Treffer: Data-based Langevin modeling of biomolecular systems

Understanding the dynamical behavior of proteins is a highly challenging area of current research. Based on the progress in algorithmic methods and the increase of computational power in the recent years, molecular dynamics simulations have emerged as powerful tool to access molecular motions on time scales from femto- to milliseconds. However, the resulting data is so overwhelming that a suitable interpretation framework is needed in order to detect and analyse the essential dynamics of the system under study. Frequently, following a dimensionality reduction to identify collective variables, the dynamics are described in terms of a diffusive motion on a low-dimensional free energy landscape. By using projection operator approaches, such as developed by Zwanzig, it is possible to derive coarse-grained equations of motions for the collective variables, such as the generalized Langevin equation. Going further, by assuming a time scale separation between the slow dynamics along the system coordinate and the fast fluctuations of the bath, this equation can be simplified to the (memory-less) Markovian Langevin equation, which describes the system dynamics in terms of a deterministic drift, a Stokes’ friction and a stochastic force. Alternatively, an additional step of coarse graining can be applied in order to account for the dynamics in terms of jumps between metastable conformational states. By furthermore assuming that those jumps are memory-free, a so-called Markov state model can be constructed. In this thesis the virtues and shortcomings of data-based Markovian modeling are investigated. In particular, two modifications of the data-driven Langevin equation are presented: the rescaled and the binned data-driven Langevin equation. While the former approach allows for the rescaling of the dissipative force of the model, the latter concept enables the analysis of extensive MD data. In addition, it is investigated under which conditions the data-driven Langevin equation can be applied in the nonequilibrium regime. ...