upon decreasing steps to [Cl^-] of 0 mM over a similar time course (Fig 9). For aspartate currents, Cl^--dependent activation was more than 10-fold slower, and followed a biexponential time course upon [Cl^-] increases or decreases with time constants of around 140 ms (Figs 9F and S8B). Despite these differences in kinetics, glutamate and aspartate currents rose with increasing external [Cl^-] with a similar concentration dependence (i.e., glutamate: K_M = 8.1 ± 2.0 mM, aspartate: 9.9 ± 2.2 mM, mean and 95% confidence interval; Fig 9H). These values are significantly lower than the K_M of 28.3 ± 0.7 mM for VGLUT1 Cl^- currents (p = 0.0097, n ≥ 10 cells, one-sample Wilcoxon signed rank test between the combined glutamate mean fit and individual cellular fits of Cl^- current).

We calculated unitary aspartate transport rates from combined whole-cell current and fluorescence amplitudes of an earlier publication: in this dataset, whole-cell current amplitudes increase linearly with cellular expression levels quantified as whole-cell fluorescence, and we compared fluorescence-normalized current values from this publication in combination with its calculated glutamate transport of 561 ± 123 s^-1 [4]. Since aspartate currents exceed glutamate by a factor 2.3 at -160 mV, without the protons exchanged with glutamate at a stoichiometry of 1:1, we obtained a transport rate of approximately 2581 s^-1.

VGLUT1 structurally resembles transporters of the Major Facilitator Superfamily [30] and operates as a secondary active glutamate transporter. Therefore, we described glutamate and aspartate transport with an alternating access mechanism that shuttles between inward-facing states that permit the binding of amino acids from the cytoplasm and outward-facing states that release amino acids to the vesicular lumen (Fig 10).

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Fig 10. Kinetic model of active glutamate and aspartate transport by VGLUT1.

The top states are outward-facing, connected to the inward-facing states at the bottom by vertical arrows. Green arrows depict Cl^- binding to the (outward-facing) black states in front, red arrows depict protonation, substrate binding is shown in horizontal blue-yellow arrows, and ligand unbinding in corresponding black arrows. Vertical black arrows with a blue-yellow fill show doubly protonated translocation with substrate, with limited rates when glutamate-bound. Pink arrows indicate the general direction of the Cl^--free (black states) and Cl^--bound (gray states) transport cycle.

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The model is based on multiple assumptions. Since the Cl^- channel is described using two protonation sites and shows a pH dependence remarkably similar to VGLUT1 transport of glutamate and aspartate, we assumed that the same number of sites are protonated when the empty transporter returns to the inward-facing conformation. Substrates then bind to the doubly protonated transporter and cross the membrane either in this protonation state or after the release of one proton. Substrate translocation in the doubly protonated state results in uncoupled uniport, and singly protonated transitions in H⁺-substrate exchange. To permit H⁺ transport, transporter protonation and deprotonation are permitted in inward- and outward-facing conformations. To ensure stoichiometrically coupled H⁺-glutamate exchange, H⁺ fluxes that are not coupled to glutamate transfer need to be prevented because they enable passive H⁺ flux. Therefore, for transporters with no substrate bound, we permitted only doubly protonated translocation.

Optimized parameters for the transporter, separated by bound glutamate and aspartate substrates, is provided in S3 Table. Cl^- is only present in the external solution, and we therefore exclusively accounted for Cl^- binding in the outward-facing conformation. Since we studied glutamate and aspartate currents at negative voltages in the absence of internal Cl^-, anion-conducting states were not added to the kinetic scheme. The scheme correctly describes the current kinetics and pH and [Cl^-] dependence of both glutamate and aspartate currents (Fig 11), with both H⁺-glutamate and aspartate transport rates similar to experimental data [4].

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Fig 11. VGLUT1_PM glutamate and aspartate currents are well described by an alternating access kinetic scheme.

(A, B) Experimental currents and predictions by the kinetic scheme for pH steps from 7.4 to 5.0 at [Cl^-]_o = 140 mM with glutamate (A) or aspartate (B). (C, D) Plots showing late currents (means ± 95% confidence interval) against pH for glutamate (C) or aspartate (D). (E, F) Experimental currents and predictions by the kinetic scheme for changes in [Cl^-]_o from 0 to 40 mM at pH 5.0 for glutamate (E) or at pH 5.5 for aspartate (F). (G, H) Plots showing late currents (means ± 95% confidence interval) against pH at [Cl^-]_o = 40 mM for glutamate (G) or aspartate (H). All panels show experimental data as the 95% confidence interval of patch clamp data (gray and black) and the fitting results of 250 simulations from parameter sets generated through exploratory mutations (blue) under the same conditions.

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Cl^- stimulates cytoplasmic glutamate binding

Fig 12 compares the kinetic parameters for coupled glutamate transport in the Cl^--free and Cl^--bound states; its voltage dependence is given by the corresponding z and d parameters in S9 Fig. VGLUT1 binds substrates from the internal solution after double protonation and translocation to the inward-facing state. At -160 mV, external Cl^- enhances the rates of glutamate binding to the inward-facing state from 6.9 × 10⁴ (3.5 × 10⁴–9.1 × 10⁴, median and parameter amplitude range) M^-1 s^-1 to 6.0 × 10⁶ (2.8 × 10⁶–2.4 × 10⁷) M^-1 s^-1 (Fig 12B). Changing the glutamate binding rate while modifying unbinding to maintain the same K_D results in sharply defined and distinct RSS values in both conformations, which shows that Cl^- increases individual association rates and not just the K_D (S10 Fig). This change in association rates suggests that the pocket needs to be primed upon Cl^- binding to permit binding of glutamate. Cl^- does not affect predicted pK_a values for protonation after glutamate binding, they are close to pH 1 without Cl^- at 1.7 (0.6–2.1) or with Cl^- at 0.3 (-0.6–1.3). These low pK_a values ensure deprotonation of the inward-facing glutamate-bound transporter at neutral cytoplasmic pH (Fig 12C).

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Fig 12. Cl^- binding changes VGLUT1 glutamate transport parameters.

(A) Kinetic scheme describing glutamate transport by VGLUT1 with or without bound Cl^-. (B–H) Cl^--induced changes in glutamate binding/unbinding in the inward-facing conformation (B), in the pK_a of the second protonation site in the inward-facing conformation (C), in the singly protonated translocation rate (D), in pK_a for the second protonation site in the outward-facing conformation (E), in glutamate binding/unbinding in the outward-facing conformation (F), and in the doubly protonated translocation rate without substrate (G) or doubly protonated translocation rate with substrate (H). Rates along the transport cycle are positively numbered and on the left, next to rates going against the transport cycle with negative numbers. Protonation is represented by pK_a violin plots; other simulated rates are given as normalized RSS representing goodness of fit for a range of amplitudes in addition to violin plots depicting the amplitude range generated by exploratory mutation. All rates are shown at -160 mV or at 0 V in purple or dashed lines.

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Outward translocation rates of transporters with glutamate bound as substrate (_iHS) did not differ with and without Cl^- (Fig 12D), and neither did the pK_a of the subsequent protonation (Fig 12E). Glutamate release to the lumen was impaired by Cl^-, from 3.1 × 10¹⁰ (1.5 × 10¹⁰–8.1 × 10¹⁰) s^-1 to 7.4 × 10⁸ (4.4 × 10⁸–3.1 × 10⁹) s^-1 (Fig 12F). With a small increase in the final substrate-free (_oH₂) inward translocation step from 3152 (2608–6165) to 9293 (7602–9966) s^-1 (Fig 12G), Cl^- provides a net positive effect on glutamate transport. We set an upper limit of 1 s^-1 to the translocation rate constant of the doubly protonated substrate-bound transporter (_oH₂S) to the inward-facing state only with glutamate as the substrate (Fig 12H).

Glutamate transport is pronouncedly voltage dependent. The comparison of kinetic parameters at 0 mV and -160 mV in the presence of Cl^- demonstrate that the main effect of voltage is stimulation of the protonation of the substrate bound transporter (Fig 12E).

Allosteric regulation of transporter protonation contributes to VGLUT1 substrate selectivity

Fig 13 compares the pK_a values and transition rates for glutamate and aspartate transport in the Cl^--bound cycle, its voltage dependence is given by the corresponding z and d parameters in S11 Fig. Glutamate and aspartate bind at comparable rates to the doubly protonated inward-facing transporter, but with 5.1 × 10⁸ (2.5 × 10⁸–2.8 × 10⁹, median and parameter amplitude range at -160 mV) s^-1 glutamate unbinding is significantly faster than aspartate unbinding with 309 (181–366) s^-1 (Fig 13A and 13B). The pK_a of the second protonation site is 0.3 (-0.6–1.3) for glutamate-bound transporters and 5.1 (5.0–5.4) for aspartate-bound transporters (Fig 13C).

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Fig 13. Differences in the VGLUT1 glutamate and aspartate transport cycle.

(A) Kinetic scheme describing Cl^--bound and protonated VGLUT1 glutamate (left) or aspartate (right) transport function. (B) rates of substrate binding/unbinding in the inward-facing conformation. (C) pK_a values for the second protonation site in the inward-facing conformation. (D) Translocation rates for the singly protonated, substrate-bound conformation. (E) pK_a values for the second protonation site in the outward-facing conformation. (F) Rates of substrate binding/unbinding in the outward-facing conformation. (G) Translocation rates for the doubly protonated, substrate-bound conformation. Protonation is described by pK_a violin plots; other simulated rates are given as normalized RSS representing goodness of fit for a range of amplitudes in addition to violin plots depicting the amplitude range generated by exploratory mutation. Data for glutamate transport are shown in blue and for aspartate transport in yellow. All rates are shown at -160 mV.

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This difference results in preferred deprotonation of the glutamate-bound than of the aspartate-bound transporter; it supports glutamate translocation in the singly protonated state and H⁺-glutamate exchange. We tested the importance of the different substrate-bound pK_a values by modifying unbinding rates in both inward- and outward-facing conformation. Increasing the low glutamate value and decreasing the high aspartate value reduces transport rates, showing how important the optimized rates are for VGLUT1 transport rates (S12 Fig).

Substrate-bound outward translocation in the singly protonated state is the same for glutamate and aspartate (Fig 13D). Outward-facing pK_a values with aspartate were the same as the glutamate-bound transporter (Fig 13E), at a value comparable to the inward-facing aspartate-bound pK_a. With 7.4 × 10⁸ (4.4 × 10⁸–3.1 × 10⁹) s^-1, outward-facing VGLUT1 releases glutamate faster than aspartate with 1.0 × 10⁴ (8.4 × 10³–1.4 × 10⁴) s^-1 with similar binding rates (Figs 13F and S12 Fig).

To ensure coupled H⁺-glutamate transport, the glutamate translocation rate constant was limited to 1 s^-1 for doubly protonated VGLUT1. Under these restrictions, translocation is much faster for aspartate with 8.5 × 10⁴ (6.9 × 10⁴–1.2 × 10⁵) s^-1 than for glutamate with 1.4 (0.3–6.2) s^-1 while singly protonated outward translocation rates are equivalent (Fig 13D). This is consistent with the larger aspartate currents at very negative voltages in whole-cell recordings [4].

Aspartate binding induces an occluded state that impairs Cl^- binding/unbinding

VGLUT1_PM binds Cl^- in different protonation and substrate-bound states (Fig 14, the corresponding z and d parameters are given in S14 Fig). In transporters with no substrate bound, Cl^- binding has more pronounced effects on protonation of inward-facing states than of outward-facing states (Fig 14A). For inward-facing conformations, Cl^- decreases the pK_a of the first protonation from 6.3 (6.0–6.6) to 0.5 (0.4–0.7), but increases the pK_a of the second protonation from 4.0 (3.8–4.0) to 7.3 (7.2–7.5). For outward-facing conformations, Cl^- slightly increases pK_a values for the first and second protonation states, from 7.8 (7.7–7.9) to 8.2 (8.1–8.4) and from 7.7 (7.5–7.9) to 8.2 (8.1–8.4), respectively. Both the pK_a values and their Cl^- dependence are different from those of the protonation sites involved in VGLUT1 anion channel opening (Fig 4), consistent with the notion that different protonation sites are used for channel activation and transporter translocation.

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Fig 14. Binding and unbinding of protons and Cl^- to VGLUT1 in its neurotransmitter transport mode.

(A) pK_a for the first and second protonation, with and without Cl^-, for inward- and outward-facing transporters without substrate. (B) pK_a of the second protonation with bound substrate, with or without bound Cl^-. (C) Cl^-binding/unbinding rates and corresponding K_D values for outward-facing transporters without substrate (light→dark red indicates increasing protonation). (D) Cl^-binding/unbinding rates and corresponding K_D values for the singly or doubly protonated, substrate-bound, outward-facing state). Protonation is represented by pK_a violin plots; other simulated rates are given as normalized RSS representing goodness of fit for a range of amplitudes in addition to violin plots depicting the amplitude range generated by exploratory mutation. All rates are shown at -160 mV.

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Cl^- unbinding from transporters without substrate is promoted by deprotonation, despite a simultaneous but smaller increase in binding. With 0.48 (0.35–0.67) mM Cl^- the non-protonated state has the highest K_D, with a lower values of 0.18 (0.12–0.28) mM in the singly protonated state and 0.051 (0.038–0.076) mM in the doubly protonated state (Fig 14C). However, statistical testing only identified significant differences in individual Cl^- association rates for substrate-bound transporters in the singly protonated state (_oHS; S15 Fig). For substrate-bound VGLUT1 in the single protonation state, Cl^- binding and unbinding is much slower with bound aspartate than with bound glutamate: Cl^- binding with 1.1 × 10⁴ (7.7 × 10²–2.2 × 10⁴) M^-1 s^-1 versus 5.6 × 10⁵ (6.8 × 10⁴–4.6 × 10⁶) M^-1 s^-1 and Cl^- unbinding at 0.529 (0.002–1.433) s^-1 versus 1.9 × 10⁵ (1.7 × 10⁴–3.1 × 10⁶) s^-1 (Fig 14D). For double protonation, the Cl^- binding/unbinding rates for the glutamate- and aspartate-bound states are much closer; however, aspartate binding results in tighter Cl^- binding with a K_D of 9.5 × 10^-8 (7.2 × 10^-8–1.6 × 10^-7) mM compared to glutamate with a K_D of 0.024 (0.003–0.078) mM (Fig 14D). These changes are directly observable in fast Cl^- application experiments (Fig 9F), and indicate that binding of aspartate, but not of glutamate, modifies the Cl^- binding site towards higher affinity and lower association rates.

Expression plasmids, mutagenesis, and heterologous expression

HEK293T cells (Sigma-Aldrich) were grown in humidified incubators at 37°C and 95% air/5% CO₂ in Dulbecco’s modified Eagle Medium supplemented with 10% FBS, and 5 mL penicillin-streptavidin at 5,000 U/ml. To express VGLUT1 as an eGFP fusion protein, we inserted the coding region of eGFP into pcDNA3.1-rVGLUT1 (kindly provided by Dr. Shigeo Takamori at Doshisha University in Kyoto, Japan) at the 3′ end of the transporter coding region and mutated various dileucine-like endocytosis motifs to alanine to promote plasma membrane insertion using PCR-based techniques [4]. The H120A mutation was introduced into VGLUT1_PM using PCR-based techniques. Cells were transiently transfected using a calcium phosphate or lipofectamine precipitation method and examined 24 h later.

Whole-cell patch clamp and fluorescence measurements

Standard whole-cell patch clamp recordings were performed using EPC10 amplifiers, controlled by HEKA PatchMaster (Multi Channel Systems MCS GmbH, Reutlingen, Germany; [4]. We used borosilicate pipettes (Harvard Apparatus, Holliston, Massachusetts, USA) with a resistance of 0.9–3 MΩ and applied series resistance compensation and capacitance cancelation, resulting in a voltage error of < 5 mV. The standard bath solution contained (in mM) 136 choline chloride, 2 MgCl₂, and 30 HEPES or 50 MES; we adjusted the osmolarity of the bath solution with glucose to values at least 5 mOsm/L higher than the internal solution. HEPES was used as the buffer for external and internal pH values between 6.5 and 7.4, and was replaced with MES for more acidic perfusion solutions; in all cases, pH was adjusted with choline hydroxide. In experiments that used glutamate or aspartate in the pipette solution, 100 mM choline chloride was replaced by choline gluconate in the bath solution; cells were held at -50 mV before all measures other than the Cl^- current. The standard pipette solution contained (in mM) 140 choline anion_X, 5 EGTA, 5 Mg(OH)₂, and 30 HEPES, adjusted to pH 7.4 with TMA-OH (anion_X = Cl^-, glutamate^- or aspartate^-). For glutamate- or aspartate-based pipette solutions, we used internal agar salt bridges (made from plastic tubing filled with 0.5 M KCl in 2% agar) to connect the Ag/AgCl electrode. Where necessary, junction potentials were calculated and corrected. To support complete intracellular dialysis, we waited at least 2 min after establishing the whole-cell mode before starting electrical recordings. Except for Cl^- dependence of the anion channel function, current recordings were corrected for leakage currents by subtracting current amplitudes obtained in the same cell with external pH 7.4 under identical conditions. In an earlier publication [4], we carefully tested whether glutamate and aspartate currents measured in this way are mediated by VGLUT1_PM: both are blocked by Rose Bengal (a high-affinity, non-competitive VGLUT blocker), only negligible currents can be recorded under these conditions in untransfected HEK293T cells, and there is a linear relationship between expression levels and transport currents.

Fast solution exchanges were achieved by moving the solution interface of continuous perfusion flow around a cell using a PiezoMove P-601.30L or P-840.40 piezoelectric actuator (Physik Instrumente, Karlsruhe, Germany) controlled via a MXPZT controller (Siskiyou, Grants Pass, Oregon, USA) or PI E-836 Piezo Driver combined with a USBPGF-S1 Instrumentation Amplifier Low Pass Filter (Alligator Technologies, Charlottesville, Virginia, USA) to smoothen the signal and reduce vibration. Actuators were connected to the EPC10 amplifier and controlled using HEKA PatchMaster software. The mean time course of solution exchange was determined to be 0.87 ± 0.2 ms (n = 19, mean and 95% confidence interval) by recording the current responses of an open pipette after changing from a high to low [Cl^-] solution and measuring the time passing between 10% and 90% of the maximum current (S1 Fig). Two back-and-forth exchanges were performed, and the on-off pair with the best resolution was chosen and averaged. Even the slowest solution exchange is less than half of the fastest solution exchange time constant of our experimental data (S1C Fig).

Kinetic modeling

VGLUT chloride or glutamate/aspartate currents were simulated using kinetic models based on subsequent conformational changes and ligand binding/reactions. Changes in state occupation were computed using a set of differential rate equations

Eq 1

in which the state of the system is represented by the vector y(t), and transitions between states are encoded in a transition matrix, which contains the rate constants that determine the dynamics of the system. A simplified example of such states and matrix are shown in Fig 15. The evolution of the system is described by numerically integrating the differential equation, using the scipy.integrate.odeint function and providing the time evolution of the protein state distribution y(t). This method avoids conversions and lag time limitations by enabling time-continuous prediction of Cl^- ion fluxes and glutamate/aspartate transport. We only used time steps to compare the simulation output to experimental time course data in order to calculate RSS. These time steps were set to the recording frequency of the experiment, except the Cl^- jumps with aspartate current, which was filtered to mitigate its substantial length.

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Fig 15. Hypothetical kinetic model and corresponding transition matrix.

Directional rate numbers are chosen arbitrarily and full matrix equations are omitted for clarity. Any ligand binding rate would additionally be multiplied by the concentration of k0X, according to the convention used, for both its appearances in the matrix.

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Solving this matrix as a series of linear algebra equations provided steady-state distributions of kinetic states. The dependence of net rates on voltage and temperature, as an adaptation of the Arrhenius equation, is calculated as

Eq 2

where k1 is the rate constant (limited to < 10⁵ s^-1 for conformation changes and to 5 × 10⁹ for binding and unbinding of ligands), z is charge movement (-1 to + 1), d is a symmetry factor (0–1 [42], V is the voltage across the cell membrane, and the other elements are constants: F is the Faraday constant, R is the gas constant, and T is the absolute temperature. The inverse reaction k10 was calculated as:

Eq 3

To ensure microscopic reversibility, one rate constant was calculated from the clockwise and counterclockwise products, and one z variable was the sum of all other z values in each cycle. To prevent transporter behavior that is incompatible with experimental data, the rate constants describing non-protonated channel opening and doubly protonated glutamate-bound transporter transition between inward- and outward-facing conformation, each with or without bound Cl^-, were limited to 1 s^-1. The calculated net rates may exceed 1 s^-1 at -160 mV depending on their voltage dependence.

We used a population-based optimization procedure inspired by biological evolution, which was adapted from the Distributed Evolutionary Algorithms in Python (DEAP) software package [43]. To allow modification in either direction with minimal initial bias, we chose an initial parameter set with intermediate starting values of 1000 s^-1 for all rate constants, except the non-protonated channel opening and doubly protonated in- or outward transitions with glutamate, which were set to 1 s^-1 and proton-binding steps, which were set to 10⁸ s^-1. This initial parameter is copied into at least 50 parameter sets. With the exception of parameters calculated from others for detailed balance, all parameter sets were allowed to be mutated (p = 0.5) by a random amount. Additionally, randomly selected pairs of parameter sets may mate (p = 0.7); i.e., exchange values of specific parameters, with exchanged parameters being randomly chosen. Rate constants are limited to 10⁵ s^-1 for conformational changes and to 5 × 10⁹ s^-1 for binding and unbinding of ligands. Charge movement can range from -1 to +1, and symmetry from 0 to 1. If mutations cause parameter values outside these bounds, individuals will be declared unfit and removed from the population. The fitness of each parameter set is evaluated as the cumulative difference between simulated and experimental data. Comparisons are made as residual sums of square for calculated values and experimental time courses. These residual sums of square are multiplied by a chosen weight factor – to adjust the category influence on fitness – and summed up. We usually increase weight multiplier for the worst fits, and scale down metrics that appear to dominate changes in fit quality. This repeated adjustment sustains a selective pressure to drive the optimization of simulation outputs where accuracy needs to be improved.

From a group of individuals, a tournament-style selection picks the parameter set with the best fitness: three parameter sets are randomly selected from the current generation, and the one with the best fitness is selected for each slot in the next generation (based on https://deap.readthedocs.io/en/devel/api/tools.html#deap.tools.selTournament).

We converted the kinetic transition rates into transition probabilities in order to allow for the calculation of preferred pathways of opening and closing of the anion channel (Figs 3L and 7L), using the reactive flux module of the Deeptime Python library which uses transition path theory [44]. Activation pathways were described starting from the apo state to any conductive state, deactivation pathways from the two most common open states (oH or oClH₂) to either of the two unprotonated closed states (apo and cCl).

For the comparison of kinetic parameters, we used two tests, and changes were only considered significant after passing both tests. The first test is based on the collection of multiple parameter set variants generated via ‘exploratory mutation’ of a modified DEAP cycle. All parameter sets with RSS values that are less than 25% larger than the optimum values for all simulated metrics and time courses are shown in violin plots, together with the median and the confidence interval that provides the range of variation generated during exploratory mutation. Parameters are considered different when there is no overlap of the confidence interval. Whereas >10,000 sets with >3000 variants for each parameter were generated for the Cl^- channel model, we limited the data size for glutamate/aspartate transport by removing individuals that did not vary parameters describing protonation and generated >980 variants from >20,000 individual sets from >50,000 generations. A second statistical test to calculate the change in the quality of fit is based on varying only the compared parameter [27]. In such a plot, a sharply defined and distinct parameter value is associated with instantly increasing RSS upon small changes in parameter values without overlap with parameter values obtained under other conditions. We assume two parameters to be indistinct when values overlap at RSS of below 150%.

For current predictions in the VGLUT1_PM channel mode, the distribution of relative state occupations in the transition matrix was used to calculate the fraction of open states, i.e., the open probability, as the output value. Numerical weights were assigned to individual simulated metrics and time courses to control the driving force optimizing simulation accuracy through parameter mutation. A large weight ensures that the WT model remains close to the calculated open probability of 0.24 at 140 mM Cl^-, pH 5.5, and -160 mV [4]. Each simulation calculates the modification of steady-state currents by [Cl^-]_o, pH, or voltage relative to this open probability and the time-dependent changes of currents relative to the highest steady-state current in each experiment. Active transport was calculated as the sum of net transition fluxes between states, multiplied by the corresponding z value. Here, a microscopic reversibility charge offset of -1 or 2 in each transport cycle accounts for current generation. Similarly to how Cl^- channel models were trained to mimic experimentally determined open probability, the active transport model uses the calculated glutamate (561 s^-1) and aspartate (2581 s^-1) transport rates.

Quantification and statistical analysis

Data are given either as the mean ± 95% confidence interval or as violin plots showing the distribution of data with the median and exploratory mutation value range. We calculated secondary binding rates for Cl^-, glutamate, and aspartate to normalize them, dividing the binding rate constant by the ligand concentration: in mM when calculating K_D (expressed in mM) and in M for the rates themselves (expressed in M^-1 s^-1).

Measurements were taken from distinct samples. Mean and confidence intervals of time courses, dependence fits, and fit parameters were either from individual fits (chloride dependence of glutamate and aspartate) or determined by bootstrapping (other dependence fits and time constants). For patch clamp electrophysiology experiments, sample sizes correspond to the number of patched cells and are given in the Figure or legend. For statistical analysis of two groups, we used two-tailed bootstrap hypothesis testing via the bootstrap t-statistic of bootstrapped means, F-tests to determine the number of exponents in current activation and deactivation, and one-sample Wilcoxon signed rank tests when comparing fits of means to distributions of groups of individually fitted cells.

We fitted time courses of VGLUT1_PM currents with mono- or biexponential functions and concentration dependence by global bootstrapping, with the Michaelis-Menten equation for Cl^- and the Hill equation for pH to better capture saturation. To generate modest and comparable confidence intervals, we used sampling of 1000 for dependence data and time constants. To ensure reliable p-values, we used higher sampling of 10,000 for bootstrap hypothesis testing between different datasets.