computer modeling in molecular biology.pdf

6 Theory of Transport in Ion Channels 137ogy is to serve as a bridge between the microscopic model and the macroscopicobservables. In the case of ion channels, Eyring Rate Theory [52] and Nernst-Planckdiffusion [53] provide an effective conceptual framework to make full use of the informationgathered from the molecular dynamics simulations.The goal of this chapter is to provide an introduction to the modern moleculardynamics simulation techniques that are particularly useful in theoretical studies ofion channels. The chapter is divided in 4 sections. The phenomenological theoriestraditionally used to describe experimental data are briefly introduced in Section 6.2.The general methodology applied to the gramicidin channel is explained in Section6.3. The chapter is concluded with an outlook at future applications in Section6.4.6.2 Traditional Phenomenological DescriptionsTraditional approaches, such as Eyring Rate Theory (ERT) [52], or the Nernst-Planck (NP) continuum diffusion equation [53], are useful phenomenological toolsto account for the experimentally observed current-voltage relation, i[A 4 [l]. Bothapproaches describe the movements of ions across membrane channels as chaoticrandom displacements driven by an electrochemical free energy potential, ’ W,,, (x).ERT describes the movements of ions as a sequence of sudden stochastic “hoppingevents” across barriers separating energetically favorable discrete wells [52] ; in contrast,the one-dimensional NP equation describes the movements of ions along theaxis of the channel as a random continuous diffusion process [53]. ERT models areexpressed in terms of a set of equations relating the net stationary flux, J, and theoccupation probability of the i-th and i + 1-th sites, Pi and Pi+l,where ki and are forward and backward jump rates, respectively [52]. It isgenerally assumed that the rates have an Arrhenius-like form with a voltage-independentdynamical pre-exponential frequency factor, Fp [52, 581,where W,,, (xi) and wot (xL) are the electrochemical free energy at the i-th barrierand well, respectively. Similarly, the NP equation relates the net stationary flux, J,to the probability density per unit length, P(x),