Sailer and Harms (2017) showed with a 12-site lattice protein model that because proteins populate a thermodynamic ensemble of interconverting conformations, each mutation redistributes the weights of the ensemble, so the effect of any later mutation depends on which mutations preceded it. This 'ensemble-induced epistasis' arises at every epistatic order, defeats trajectory prediction even when the effects of all mutations in the ancestor are known, and cannot be removed by pairwise corrections. The authors explicitly left open how this maps quantitatively onto real biological systems. The open problem is fourfold and coherent: measure the magnitude and order distribution of ensemble-attributed epistasis in real experimentally characterized protein genotype-phenotype maps (as distinct from contact interactions and global nonlinearities); determine how many sequential substitutions can be predicted in real proteins before trajectories diverge; determine whether the required state-resolved mutational effects can be measured, inferred, or otherwise constrained; and determine whether an analogous ensemble mechanism operates at higher levels of biological organization such as signaling networks. Later work has demonstrated the mechanism experimentally only at small scale (lac repressor mutant cycles, a riboswitch), measured drift of mutational effects along real protein histories without ensemble attribution, and found high-order epistasis in real maps to be rarer than the lattice model suggests — so the quantitative real-protein account and its cross-scale generalization remain open.

Background

A long-standing goal in evolutionary biology is to predict evolution before it happens — for example, to forecast which mutational paths a protein will take under selection. The central obstacle is epistasis: the effect of a mutation on a trait depends on which other mutations are already present, so effects measured in one genetic background do not transfer to another. Epistasis is called pairwise when it involves two sites and higher-order when it involves three or more sites jointly; a genotype-phenotype map is the function from amino-acid sequences to a measured property such as binding affinity, stability, or activity. Deep mutational scanning (DMS) is the high-throughput experimental method that measures the effects of very many mutations or mutation combinations simultaneously. The physical origin of epistasis within a single protein was clarified by Sailer and Harms (2017) using a lattice protein model — a simplified computational protein representation in which residues occupy sites on a two-dimensional grid with pairwise contact energies (Miyazawa-Jernigan parameters) and folding stability is computed exactly over all conformations. Under physiological conditions a real protein does not adopt one structure: it populates a thermodynamic (conformational) ensemble, a Boltzmann-weighted set of interconverting conformations, and any observable property is an average over that ensemble. Because a mutation changes the stability of each conformation slightly differently, it redistributes the ensemble's probabilities; a subsequent mutation then acts on a shifted distribution of states, so its measured (ensemble-averaged) effect differs from its effect in the original background. This mechanism, ensemble-induced epistasis, is directly analogous to ensemble allostery, in which binding at one site shifts conformational populations and changes behavior at another site. In their virtual deep mutational scan of 12-site lattice proteins evolved to a fraction folded of about 0.7, Sailer and Harms found that ensemble-induced epistasis arises at every order, that phenotype values remain highly predictable even while evolutionary trajectories do not (small phenotype errors amplify into large trajectory uncertainties because evolution is a contingent series of steps), and that adding pairwise epistatic terms does not rescue trajectory prediction. The mechanism requires only that the molecule populate three or more conformations whose stabilities respond differently to mutation. Independent surveys had found high-order epistasis in every combinatorial protein genotype-phenotype map analyzed (Sailer and Harms 2017, Genetics), and ensemble-induced epistasis offered a simple universal explanation, though without direct mechanistic evidence in real data. Two neighboring concepts must be distinguished from it: contact epistasis, arising from direct physical interaction between the mutated residues themselves, and global epistasis, a single nonlinear function relating an additive underlying trait to the observed phenotype (for example the sigmoidal mapping of folding stability to fraction folded). The paper's own Discussion formulates what remains unresolved: the magnitude of ensemble-induced epistasis in real systems, how many steps of real evolutionary prediction are possible before divergence, the fact that predicting a mutation's effect in a future background 'requires knowing its effect on every member of the ensemble ... in practice, impossible to measure', and whether something analogous exists on a larger scale, such as in a signaling network whose molecular components populate a collection of configurations that rearrange in response to stimuli.

Problem Statement

Determine, quantitatively, how conformational-ensemble-induced epistasis limits evolutionary prediction in real biological systems, translating the lattice-model result of Sailer and Harms (2017) into measured fact. The problem has one scientific objective and four linked deliverables. (1) Real-map structure: in experimentally characterized protein genotype-phenotype maps, measure the magnitude distribution and order distribution of epistasis that is attributable to redistribution of the conformational ensemble — distinguished explicitly from contact epistasis between the mutated sites and from global (single-nonlinear-transform) epistasis — and establish whether ensemble-induced terms of third and higher order are pervasive, as the lattice model predicts. (2) Predictive horizon: determine how many sequential substitutions can be reliably predicted in real proteins before predicted and actual evolutionary trajectories diverge, and how that horizon depends on the ensemble properties of the sequence background. (3) State-resolved information: determine whether the effect of a mutation on each populated conformational state — the information long-range prediction requires — can be measured, inferred, or otherwise practically constrained, and, if full state resolution is unattainable, which partial measurements most improve long-range predictions. (4) Cross-scale generality: determine whether an analogous ensemble mechanism (a population of configurations redistributed by perturbations, changing the effects of subsequent perturbations) operates at higher levels of biological organization such as signaling networks or multi-protein assemblies, and how ensemble complexity at those scales affects predictability. Deliverables (2) and (3) quantify the practical consequence of (1) and share its causal target; (4) tests the same mechanism beyond single macromolecules. The four parts are jointly posed; an epistasis quantification without ensemble attribution, or an effect-drift measurement without trajectory-level or mechanistic resolution, addresses only part of the objective.

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