Prediction of protein conformation on the basis of a search for compact structures: Test on avian pancreatic polypeptide

Liwo, Adam; Pincus, Matthew R.; Wawak, Ryszard J.; Rackovsky, S.; Scheraga, Harold A.

doi:10.1002/pro.5560021016

Cited by 143 publications

(288 citation statements)

References 52 publications

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“…In the UNRES model (22)(23)(24)(25)(26), a polypeptide chain is represented as a sequence of ␣-carbon (C ␣ ) atoms. The C ␣ atoms are linked together by backbone virtual bonds (designated as dCs), which constitute the backbone.…”

Section: Unres Forcementioning

confidence: 99%

“…Also, Monte Carlo dynamics with lattice mesoscopic models and knowledge-based potentials is applied with success to study folding of real proteins (20). A physics-based mesoscopic model and MD algorithm based on generalized Lagrange equations of motion were developed recently for nucleic acids by Rudnicki et al (21) For the past several years, we have been developing a physicsbased united-residue (UNRES) force field (22)(23)(24)(25)(26). Each amino acid residue is represented by only two interaction sites, which makes the model simple enough to carry out large-scale simulations.…”

mentioning

confidence: 99%

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Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains

Liwo

Khalili²,

Scheraga³

2005

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

258

345

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We report the application of Langevin dynamics to the physicsbased united-residue (UNRES) force field developed in our laboratory. Ten trajectories were run on seven proteins [PDB ID codes 1BDD (␣; 46 residues), 1GAB (␣; 47 residues), 1LQ7 (␣; 67 residues), 1CLB (␣; 75 residues), 1E0L (␤; 28 residues), and 1E0G (␣؉␤; 48 residues), and 1IGD (␣؉␤; 61 residues)] with the UNRES force field parameterized by using our recently developed method for obtaining a hierarchical structure of the energy landscape. All ␣-helical proteins and 1E0G folded to the native-like structures, whereas 1IGD and 1E0L yielded mostly nonnative ␣-helical folds although the native-like structures are lowest in energy for these two proteins, which can be attributed to neglecting the entropy factor in the current parameterization of UNRES. Average folding times for successful folding simulations were of the order of nanoseconds, whereas even the ultrafast-folding proteins fold only in microseconds, which implies that the UNRES time scale is approximately three orders of magnitude larger than the experimental time scale because the fast motions of the secondary degrees of freedom are averaged out. Folding with Langevin dynamics required 2-10 h of CPU time on average with a single AMD Athlon MP 2800؉ processor depending on the size of the protein. With the advantage of parallel processing, this process leads to the possibility to explore thousands of folding pathways and to predict not only the native structure but also the folding scenario of a protein together with its quantitative kinetic and thermodynamic characteristics.Langevin dynamics ͉ mesoscopic models ͉ restricted free energy T here are two protein-folding problems in contemporary computational biology. The first problem is to predict protein structure from sequence, and the second one is to predict protein-folding pathways. There are many approximate methods to attack the folding problem, which belong to two broad categories of physics and knowledge-based methods (1-3). Molecular dynamics (MD) is the only computational method that provides a time-dependent analysis of a system in molecular biology and, consequently, can be implemented to solve the second protein-folding problem.Ideally, both the protein and the surrounding solvent should be represented at the all-atom level (4) because this approach is the closest to experiment. However, there are two severe limitations to such a treatment, namely the multidimensionality of the system (typically, Ͼ10 4 degrees of freedom with explicit solvent) and the small values of the time step in integrating the equations of motion (of the order of femtoseconds). Because of these two limitations, explicit-solvent all-atom MD algorithms can simulate events in the range of 10 Ϫ9 to 10 Ϫ8 s for typical proteins and 10 Ϫ6 s for very small proteins (4-6). These time scales are at least one order of magnitude smaller than the folding times of proteins (4). Consequently, all-atom simulations of real-size proteins are usually limited to unfolding the nati...

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Section: Unres Forcementioning

confidence: 99%

mentioning

confidence: 99%

Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains

Liwo

Khalili²,

Scheraga³

2005

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

258

345

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“…Let the resulting coordinates and velocities be denoted by q 2 and q˙2, respectively, q 2 = q(t + δt L ) being the final coordinates at the end of the RESPA step. (35) where U S denotes the sum of the short-range energy components of the UNRES energy function.…”

Section: Integrating the Equations Of Motionmentioning

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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“…1). The ith dipole is placed between Cy and Cia+] (Liwo et al, 1993). We assume that all the peptide groups are in the planar trans conformation, which means that the virtual-bond lengths are fixed at 3.8 A (Nishikawa et al, 1974).…”

Section: Description Of the Virtual-bond Chainmentioning

confidence: 99%

“…The problem of conversion of the virtual-bond chain to an all-atom backbone can now be identified with min- Table 2 of the accompanying paper (Liwo et al, 1993).…”

Section: Energy Of Interaction Of Peptide-group Dipolesmentioning

confidence: 99%

Calculation of protein backbone geometry from α‐carbon coordinates based on peptide‐group dipole alignment

et al. 1993

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An algorithm is proposed for the conversion of a virtual-bond polypeptide chain (connected C" atoms) to an allatom backbone, based on determining the most extensive hydrogen-bond network between the peptide groups of the backbone, while maintaining all of the backbone atoms in energetically feasible conformations. Hydrogen bonding is represented by aligning the peptide-group dipoles. These peptide groups are not contiguous in the amino acid sequence. The first dipoles to be aligned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to optimize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable amino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipoles are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is used to keep the geometry of the a-carbon trace of the resulting backbone close to that of the input virtual-bond chain. This procedure is sufficient to convert the virtual-bond chain to a real chain; in applications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry resulting from the solution of the alignment equations. When applied to model a-helical and &sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone geometry characteristic of these a-helical and P-sheet structures. Application to the a-carbon trace of the backbone of the crystallographic SPTI structure of bovine pancreatic trypsin inhibitor, followed by ECEPP/2 energy minimization with C"-distance constraints, led to a structure with almost as low energy and root mean square deviation as the ECEPP/2 geometry analog of SPTI, the best agreement between the crystal and reconstructed backbone being observed for the residues involved in the dipole-path network.

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Prediction of protein conformation on the basis of a search for compact structures: Test on avian pancreatic polypeptide

Cited by 143 publications

References 52 publications

Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains

Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains

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

Calculation of protein backbone geometry from α‐carbon coordinates based on peptide‐group dipole alignment

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