Percolation in protein sequence space

The currently known protein sequences are not distributed equally in sequence space, but cluster into families. Analyzing the cluster size distribution gives a glimpse of the large and unknown extant protein sequence space, which has been explored during evolution. For six protein superfamilies with different fold and function, the cluster size distributions followed a power law with slopes between 2.4 and 3.3, which represent upper limits to the cluster distribution of extant sequences. The power law distribution of cluster sizes is in accordance with percolation theory and strongly supports connectedness of extant sequence space. Percolation of extant sequence space has three major consequences: (1) It transforms our view of sequence space as a highly connected network where each sequence has multiple neighbors, and each pair of sequences is connected by many different paths. A high degree of connectedness is a necessary condition of efficient evolution, because it overcomes the possible blockage by sign epistasis and reciprocal sign epistasis. (2) The Fisher exponent is an indicator of connectedness and saturation of sequence space of each protein superfamily. (3) All clusters are expected to be connected by extant sequences that become apparent as a higher portion of extant sequence space becomes known. Being linked to biochemically distinct homologous families, bridging sequences are promising enzyme candidates for applications in biotechnology because they are expected to have substrate ambiguity or catalytic promiscuity.