Inferring the shape of global epistasis

Abstract

Genotype-phenotype relationships are notoriously complicated. Idiosyncratic interactions between specific combinations of mutations occur and are difficult to predict. Yet it is increasingly clear that many interactions can be understood in terms of global epistasis. That is, mutations may act additively on some underlying, unobserved trait, and this trait is then transformed via a nonlinear function to the observed phenotype as a result of subsequent biophysical and cellular processes. Here we infer the shape of such global epistasis in three proteins, based on published high-throughput mutagenesis data. To do so, we develop a maximum-likelihood inference procedure using a flexible family of monotonic nonlinear functions spanned by an I-spline basis. Our analysis uncovers dramatic nonlinearities in all three proteins; in some proteins a model with global epistasis accounts for virtually all of the measured variation, whereas in others we find substantial local epistasis as well. This method allows us to test hypotheses about the form of global epistasis and to distinguish variance components attributable to global epistasis, local epistasis, and measurement error.

Minimum epistasis interpolation for sequence-function relationships

“…in partial factorial designs where they are purposefully confounded with main effects and lower-order interactions, [63]). However, there is a growing consensus that such higher-order interactions are not only common in genotype-phenotype maps [10,18,29,32,38] but are expected even for very simple, smooth genotype-phenotype relationships such as where the observed phenotype is just an additive trait that has been run through a nonlinear transformation [31,32,40,[64][65][66]. Our results contribute to this view by showing that the incorporation of higher-order interactions in fact allows substantially less epistatic fits than standard pairwise models.…”

“…In principle, these "higher-order" interactions can be captured by adding interactions between three or more sites to standard regression models, but this leads to problems in interpretability and overfitting because the number of such terms grows rapidly with increasing interaction order [26]. Another strategy has been to assume that the observed phenotype is a simple non-linear function of some underlying nonepistatic trait [32,40], a pattern of epistasis known as univariate [8,24], non-specific [31] or global [40,41] epistasis, which appears to be well suited-primarily to sequence-function relationships that are essentially noised versions of single-peaked landscapes. Finally, a variety of machine-learning techniques [8,12,[42][43][44][45] have been employed that can fit more complex forms of epistasis than global epistasis or pairwise interaction models.…”

Recent insights into the genotype–phenotype relationship from massively parallel genetic assays

“…Of course, as for the DME, many specific cases will deviate from these general expectations and vary across proteins. For example, specific structural interactions could generate sign epistasis when mutations do not act additively on the level of folding energy (ΔG) (Otwinowski, McCandlish, & Plotkin, 2018;Starr & Thornton, 2016 F I G U R E 5 Expression-fitness functions for a diverse set of protein-coding yeast genes. Red lines mark wild-type expression levels.…”

Lexical landscapes as largein silicodata for examining advanced properties of fitness landscapes

“…Epistasis remains a cutting-edge topic in evolutionary biology that continues to be the object of study for a variety of reasons, and measured using diverse methods [10,[19][20][21]. For our purposes, we use a Walsh-Hadamard transformation of the fitness values, scaled by an additional diagonal matrix, as presented in Poelwijk et al [19].…”