Network Analysis of Protein Topology and Folding Kinetics

It is a challenging task to investigate the different influence of long-range and short-range interactions on two-state and three-state folding kinetics of protein. The networks of the 30 two-state proteins and 15 three-state proteins are constructed at three length scales: protein contact networks, long-range interaction networks and short-range interaction networks, using complex networks analysis. To uncover the relationship between structural properties and folding kinetics of the proteins, the correlations of protein network parameters with protein folding rate and topology parameters contact order are analyzed. The results show that protein contact networks and short-range interaction networks (for both two-state and three-state proteins) exhibit the dasiasmall-worldpsila property and long-range interaction networks indicate dasiascale-freepsila behavior. Our results further indicate that all protein contact networks and short-range interaction networks are assortative type. While some of long-range interaction networks are of assortative type, the others are of disassortative type. For two-state proteins, the clustering coefficients of short-range interaction networks show prominent correlation with folding rate and contact order. The assortativity coefficients of short-range interaction networks also show remarkable correlation with folding rate and contact order. Similar correlations exist in protein contact networks of three-state proteins. For two-state proteins, the correlation between contact order and folding rate is determined by the numbers of local contacts. Short-range interactions play a key role in determining the connecting trend among amino acids and they influence directly the folding rate of two-state proteins. For three-state proteins, the folding rate is determined by short-range and long-range interactions among residues together.