Adaptation in protein fitness landscapes is facilitated by indirect paths
The structure of fitness landscapes is critical for understanding adaptive protein evolution (e.g. antimicrobial resistance, affinity maturation, etc.). Due to limited throughput in fitness measurements, previous empirical studies on fitness landscapes were confined to either the neighborhood around the wild type sequence, involving mostly single and double mutants, or a combinatorially complete subgraph involving only two amino acids at each site. In reality, however, the dimensionality of protein sequence space is higher (20L, L being the length of the relevant sequence) and there may be higher-order interactions among more than two sites. To study how these features impact the course of protein evolution, we experimentally characterized the fitness landscape of four sites in the IgG-binding domain of protein G, containing 204 = 160,000 variants. We found that the fitness landscape was rugged and direct paths of adaptation were often constrained by pairwise epistasis. However, while direct paths were blocked by reciprocal sign epistasis, we found systematic evidence that such evolutionary traps could be circumvented by \"extra-dimensional bypass\". Extra dimensions in sequence space - with a different amino acid at the site of interest or an additional interacting site - open up indirect paths of adaptation via gain and subsequent loss of mutations. These indirect paths alleviate the constraint on reaching high fitness genotypes via selectively accessible trajectories, suggesting that the heretofore neglected dimensions of sequence space may completely change our views on how proteins evolve.