The scale-free nature of protein sequence space.

The sequence space of five protein superfamilies was investigated by constructing sequence networks. The nodes represent individual sequences, and two nodes are connected by an edge if the global sequence identity of two sequences exceeds a threshold. The networks were characterized by their degree distribution (number of nodes with a given number of neighbors) and by their fractal network dimension. Although the five protein families differed in sequence length, fold, and domain arrangement, their network properties were similar. The fractal network dimension Df was distance-dependent: a high dimension for single and double mutants (Df = 4.0), which dropped to Df = 0.7-1.0 at 90% sequence identity, and increased to Df = 3.5-4.5 below 70% sequence identity. The distance dependency of the network dimension is consistent with evolutionary constraints for functional proteins. While random single and double mutations often result in a functional protein, the accumulation of more than ten mutations is dominated by epistasis. The networks of the five protein families were highly inhomogeneous with few highly connected communities ("hub sequences") and a large number of smaller and less connected communities. The degree distributions followed a power-law distribution with similar scaling exponents close to 1. Because the hub sequences have a large number of functional neighbors, they are expected to be robust toward possible deleterious effects of mutations. Because of their robustness, hub sequences have the potential of high innovability, with additional mutations readily inducing new functions. Therefore, they form hotspots of evolution and are promising candidates as starting points for directed evolution experiments in biotechnology.

Network Analysis of Sequence-Function Relationships and Exploration of Sequence Space of TEM ß-Lactamases.

The Lactamase Engineering Database (www.LacED.uni-stuttgart.de) was developed to facilitate the classification and analysis of TEM ß-lactamases. The current version contains 474 TEM variants. Two hundred fifty-nine variants form a large scale-free network of highly connected point mutants. The network was divided into three subnetworks which were enriched by single phenotypes: one network with predominantly 2be and two networks with 2br phenotypes. Fifteen positions were found to be highly variable, contributing to the majority of the observed variants. Since it is expected that a considerable fraction of the theoretical sequence space is functional, the currently sequenced 474 variants represent only the tip of the iceberg of functional TEM ß-lactamase variants which form a huge natural reservoir of highly interconnected variants. Almost 50% of the variants are part of a quartet. Thus, two single mutations that result in functional enzymes can be combined into a functional protein. Most of these quartets consist of the same phenotype, or the mutations are additive with respect to the phenotype. By predicting quartets from triplets, 3,916 unknown variants were constructed. Eighty-seven variants complement multiple quartets and therefore have a high probability of being functional. The construction of a TEM ß-lactamase network and subsequent analyses by clustering and quartet prediction are valuable tools to gain new insights into the viable sequence space of TEM ß-lactamases and to predict their phenotype. The highly connected sequence space of TEM ß-lactamases is ideally suited to network analysis and demonstrates the strengths of network analysis over tree reconstruction methods.