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WIREs Comput Mol Sci
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Coarse‐grained models of protein folding as detailed tools to connect with experiments

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Abstract Protein folding, a process that spans a wide range of timescales and that involves complex conformational dynamics, is an extremely challenging problem to decode at the atomic level. Over the past decade, coarse‐grained (CG) models that rely on a reduced representation of the polymer chain as dictated by the native structure have been quite successful in characterizing and predicting a variety of aspects of the folding mechanism of single‐domain proteins. The ever‐increasing ability of this minimalist treatment is a primarily due to the rapid and efficient sampling afforded by coarse‐graining that smoothens the folding landscape and the simple nature of the constituent physical energy functions that can be easily cast in various forms or parameterized using experimental or knowledge‐based approaches. With the advances in computational power we have now reached a stage where CG simulations can be routinely performed to test various mechanistic hypothesis, to interpret intricate experimental observables and even suggest new experimental avenues. Here, we provide an overview of recent CG developments that have predicted experiments quantitatively and others that have sought to use experimental information as constraints to tune the energetics and answer fundamental questions in folding and conformational behavior of proteins. We further discuss open issues and point to new directions that can drive the CG models toward better agreement with experiments and to a better understanding of folding mechanisms in general. © 2012 John Wiley & Sons, Ltd. This article is categorized under: Electronic Structure Theory > Density Functional Theory

The diversity of coarse‐grained representations and energetic treatments currently employed by the protein folding community.

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Generating an experimentally constrained native ensemble. The small‐angle X‐ray scattering profile (a), far‐UV circular dichroism (CD) signal (b) and the long‐range correlation between α‐carbons (c) as generated from the coarse‐grained (CG) ensemble that best reproduces all the three experimental constraints simultaneously (T = 1.04 Tm where Tm is the melting temperature from the Cα‐based CG model; red in panels a and b). The results of prediction from a low temperature ensemble are shown in green in panels (a) and (b) for comparison. (d) The distribution of root mean‐square deviation (RMSD) between the PDB structure and that of the native ensemble for a two‐state protein (Im9; blue) and the molten‐globular NCBD (red). (e) A representation of the native‐ensemble in a two‐dimensional logarithmic probability density plot with the black square indicating the alternate orientation of helices in some members of the ensemble that resemble the 1ZOQ conformation (panel f). (g) A representative of the ensemble that resembles a conformation similar to the PDB structure 1JJS that is also a proposed structure for NCBD. (Reproduced with permission from Ref 44. Copyright 2011, American Chemical Society.)

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Predicting local dynamics. The predicted natural logarithm of the protection factors (Pf; purple) as a function of the residue index for the three proteins ubiquitin (a), CI2 (b), and staphylococcal nuclease (c) together with the experimental values (blue). Proline residues are marked with an asterisk. (Adapted with permission from Ref 40. Copyright 2011, American Chemical Society.)

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Reproducing chemical denaturant effects. (a) The predicted fraction folded population for Src SH3 domain in the native basin of attraction (fNBA) from the coarse‐grained model as a function of urea (green) and guanidinium hydrochloride (red) compared against the experiment (black circles). (b) The predicted chevron plot (red and right axis) together with the experimental measurements (black and left axis). (Reproduced with permission from Ref 35. Copyright 2011, National Academy of Sciences.)

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Roll‐overs in chevron plots and frustration. Effects of increasing the strength of nonnative hydrophobic interactions on a designed (Top7; panel a) and a natural protein (S6; panel b) compared against experimental relaxation rates (black crosses; right axis). The simulated chevron‐like plots of the mean first‐passage time (MFPT) in the folding (filled symbols; left axis) and unfolding direction (open symbols) are for the nonnative hydrophobic interaction energies of zero (red; purely native centric), equal to the native interaction energy (blue) and 10% higher than the native energy (green). The agreement between the model and predictions are the best when the nonnative interaction energy exceeds that of the native energy for the designed protein Top7. (Reproduced with permission from Ref 18. Copyright 2010, National Academy of Sciences.)

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Quantifying probability distributions (upper; red curves and right axes) and representative simulated structures (lower) of specific nonnative hydrophobic () interactions in the double mutants N53I‐L3I (a) and N53I‐T47I (b) of fyn SH3. The free‐energy surfaces as a function of an order parameter (the fraction of native contacts; Q) of the respective mutants are shown at the folding midpoint temperature (upper; green curves and left axes). The nonnative interaction between N53 and L3 forms early and persists throughout as viewed by Q with the maximum probability around the folding transition state thus speeding up the folding process. (Reproduced with permission from Ref 17. Copyright 2008, National Academy of Sciences.)

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