Learning generative models of molecular dynamics

Systematic Testing of Belief-Propagation Estimates for Absolute Free Energies in Atomistic Peptides and Proteins

Motivated by the extremely high computing costs associated with estimates of free energies for biological systems using molecular simulations, we further the exploration of existing "belief propagation" (BP) algorithms for fixed-backbone peptide and protein systems. The precalculation of pairwise interactions among discretized libraries of side-chain conformations, along with representation of protein side chains as nodes in a graphical model, enables direct application of the BP approach, which requires only ∼1 s of single-processor run time after the precalculation stage. We use a "loopy BP" algorithm, which can be seen as an approximate generalization of the transfer-matrix approach to highly connected (i.e., loopy) graphs, and it has previously been applied to protein calculations. We examine the application of loopy BP to several peptides as well as the binding site of the T4 lysozyme L99A mutant. The present study reports on (i) the comparison of the approximate BP results with estimates from unbiased estimators based on the Amber99SB force field; (ii) investigation of the effects of varying library size on BP predictions; and (iii) a theoretical discussion of the discretization effects that can arise in BP calculations. The data suggest that, despite their approximate nature, BP free-energy estimates are highly accurate-indeed, they never fall outside confidence intervals from unbiased estimators for the systems where independent results could be obtained. Furthermore, we find that libraries of sufficiently fine discretization (which diminish library-size sensitivity) can be obtained with standard computing resources in most cases. Altogether, the extremely low computing times and accurate results suggest the BP approach warrants further study.

Learning sequence determinants of protein:protein interaction specificity with sparse graphical models

In studying the strength and specificity of interaction between members of two protein families, key questions center on which pairs of possible partners actually interact, how well they interact, and why they interact while others do not. The advent of large-scale experimental studies of interactions between members of a target family and a diverse set of possible interaction partners offers the opportunity to address these questions. We develop here a method, DgSpi (data-driven graphical models of specificity in protein:protein interactions), for learning and using graphical models that explicitly represent the amino acid basis for interaction specificity (why) and extend earlier classification-oriented approaches (which) to predict the ΔG of binding (how well). We demonstrate the effectiveness of our approach in analyzing and predicting interactions between a set of 82 PDZ recognition modules against a panel of 217 possible peptide partners, based on data from MacBeath and colleagues. Our predicted ΔG values are highly predictive of the experimentally measured ones, reaching correlation coefficients of 0.69 in 10-fold cross-validation and 0.63 in leave-one-PDZ-out cross-validation. Furthermore, the model serves as a compact representation of amino acid constraints underlying the interactions, enabling protein-level ΔG predictions to be naturally understood in terms of residue-level constraints. Finally, the model DgSpi readily enables the design of new interacting partners, and we demonstrate that designed ligands are novel and diverse.

Learning Sequence Determinants of Protein:protein Interaction Specificity with Sparse Graphical Models

In studying the strength and specificity of interaction between members of two protein families, key questions center on which pairs of possible partners actually interact, how well they interact, and why they interact while others do not. The advent of large-scale experimental studies of interactions between members of a target family and a diverse set of possible interaction partners offers the opportunity to address these questions. We develop here a method, DgSpi (Data-driven Graphical models of Specificity in Protein:protein Interactions), for learning and using graphical models that explicitly represent the amino acid basis for interaction specificity (why) and extend earlier classification-oriented approaches (which) to predict the ΔG of binding (how well). We demonstrate the effectiveness of our approach in analyzing and predicting interactions between a set of 82 PDZ recognition modules, against a panel of 217 possible peptide partners, based on data from MacBeath and colleagues. Our predicted ΔG values are highly predictive of the experimentally measured ones, reaching correlation coefficients of 0.69 in 10-fold cross-validation and 0.63 in leave-one-PDZ-out cross-validation. Furthermore, the model serves as a compact representation of amino acid constraints underlying the interactions, enabling protein-level ΔG predictions to be naturally understood in terms of residue-level constraints. Finally, as a generative model, DgSpi readily enables the design of new interacting partners, and we demonstrate that designed ligands are novel and diverse.

Generative models of conformational dynamics

Atomistic simulations of the conformational dynamics of proteins can be performed using either Molecular Dynamics or Monte Carlo procedures. The ensembles of three-dimensional structures produced during simulation can be analyzed in a number of ways to elucidate the thermodynamic and kinetic properties of the system. The goal of this chapter is to review both traditional and emerging methods for learning generative models from atomistic simulation data. Here, the term 'generative' refers to a model of the joint probability distribution over the behaviors of the constituent atoms. In the context of molecular modeling, generative models reveal the correlation structure between the atoms, and may be used to predict how the system will respond to structural perturbations. We begin by discussing traditional methods, which produce multivariate Gaussian models. We then discuss GAMELAN (GRAPHICAL MODELS OF ENERGY LANDSCAPES), which produces generative models of complex, non-Gaussian conformational dynamics (e.g., allostery, binding, folding, etc.) from long timescale simulation data.