computer modeling in molecular biology.pdf

164 Benoft RouxTable 6-3. Pre-exponential frequency factors.ExpressionActivated dynamicsHigh friction limitEyring’s Transition State TheoryGas phase k,T/hFp in ps-’0.440.324.006.25coupling contribute equally to the total static friction acting on Na’ . The importanceof the water-channel cross-coupling contribution suggests that the ion-ligandcomplex is tightly structured.It is of interest to compare the pre-exponential factor, Fp, obtained from approximateexpressions with the “exact” result of the activated dynamics trajectories.Various expressions for Fp are given in Table 6-3. It is seen that the TST rate iswrong by one order of magnitude in the case of Na’ movements in the interior ofthe &helix. The reason is that the TST pre-exponential dynamical factor, solelydetermined by the potential of mean force and the mass of the ion, ignores all frictionaland collisional effects and represents an upper bound to the exact Fp.Generally the TST rate overestimates the exact rate in dense liquid systems [94].Although it does not yield the exact result, the high friction limit provides a muchbetter estimate than TST in the present case. Inertial and “memory” effects due tothe finite decay time of the time-dependent friction, neglected in the high frictionapproximation, are responsible for the remaining discrepancy. More sophisticatedapproximations have been proposed to account for such effects [94, 951. One expressionfor the pre-exponential dynamical factor, often mentioned in early publicationsusing ERT models to describe ion channels [52] is k,T/h, where h is Planck’s constant.This expression, designed for gas phase, is not valid for reactions taking placein dense liquids and yields a Fp that is largely overestimated.6.4 ConclusionsA coherent, though incomplete, picture of the permeation process through thegramicidin channel has emerged from molecular dynamics simulations based ondetailed atomic models with realistic microscopic interactions. Based on our experiencewith the gramicidin channel, it is possible to propose a general strategy fortheoretical studies of ion transport in complex biological systems. First, the importantmicroscopic interactions should be identified, and an accurate empirical energyfunction developed, based on available experimental data in combination with ac-