Time-Varying Gaussian Graphical Models of Molecular Dynamics Data

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 L1regularization 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.