Characterizing Energy Landscapes of Proteins and Identifying Shape-Determining Factors

Abstract

Protein folding is a long standing problem in biology, whose mechanism is still not completely understood. Funnel-shape energy landscape has been proposed as a plausible folding mechanism. However, the factors that determine the funnel-shape energy landscapes is largely unknown. In this study, we use hydrophobic-hydrophilic (HP) model to investigate the factors that affect the funnel-shape of protein energy landscapes. We designed a clustering method based on graph theory to analyze the conformations sampled using a recently developed Monte Carlo method, FRESS. We found that the way conformations move from one to another defined by a particular sampling method (move set) has a significant effect on the shape of protein energy landscapes. To our surprise, both protein-like sequences and random sequences with around 50% hydrophobic residues have a stable state represented by a single dominant cluster, consisting of a large number of similar conformations. The energy landscapes resemble a funnel, where there are many paths to minimum energy conformations in the dominant cluster from conformations of higher energies. We also found that sequences with hydrophobic residues above or below the optimal range around 50% do not have a single stable state. In stead, there are many much smaller clusters, representing multiple local energy minima. Our finding is consistent with the compositions of hydrophobic and polar residues in globular proteins (fold to unique structures) and intrinsically disordered proteins (IDPs). Our study suggests that in computational simulations, move sets affect significantly the shape of protein energy landscapes; hydrophobic interaction is likely a major force leading to the funnel-shape energy landscape of proteins; and the composition of hydrophobic and polar residues is an important sequence feature for the formation of funnel-shape of protein energy landscapes.