Higher-order genetic interactions in sequence-function relationships

Pairwise interaction models, such as the Potts model, have been extensively applied to study sequence-function relationships. However, modern high-throughput phenotyping assays have shown that genetic interactions among three or more loci also frequently occur. In this talk, I will present ongoing work on modeling these higher-order interactions based on either high-throughput experimental assays or the analysis of collections of functional sequences. We will first present a semi-parametric generalization of the Potts model for estimating probability distributions over sequence space. This generalization is based on a family of linear operators constructed using spectral transformations of the graph Laplacian for the Hamming graph. Such linear operators can then be used to define a prior over the type of higher-order associations that are assumed to be absent in typical maximum entropy models such as the Potts and independent sites models. Next, we will show how higher-order interactions influence the distance correlation structure of local epistatic coefficients, and use these observations to build Gaussian process priors for reconstructing full fitness landscapes from noisy and incomplete experimental data. Finally, we will present new results showing how the above approaches can be generalized to accommodate diploid genotypes as well as a method for building priors over sequence-function relationships with variable allelic weights in order to incorporate a greater degree of anisotropy.