Determination of the Potentials of Mean Force for Rotation about C<sup>α</sup>−C<sup>α</sup> Virtual Bonds in Polypeptides from the ab Initio Energy Surfaces of Terminally Blocked Glycine, Alanine, and Proline

Ołdziej, Stanisław; Kozłowska, Urszula; Liwo, Adam; Scheraga, Harold A.

doi:10.1021/jp0223410

Cited by 63 publications

(191 citation statements)

References 72 publications

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“…The RFE is defined as the free energy of a given coarse-grain conformation obtained by integrating the Boltzmann factor of the all-atom (i.e., the polypeptide chain plus solvent) energy over the degrees of freedom that are neglected in the united-residue model. 38,40,45,46 The complete UNRES potential-energy function is expressed by eq 1. The terms U SC i SC j correspond to the mean free energy of hydrophobic (hydrophilic) interactions between the side chains.…”

Section: United-residue Force Fieldmentioning

confidence: 99%

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

et al. 2005

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The Lagrange formalism was implemented to derive the equations of motion for the physics-based united-residue (UNRES) force field developed in our laboratory. The C α… C α and C α… SC (SC denoting a side-chain center) virtual-bond vectors were chosen as variables. The velocity Verlet algorithm was adopted to integrate the equations of motion. Tests on the unblocked Ala 10 polypeptide showed that the algorithm is stable in short periods of time up to the time step of 1.467 fs; however, even with the shorter time step of 0.489 fs, some drift of the total energy occurs because of momentary jumps of the acceleration. These jumps are caused by numerical instability of the forces arising from the U rot component of UNRES that describes the energetics of side-chain-rotameric states. Test runs on the Gly 10 sequence (in which U rot is not present) and on the Ala 10 sequence with U rot replaced by a simple numerically stable harmonic potential confirmed this observation; oscillations of the total energy were observed only up to the time step of 7.335 fs, and some drift in the total energy or instability of the trajectories started to appear in long-time (2 ns and longer) trajectories only for the time step of 9.78 fs. These results demonstrate that the present U rot components (which are statistical potentials derived from the Protein Data Bank) must be replaced with more numerically stable functions; this work is under way in our laboratory. For the purpose of our present work, a nonsymplectic variable-time-step algorithm was introduced to reduce the energy drift for regular polypeptide sequences. The algorithm scales down the time step at a given point of a trajectory if the maximum change of acceleration exceeds a selected cutoff value. With this algorithm, the total energy is reasonably conserved up to a time step of 2.445 fs, as tested on the unblocked Ala 10 polypeptide. We also tried a symplectic multiple-time-step reversible RESPA algorithm and achieved satisfactory energy conservation for time steps up to 7.335 fs. However, at present, it appears that the reversible RESPA algorithm is several times more expensive than the variable-time-step algorithm because of the necessity to perform additional matrix multiplications. We also observed that, because Ala 10 folds and unfolds within picoseconds in the microcanonical mode, this suggests that the effective (event-based) time unit in UNRES dynamics is much larger than that of all-atom dynamics because of averaging over the fast-moving degrees of freedom in deriving the UNRES potential.

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Section: United-residue Force Fieldmentioning

confidence: 99%

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

et al. 2005

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“…The UNRES model of polypeptide chains and the associated energy function are described in our earlier papers (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29), and only a brief summary is presented here. The polypeptide chain is represented as a sequence of ␣-carbon atoms (C ␣ ) linked by virtual bonds of length 3.8 Å corresponding to trans peptide groups.…”

Section: Methodsmentioning

confidence: 99%

“…14). The parameters of U SCSC , U b , and U rot were derived (14,15) from the distribution and correlation functions calculated from the PDB (38), whereas those of U corr (i) , Ϫi ϭ 3,4,5,6, U tor , U tord , and U pp were calculated by fitting the corresponding analytical expression to the restricted free energy surfaces of model all-atom systems calculated by using high-level quantum-mechanical ab initio methods (25,26). Use of protein-structural data is not, however, necessary to derive the parameters of U SCSC , U b , and U rot , and was motivated only by lack of sufficient resources; these terms are currently being reparameterized based on the results of our simulation studies of the potentials of mean force of models of SC in water (39,40) and quantum-mechanical calculations of the energy surfaces of terminally blocked amino acid residues (25), respectively.…”

Section: Methodsmentioning

confidence: 99%

“…1 (25), reparameterization of the torsional, correlation, and backbone-electrostatic terms based on free-energy surfaces of model systems calculated by using a quantum-mechanical ab initio method (26), and by developing a hierarchical procedure to obtain hierarchical well-searchable energy landscapes (24). However, the hierarchical-optimization procedure was still being developed during CASP5, and the force field used in that experiment was not refined, having an overwhelming preference for ␤-structure (26,27).…”

Section: Casp Exercise Prediction Methodologymentioning

confidence: 99%

“…We, therefore, designed a hierarchical approach (11)(12)(13) in which the conformational space is searched extensively by using the physics-based united-residue (UNRES) force field (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29) developed in our laboratory, which is the key component of the method. The UNRES force field has been derived (11,18,21,25,26) by averaging the all-atom energy of a system composed of protein plus solvent with implementation (21) of Kubo's theory of cluster cumulants (30). Furthermore, it has been parameterized (24,27,28) to achieve a hierarchical structure of the potential-energy landscape, which is the fundamental feature of the energy landscapes of proteins (31) and the necessary condition for foldability (31,32).…”

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Physics-based protein-structure prediction using a hierarchical protocol based on the UNRES force field: Assessment in two blind tests

Ołdziej

Czaplewski

Liwo

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

134

119

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Recent improvements in the protein-structure prediction method developed in our laboratory, based on the thermodynamic hypothesis, are described. The conformational space is searched extensively at the united-residue level by using our physics-based UNRES energy function and the conformational space annealing method of global optimization. The lowest-energy coarse-grained structures are then converted to an all-atom representation and energyminimized with the ECEPP͞3 force field. The procedure was assessed in two recent blind tests of protein-structure prediction. During the first blind test, we predicted large fragments of ␣ and ␣؉␤ proteins [60 -70 residues with C ␣ rms deviation (rmsd) <6 Å]. However, for ␣؉␤ proteins, significant topological errors occurred despite low rmsd values. In the second exercise, we predicted whole structures of five proteins (two ␣ and three ␣؉␤, with sizes of 53-235 residues) with remarkably good accuracy. In particular, for the genomic target TM0487 (a 102-residue ␣؉␤ protein from Thermotoga maritima), we predicted the complete, topologically correct structure with 7.3-Å C ␣ rmsd. So far this protein is the largest ␣؉␤ protein predicted based solely on the amino acid sequence and a physics-based potential-energy function and search procedure. For target T0198, a phosphate transport system regulator PhoU from T. maritima (a 235-residue mainly ␣-helical protein), we predicted the topology of the whole six-helix bundle correctly within 8 Å rmsd, except the 32 C-terminal residues, most of which form a ␤-hairpin. These and other examples described in this work demonstrate significant progress in physics-based protein-structure prediction.global optimization ͉ thermodynamic hypothesis T o date, the great majority of successful algorithms for proteinstructure prediction are knowledge-based approaches; they make explicit use of homology modeling (1, 2) or fold recognition methods (2-6). This feature even pertains to most of the methods considered as ab initio (7,8), which, in theory, should not make explicit use of structural databases. However, in-depth understanding of the physical principles of formation of protein structure requires the development of physics-based methods for proteinstructure prediction (9). Moreover, such methods will be independent of structural databases used in the training of knowledgebased methods. Furthermore, physics-based methods will enable us to study the structures of proteins that seem to possess a degenerate native state, such as the prion proteins, to simulate protein-folding pathways, to understand the mechanisms of protein folding, and to study interactions of proteins with other biomacromolecules and their assemblies (e.g., nucleic acids, polysaccharides, lipids, etc.). The underlying principle of physics-based methods for proteinstructure prediction is Anfinsen's thermodynamic hypothesis (10), according to which protein molecules adopt the conformations that are the global minima of their potential-energy surfaces. The methods based on this hypoth...

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Hydrogen Bonding and Proton Transfer in ionized DNA Base Pairs, Amino Acids and Peptides

Rodrı́guez-Santiago

Noguera

Bertrán

et al. 2010

Quantum Biochemistry

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Determination of the Potentials of Mean Force for Rotation about C^α−C^α Virtual Bonds in Polypeptides from the ab Initio Energy Surfaces of Terminally Blocked Glycine, Alanine, and Proline

Cited by 63 publications

References 72 publications

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

Physics-based protein-structure prediction using a hierarchical protocol based on the UNRES force field: Assessment in two blind tests

Hydrogen Bonding and Proton Transfer in ionized DNA Base Pairs, Amino Acids and Peptides

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Determination of the Potentials of Mean Force for Rotation about Cα−Cα Virtual Bonds in Polypeptides from the ab Initio Energy Surfaces of Terminally Blocked Glycine, Alanine, and Proline

Cited by 63 publications

References 72 publications

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

Physics-based protein-structure prediction using a hierarchical protocol based on the UNRES force field: Assessment in two blind tests

Hydrogen Bonding and Proton Transfer in ionized DNA Base Pairs, Amino Acids and Peptides

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Determination of the Potentials of Mean Force for Rotation about C^α−C^α Virtual Bonds in Polypeptides from the ab Initio Energy Surfaces of Terminally Blocked Glycine, Alanine, and Proline