Total charge movement per channel. The relation between gating charge displacement and the voltage sensitivity of activation - PubMed (original) (raw)

Total charge movement per channel. The relation between gating charge displacement and the voltage sensitivity of activation

D Sigg et al. J Gen Physiol. 1997 Jan.

Abstract

One measure of the voltage dependence of ion channel conductance is the amount of gating charge that moves during activation and vice versa. The limiting slope method, introduced by Almers (Almers, W. 1978. Rev. Physiol. Biochem. Pharmacol. 82:96-190), exploits the relationship of charge movement and voltage sensitivity, yielding a lower limit to the range of single channel gating charge displacement. In practice, the technique is plagued by low experimental resolution due to the requirement that the logarithmic voltage sensitivity of activation be measured at very low probabilities of opening. In addition, the linear sequential models to which the original theory was restricted needed to be expanded to accommodate the complexity of mechanisms available for the activation of channels. In this communication, we refine the theory by developing a relationship between the mean activation charge displacement (a measure of the voltage sensitivity of activation) and the gating charge displacement (the integral of gating current). We demonstrate that recording the equilibrium gating charge displacement as an adjunct to the limiting slope technique greatly improves accuracy under conditions where the plots of mean activation charge displacement and gross gating charge displacement versus voltage can be superimposed. We explore this relationship for a wide variety of channel models, which include those having a continuous density of states, nonsequential activation pathways, and subconductance states. We introduce new criteria for the appropriate use of the limiting slope procedure and provide a practical example of the theory applied to low resolution simulation data.

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Figures

Figure 1

Figure 1

(A) An example of a kinetic model satisfying Almers' criterion for Eq. 1. It consists of a linear sequence of discrete closed states followed by a single open state. The total range in gating charge displacement is Δ_q_. A more generalized model (B) includes degeneracies produced by additional degrees of freedom (indicated by the variable ξ), multiple open states, and peripheral charge movement. In a discrete model with no subconductance states we can graphically display the range in essential charge movement, Δ_q_ e, as a sum of its components; Δ_q_ a+ and Δ_q_ a− are the range in positive and negative activation charge displacement, respectively, and Δ_q_ l is the range in latent charge displacement. The peripheral charge movement, Δ_q_ p, is shown on the lower panel with its own reaction coordinate, indicating independence from the main activation sequence. The total charge movement per channel is Δ_q_ = Δ_q_ e + Δ_q_ p, which is the value obtained from the Q/N procedure (Δ_q_ Q/N). Use of the limiting slope procedure estimates the value of Δ_q_ a+ in the hyperpolarizing direction and Δ_q_ a− in the depolarizing direction. In a saturated channel, Δ_q_ l and Δ_q_ p are zero.

Figure 4

Figure 4

(A and B) Model a represents a saturated channel with a closed loop of nonconducting states followed by one open state; Δ_q_ = 4 eu. By severing the connections indicated by the vertical lines (model b), we obtain two independent charge relay systems: one essential, moving 4 eu of gating charge (Δ_q_ e), and the other peripheral, moving 2 eu (Δ_q_ p). In addition to a slight shift to the right of the P o-V (C ), the channel becomes unsaturated (D), though use of the limiting slope procedure in this case would produce the correct estimate of essential gating charge movement (Δ_qa_ = Δ_q_ e).

Figure 9

Figure 9

(A) Representative single channel traces (thin line) of simulated gating (top) and ionic (middle) currents using a voltage ramp protocol (bottom). The model (shown at the lower right of the figure) is discrete and saturated; Δ_q_ = 10 eu. The forward and backward rates at zero potential for all transitions were 5 and 1 ms−1, respectively. The transition charge movements were 2 eu. Symmetric barriers were used. The times of transition events were obtained using Eq. 14. Single channel traces were then constructed and discretized at 101.3 μ_s_ with 4,000 points, and subsequently filtered (cutoff frequency 1 kHz) using a digital Gaussian filter with 0.5-ms delay. The mean of 106 accumulated single channel gating and ionic currents (thick line) are superimposed onto a corresponding representative single channel trace (noisy thin line). The mean gating current was scaled up by a factor of 50 to make it comparable to the single channel trace. (B) The sample estimate of the mean activation charge displacement q – a ( solid line) and the _Q_-V curve (dashed line) were derived from the ramp data (see

methods

). The true _Q_-V (unfilled circles) was calculated numerically every 1 mV using the formula for 〈_q_〉 given in the theory section. Both _Q_-V curves were inverted and independently rescaled to superimpose on the smooth region of q – a.

Figure 7

Figure 7

A continuum model that approximates a two-state discrete model. The probability density p(q) for zero voltage is calculated from the potential of mean force G(q) using the Boltzmann distribution. The channel opens when the gating charge displacement reaches 0.9 · Δ_q_. Panels A and B are comparable to those of Fig. 2, model 2_a_.

Figure 2

Figure 2

(A) Plots of open probability (P o) and normalized gating charge displacement (Q) vs. voltage for a two-state model a and two models with degenerate states (b and c). (B) In each case, the mean activation charge displacement, 〈q a〉, and the mean gating charge displacement, 〈q_〉 (inverted and displaced by Δ_q), lie on the same plot, indicating that the channels are saturated.

Figure 3

Figure 3

Model a is a linear three state scheme satisfying Almers' criterion. The P o is displaced to the right of center (A), though the channel is saturated (B). The open probability in model b vanishes at both ends of the voltage axis (C). Consequently, it has a nonvanishing value for the latent charge displacement, splitting the activation charge displacement into positive and negative components (D). Model c has two open states, displacing P o(V ) to the left of the Q -V (E ), and resulting in a limiting slope estimate of only 50% of the total gating charge movement (F ).

Figure 5

Figure 5

Predictions from a continuum model with a flat potential landscape. The transition from closed to open pore is abrupt and occurs at the value a_Δ_q, where a ranges from 0.1 to 0.9 in increments of one-tenth. (A) As the value of a decreases, the P o -V curve crosses the Q -V at increasingly negative potentials. (B) The limiting value of 〈q a〉 is equal to range of gating charge movement that occurs when the channel is closed.

Figure 6

Figure 6

A continuum model with a slower rise of the fractional conduction along the q axis. The equation used for f(q) is [1 + exp(−b(q − a_Δ_q)]−1 where the slope factor b takes on the values: 2, 5, 10, 15, 20, 50, and infinity. The case of b = infinity is identical to the model in Fig. 5 with a = 0.9. A shallow slope lowers the open probability at extreme depolarizing potentials (A) and produces a downward shift in the mean activation charge displacement at hyperpolarized potentials (B).

Figure 8

Figure 8

A 5-state model with subconductance states and varying potential landscape. The values of G and f in increasing order of q are G i = {4, −1, 3, 0, 4}kT and f i = {0, 0.1, 0.3, 0.6, 1.0}. (B) The initial rise in 〈q a〉 at V ≃ 0 mV could be mistaken for the value of the limiting slope under conditions of poor experimental resolution, but knowledge of the Q -V would indicate that the gating charge had not yet saturated.

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