Computer Science Department
School of Computer Science, Carnegie Mellon University


Time-Varying Gaussian Graphical Models
of Molecular Dynamics Data

Narges Sharif Razavian*, Subhodeep Moitra*,
Hetunandan Kamisetty**, Arvind Ramanathan***, Christopher James Langmead+

May 2010


Keywords: Structure learning, generative models, probabilistic graphical models, L-1 regularization, time-varying, proteins, molecular dynamics

We introduce an algorithm for learning sparse, time-varying undirected probabilistic graphical models of Molecular Dynamics (MD) data. Our method computes a maximum a posteriori (MAP) estimate of the topology and parameters of the model (i.e., structure learning) using L1-regularization of the negative log-likelihood (aka 'Graphical Lasso') to ensure sparsity, and a kernel to ensure smoothly varying topology and parameters over time. The learning problem is posed as a convex optimization problem and then solved optimally using block coordinate descent. The resulting model encodes the time-varying joint distribution over all the dihedral angles in the protein. We apply our method to three separate MD simulations of the enzyme Cyclophilin A, a peptidylprolyl isomerase. Each simulation models the isomerization of a different substrate. We compare and contrast the graphical models constructed from each data set, providing insights into the differences in the dynamics experienced by the enzyme for the different substrate.

21 pages

*Language Technologies Institute
**Computer Science Department
***Lane Center for Computational Biology
+Computer Science Department and Lane Center for Computational Biology

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