Long-Range epistasis mediated by structural change in a model of ligand binding proteins

Recent analyses of amino acid mutations in proteins reveal that mutations at many pairs of sites are epistatic-i.e., their effects on fitness are non-additive-the combined effect of two mutations being significantly larger or smaller than the sum of their effects considered independently. Interestingly, epistatic sites are not necessarily near each other in the folded structure of a protein, and may even be located on opposite sides of a molecule. However, the mechanistic reasons for long-range epistasis remain obscure. Here, we study long-range epistasis in proteins using a previously developed model in which off-lattice polymers are evolved under ligand binding constraints. Epistatic effects in the model are qualitatively similar to those recently reported for small proteins, and many are long-range. We find that a major reason for long-range epistasis is conformational change-a recurrent theme in both positive and negative epistasis being the transfer, or exchange of material between the ordered nucleus, which supports the binding site, and the liquid-like surface of a folded molecule. These local transitions in phase and folded structure are largely responsible for long-range epistasis in our model.