On inferring epistatic complexity in protein sequence-function landscapes

The extent to which epistatic interactions create complexity in protein sequence-function landscapes is highly contested. Numerous empirical studies have found evidence for complex landscapes with widespread high-order epistasis. However, recent work has argued that many of these empirical sequence-function landscapes are in fact much simpler and less epistatic than previously appreciated, based on analysis using a "reference-free" rather than "reference-based" framework for the inference of protein architecture. Here, we show that reference-free and reference-based frameworks are exactly equivalent when inferred using least-squares regression. Because the landscapes analyzed by these approaches are in fact identical, the different conclusions drawn based on the reference-free approach instead reflect different interpretations of the parameters describing the inferred landscapes. Thus, we argue that the choice of framework, the inference method, and the interpretation of the resulting parameters should be driven by the nature of the sequence-function dataset (e.g. the specific protein function being measured) and the motivating biological question (e.g. whether we are interested in explaining phenotypic variance, understanding biochemical properties, or analyzing evolutionary trajectories).