Abstract

Mutations in non-coding regulatory DNA sequences can alter gene expression, organismal phenotype and fitness(1,3). Constructing complete fitness landscapes, in which DNA sequences are mapped to fitness, is a long-standing goal in biology, but has remained elusive because it is challenging to generalize reliably to vast sequence spaces(4-6). Here we build sequence-to-expression models that capture fitness landscapes and usethem to decipher principles of regulatory evolution. Using millions of randomly sampled promoter DNA sequences and their measured expression levels in the yeast Saccharomyces cerevisiae, we learn deep neural network models that generalize with excellent prediction performance, and enable sequence design for expression engineering. Using our models, we study expression divergence under genetic drift and strong-selection weak-mutation regimes to find that regulatory evolution is rapid and subject to diminishing returns epistasis; that conflicting expression objectives in different environments constrain expression adaptation; and that stabilizing selection on gene expression leadsto the moderation of regulatory complexity. We present an approach for using such modelsto detect signatures of selection on expression from natural variation in regulatory sequences and use it to discover an instance of convergent regulatory evolution. We assess mutational robustness, finding that regulatory mutation effect sizes follow a power law, characterize regulatory evolvability, visualize promoter fitness landscapes, discover evolvability archetypes and illustrate the mutational robustness of natural regulatory sequence populations. Our work provides a general framework for designing regulatory sequences and addressing fundamental questions in regulatory evolution.