Equilibrium simulations

VER in liquid O 2 is far too slow to be studied directly by nonequilibrium simulations. The force-correlation function, equation (C3.5.2), was computed from an equilibrium simulation of rigid O2. The VER rate constant given in equation (C3.5.3) is proportional to the Fourier transfonn of the force-correlation function at the Oj frequency. Fiowever, there are two significant practical difficulties. First, the Fourier transfonn, denoted [Pg.3041]

Equilibrium Simulation. The equilibrium simulations described here were carried out by Magda et ai (12.). The pore walls modelled are two flat, seml-lnflnlte solids separated by a distance h In the x-dlrectlon. The wall-fluid potential Is the 10-4 or 10-4-3 potential, l.e.. 

The structure is induced by a pore wall potential, which has the form of the potential used In the equilibrium simulations (Equation 41) with 6 = 0, = 4e and = a, (e, a are the parameters of the truncated 12-6... 

The density profile for the micropore fluid was determined as In the equilibrium simulations. In a similar way the flow velocity profile for both systems was determined by dividing the liquid slab Into ten slices and calculating the average velocity of the particles In each slice. The velocity profile for the bulk system must be linear as macroscopic fluid mechanics predict. 

Daura, X., van Gunsteren, W. F., and Mark, A. E. (1999b). Folding-unfolding thermodynamics of a /3-heptapeptide from equilibrium simulations. Proteins Strud. Fund. 

Create an equilibrium ensemble of starting configurations. To create N initial conformations representative of the equilibrium ensemble for Hamiltonian - // (z. A = 0), one can, for instance, save conformations at regular intervals during a long equilibrium simulation. In some cases, accelerated sampling procedures may be necessary. 

The other major limitation of membrane simulations is the time and length scale we are able to simulate. We are currently able to reach a microsecond, but tens to hundreds of nanosecond simulations are more common, especially in free energy calculations. The slow diffusion of lipids means we are not able to observe many biologically interesting phenomena using equilibrium simulations. For example, we would not observe pore formation in an unperturbed bilayer system during an equilibrium simulation, and even pore dissipation is at the limits of current computational accessibility. 

Using preformed pores in a DMPC bilayer, Gurtovenko and Vattulainen [82] investigated the translocation of DMPC across a pore. It was shown that multiple lipids diffused across the pore before it dissipated, providing support for pore-mediated flip-flop as mechanism for passive flip-flop. The timescale for pore dissipation was found to be 35-200 ns, at the limits of current computational capability for equilibrium simulations. 

The results reported below were obtained from equilibrium simulations that were performed for a single polypeptide which is either freely diffusing or surface-immobilized. The surface was assumed to be planar, and to consist of beads of diameter a that were arranged on a 2D square lattice with distance a between nearest neighbors. Surface-immobilization was introduced by fixing the position of the 40-th bead such that it lies a distance a above a surface bead. The interaction between the polypeptide and surface beads is described by a pair-wise potential of the form ... 

While the results presented in Fig. 11 and 12 are clearly in the regime yxz 1, the question is how close do they correspond to the experimental situation studied by Klein et al. [16]. From earlier work on mapping the equilibrium simulations to the experiments of Taunton et al. [37], we [46] found that a—1.5 nm for the case of polystyrene of MW= A X105 in toluene. (The analysis was done for a continuum solvent simulation but the results will not change sig-... 

IV.2. Monte Carlo equilibrium simulations of ligand-protein thermodynamics... 

Figure 7 The time-dependent history of the SB203386-HIV-1 protease system as a function of rmsd of the current ligand conformation relative to the crystal structure versus Monte Carlo cycle at 300K during equilibrium simulations with the ensemble of 6 protein conformations (a) and the ensemble of 32 protein conformations (b). The frequency of protein conformations for the SB203386-HIV-1 protease complex at T=300K in equilibrium simulations with the ensemble of 6 protein conformations (c) and the ensemble of 32 protein conformations (d). The piecewise energy function is used. The unfilled histogram is the total frequency for each conformation, the filled histogram is the frequency for ligand conformations that are within 2.0 A RMSD of the crystal structure.

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