title: Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding.
abstract: The energy landscape approach has played a fundamental role in advancing our understanding of protein folding. Here, we quantify protein folding energy landscapes by exploring the underlying density of states. We identify three quantities essential for characterizing landscape topography: the stabilizing energy gap between the native and nonnative ensembles δE, the energetic roughness ΔE, and the scale of landscape measured by the entropy S. We show that the dimensionless ratio between the gap, roughness, and entropy of the system Λ=δE/(ΔE√(2S)) accurately predicts the thermodynamics, as well as the kinetics of folding. Large Λ implies that the energy gap (or landscape slope towards the native state) is dominant, leading to more funneled landscapes. We investigate the role of topological and energetic roughness for proteins of different sizes and for proteins of the same size, but with different structural topologies. The landscape topography ratio Λ is shown to be monotonically correlated with the thermodynamic stability against trapping, as characterized by the ratio of folding temperature versus trapping temperature. Furthermore, Λ also monotonically correlates with the folding kinetic rates. These results provide the quantitative bridge between the landscape topography and experimental folding measurements.
authors.affiliation: State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences Changchun, Jilin, China. jin.wang.1@stonybrook.edu
authors.forename: Jin
authors.initials: J
authors.lastname: Wang
authors.forename: Ronaldo J
authors.initials: RJ
authors.lastname: Oliveira
authors.forename: Xiakun
authors.initials: X
authors.lastname: Chu
authors.forename: Paul C
authors.initials: PC
authors.lastname: Whitford
authors.forename: Jorge
authors.initials: J
authors.lastname: Chahine
authors.forename: Wei
authors.initials: W
authors.lastname: Han
authors.forename: Erkang
authors.initials: E
authors.lastname: Wang
authors.forename: José N
authors.initials: JN
authors.lastname: Onuchic
authors.forename: Vitor B P
authors.initials: VB
authors.lastname: Leite
mesh_terms: D019277:Entropy; D008956:Models, Chemical; D017510:Protein Folding; D011506:Proteins / Q000737:chemistry*
chemical_list: D011506:Proteins