Long-range correlation and critical fluctuations in coevolution networks of protein sequences

Abstract Stability and adaptability are two conflicting requirements of living systems. Previous statistical survey on the structural ensembles of folded proteins showed that natural proteins have evolved to critical point, at which the proteins have the maximal adaptability but simultaneously maintaining the structural integrity. Here we study the correlation and fluctuation properties of natural proteins from the sequence level by using complex network methods. By performing direct coupling analysis to the amino acid sequences of homologous proteins, we constructed the coevolution networks for the protein families and analyzed the statistical and correlation properties. The results showed that the edge weights of the networks, which were characterized by the direct information of the coevolutionary analysis, have power law distributions. In addition, the correlation length of the fluctuations is proportional to the topological sizes of the proteins, demonstrating scale-free feature of the correlated fluctuations. Our results provide new signature of critical behaviors of the proteins based on the information of amino acid sequences, supporting the previous proposal that natural proteins have evolved to the vicinity of critical point.