The mechanism of fast-gate opening in ClC-0

Abstract

ClC-0 is a chloride channel whose gating is sensitive to both voltage and chloride. Based on analysis of gating kinetics using single-channel recordings, a five-state model was proposed to describe the dependence of ClC-0 fast-gate opening on voltage and external chloride (Chen, T.-Y., and C. Miller. 1996. J. Gen. Physiol. 108:237-250). We aimed to use this five-state model as a starting point for understanding the structural changes that occur during gating. Using macroscopic patch recordings, we were able to reproduce the effects of voltage and chloride that were reported by Chen and Miller and to fit our opening rate constant data to the five-state model. Upon further analysis of both our data and those of Chen and Miller, we learned that in contrast to their conclusions, (a) the features in the data are not adequate to rule out a simpler four-state model, and (b) the chloride-binding step is voltage dependent. In order to be able to evaluate the effects of mutants on gating (described in the companion paper, see Engh et al. on p. 351 of this issue), we developed a method for determining the error on gating model parameters, and evaluated the sources of this error. To begin to mesh the kinetic model(s) with the known CLC structures, a model of ClC-0 was generated computationally based on the X-ray crystal structure of the prokaryotic homolog ClC-ec1. Analysis of pore electrostatics in this homology model suggests that at least two of the conclusions derived from the gating kinetics analysis are consistent with the known CLC structures: (1) chloride binding is necessary for channel opening, and (2) chloride binding to any of the three known chloride-binding sites must be voltage dependent.

Figure 1.

Effects of external chloride on gating. (A) Voltage pulse protocol (top left) and current responses in 5, 110, and 310 mM external chloride. (B) Tail-current analysis was used to determine the apparent open probability (P_o) as a function of voltage (V) (see Materials and methods) (n = 5–26 for external chloride concentrations <600 mM, and n = 2–5 for 610 mM). These plots were fit as described in Materials and methods (solid lines), and gating parameters were derived (Table II).

Figure 2.

Effect of voltage and external chloride on the kinetics of fast gating. (A and C) opening (α) and closing (β) rate constants for each test voltage. For test pulses (see examples in Fig. 1 A) where current decay could be seen, the decay was fit to a single exponential to derive the decay constant (1/τ). This was used in conjunction with the open probability (P_o) to calculate α and β (Chen and Chen, 2001): α = P _o/τ ; β = (1/τ) − α. For each condition (voltage (V), external chloride activity ([Cl]_ext), we recorded from at least five patches and derived the rate constant for each patch. For the 610 mM chloride condition, we recorded two to five patches for each voltage. For a given condition, the rate constants from all patches were averaged; the error bars show the SEM. (B) For comparison, opening rate constant data were taken from the graphs published by Chen and Miller (1996) and replotted. (A and B) Each opening rate constant dataset was globally fit to the five-state model (Scheme 2, Eqs. S5–S8 in the online supplemental material) either holding z _c constant (dashed lines) or letting all six parameters find their best-fit values (solid lines). In the case where z _c was held constant, the values of z _c (0.09 in [A] and 0.08 in [B]) were chosen based on the analysis using the Method 1 and the four-state model, where only a subset of voltages were included (see analysis in the supplemental material and parameter values in Fig. 3). The parameters derived from all of these fits are shown in Fig. 5.

Figure 3.

Parameter values for the four-state gating model. Values for the four-state model parameters were derived for both the dataset published by Chen and Miller in 1996 (CM) and for the dataset we obtained using macroscopic recordings (EM). These parameter values were derived using two different fitting methods: (1) Method 1, used by Chen and Miller, shown in Figure S4; and (2) Method 2, globally fitting the opening rate constant as a function of voltage and external chloride (α(V, [Cl]_ext)), allowing all six parameters to be free, shown as solid lines in Fig. S5, C and F. Method 1 was performed including either all the voltages (all) or some subset of the voltages (sub). For Method 1, the error bars show the standard deviation calculated by the fitting algorithm (for fits shown in Fig. S4, B and D); for Method 2, the error bars show the 95% confidence limits determined as described in the text. For comparison, the first column shows the parameter values (z ₁ ^*, z ₂ ^*, and z _c) published by Chen and Miller (pub. val.); values for α₁ ^*(0), α₂ ^*(0), and K _c(0) were not reported.

Figure 4.

Error analysis on fits to the five-state model. To determine the certainty of the best-fit values found when globally fitting α(V, [Cl]_ext) to the five-state model (Method 2), we used the procedure described in the text. Each of the plots shows how varying one of the six parameters affects the goodness of fit to our data as given by the sum of squares (solid lines). The sum of squares at 95% confidence is shown as a dashed line, and the parameter values at the intersections of the solid line and dashed line represent the 95% confidence limits, shown as error bars in Fig. 5. A similar procedure was used to calculate the 95% confidence limits on the four-state model parameter values, which are shown as error bars in Fig. 3, columns 6 and 7 of each graph.

Figure 5.

Parameter values for the five-state gating model. Values for the five-state model parameters were derived for both the dataset published by Chen and Miller in 1996 (CM) and for the dataset we obtained using macroscopic recordings (EM). In both cases, parameter values were derived by globally fitting the opening rate constant as a function of voltage and external chloride (α(V, [Cl]_ext)) (Method 2) (fits shown in Fig. 2, A and B), either with all six parameters free (free) or while holding z _c at 0.08 (held) (see the supplemental material for explanation, and Figs. 3 and S4, subset of voltages). The error bars show the 95% confidence limits determined as described in the text. For comparison, the first column shows the parameter values published by Chen and Miller (*).

Figure 6.

Chloride binding and movement in the pore. (A) The ClC-0 homology models created as described in Materials and methods were used to calculate the electrostatic potential at various positions in the pore (V/V _tm) under an externally applied transmembrane voltage of −200 mV. Shown here is the fraction of the transmembrane voltage along a hypothetical permeation pathway, with S _int, S _cen, S _ext at sites 10, 14, and 16, respectively. (B) The ClC-0 homology model was used to calculate the electrostatic contribution to the free energy of chloride binding (ΔG _b) to each site in the pore (starting from the cytoplasmic side: S _int, S _cen, S _ext) with either zero (circles) or two (squares) chlorides already bound in the pore. The dielectric constant used for the protein was 4. In both A and B, lines connect data points for ease in viewing, and error bars represent an estimate of the discretization error arising from the grid-based Poisson-Boltzmann calculations (see Materials and methods).

Figure 7.

Possible models for chloride movement during depolarization-activated fast gating. Evidence from previously published papers and our kinetic and homology model analysis was used to narrow down the possible models for chloride movement during depolarization-activated fast-gate opening to those shown (see text). The channel begins in the closed state C, binds chloride to reach the closed state C·Cl, and then goes through another depolarization-activated transition to reach the open state O. This is depicted at the top of both A and B. K _c is the apparent equilibrium constant for chloride dissociation, and α₂ ^* is the rate constant for the second step, C·Cl→O. In A, depicted below each of these states (C, C·Cl, and O) are their possible chloride occupancy states, with empty circles depicting vacant chloride binding sites, and filled circles depicting filled chloride binding sites. Lines between these chloride-occupancy states indicate transitions corresponding to either C→C·Cl or C·Cl→O. Dashed lines indicate C·Cl→O transitions that involve chloride binding to the pore. Evidence from our analysis of gating kinetics and the ClC-0 homology models further narrowed the possibilities to those shown in B. In Model 1, the dashed line outlines the microstates that are all part of C·Cl. K ₁, K ₂, and K ₃ are microscopic equilibrium constants, and k ₄ is a microscopic rate constant. In Model 2, the second step has to involve some conformational change that opens the channel but does not change chloride occupancy.