Eike Meerbach

Identification of biomolecular conformations from incomplete torsion angle observations by hidden markov models

We present a novel method for the identification of the most important conformations of a biomolecular system from molecular dynamics or Metropolis Monte Carlo time series by means of Hidden Markov Models (HMMs). We show that identification is possible based on the observation sequences of some essential torsion or backbone angles. In particular, the method still provides good results even if the conformations do have a strong overlap in these angles. To apply HMMs to angular data, we use von Mises output distributions. The performance of the resulting method is illustrated by numerical tests and by application to a hybrid Monte Carlo time series of trialanine and to MD simulation results of a DNA–oligomer.

Multiscale modelling in molecular dynamics : Biomolecular conformations as metastable states

We report on a novel approach to the automatic identification of metastable states from long term simulation of complex molecular systems. The new approach is based on a hierarchical concept of metastability: metastable states are understood as subsets of state or configuration space from which the dynamics exits only very rarely; subsets with the smallest exit probabilities are of most interest, their further decomposition then may reveal subsets from which exiting is less but comparably difficult for the system under investigation. The article gives a survey of the theoretical foundation of the approach and its algorithmic realization that generalizes the well-known concept of Hidden Markov Models. The performance of the resulting algorithm are illustrated by application to a 100 ns simulation of penta-alanine with explicit water. We demonstrate the resulting metastable states allow to reveal the conformation dynamics of the moelcule.

Sequential Change Point Detection in Molecular Dynamics Trajectories

Motivated from a molecular dynamics context we propose a sequential change point detection algorithm for vector-valued autoregressive models based on Bayesian model selection. The algorithm does not rely on any sampling procedure or assumptions underlying the dynamics of the transitions and is designed to cope with high-dimensional data. We show the applicability of the algorithm on a time series obtained from numerical simulation of a penta-peptide molecule.

Uncoupling-Coupling Techniques for Metastable Dynamical Systems

We shortly review the uncoupling-coupling method, a Markov chain Monte Carlo based approach to compute statistical properties of systems like medium-sized biomolecules. This technique has recently been proposed for the efficient computation of biomolecular conformations. One crucial step of UC is the decomposition of reversible nearly uncoupled Markov chains into rapidly mixing subchains. We show how the underlying scheme of uncoupling-coupling can also be applied to stochastic differential equations where it can be translated into a domain decomposition technique for partial differential equations.

Biological systems: applications and perspectives

Viable biological systems occur on a wide scale of dimensions ranging from sizes of 30 meters for mammals (blue whale), and 120 meters for plants (sequoia tree), down to 10−6 meters for single cellular organisms.