Partition function estimation in computational protein design with continuous-label Markov random fields

Abstract

Proteins perform a variety of biological tasks, and drive many of the dynamic processes that make life possible. Computational structure-based protein design (CSPD) involves computing optimal sequences of amino acids with respect to particular backbones, or folds, in order to produce proteins with novel functions. In particular, it is crucial to be able to accurately model protein-protein interfaces (PPIs) in order to realize desired functionalities. Accurate modeling of PPIs raises two significant considerations. First, incorporating continuous side-chain flexibility in the design process has been shown to significantly improve the quality of designs. Second, because proteins exist as ensembles of structures, many of the properties we wish to design, including binding affinity, require the computation of ensemble properties as opposed to features of particular conformations. The bottleneck in many design algorithms that attempt to handle the ensemble nature of protein structure, including the Donald Lab’s K ∗ algorithm, is the computation of the partition function, which is the sum of the Boltzmann-weighted energies of all the conformational states of a protein or protein-ligand complex. Protein design can be formulated as an inference problem on Markov random fields (MRFs), where each residue to be designed is represented by a node in the MRF and an edge is placed between nodes corresponding to interacting residues. Label sets on each vertex correspond to allowed flexibility in the underlying design problem. The aim of this work is to extend message-passing algorithms that estimate the partition function for Markov random fields with discrete label sets to MRFs with continuous label sets in order to compute the partition function for PPIs with continuous flexibility and continuous entropy.