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A method for optimizing potential-energy functions by a hierarchical design of the potential-energy landscape: application to the UNRES force field.

ABSTRACT: A method for optimizing potential-energy functions of proteins is proposed. The method assumes a hierarchical structure of the energy landscape, which means that the energy decreases as the number of native-like elements in a structure increases, being lowest for structures from the native family and highest for structures with no native-like element. A level of the hierarchy is defined as a family of structures with the same number of native-like elements (or degree of native likeness). Optimization of a potential-energy function is aimed at achieving such a hierarchical structure of the energy landscape by forcing appropriate free-energy gaps between hierarchy levels to place their energies in ascending order. This procedure is different from methods developed thus far, in which the energy gap and/or the Z score between the native structure and all non-native structures are maximized, regardless of the degree of native likeness of the non-native structures. The advantage of this approach lies in reducing the number of structures with decreasing energy, which should ensure the searchability of the potential. The method was tested on two proteins, PDB ID codes and, with an off-lattice united-residue force field. For, the search of the conformational space with the use of the conformational space annealing method and the newly optimized potential-energy function found the native structure very quickly, as opposed to the potential-energy functions obtained by former optimization methods. After even incomplete optimization, the force field obtained by using located the native-like structures of two peptides, and betanova (a designed three-stranded beta-sheet peptide), as the lowest-energy conformations, whereas for the 46-residue N-terminal fragment of staphylococcal protein A, the native-like conformation was the second-lowest-energy conformation and had an energy 2 kcal/mol above that of the lowest-energy structure.

SUBMITTER: Liwo A

PROVIDER: S-EPMC122298 | biostudies-literature | 2002 Feb

REPOSITORIES: biostudies-literature

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A method for optimizing potential-energy functions by a hierarchical design of the potential-energy landscape: application to the UNRES force field.

Liwo Adam A Arłukowicz Piotr P Czaplewski Cezary C Ołdziej Stanislaw S Pillardy Jaroslaw J Scheraga Harold A HA

Proceedings of the National Academy of Sciences of the United States of America 20020201 4

A method for optimizing potential-energy functions of proteins is proposed. The method assumes a hierarchical structure of the energy landscape, which means that the energy decreases as the number of native-like elements in a structure increases, being lowest for structures from the native family and highest for structures with no native-like element. A level of the hierarchy is defined as a family of structures with the same number of native-like elements (or degree of native likeness). Optimiz ...[more]

PMID: 11854494

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Project description:Three algorithms, namely a Replica Exchange method (REM), a Replica Exchange Multicanonical method (REMUCA), and Replica Exchange Multicanonical with Replica Exchange (REMUCAREM), were implemented with the coarse-grained united-residue force field (UNRES) in both Monte Carlo and Molecular Dynamics versions. The MD algorithms use the constant-temperature Berendsen thermostat, with the velocity Verlet algorithm and variable time step. The algorithms were applied to one peptide (20 residues of Alanine with free ends; ala(20)) and two small proteins, namely an ?-helical protein of 46 residues (the B-domain of the staphylococal protein A; 1BDD), and an ?+?-protein of 48 residues (the E. Coli Mltd Lysm Domain; 1E0G). Calculated thermodynamic averages, such as canonical average energy and heat capacity, are in good agreement among all simulations for poly-L-alanine, showing that the algorithms were implemented correctly, and that all three algorithms are equally effective for small systems. For protein A, all algorithms performed reasonably well, although some variability in the calculated results was observed whereas, for a more complicated ?+?-protein (1E0G), only Replica Exchange was capable of producing reliable statistics for calculating thermodynamic quantities. Finally, from the Replica Exchange molecular dynamics results, we calculated free energy maps as functions of RMSD and radius of gyration for different temperatures. The free energy calculations show correct folding behavior for poly-L-alanine and protein A while, for 1E0G, the native structure had the lowest free energy only at very low temperatures. Hence, the entropy contribution for 1E0G is larger than that for protein A at the same temperature. A larger contribution from entropy means that there are more accessible conformations at a given temperature, making it more difficult to obtain an efficient coverage of conformational space to obtain reliable thermodynamic properties. At the same temperature, ala(20) has the smallest entropy contribution, followed by protein A, and then by 1E0G.

Project description:Coarse-grained molecular dynamics simulations offer a dramatic extension of the time-scale of simulations compared to all-atom approaches. In this article, we describe the use of the physics-based united-residue (UNRES) force field, developed in our laboratory, in protein-structure simulations. We demonstrate that this force field offers about a 4000-times extension of the simulation time scale; this feature arises both from averaging out the fast-moving degrees of freedom and reduction of the cost of energy and force calculations compared to all-atom approaches with explicit solvent. With massively parallel computers, microsecond folding simulation times of proteins containing about 1000 residues can be obtained in days. A straightforward application of canonical UNRES/MD simulations, demonstrated with the example of the N-terminal part of the B-domain of staphylococcal protein A (PDB code: 1BDD, a three-alpha-helix bundle), discerns the folding mechanism and determines kinetic parameters by parallel simulations of several hundred or more trajectories. Use of generalized-ensemble techniques, of which the multiplexed replica exchange method proved to be the most effective, enables us to compute thermodynamics of folding and carry out fully physics-based prediction of protein structure, in which the predicted structure is determined as a mean over the most populated ensemble below the folding-transition temperature. By using principal component analysis of the UNRES folding trajectories of the formin-binding protein WW domain (PDB code: 1E0L; a three-stranded antiparallel beta-sheet) and 1BDD, we identified representative structures along the folding pathways and demonstrated that only a few (low-indexed) principal components can capture the main structural features of a protein-folding trajectory; the potentials of mean force calculated along these essential modes exhibit multiple minima, as opposed to those along the remaining modes that are unimodal. In addition, a comparison between the structures that are representative of the minima in the free-energy profile along the essential collective coordinates of protein folding (computed by principal component analysis) and the free-energy profile projected along the virtual-bond dihedral angles gamma of the backbone revealed the key residues involved in the transitions between the different basins of the folding free-energy profile, in agreement with existing experimental data for 1E0L .

Project description:Coarse-grained force fields for protein simulations are usually designed and parameterized to treat proteins composed of natural L-amino-acid residues. However, D-amino-acid residues occur in bacterial, fungal (e.g., gramicidins), as well as human-designed proteins. For this reason, we have extended the UNRES coarse-grained force field developed in our laboratory to treat systems with D-amino-acid residues. We developed the respective virtual-bond-torsional and double-torsional potentials for rotation about the C (?) · · · C (?) virtual-bond axis and two consecutive C (?) · · · C (?) virtual-bond axes, respectively, as functions of virtual-bond-dihedral angles ?. In turn, these were calculated as potentials of mean force (PMFs) from the diabatic energy surfaces of terminally-blocked model compounds for glycine, alanine, and proline. The potential-energy surfaces were calculated by using the ab initio method of molecular quantum mechanics at the Møller-Plesset (MP2) level of theory and the 6-31G(d,p) basis set, with the rotation angles of the peptide groups about [Formula: see text] and [Formula: see text] used as variables, and the energy was minimized with respect to the remaining degrees of freedom. The PMFs were calculated by numerical integration for all pairs and triplets with all possible combinations of types (glycine, alanine, and proline) and chirality (D or L); however, symmetry relations reduce the number of non-equivalent torsional potentials to 13 and the number of double-torsional potentials to 63 for a given C-terminal blocking group. Subsequently, one- (for torsional) and two-dimensional (for double-torsional potentials) Fourier series were fitted to the PMFs to obtain analytical expressions. It was found that the torsional potentials of the x-Y and X-y types, where X and Y are Ala or Pro, respectively, and a lowercase letter denotes D-chirality, have global minima for small absolute values of ?, accounting for the double-helical structure of gramicidin A, which is a dimer of two chains, each possessing an alternating D-Tyr-L-Tyr sequence, and similar peptides. The side-chain and correlation potentials for D-amino-acid residues were obtained by applying the reflection about the [Formula: see text] plane to the respective potentials for the L-amino-acid residues.

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A method for optimizing potential-energy functions by a hierarchical design of the potential-energy landscape: application to the UNRES force field.

Publications

A method for optimizing potential-energy functions by a hierarchical design of the potential-energy landscape: application to the UNRES force field.

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