# Extracting Markov Models of Peptide Conformational Dynamics from Simulation Data

journal contribution

posted on 12.07.2005, 00:00 by Verena Schultheis, Thomas Hirschberger, Heiko Carstens, Paul TavanA high-dimensional time series obtained by simulating a complex and stochastic
dynamical system (like a peptide in solution) may code an underlying multiple-state Markov
process. We present a computational approach to most plausibly identify and reconstruct this
process from the simulated trajectory. Using a mixture of normal distributions we first construct
a maximum likelihood estimate of the point density associated with this time series and thus
obtain a density-oriented partition of the data space. This discretization allows us to estimate
the transfer operator as a matrix of moderate dimension at sufficient statistics. A nonlinear
dynamics involving that matrix and, alternatively, a deterministic coarse-graining procedure are
employed to construct respective hierarchies of Markov models, from which the model most
plausibly mapping the generating stochastic process is selected by consideration of certain
observables. Within both procedures the data are classified in terms of prototypical points, the
conformations, marking the various Markov states. As a typical example, the approach is applied
to analyze the conformational dynamics of a tripeptide in solution. The corresponding high-dimensional time series has been obtained from an extended molecular dynamics simulation.