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WIREs Comput Mol Sci
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Accelerating physical simulations of proteins by leveraging external knowledge

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It is challenging to compute structure‐function relationships of proteins using molecular physics. The problem arises from the exponential scaling of the computational searching and sampling of large conformational spaces. This scaling challenge is not met by today's methods, such as Monte Carlo, simulated annealing, genetic algorithms, or molecular dynamics (MD) or its variants such as replica exchange. Such methods of searching for optimal states on complex probabilistic landscapes are referred to more broadly as Explore‐and‐Exploit (EE), including in contexts such as computational learning, games, industrial planning, and modeling military strategies. Here, we describe a Bayesian method, called MELD, that ‘melds’ together EE approaches with externally added information that can be vague, combinatoric, noisy, intuitive, heuristic, or from experimental data. MELD is shown to accelerate physical MD simulations when using experimental data to determine protein structures; for predicting protein structures by using heuristic directives; and when predicting binding affinities of proteins from limited information about the binding site. Such Guided EE approaches might also be useful beyond proteins and beyond molecular science. WIREs Comput Mol Sci 2017, 7:e1309. doi: 10.1002/wcms.1309

Explore‐and‐exploit is a general strategy for seeking a global optimum of an objective function (in this case, a free‐energy minimum), on a landscape that is usually bumpy and high dimensional.
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Search space increases exponentially with protein size. Bigger computers alone have not been the solution to the game of Go nor to protein folding. Alternative algorithms that can incorporate intuition and current knowledge can help improve scaling.
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Swapping the different peptides (red and blue) in and out of the protein‐binding site. Two possible states (a) in which one peptide (blue structure) is bound to the target protein (gray surface) and the other (red structure) is kept unbound and (b) in which the roles of the peptides are reversed. Each peptide may favor different binding modes. The ratio of the populations between these two cases p B / p A can be related to the relative free energy of binding by the equation given here.
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The CASP blind test of protein structure prediction. The x‐axis represents the degree to which known proteins can be used as starting models for predicting target protein structure. Blue band represents the historical average over 20 years of CASP events, showing that bioinformatics methods have been challenged to predict protein structures. The triangles shows that, when given some additional information beyond the amino acid sequence, the MELD physical method (black triangles) gives comparable predictions to the best bioinformatics methods (one of which is Rosetta, red triangles).
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Blind predictions from CASP 11. TOP: The name of the targets is denoted according to CASP numbering T0 and can be accessed through http://www.predictioncenter.org. We are the ‘Laufer’ group (number 428). The number on top of the name is the RMSD of our number one submission: centroid structure of the highest population cluster from MELD trajectories. BOTTOM: Hubbard plots representing our prediction accuracy (blue) compared to predictions by all other groups in CASP (gray lines). The best results are shown by the shoulder in the line (where the slope changes upward) being more to the right and low RMSD values (higher % of the structure being less than X Å away from native). Adapted from Ref .
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MELD speeds up folding simulations. Simulation time required to sample native states starting from fully unfolded states. Adapted with permission from Ref .
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Coarse physical insights based on hydrophobic residues. All possible hydrophobic restraints are shown for a structured sampled at high temperature in a MELD simulation. Only a subset of these (the ones with the lowest restraint energy) will be used to guide the structure to the next time step.
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MELD can make accurate predictions starting from sequence using noisy data. The figure shows evolutionary data from EvFold superposed on the native structure (a) and our top prediction with this data superposed on the native structure (PDBid 5P21) (b).
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The MELD method explained using a toy HP lattice model. Adapted with permission from Ref . Copyright 2015 National Academy of Sciences, USA.
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The MELD method. (a) The energy function given by the force field at the lowest replica in a traditional replica‐exchange Molecular Dynamics (REMD) approach. (b) The same energy function with an arbitrary energy penalty in regions that are not compatible with data (red). MELD uses a one‐dimensional replica‐exchange ladder approach in which the Hamiltonian and the temperature are both changed together. At the top replica, the highest temperature is enforced and the Hamiltonian is the one determined by the force field—exactly the same as in a traditional temperature replica‐exchange approach.
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Structure and Mechanism > Computational Biochemistry and Biophysics

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