Figure 1.

Mechanistic and mathematical descriptions of epistasis. (A) The mathematical description of epistasis (ε) in ligand binding free energy ($\Delta G_{\mathit{obs}}$) for the mutant cycle between genotypes ab and AB. $\Delta G_{\mathit{obs}}$ measures the strength of the binding interaction between protein (gray) and ligand (orange). We indicate genotypes as superscripts. ε is defined as the difference in the effect of mutation $a\to A$ in the aB background (red text), vs its effect in the ab background (blue text). (B) Mutant cycle where epistasis is readily understood: the $a\to A$ and $b\to B$ mutations introduce charges into the hydrophobic core, destabilizing the protein and disrupting binding of the orange square. Mutations $a\to A$ and $b\to B$ lead to a new electrostatic interaction when introduced together (minus and plus signs) restoring stability and binding. (C) Mutant cycle with difficult-to-understand epistasis. Mutations at two distant sites (green and yellow spheres) have no effect on binding of the orange square when introduced independently, but disrupt binding when introduced together.