Epistasis meets pleiotropy in shaping biophysical protein subspaces associated with antimicrobial resistance.

Protein space is a rich analogy for genotype-phenotype maps, where amino acid sequence is organized into a high-dimensional space that highlights the connectivity between protein variants. It is a useful abstraction for understanding the process of evolution, and for efforts to engineer proteins towards desirable phenotypes. Few framings of protein space consider how higher-level protein phenotypes can be described in terms of their biophysical dimensions, nor do they rigorously interrogate how forces like epistasis-describing the nonlinear interaction between mutations and their phenotypic consequences-manifest across these dimensions. In this study, we deconstruct a low-dimensional protein space of a bacterial enzyme (dihydrofolate reductase; DHFR) into "subspaces" corresponding to a set of kinetic and thermodynamic traits [(, , , and (melting temperature)]. We then examine how three mutations (eight alleles in total) display pleiotropy in their interactions across these subspaces. We extend this approach to examine protein spaces across three orthologous DHFR enzymes ( and ), adding a genotypic context dimension through which epistasis occurs across subspaces. In doing so, we reveal that protein space is a deceptively complex notion, and that the process of protein evolution and engineering should consider how interactions between amino acid substitutions manifest across different phenotypic subspaces.