A Strategy to Simulate the Dynamics of Molecular Assemblies Over Long Times
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A Strategy to Simulate the Dynamics of Molecular Assemblies Over Long Times Julius T. Su1 1 Materials and Process Simulation Center, Caltech, Pasadena, CA 91125, U.S.A. ABSTRACT We propose a strategy to simulate the dynamics of molecular assemblies over long times, provided they have a hierarchical and modular nature. In the scheme, fast fluctuations are averaged into a set of effective potentials (fluctuation softened potentials or FSPs), and the remaining slower dynamics are propagated in a drastically reduced configuration space (coupled energy landscapes or CEL). As a preliminary validation of the FSPs we compute the free energy of binding of a protein complex (RNase:barstar) for different relative positionings of the proteins. As a demonstration of CEL, we simulate the dynamics of microtubule unraveling upon hydrolysis of bound nucleotides. The method should allow the use of time steps hundreds to thousands of times longer than in conventional molecular dynamics, so that with only atomic structures and interactions as input, motions over human time scales (>ms) could be simulated. INTRODUCTION In all living organisms, key cellular processes are performed and regulated by assemblies of macromolecules. For example, proteins in E. coli bacteria are synthesized by their ribosomes, 82 proteins enmeshed in 3 RNA molecules that collectively form a molecular machine. Understanding better how such assemblies function and misfunction is a critical step toward developing new and effective therapeutics for a broad range of human diseases. Computation has long held out the tantalizing prospect of being able to simulate biological function starting from atomic structures and interactions, via a suitable series of approximations and step-by-step dynamics. As yet, however, such approaches have been stymied by the huge gap between the fast time scales of atomic motions (10−15 seconds), and the relatively slow time scale of interesting biological motions (10−3 seconds and beyond) – simply too many intermediate computations need to be performed. This difficulty has been colloquially termed the “time scale problem.” In this paper, we do not propose a solution for the time scale problem in general, but suggest instead that for a certain class of systems, vast accelerations in the speed of dynamics simulations ought to be possible, making simulations over biological time scales practical. We focus on simulating molecular assemblies with the following two characteristics: (1) hierarchy, i.e. there is a nesting of components within components over a range of time and length scales, and (2) modularity, i.e. the components of the assembly retain characteristics of their individual dynamics, even in the context of the complex. These properties may be exploited to make long time dynamics simulations feasible as follows. First, hierarchy imposes a nested separation of time scales. We pick the time scale of protein conformational transitions (> µs) as a dividing point. Fluctuations faster than that are averaged out into effect
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