Direct Coupling Analysis of Epistasis in Allosteric Materials

Abstract

In allosteric proteins, the binding of a ligand modifies function at a distant active site. Such allosteric pathways can be used as target for drug design, generating considerable interest in inferring them from sequence alignment data. Currently, different methods lead to conflicting results, in particular on the existence of long-range evolutionary couplings between distant amino-acids mediating allostery. Here we propose a resolution of this conundrum, by studying epistasis and its inference in models where an allosteric material is evolved in silico to perform a mechanical task. We find in our model the four types of epistasis (Synergistic, Sign, Antagonistic, Saturation), which can be both short or long-range and have a simple mechanical interpretation. We perform a Direct Coupling Analysis (DCA) and find that DCA predicts well the cost of point mutations but is a rather poor generative model. Strikingly, it can predict short-range epistasis but fails to capture long-range epistasis, in consistence with empirical findings. We propose that such failure is generic when function requires subparts to work in concert. We illustrate this idea with a simple model, which suggests that other methods may be better suited to capture long-range effects.

arXiv comment22 pages, 9 figures

References in corpus (20)

• Direct-coupling analysis of residue co-evolution captures native contacts across many protein families
• Quantification of the effect of mutations using a global probability model of natural sequence variation
• Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models
• Coevolutionary landscape inference and the context-dependence of mutations in beta-lactamase TEM-1
• Inverse statistical problems: from the inverse Ising problem to data science
• Inverse Statistical Physics of Protein Sequences: A Key Issues Review
• Designing allostery-inspired response in mechanical networks
• How pairwise coevolutionary models capture the collective residue variability in proteins
• Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy Data
• Architecture and Co-Evolution of Allosteric Materials
• Adaptive cluster expansion for the inverse Ising problem: convergence, algorithm and tests
• Benchmarking inverse statistical approaches for protein structure and design with exactly solvable models
• Green function of correlated genes in a minimal mechanical model of protein evolution
• Principles for optimal cooperativity in allosteric materials
• Revealing evolutionary constraints on proteins through sequence analysis
• Evolution of sparsity and modularity in a model of protein allostery
• Large Pseudo-Counts and $L_2$-Norm Penalties Are Necessary for the Mean-Field Inference of Ising and Potts Models
• Improving landscape inference by integrating heterogeneous data in the inverse Ising problem
• A statistical physics approach to learning curves for the Inverse Ising problem
• Design of elastic networks with evolutionary optimised long-range communication as mechanical models of allosteric proteins

Cited by in corpus (4)

• Revealing evolutionary constraints on proteins through sequence analysis
• Mechanics of allostery: contrasting the induced fit and population shift scenarios
• Impact of phylogeny on structural contact inference from protein sequence data
• Impact of phylogeny on the inference of functional sectors from protein sequence data