The composition of biophysical constraints generates complex, rugged regions of protein fitness landscapes

The ruggedness of a proteins fitness landscape constrains how it can evolve and how effectively it can be engineered. What determines whether a fitness landscape is rugged, and where in sequence space that ruggedness concentrates, remains poorly understood. Existing measures of ruggedness rely on complete combinatorial datasets and cannot be applied to landscapes in which only a fraction of possible sequences have been characterized. Here, we introduce a graph-based measure of ruggedness based on how quickly fitness differences diffuse across a landscape, which can be applied to sparse datasets. Applying this measure to 64 protein domains and several experimental systems with characterized folding and binding constraints, we show that ruggedness is not uniformly distributed but concentrates at regions where the dominant constraint on fitness changes. These results establish that the composition of individually simple constraints can generate localized ruggedness, providing a mechanistic basis for the complexity of protein fitness landscapes.