Nonlinear drift-diffusion model of gating in K and nACh ion channels

Nonlinear drift-diffusion model of gating in the fast Cl channel

“…The distribution function f c (t) = −dP c (t)/dt obtained from Eq. ( 7) is also in good agreement with the approximate power law distributions of closed times from a K channel and a nACh channel when ν ≈ −0.5 [16], and a fast Cl channel when ν ≈ −0.3 (see Fig. 3).…”

“…The voltage dependence of the channel opening and closing rate functions may be derived from the mean state residence time for an interacting diffusion regime [11,12] or from an expression for the quasi-stationary diffusion current between the open and closed regions at each membrane surface, and in the latter case, the interaction between the open state probability and the membrane potential may be described by a Lagrangian (see Appendix). It may be shown that the closed state dwell-time distribution f c (t) derived from a Fokker-Planck equation with a nonlinear diffusion coefficient D(x) = D c exp(−γx), γ > 0 and a linear potential U c (x) is in good agreement with experimental data from a K and nACh channel and for intermediate times, f c (t) ∝ t −1.5 when ν = U ′ c /γ = −0.5 where U ′ c = ∂U c (x)∂x is a constant [16]. In this paper, it is shown analytically that if γ is sufficiently large, the solution of the Fokker-Planck equation has an intermediate power law approximation f c (t) ∝ t −2−ν , and provides a good description of the data from a fast Cl channel when ν ≈ −0.3.…”

“…∂x is a constant [16]. In this paper, it is shown analytically that if γ is sufficiently large, the solution of the Fokker-Planck equation has an intermediate power law approximation f c (t) ∝ t −2−ν , and provides a good description of the data from a fast Cl channel when ν ≈ −0.3.…”

“…When ν = −0.5 this expression reduces to P c (t) ≈ τ c /πt/r c which describes the power law approximation for a K and nACh ion channel [16] whereas for a fast Cl channel, ν ≈ −0.3 and P c (t) ≈ 0.1(τ c /t) 0.7 /r c π. If t > τ c , P c (t) ≈ a 1 exp(−D c µ 2 1 t) where µ 1 is a solution of Eq.…”

Stochastic diffusion model of multistep activation in a voltage-dependent K channel

“…18 An analytical solution of the stochastic diffusion equation also has an exponential relaxation for a large ramp potential, but as the voltage dependent barrier is attenuated, the response to a membrane depolarization is characterized by a power law for intermediate times, and therefore is in accord with the distribution of closed times recorded during a patch clamp of an ion channel. [19][20][21][22][23][24] If it is assumed that the diffusion barrier is sufficiently large at the entrance to the protein region of the gating pore, the activation process may be described by a rate equation for each membrane depolarization. 25 In this paper, an expression for the energy of an S4 helix is derived which is dependent on the transverse displacement and rotation of the sensor within a gating pore.…”