Folding energy landscape and network dynamics of small globular proteins

Abstract

The folding energy landscape of proteins has been suggested to be funnel-like with some degree of ruggedness on the slope. How complex the landscape, however, is still rather unclear. Many experiments for globular proteins suggested relative simplicity, whereas molecular simulations of shorter peptides implied more complexity. Here, by using complete conformational sampling of 2 globular proteins, protein G and src SH3 domain and 2 related random peptides, we investigated their energy landscapes, topological properties of folding networks, and folding dynamics. The projected energy surfaces of globular proteins were funneled in the vicinity of the native but also have other quite deep, accessible minima, whereas the randomized peptides have many local basins, including some leading to seriously misfolded forms. Dynamics in the denatured part of the network exhibited basin-hopping itinerancy among many conformations, whereas the protein reached relatively well-defined final stages that led to their native states. We also found that the folding network has the hierarchic nature characterized by the scale-free and the small-world properties.contact maps ͉ folding pathways ͉ multiple pathways ͉ principal coordinates P roteins fold on large-dimensional energy landscapes through myriads of conformations. One energy-landscape theory suggests that the global shape of the landscape is primarily funnel-like with some degree of ruggedness on the slope of the funnel (1, 2). How complex/rugged the energy landscape is and how diverse the folding-pathway ensemble is are still rather controversial. Experimentally, many small fast-folding proteins exhibit single-exponential behavior, suggesting simplicity (3). For such proteins, a perfect funnel model, Go model, has been used, as an extreme of simplicity, to model folding routes, often showing modestly good agreement with experiments (4). Conversely, there exist several clear evidences of complexity in folding. Under some conditions, proteins show strange and glassy kinetics, suggesting ruggedness of the landscape (5). Some ␤-sheet proteins, such as ␤-lactoglobulin, form nonnative ␣-helices at early stages of folding (6, 7).The computational approach has been the most direct to elucidate the complexity of folding energy landscapes. Methods developed in other areas, such as atomic clusters, have been applied to peptides and proteins, illustrating the multiple minima on the landscape (8-11). Recently, with background (10, 11), Krivov and Karplus developed the transition disconnectivity graph to visualize quantitatively the free-energy landscape and applied it for peptides finding a highly rugged non-funnel-like landscape with competing minima (12, 13). Caflisch and coworkers (14, 15) constructed a folding network for a designed peptide and uncovered a highly heterogeneous denatured ensemble. They both used network analyses without the data reduction to lower dimension and warned that the projection to low dimension, as is often done in conventional folding studies, can hide the co...

Complex Pathways in Folding of Protein G Explored by Simulation and Experiment

“…Indeed, Camilloni et al has found nonnative contacts as well as three separate pathways in a ratcheted simulation of protein G folding (36). On the other hand, Hori et al have constructed a free energy landscape of protein G using a coarse-grained model that shows a reasonably funneled landscape near the native state but many energy minima far from the native state, including a completely misfolded state that must largely unfold before progressing to the native state (37). Different trajectories show different pathways to the native state.…”

A virtual-system coupled multicanonical molecular dynamics simulation: Principles and applications to free-energy landscape of protein–protein interaction with an all-atom model in explicit solvent

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] A multicanonical Monte Carlo sampling, was introduced to study a physical system, a two-dimensional Potts model, 16 and was subsequently applied to biological systems. [17][18][19] Nakajima et al extended the multicanonical sampling to molecular dynamics (MD), which solves the equations of motion in a Cartesian coordinate space. 20 We designate this method a multicanonical molecular dynamics (McMD).…”

Virtual‐system‐coupled adaptive umbrella sampling to compute free‐energy landscape for flexible molecular docking

“…[4][5][6][7] Nakajima et al extended the multicanonical MonteCarlo sampling to Cartesian-coordinate-based molecular dynamics, [8] and this method was abbreviated to McMD.…”