Biophysical Inference of Epistasis and the Effects of Mutations on Protein Stability and Function

Abstract

Understanding the relationship between protein sequence, function, and stability is a fundamental problem in biology. The essential function of many proteins that fold into a specific structure is their ability to bind to a ligand, which can be assayed for thousands of mutated variants. However, binding assays do not distinguish whether mutations affect the stability of the binding interface or the overall fold. Here, we introduce a statistical method to infer a detailed energy landscape of how a protein folds and binds to a ligand by combining information from many mutated variants. We fit a thermodynamic model describing the bound, unbound, and unfolded states to high quality data of protein G domain B1 binding to IgG-Fc. We infer distinct folding and binding energies for each mutation providing a detailed view of how mutations affect binding and stability across the protein. We accurately infer the folding energy of each variant in physical units, validated by independent data, whereas previous high-throughput methods could only measure indirect changes in stability. While we assume an additive sequence-energy relationship, the binding fraction is epistatic due its nonlinear relation to energy. Despite having no epistasis in energy, our model explains much of the observed epistasis in binding fraction, with the remaining epistasis identifying conformationally dynamic regions.

Uninterpretable interactions: epistasis as uncertainty

“…The third is to attempt to model the underlying mechanistic process that leads to the 405 map (Tokuriki et al, 2012;Schenk et al, 2013;Otwinowski, 2018;Dutta et al, 2018). 406 Rather than taking a "top-down" approach, in which one dissects epistasis into statistical 407 interactions that are hopefully meaningful, one can instead take a "bottom-up" approach, 408 in which one calculates phenotypes from genotypes using a mechanistic biological model.…”

Minimum epistasis interpolation for sequence-function relationships

“…Application to protein G. Having explored the behavior of our interpolation method on simulated data, we now turn to analyzing empirical data. We begin by considering a combinatorial mutagenesis study of the IgG-binding domain of streptococcal protein G (GB1) 34 , which is a model system for studying protein folding stability and binding affinity 5,34,61,62 . By sequencing a library of protein variants before and after binding to IgG-Fc beads, this experiment 34 attempted to assay all possible combinations of mutations at four sites (V39, D40, G41, and V54; 20 4 = 160,000 protein variants) that had previously been shown to harbor a particularly strong and complex pattern of genetic interactions 5 .…”

DiMSum: an error model and pipeline for analyzing deep mutational scanning data and diagnosing common experimental pathologies

“…DMS datasets for leave-one-out cross validation were processed with DiMSum v1.1.3 except the data for Protein G B1 domain (GB1 [5] ) whose variant counts were obtained from Otwinoski 2019 [59] . tRNA datasets [50] obtained from SRA (SRP134087) were analysed using DiMSum with default parameters except fitnessMinInputCountAll = 2000 and fitnessMinOutputCountAll = 200 to remove flaps likely due to DNA extraction bottlenecks, resulting in an average number of 2400 variants that could be analysed per selection experiment.…”