A continuous epistasis model for predicting growth rate given combinatorial variation in gene expression and environment

The ability to predict changes in cellular growth rate given variation in gene expression is critical to engineer biosynthetic pathways and understand evolutionary constraints on mRNA abundance. However, the relationship between gene expression and growth rate is nonlinear and shaped by environmental and genetic context. To address these challenges, we examined the relationship between enzyme expression and E. coli growth rate for 36 metabolic gene pairs by measuring growth following 4,404 pairwise, titrated changes in enzyme abundance under varied environmental contexts. Using 20% of these data, we trained an interpretable epistatic model to predict growth rate following simultaneous expression and environmental perturbations. The models predictions were robust to significant genetic and environmental epistasis and at times approached the accuracy of biological replicates. Based on these results, we propose a strategy using sparsely sampled, low-order measurements to quantify genetic interaction landscapes on the pathway-wide or genomic scale in a single assay.