Reduced Stochastic Models for Complex Molecular Systems

We present a new numerical method for the identification of the most important metastable states of a system with complicated dynamical behavior from time series information. The approach is based on the representation of the effective dynamics of the full system by a Markov jump process between metastable states, and the dynamics within each of these metastable states by rather simple stochastic differential equations (SDEs). Its algorithmic realization exploits the concept of hidden Markov models (HMMs) with output behavior given by SDEs. A first complete algorithm including an explicit Euler–Maruyama-based likelihood estimator has already been presented in Horenko et al. (MMS, 2006a). Herein, we present a semi-implicit exponential estimator that, in contrast to the Euler–Maruyama-based estimator, also allows for reliable parameter optimization for time series where the time steps between single observations are large. The performance of the resulting method is demonstrated for some generic examples, in detail compared to the Euler–Maruyama-based estimator, and finally applied to time series originating from a 100 ns B-DNA molecular dynamics simulation.Dedicated to Peter Deuflhard on the occassion of his sixtieth birthday.Supported by the SfB 450 and DFG research center “Mathematics for key technologies” (FZT 86) in Berlin.