Epistasis and pleiotropy shape biophysical protein subspaces associated with drug 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 mentions of protein space consider how protein phenotypes can be described in terms of their biophysical components, nor do they rigorously interrogate how forces like epistasis---describing the nonlinear interaction between mutations and their phenotypic consequences---manifest across these components. 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 [${k}_{\mathrm{cat}}, {K}_{M}, {K}_{i}$, and ${T}_{m}$ (melting temperature)]. We then examine how combinations of three mutations (eight alleles in total) display pleiotropy, or unique effects on individual subspace traits. We examine protein spaces across three orthologous DHFR enzymes (Escherichia coli, Listeria grayi, and Chlamydia muridarum), 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 future applications to bioengineering should consider how interactions between amino acid substitutions manifest across different phenotypic subspaces.