Minimum epistasis interpolation for sequence-function relationships

Abstract

Massively parallel phenotyping assays have provided unprecedented insight into how multiple mutations combine to determine biological function. While such assays can measure phenotypes for thousands to millions of genotypes in a single experiment, in practice these measurements are not exhaustive, so that there is a need for techniques to impute values for genotypes whose phenotypes have not been directly assayed. Here, we present an imputation method based on inferring the least epistatic possible sequence-function relationship compatible with the data. In particular, we infer the reconstruction where mutational effects change as little as possible across adjacent genetic backgrounds. The resulting models can capture complex higher-order genetic interactions near the data, but approach additivity where data is sparse or absent. We apply the method to high-throughput transcription factor binding assays and use it to explore a fitness landscape for protein G.

Inferring a complete genotype-phenotype map from a small number of measured phenotypes

“…Finally, a recent paper has identified a regression strategy that yielded predictive epistatic coefficients [ 66 ]. Such strategies, in combination with approaches such as classifiers and nonlinear splines, could allow the extraction of further information—and thus the development of better predictive models—from large genotype-phenotype maps.…”

Higher-order epistasis and phenotypic prediction

“…The method we propose here also has some commonalities with minimum epistasis interpolation [48], another method we recently proposed for phenotypic prediction that includes genetic interactions of all orders. The most important di↵erence is based on the criterion for parsimony being employed in each instance.…”

“…Importantly, various previously developed methods can be subsumed as particular (limiting) cases of inference under this class of priors. For example, the additive model and our recently proposed method of minimum epistasis interpolation [48] both arise as particular limiting cases where the fraction of variance due to additive e↵ects goes to 1, and the pair-wise interaction model [42] arises as a limiting case where the total fraction of variance due to additive and pairwise e↵ects goes to 1 (see Supplemental Figure 1). Thus, in a rigorous manner we can view these previously proposed methods as encoding specific assumptions about how the predictability of mutational e↵ects, epistatic coe cients and phenotypic values changes as we move through sequence space, where these assumptions take the form of particular shapes for the curves in Figure 1.…”

Non-additive polygenic models improve predictions of fitness traits in three eukaryote model species

“…The evidence for non-addi ve gene c architecture presented here may not be surprising given the growing literature of experiments that require genome-wide epistasis to explain asymmetric responses to ar ficial selec on (33) , line-dependent effects of muta ons in Drosophila (14,34) , or significant quan ta ve trait loci hubs in yeast (35) . This has sparked recent development of various sta s cal approaches to test epistasis more generally, by studying the emergent pa erns of epistasis as its contribu on to variance (36) , or one genotype-to-trait map (24,25,31,37,38) as in this study. Recent systems biology approaches for crea ng massively-parallel muta ons using CRISPR/Cas9 techniques (39) , as recently aimed in yeast experiments (40) , should further enable researchers to test the underlying addi ve or epista c interac ons of muta ons.…”