computer modeling in molecular biology.pdf

136 Benoit Roux[18-201. The gramicidin channel exhibits functional behavior similar to far morecomplex macromolecular biological structures, and for this reason, has proved to bean extremely useful model system to study the principles governing ion transportacross lipid membranes. It has been the object of numerous experimental [21-271 aswell as theoretical investigations [28-401, and a great wealth of information is knownabout its membrane-bound ion-conducting conformation [41-501. Gramicidin is atthis moment the best characterized molecular pore [51].Comprehension of how any ion channel works in terms of its underlying atomicstructure, even the one formed by the relatively simple gramicidin molecule, representsan outstanding challenge. Research on ion channels has now reached the pointwhere the design and interpretation of experiments depends upon the availability oftheoretical calculations to help formulate and develop a detailed realistic microscopicpicture of ion permeation. Despite their usefulness, traditional phenomenologicaldescriptions of ion permeation based on Eyring Rate Theory [52] or Nernst-Planckdiffusion [53] cannot fulfill this purpose. For example, attempts to explain theobserved effects of amino acid substitution on current-voltage measurements oftenneed to rely on atomic models of the channel structure [8-10, 54, 551. Moleculardynamics simulation is a powerful theoretical approach to investigate the functionof complex macromolecular structures [56]. It consists in calculating the position ofthe atoms as a function of time, using detailed models of the microscopic forcesoperating between them, by integrating numerically the classical equations ofmotion. Although molecular dynamics is used to study biological systems of increasingcomplexity [56], theoretical investigations of ion transport are faced with particularlydifficult and serious problems. A first problem arises from the magnitudeof the interactions involved. The large hydration energies of ions, around-400 kJ/mol for Na’, contrast with the activation energies deduced from experimentallyobserved ion-fluxes, which generally do not exceed 10 k,T [l]. Thisimplies that the energetics of ion transport results from a delicate balance of verylarge interactions. Therefore, special care must be taken to construct an accurate andrealistic potential energy function to be used in the calculations. A second problemarises from the time-scales involved. The passage of one ion across a channel takesplace on a microsecond time-scale and realistic simulations of biological systems,which typically do not exceed a few nanoseconds, are insufficiently short. Althoughthe most exact and realistic information is provided by straight molecular dynamicstrajectories, simple “brute force” simulations cannot account for the time-scales ofion permeation. A variety of special computational approaches called “biasedsampling” techniques are necessary to extract information about these slower andmore complex processes. A last difficulty is the translation of the results obtainedfrom a microscopic model into macroscopic observables such as channel conductanceand current-voltage relations. Here, the traditional phenomenologies play animportant role. As in the fundamental formulation of non-equilibrium statisticalmechanical theories of transport coefficients [57], the purpose of the phenomenol-