Principles for Evolutionary Paths to New Folds

Experiments have identified particular evolutionary paths that switch from one fold structure to another via a single mutation, for both RNA and protein folds. However, the broader principles of fold switching through sequence space remain mysterious. To probe this, we simulate combinatorial paths between RNA and protein sequences with different folds, and characterize the frequency and properties of viable paths. We develop a simple model that incorporates both a Boltzmann global non-linearity and specific epistasis to understand the properties of viable paths. We show how the distribution of mutation effect sizes and their correlations between the two structures drive the probability of finding viable paths.