computer modeling in molecular biology.pdf

6 Theory of Transport in Zon Channels 139saturation as a function of the permeant ion concentration. With the same concentration,[C], on both sides of the membrane the concentration-dependent conductance,A([C]), is,where Kb is the equilibrium binding constant to the pore. This Michaelis-Mentenform is obtained from both the NP and the ERT approaches and follows from theone-ion pore assumption. The maximum conductance, Amax , reached at saturatingconcentrations can be written as,q2 keff/(n + l)n ERTAmax = - k,T [Deff/L2 (6-9)NPIn Eq. (6-9), k,, is an effective hopping rate constant, defined in terms of theweighted averages over all the discrete sites of the pore,(6-10)obtained by assuming that sites 1 to n are inside the pore and sites 0 and n + 1 belongto the aqueous phases [52]; Deff is an effective diffusion constant of the ion insidethe pore, defined in terms of weighted spatial averages over the full length of thepore,These expressions, which may seem unwieldy and difficult to understand, deserve afew explanations. First, it is observed that the expression for Amax-ERT is considerablysimpler in the special case where the transition rates are all equal since k,,,reduces to k. Moreover, despite their very different appearances the expressions forA,,, from ERT and NP are closely related. For example, a Deff corresponding tokL2/n2 is obtained if the diffusion takes place as a sequence of random jumps occurringat a rate, k, between a large number of identical site, n, separated by L/n (seealso Section 6.3.5). Lastly, a simple physical interpretation of A,,-NP can begiven. It is the conductance of a cylinder of length, L, and area, S, containing a