computer modeling in molecular biology.pdf

110 E. Westhof; C. Rubin-Carrez, and K Fritschwhere I/K is the Debye screening distance, or distance at which the electrostaticpotential is reduced to l/e of its value in the absence of screening by the mobile ions,and G the ionic radius of the counterions. At the physiological ionic strength of100 mM, the Debye screening distance is about 10 A. With filamentous-like polyionslike DNA, the phenomenum of counterion condensation must be considered. Whenthe polyion is modelled as an infinitely long and uniformly spaced line of charges,there is a condensed fraction of counterions which depends only on the linear chargedensity of the polyion and the valence of the counterion and which is invariant tosalt concentrations in excess of 0.1 M. For NaCl aqueous solutions of B-DNA, 76%of the phosphate charge is theoretically compensated by condensed counterions. Ina recent work, Fenley et al. [23] have investigated the effect of the finite length ofthe polyion: at 10-5 M, a 10 bp DNA oligomer has about 45% of its phosphatecharge compensated. These two macroscopic approaches are incorporated in twoways in MD simulations. First, the cut-off for the calculations of the electrostaticterms is set to about 10 A and, secondly, phosphate charges are scaled down to about-0.2. When applied brutally, the latter change has the drawback of decreasing thecharges on the phosphate to values below those of some polar atoms in the bases(e. g. the amino group of guanine residues).We have recently described a fast algorithm for calculating any dielectric functionin MD simulations of biological macromolecules [24]. With no increase in CPUtime, one can add a constant to take care of ion condensation, a term for representingDebye-Huckel screening, and any dielectric function which accounts for saturationof water dipoles.5.6 Explicit Treatment of the SolventThe complete microscopic description of the solvent is theoretically the only firmlygrounded method. Principally, it sounds easy to implement although practically itis fraught with difficulties. A long period of equilibration and thermalization isnecessary in order to avoid strongly unfavorable energetic interactions between thesolute and the solvent molecules with concomitant deformation of the solute.Generally, the conformational changes introduced by collisions between the soluteand the solvent molecules are irreversible and the ensuing simulation does not reflectmolecular dynamics around the equilibrium (Figures 5-2 and 5-3).For DNA systems [25] the following equilibration protocol was developped(Figure 5-4). First, in order to eliminate close contacts and unfavorable geometricstrains in the initial system, 200 steps of steepest descent minimization are appliedon the water molecules. To disorder the periodicity of the box, which is built fromsmaller boxes (each box containing 216 Monte Carlo water molecules), this step is