Folding-unfolding energy change of a simple sphere model protein and an energy landscape of the folding process

Abstract

We have calculated the free energy of a spherical model of a protein or part of a protein generated in the way of protein folding. Two spherical models are examined; one is a homogeneous model consisting of only one residue type--hydrophobic. The other is a heterogeneous model consisting of two residue types--strong hydrophobic and weak hydrophobic. Both models show a folding transition state, and the latter model reproduces the trend of the experimental folded-unfolded energy change. The heterogeneous model suggests that in the folding process of a protein of more than 70 residues, a specific region of the protein folds first to form a stable region, then the other residues follow the folding process. The energy landscape of folding of a small protein is approximately a funnel model, whereas a flatter energy landscape is suggested for larger proteins of more than 55-70 residues.

The Highly Cooperative Folding of Small Naturally Occurring Proteins Is Likely the Result of Natural Selection

“…This would produce a rugged folding free energy landscape in which the folding of a polypeptide chain could be slowed by trapping in nonnative minima. In agreement with this picture, many theoretical models predict that protein folding should be a complex, slow process characterized by the trapping of the polypeptide chain in nonnative minima (Chan, 2000;Fukunishi, 1998;Go, 1984;Kaya and Chan, 2003;Sali et al, 1994). However, a large body of work carried out over the past 15 years suggests that rugged folding free energy landscapes are quite rare in small, naturally occurring proteins; these proteins generally have highly cooperative folding transitions in which nonnative states are not significantly populated (Jackson, 1998;Jackson and Fersht, 1991;Krantz et al, 2002;Krantz and Sosnick, 2000).…”

Combining pressure and temperature control in dynamics on energy landscapes

“…These stable regions correspond to e.g. (meta)stable chemical compounds [6,11,12], folded or unfolded states of a protein [13][14][15][16][17][18], magnetic phases [19], stable attractors [20], or (sub)optimal solutions of combinatorial optimization problems [21,22], while the flows characterize the likelihood of transitions between stable regions [23,24], the relaxation towards equilibrium [25,26], and the progress of optimization algorithms [22,27]. The determination of such regions and flows requires finding the minima of the landscape and measuring the local volume in state space contained within the basins of the landscape, and furthermore the analysis of the connectivity of the landscape including the derivation of the energetic, entropic and kinetic barriers [10,28] that separate individual minima and the multi-minima basins [2].…”