A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data

To demonstrate the utility of the coarse-grained united-residue (UNRES) force field to compare experimental and computed kinetic data for folding proteins, we have performed long-time millisecondtimescale canonical Langevin molecular dynamics simulations of the triple β-strand from the Formin binding protein 28 WW domain and six nonnatural variants, using UNRES. The results have been compared with available experimental data in both a qualitative and a quantitative manner. Complexities of the folding pathways, which cannot be determined experimentally, were revealed. The folding mechanisms obtained from the simulated folding kinetics are in agreement with experimental results, with a few discrepancies for which we have accounted. The origins of single-and double-exponential kinetics and their correlations with two-and three-state folding scenarios are shown to be related to the relative barrier heights between the various states. The rate constants obtained from time profiles of the fractions of the native, intermediate, and unfolded structures, and the kinetic equations fitted to them, correlate with the experimental values; however, they are about three orders of magnitude larger than the experimental ones for most of the systems. These differences are in agreement with the timescale extension derived by scaling down the friction of water and averaging out the fast degrees of freedom when passing from all-atom to a coarse-grained representation. Our results indicate that the UNRES force field can provide accurate predictions of folding kinetics of these WW domains, often used as models for the study of the mechanisms of proein folding.FBP28 WW domain | nonnatural variants | folding rates | free-energy landscapes | millisecond-timescale canonical MD simulations R ecent advances in computer simulation techniques have facilitated the direct study of the folding process of small fastfolding proteins, using all-atom force fields (1). However, it is important to validate the simulation methodologies, and the only way to accomplish this is a quantitative comparison with experimental data with proper statistics. The validation of all-atom simulation methodologies is still a major problem because of the differences between the experimental timescale (from multiple microseconds to seconds) and the theoretical one (from hundreds of nanoseconds to microseconds). To overcome this problem, many approximate coarse-grained methods have been developed during the past decade (2-5). One of them makes use of a physics-based united-residue (UNRES) force field developed in our group over the past years (6-14) (SI Appendix, Fig. S1 and SI Materials and Methods).The folding and unfolding rates are among the most accessible quantitative observables for two-and multistate folding proteins; therefore, a study of protein folding kinetics can bridge microscopic motions and the world of experimental measurements. In analyzing protein folding kinetics, the differential rate equations and their integrated forms become more complex as the num...

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confidence: 99%

Folding kinetics of WW domains with the united residue force field for bridging microscopic motions and experimental measurements

Zhou

Maisuradze

Suñol

et al. 2014

“…By reducing the number of degrees of freedom, coarse-grained models of proteins can drastically reduce the intrinsic cost of simulating a time step, as well as increasing the duration of each step. The strategy has been pursued for many different problems over the years from protein folding to aggregation to conformational change (8,(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27). Although coarse-grained models fail to capture atomistic detail and may have limited biochemical accuracy, recent work may permit the use of simplified ensembles in accelerating atomistic sampling (28,29).…”

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confidence: 99%

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

Zhang

Jasnow

Zuckerman

2007

120

165

The computational sampling of rare, large-scale, conformational transitions in proteins is a well appreciated challenge-for which a number of potentially efficient path-sampling methodologies have been proposed. Here, we study a large-scale transition in a united-residue model of calmodulin using the ''weighted ensemble'' (WE) approach of Huber and Kim. Because of the model's relative simplicity, we are able to compare our results with bruteforce simulations. The comparison indicates that the WE approach quantitatively reproduces the brute-force results, as assessed by considering (i) the reaction rate, (ii) the distribution of event durations, and (iii) structural distributions describing the heterogeneity of the paths. Importantly, the WE method is readily applied to more chemically accurate models, and by studying a series of lower temperatures, our results suggest that the WE method can increase efficiency by orders of magnitude in more challenging systems.transition path ͉ path sampling ͉ weighted ensemble ͉ conformational transition

“…For reducing complexity in proteins, C␣-only models have been the most popular, but other coarse-graining approaches have also been taken, such as the inclusion of side-chain centroids (SCs) (13). An important aspect of coarse-grained analysis is the use of an appropriate pseudoforce field to model the forces and constraints exerted on the molecular system.…”

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confidence: 99%

“…The first major approach to a realistic coarse-grained force field is the united residue (UNRES) potential developed by Scheraga and coworkers (13,15). It has been used mainly in ab initio protein prediction by means of global conformational searches with energy evaluations.…”

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A force field for virtual atom molecular mechanics of proteins

Korkut¹,

Hendrickson

2009

Activities of many biological macromolecules involve large conformational transitions for which crystallography can specify atomic details of alternative end states, but the course of transitions is often beyond the reach of computations based on full-atomic potential functions. We have developed a coarse-grained force field for molecular mechanics calculations based on the virtual interactions of C␣ atoms in protein molecules. This force field is parameterized based on the statistical distribution of the energy terms extracted from crystallographic data, and it is formulated to capture features dependent on secondary structure and on residue-specific contact information. The resulting force field is applied to energy minimization and normal mode analysis of several proteins. We find robust convergence in minimizations to low energies and energy gradients with low degrees of structural distortion, and atomic fluctuations calculated from the normal mode analyses correlate well with the experimental B-factors obtained from high-resolution crystal structures. These findings suggest that the virtual atom force field is a suitable tool for various molecular mechanics applications on large macromolecular systems undergoing large conformational changes.energy minimization ͉ normal modes ͉ transition pathways A ccurate understanding of the dynamic properties of proteins has been a major challenge in biophysics (1, 2). With advances in macromolecular crystallography, structural information has been obtained on very large complexes such as ribosome particles (3), chaperone complexes (4), virus particles (5), and RNA polymerases (6) as well as on thousands of individual proteins. In addition, snapshots of protein structures in different states of activity demonstrate the existence of very large conformational changes (7,8). Computational analysis of the dynamics of such systems is extremely difficult, if not impossible, when using full-atomic computational approaches, due not only to computational limitations but also to the complexity of the resulting information. Thus, coarse-grained approaches have gained importance for addressing large systems and large conformational changes (9-11).Coarse graining reduces computational complexity by greatly decreasing degrees of freedom of a molecular system with appropriate assumptions to achieve simplification without compromise of essential features (12). For reducing complexity in proteins, C␣-only models have been the most popular, but other coarse-graining approaches have also been taken, such as the inclusion of side-chain centroids (SCs) (13). An important aspect of coarse-grained analysis is the use of an appropriate pseudoforce field to model the forces and constraints exerted on the molecular system.The use of simple harmonic potentials to model the C␣-to-C␣ interactions in proteins as flexible springs has been most popular (14). Such simple harmonic potentials are very effective in defining the near-native-state fluctuations of proteins calculated by elastic network models...