Abstract: An intriguing feature of protein folding is that the overall behavior obeys simple physical rules, but the finer details show a great deal of complexity. The scaling of thermodynamic and kinetic properties with protein size is one such rule. However, it is not clear to what extent biologically relevant folding properties (i.e., rates and stabilities) depend on size and/or on other factors such as structure and amino acid sequence. Here we address this question analyzing experimental data on 52 nonmultistate folding proteins with a simple theoretical model. We find that size scaling is the primary factor in determining folding rates, and more surprisingly also protein stability. Furthermore, our analysis reveals that the experimental deviations from size predictions are due to minute differences in the fundamental parameters (e.g., less than 2% for the stability). Folding is thus highly sensitive to little changes in protein energetics, but at the same time the folding properties of natural proteins are remarkably homogeneous. These results suggest that evolution has selected a small subset of possibilities from the physically plausible folding catalog and highlight the need for highly accurate protein force fields to predict rates and stabilities beyond general trends.

Abstract: New force fields that are both simple and accurate are needed for computationally efficient molecular simulation studies to give insight into the actual features of the protein folding process. In this work, we assess a force field based on a new combination of two coarse-grained potentials taken from the bibliography. These potentials have already been proved efficient in representing different types of interactions, namely the side-chain interactions and the backbone hydrogen bonds. Now we combine them weighing their contribution to the global energy with a very simplified parameterization. To assess this combination of potentials, we use our evolutionary method to carry out energy minimization experiments for a set of all-alpha, all-beta, and (alpha + beta) protein structures. Our results, based on the assembly of short rigid native fragments, suggest that this combination of potentials can be successfully employed in coarse-grained folding simulations.

Abstract: Traditionally, folding experiments have been directed at determining equilibrium and relaxation rate constants of proteins that fold with two-state-like kinetics. More recently, the combination of free energy surface approaches inspired by theory with the discovery of proteins that fold in the downhill regime has greatly widened the battlefield for experimentalists. Downhill folding proteins cross very small or no free energy barrier at all so that all relevant partially folded conformations become experimentally accessible. From these combined efforts we now have tools to estimate the height of thermodynamic and kinetic folding barriers. Procedures to measure with atomic resolution the structural heterogeneity of conformational ensembles at varying unfolding degrees are also available. Moreover, determining the dynamic modes driving folding and how they change as folding proceeds is finally at our fingertips. These developments allow us to address via experiment fundamental questions such as the origin of folding cooperativity, the relationship between structure and stability, or how to engineer folding barriers. Moreover, the level of detail attained in this new breed of experiments should provide powerful benchmarks for computer simulations of folding and force-field refinement.

Abstract: Backbone hydrogen bonds contribute very importantly to the stability of proteins and therefore they must be appropriately represented in protein folding simulations. Simple models are frequently used in theoretical approaches to this process, but their simplifications are often confronted with the need to be true to the physics of the interactions. Here we study the effects of different levels of coarse graining in the modeling of backbone hydrogen bonds. We study three different models taken from the bibliography in a twofold fashion. First, we calculate the hydrogen bonds in 2gb1, an (alpha + beta)-protein, and see how different backbone representations and potentials can mimic the effects of real hydrogen bonds both in helices and sheets. Second, we use an evolutionary method for protein fragment assembly to locate the global energy minimum for a set of small beta-proteins with these models. This way, we assess the effects of coarse graining in hydrogen bonding models and show what can be expected from them when used in simulation experiments.

Abstract: We use Monte Carlo simulations to analyze the behavior of a family of previously reported, statistically derived, mean field potentials for protein folding (the DFIRE potentials from the Zhou laboratory). The potentials may consider different interaction centers (alpha carbons, beta carbons, or side-chain centroids), depending on the details of the coarse-grained model simulated. The type of association of the helices in different simulated coiled-coil proteins provides interesting information on the real capabilities of these interaction schemes along the sampling of the topological space available to the protein model.

Abstract: Many different protein folding potentials have been developed in the last decades, based upon knowledge of experimentally determined protein structures. Decoy-based techniques are frequently used to assess these force fields, but other methods can explore different features in the performance of the interaction schemes, thus helping in their evaluation. Here, we propose an evolutionary strategy to efficiently assess folding potentials. We apply it to three potentials with different characteristics, taken from the bibliography. A search for minimum energy protein topologies, treated as arrangements of rigid protein fragments, is performed. The method, applied to a set of helix bundle proteins, shows the different behavior of the studied potentials, providing a reasonably fast tool to evaluate their advantages and limitations.

Abstract: Go-type potentials, based on the inter-residue contacts present in the native structure of a protein, are frequently used to predict dynamic and structural features of the folding pathways through computer simulations. However, the mathematical form used to define the model interactions includes several arbitrary choices, whose consequences are not usually analyzed. In this work, we use a simple off-lattice protein model and a parallel tempering Monte Carlo simulation technique to carry out such analysis, centered in the thermodynamic characteristics of the folding transition. We show how the definition of a native contact has a deep impact on the presence of simple or complex transitions, with or without thermodynamic intermediates. In addition, we have checked that the width of the attractive wells has a profound effect on the free-energy barrier between the folded and unfolded states, mainly through its influence on the entropy of the denatured state.

Abstract: Genetic algorithms constitute a powerful optimization method that has already been used in the study of the protein folding problem. However, they often suffer from a lack of convergence in a reasonably short time for complex fitness functions. Here, we propose an evolutionary strategy that can reproducibly find structures close to the minimum of a potential function for a simplified protein model in an efficient way. The model reduces the number of degrees of freedom of the system by treating the protein structure as composed of rigid fragments. The search incorporates a double encoding procedure and a merging operation from subpopulations that evolve independently of one another, both contributing to the good performance of the full algorithm. We have tested it with protein structures of different degrees of complexity, and present our conclusions related to its possible application as an efficient tool for the analysis of folding potentials.