Causality Analysis of Molecular Dynamics Events with Mathematica 7

Piotr Majka and Bogdan Lesyng

Center of Excellence BioExploratorium and Department of Biophysics, Faculty of Physics, University of Warsaw, Zwirki i Wigury 93, 02-089 Warsaw, Poland

Abstract

Detecting causality relationships between events which are observed in molecular dynamics (MD) simulations of biomolecular and nano systems is of crucial importance for the description of molecular mechanisms and understanding the logic of their functioning—for an overview see: A. Gorecki, J. Trylska & B. Lesyng, Causality and Correlation Analyses of Molecular Dynamics, in “From Computational Biophysics to Systems Biology”, NIC Series, 36, pp. 25-30, 2007 (ISBN 978-3-9810843-2-0, http://www.fz-juelich.de/nic-series/volume36/volume36.html). Signals extracted from MD simulation data are time-dependent atomic positions or momenta, or their functions. Quantum degrees of freedom can also be incorporated in the analysis. In multidimensional cases (larger systems) selection or construction of the most important information channels to be analyzed is nontrivial mathematical and computational problem.

Based on Mathematica 7, a computational environment (CausalMD) for the time-series analysis extracted from MD simulation data was designed and tested for a model molecular system with intramolecular proton transfer. Parallel solutions using gridMathematica were implemented.

In the current study, three different methodologies were implemented with two parametric approaches:
   • the conventional Granger causality method,
   • a Multi-Variate Autoregressive Model (MVAR) with a Directed Transfer Function (DTF), and
   • a nonparametric wavelet approach.

The first two approaches appeared to be effective to study stationary time series, and the third one to study nonstationary ones, which accounts for proton transfer processes in (bio)molecular systems.

Acknowledgements: Studies are supported by MNiSW - grant N519 384736.