Topological features of rugged fitness landscapes in sequence space

•We review the concept of fitness landscapes in sequence space.•The genotype–phenotype relationship of a protein is complex and multidimensional.•Several experimental approaches are used to study fitness landscapes.•Fitness landscapes should be studied from a global perspective of sequence space.

The factors that determine the tempo and mode of protein evolution continue to be a central question in molecular evolution. Traditionally, studies of protein evolution focused on the rates of amino acid substitutions. More recently, with the availability of sequence data and advanced experimental techniques, the focus of attention has shifted toward the study of evolutionary trajectories and the overall layout of protein fitness landscapes. In this review we describe the effect of epistasis on the topology of evolutionary pathways that are likely to be found in fitness landscapes and develop a simple theory to connect the number of maladapted genotypes to the topology of fitness landscapes with epistatic interactions. Finally, we review recent studies that have probed the extent of epistatic interactions and have begun to chart the fitness landscapes in protein sequence space.