Time scales molecular dynamics simulations, protein

Molecular dynamics simulations ([McCammon and Harvey 1987]) propagate an atomistic system by iteratively solving Newton s equation of motion for each atomic particle. Due to computational constraints, simulations can only be extended to a typical time scale of 1 ns currently, and conformational transitions such as protein domains movements are unlikely to be observed. 

For 25 years, molecular dynamics simulations of proteins have provided detailed insights into the role of dynamics in biological activity and function [1-3]. The earliest simulations of proteins probed fast vibrational dynamics on a picosecond time scale. Fifteen years later, it proved possible to simulate protein dynamics on a nanosecond time scale. At present it is possible to simulate the dynamics of a solvated protein on the microsecond time scale [4]. These gains have been made through a combination of improved computer processing (Moore s law) and clever computational algorithms [5]. 

How well has Dill s prediction held up In 2000, the first ever microsecond-long molecular dynamics simulation of protein folding was reported. It required 750,000 node hours (equal to the product of the number of hours times the number of processors) of computer time on a Cray T3 supercomputer. According to Dill s prediction, this length of simulation was not to be expected until around 2010. However, as noted above, Dill s analysis does not take into account large-scale parallelization—which, unless the computation is communications-limited, will effectively increase the speed of a computation in proportion to the number of processors available. 

Which model provides the best representation for local mobility in a particular group remains unclear, as a detailed picture of protein dynamics is yet to be painted. This information is not directly available from NMR measurements that are necessarily limited by the number of experimentally available parameters. Additional knowledge is required in order to translate these experimental data into a reliable motional picture of a protein. At this stage, molecular dynamic simulations could prove extremely valuable, because they can provide complete characterization of atomic motions for all atoms in a molecule and at all instants of the simulated trajectory. This direction becomes particularly promising with the current progress in computational resources, when the length of a simulated trajectory approaches the NMR-relevant time scales [23, 63, 64]. 

At present we are far from an understanding of the protein folding process. Even numerical methods as e.g. molecular dynamics simulations do not lead to realistic predictions. Experiments on the folding process have been performed initially on the millisecond time-scale. It was only recently that new techniques - temperature jump or triplet-triplet quenching experiments - allowed a first access to the nanosecond time domain [2-4]. However, the elementary reactions in protein folding occur on the femto- to picosecond time-scale (femtobiology). In order to allow experiments in this temporal range we developed a new... 

The general principle of BD is based on Brownian motion, which is the random movement of solute molecules in dilute solution that result from repeated collisions of the solute with solvent molecules. In BD, solute molecules diffuse under the influence of systematic intermolecular and intramolecular forces, which are subject to frictional damping by the solvent, and the stochastic effects of the solvent, which is modeled as a continuum. The BD technique allows the generation of trajectories on much longer temporal and spatial scales than is feasible with molecular dynamics simulations, which are currently limited to a time of about 10 ns for medium-sized proteins. 

The motions of proteins are usually simulated in aqueous solvent. The water molecules can be represented either explicitly or implicitly. To include water molecules explicitly implies more time-consuming calculations, because the interactions of each protein atom with the water atoms and the water molecules with each other are computed at each integration time step. The most expensive part of the energy and force calculations is the nonbonded interactions because these scale as 77 where N is the number of atoms in the system. Therefore, it is common to neglect nonbonded interactions between atoms separated by more than a defined cut-off ( 10 A). This cut-off is questionable for electrostatic interactions because of their 1/r dependence. Therefore, in molecular dynamics simulations, a Particle Mesh Ewald method is usually used to approximate the long-range electrostatic interactions (71, 72). 

Molecular dynamics methods are primarily used for the refinement of structural models (Li et al., 1997) or the analysis of molecular interactions (Cappelli et al., 1996 Kothekar et al., 1998). In both cases the time scales to be simulated are within range of current computing technology. Another application area is the study of allosteric movements of proteins (Tanner et al., 1993). Molecular Dynamics approaches to protein-ligand docking are described in Chapter 7 of Volume I. 

All of the simulation approaches, other than harmonic dynamics, include the basic elements that we have outlined. They differ in the equations of motion that are solved (Newton s equations, Langevin equations, etc.), the specific treatment of the solvent, and/or the procedures used to take account of the time scale associated with a particular process of interest (molecular dynamics, activated dynamics, etc.). For example, the first application of molecular dynamics to proteins considered the molecule in vacuum.15 These calculations, while ignoring solvent effects, provided key insights into the important role of flexibility in biological function. Many of the results described in Chapts. VI-VIII were obtained from such vacuum simulations. Because of the importance of the solvent to the structure and other properties of biomolecules, much effort is now concentrated on systems in which the macromolecule is surrounded by solvent or other many-body environments, such as a crystal. 

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