Multidimensional Langevin modeling of biomolecular dynamics

A systematic computational approach to describe the conformational dynamics of biomolecules in reduced dimensionality is presented. The method is based on (i) the decomposition of a high-dimensional molecular dynamics trajectory into a few "system" and (many) "bath" degrees of freedom and (ii) a Langevin simulation of the resulting model. Employing principal component analysis, the dimension of the system is chosen such that it contains all slow large-amplitude motions of the molecule, while the bath coordinates only account for its high-frequency fluctuations. It is shown that a sufficiently large dimension of the model is essential to ensure a clear time scale separation of system and bath variables, which warrants the validity of the memory-free Langevin equation. Applying methods from nonlinear time series analysis, a practical Langevin algorithm is presented which performs a local estimation of the multidimensional Langevin vector fields describing deterministic drift and stochastic driving. Adopting a 800 ns molecular dynamics simulation of the folding of heptaalanine in explicit water, it is shown that a five-dimensional Langevin model correctly reproduces the structure and conformational dynamics of the system. The virtues and limits of the approach are discussed in some detail.