Langevin Modeling of Rare Biomolecular Processes

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The in silico prediction of rare biomolecular events represents a long-standing problem, because slow (say, millisecond timescale) processes are typically out of reach of current all-atom molecular dynamics (MD) simulations. To circumvent this time scale problem, one often invokes massive parallel computing strategies or various enhanced sampling techniques such as replica exchange, steered or targeted MD. While these approaches may provide an efficient sampling of the system's free energy landscape, a dynamical description requires some coarse-grained "post-simulation'' model that is capable of rebuilding the kinetics from the sampled data. To this end, we have recently proposed a data-driven Langevin equation (dLE) approach that constructs a low-dimensional dynamical model from a given MD trajectory. Now, the challenge is to exploit the virtues of the dLE formulation to facilitate its practical application to various biomolecular systems, ranging from polypeptides to multidomain proteins. Here two viable and promising routes will be followed: (1) Using temperature as driving force to overcome energy barriers, we will construct a dLE model from replica exchange MD simulations. Moreover, we will exploit a fluctuation-dissipation theorem in order to make low-temperature predictions from high-temperature simulations. (2) Employing enhanced sampling methods such as metadynamics and steered or targeted MD, we perform an efficient sampling of the overall free energy landscape and choose a number of starting configurations for subsequent short MD trajectories, which generate input data for the dLE model. Adopting protein systems of increasing size and dynamical complexity, we will ultimately consider the systems studied by our experimental collaborators and aim to compare computational and experimental predictions of molecular structures and conformational transition rates.