The scale-free nature of protein sequence space

Abstract

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.

The modular structure of α/β‐hydrolases

“…The scale‐free distribution of the number of neighbours of a protein sequence demonstrates the existence of a few hubs and a large number of loosely connected sequences, as found previously for five different protein families. The scaling exponent of the α/β‐hydrolase sequence network (γ = 1.4) is similar to other protein families which had scaling exponents between 1.1 and 1.3 . The members of the homologous family 1011 (annotated as ‘protease 2’ or ‘oligopeptidase B’) had the highest number of neighbours (Table S1) and thus formed the largest hub region of the α/β‐hydrolase network.…”

“…Linear regression was performed for n ≤ 80 resulting in a scaling exponent γ = 1.4 (Fig. ), which is similar to the values of γ between 1.1 and 1.3 determined previously for five different protein families . All sequences in the hub region, ( n ≥ 300) belong to a single homologous family, the protease 2 homologous family number 1011, which are Y‐type α/β‐hydrolases from the N‐terminal domain superfamily number 8 (Table S1).…”

“…The number of neighbouring nodes n at a given threshold is called the degree of a node. The number of nodes N ( n ) having a degree of n was fitted by a power law N ( n ) ~ n − γ , and the scaling exponent γ was derived from a log‐log plot . Distributions of cluster sizes and degrees were analysed by linear fitting via the fitlm function from the Statistics and Machine Learning Toolbox (version 11.5) in MATLAB (version R2019a The MathWorks, Natick, MA, USA).…”

The Short‐chain Dehydrogenase/Reductase Engineering Database (SDRED): A classification and analysis system for a highly diverse enzyme family

“…Previously, the analysis of protein sequence networks has demonstrated that in several protein families, a small number of sequences are densely connected to other sequences within hub regions, whereas a large number of sequences are rather loosely connected . In the current SDRED, sequences annotated as serine 3‐dehydrogenase or ADP‐glycero‐manno‐heptose‐6‐epimerase from Helicobacter pylori were among these hub sequences, since they had many neighboring sequences at a threshold of 95% pairwise sequence identity.…”

Linking molecular evolution to molecular grafting

“…This alternative method is based on the hypothesis that ancestral proteins have higher thermal stability than those observed today, with the notion that environmental temperatures were higher in the Precambrian era as one possible explanation, although the origins of the stability and trends across evolutionary time are still under debate ( 84 ). Not directly related to stability is the method of identifying hub sequences for use as starting scaffolds ( 85 ). These sequences are highly connected to related sequences through mutational space.…”