Biomedical subjects

Harold A Scheraga

Publications and source records attributed to Harold A Scheraga.

At least 19 recordsLinked to original sources

PubMed2007

Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins.

We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta

Biophysics↗

PubMed2007

Molecular dynamics with the United-residue force field: ab initio folding simulations of multichain proteins.

The implementation of molecular dynamics with the united-residue (UNRES) force field is extended to treat multichain proteins. Constant temperature was maintained in the simulations with Berendsen or Langevin thermostats. The method was tested on three alpha-helical proteins (1G6U and GCN4-p1, each with two chains, and 1C94, with four chains). Simulations were carried out for both the isolated single chains and the multichain complexes. The proteins were folded by starting from the extended conformation with random initial velocities and with the chains parallel to each other. No symmetry constraints or structure information were included for the single chains or the multichain complexes. In the case of single-chain simulations, a high percentage of the trajectories (100% for 1G6U, 90% for GCN4-p1, and 80% for 1C94) converged to nativelike structures (assumed as the experimental structure of a monomer in the multichain complex), showing that, for the proteins studied in this work with the UNRES force field, the interactions between chains are not critical for stabilization of the individual chains. In the case of multichain simulations, the native structures of the 1G6U and GCN4-p1 complexes, but not that of 1C94, are predicted successfully. The association of the subunits does not follow a unique mechanism; the monomers were observed to fold both before and simultaneously with their association.

Biophysics↗

PubMed2007

Protein-folding dynamics: overview of molecular simulation techniques.

Molecular dynamics (MD) is an invaluable tool with which to study protein folding in silico. Although just a few years ago the dynamic behavior of a protein molecule could be simulated only in the neighborhood of the experimental conformation (or protein unfolding could be simulated at high temperature), the advent of distributed computing, new techniques such as replica-exchange MD, new approaches (based on, e.g., the stochastic difference equation), and physics-based reduced models of proteins now make it possible to study protein-folding pathways from completely unfolded structures. In this review, we present algorithms for MD and their extensions and applications to protein-folding studies, using all-atom models with explicit and implicit solvent as well as reduced models of polypeptide chains.

Algorithms↗

PubMed2006

Effects of side-chain orientation on the 13C chemical shifts of antiparallel beta-sheet model peptides.

The dependence of the (13)C chemical shift on side-chain orientation was investigated at the density functional level for a two-strand antiparallel beta-sheet model peptide represented by the amino acid sequence Ac-(Ala)(3)-X-(Ala)(12)-NH(2) where X represents any of the 17 naturally occurring amino acids, i.e., not including alanine, glycine and proline. The dihedral angles adopted for the backbone were taken from, and fixed at, observed experimental values of an antiparallel beta-sheet. We carried out a cluster analysis of the ensembles of conformations generated by considering the side-chain dihedral angles for each residue X as variables, and use them to compute the (13)C chemical shifts at the density functional theory level. It is shown that the adoption of the locally-dense basis set approach for the quantum chemical calculations enabled us to reduce the length of the chemical-shift calculations while maintaining good accuracy of the results. For the 17 naturally occurring amino acids in an antiparallel beta-sheet, there is (i) good agreement between computed and observed (13)C(alpha) and (13)C(beta) chemical shifts, with correlation coefficients of 0.95 and 0.99, respectively; (ii) significant variability of the computed (13)C(alpha) and (13)C(beta) chemical shifts as a function of chi(1) for all amino acid residues except Ser; and (iii) a smaller, although significant, dependence of the computed (13)C(alpha) chemical shifts on chi(xi) (with xi > or = 2) compared to chi(1) for eleven out of seventeen residues. Our results suggest that predicted (13)C(alpha) and (13)C(beta) chemical shifts, based only on backbone (phi,psi) dihedral angles from high-resolution X-ray structure data or from NMR-derived models, may differ significantly from those observed in solution if the dihedral-angle preferences for the side chains are not taken into account.

Amino Acid Sequence↗

PubMed2006

Implementation of a symplectic multiple-time-step molecular dynamics algorithm, based on the united-residue mesoscopic potential energy function.

A symplectic multiple-time-step (MTS) algorithm has been developed for the united-residue (UNRES) force field. In this algorithm, the slow-varying forces (which contain most of the long-range interactions and are, therefore, expensive to compute) are integrated with a larger time step, termed the basic time step, and the fast-varying forces are integrated with a shorter time step, which is an integral fraction of the basic time step. Based on the split operator formalism, the equations of motion were derived. Separation of the fast- and slow-varying forces leads to stable molecular dynamics with longer time steps. The algorithms were tested with the Ala(10) polypeptide chain and two versions of the UNRES force field: the current one in which the energy components accounting for the energetics of side-chain rotamers (U(rot)) can lead to numerically unstable forces and a modified one in which the the present U(rot) was replaced by a numerically stable expression which, at present, is parametrized only for polyalanine chains. With the modified UNRES potential, stable trajectories were obtained even when extending the basic time step to 15 fs and, with the original UNRES potentials, the basic time step is 1 fs. An adaptive multiple-time-step (A-MTS) algorithm is proposed to handle instabilities in the forces; in this method, the number of substeps in the basic time step varies depending on the change of the magnitude of the acceleration. With this algorithm, the basic time step is 1 fs but the number of substeps and, consequently, the computational cost are reduced with respect to the MTS algorithm. The use of the UNRES mesoscopic energy function and the algorithms derived in this work enables one to increase the simulation time period by several orders of magnitude compared to conventional atomic-resolution molecular dynamics approaches and, consequently, such an approach appears applicable to simulating protein-folding pathways, protein functional dynamics in a real molecular environment, and dynamical molecular recognition processes.

Algorithms↗

PubMed2006

Correlation of folding kinetics with the number and isomerization states of prolines in three homologous proteins of the RNase family.

Several studies attribute the slower phases in protein folding to prolyl isomerizations, and several others do not. A correlation exists between the number of prolines in a protein and the complexity of the mechanism with which it folds. In this study, we have demonstrated a direct correlation between the number of cis-prolyl bonds in a native protein and the complexity with which it folds via slower phases by studying the folding of three structurally homologous proteins of the ribonuclease family, namely RNase A, onconase and angiogenin, which differ in the number and isomerization states of their proline residues.

Animals↗

PubMed2006

The role of hydrophobic interactions in initiation and propagation of protein folding.

Globular proteins fold by minimizing the nonpolar surface that is exposed to water, while simultaneously providing hydrogen-bonding interactions for buried backbone groups, usually in the form of secondary structures such as alpha-helices, beta-sheets, and tight turns. A primary thermodynamic driving force for the formation of globular structure is thus the sequestration of nonpolar groups, but the correlation between the parts of proteins that are observed to fold first (termed folding initiation sites) and the "hydrophobicity" (as customarily defined) of the amino acids in these regions has been quite weak. It has previously been noted that many amino acid side chains contain considerable nonpolar sections, even if they also contain polar or charged groups. For example, a lysine side chain contains four methylenes, which may undergo hydrophobic interactions if the charged epsilon-NH(3)(+) group is salt-bridged or hydrogen-bonded. Folding initiation sites might therefore contain not only accepted "hydrophobic" amino acids, but also larger charged side chains. Recent experiments on the folding of mutant apomyoglobins provides corroboration for models based on the hypothesis that folding initiation sites arise from hydrophobic interactions. A near-perfect correlation was observed between the areas of the molecule that are present in the burst-phase kinetic intermediate and both the free energy of formation of hydrophobic initiation sites and the parameter "average area buried upon folding," which pinpoints large side chains, even those containing charged or polar portions. These results provide a putative mechanism for the control of protein-folding initiation and growth by polar/nonpolar sequence propensity alone.

Animals↗

PubMed2006

A new force field (ECEPP-05) for peptides, proteins, and organic molecules.

Parametrization and testing of a new all-atom force field for organic molecules and peptides with fixed bond lengths and bond angles are described. The van der Waals parameters for both the organic molecules and the peptides were taken from J. Phys. Chem. B 2003, 107, 7143 and J. Phys. Chem. B 2004, 108, 12181. First, the values of the 1-4 nonbonded and electrostatic scale factors appropriate to the new force field were determined by computing the conformational energies of six model molecules, namely, ethanol, ethylamine, propanol, propylamine, 1,2-ethanediol, and 1,3-propanediol with different values of these factors. The partial atomic charges of these molecules were obtained by fitting to the electrostatic potentials calculated with the HF/6-31G quantum-mechanical method. Two different charge models (single- and multiple-conformation-derived) were also considered. We demonstrated that the charge model has a stronger effect on the conformational energies than the 1-4 scaling. The choice of a charge model affected the conformational energies of even the smallest molecules considered, whereas the effect of the 1-4 electrostatic or nonbonded scaling was apparent only for 1,3-propanediol. The best agreement with high-level ab initio data was obtained with the multiple-conformation-derived charges and with no scaling of the 1-4 nonbonded or electrostatic interactions (scale factors of 1.0). Next, the torsional parameters of a large number of neutral and charged organic molecules, assumed to be models of the side chains of the 20 naturally occurring amino acids, were computed by fitting to rotational energy profiles obtained from ab initio MP2/6-31G calculations. The quality of the fits was high with average errors for torsional profiles of less than 0.2 kcal/mol. To derive the torsional parameters for the peptide backbone, the partial atomic charges of the 20 neutral and charged amino acids were obtained by fitting to the electrostatic potentials of terminally blocked amino acids using the HF/6-31G quantum-mechanical method. Then, the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe were computed using MP2/6-31G//HF/6-31G quantum-mechanical methods. The phi-psi energy map of Ac-Ala-NMe was used for refinement of the nonbonded parameters for the backbone nitrogen and hydrogen bonded to it. Subsequently, the main-chain torsional parameters were obtained by fitting the molecular mechanics energies to the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe. The transferability of the entire force field was demonstrated by reproducing the main energy minima of terminally blocked Ala3 from the literature. The performance of the force field was also evaluated by simulating crystal structures of small peptides. By comparison of simulated and experimental data, examination of the torsional-angle and atom-positional root-mean-square deviations of the energy-minimized crystal structures from the corresponding X-ray model structures demonstrated high accuracy of the force field.

Algorithms↗

PubMed2006

Assessment of two theoretical methods to estimate potentiometric titration curves of peptides: comparison with experiment.

We compared the ability of two theoretical methods of pH-dependent conformational calculations to reproduce experimental potentiometric titration curves of two models of peptides: Ac-K5-NHMe in 95% methanol (MeOH)/5% water mixture and Ac-XX(A)7OO-NH2 (XAO) (where X is diaminobutyric acid, A is alanine, and O is ornithine) in water, methanol (MeOH), and dimethyl sulfoxide (DMSO), respectively. The titration curve of the former was taken from the literature, and the curve of the latter was determined in this work. The first theoretical method involves a conformational search using the electrostatically driven Monte Carlo (EDMC) method with a low-cost energy function (ECEPP/3 plus the SRFOPT surface-solvation model, assumming that all titratable groups are uncharged) and subsequent reevaluation of the free energy at a given pH with the Poisson-Boltzmann equation, considering variable protonation states. In the second procedure, molecular dynamics (MD) simulations are run with the AMBER force field and the generalized Born model of electrostatic solvation, and the protonation states are sampled during constant-pH MD runs. In all three solvents, the first pKa of XAO is strongly downshifted compared to the value for the reference compounds (ethylamine and propylamine, respectively); the water and methanol curves have one, and the DMSO curve has two jumps characteristic of remarkable differences in the dissociation constants of acidic groups. The predicted titration curves of Ac-K5-NHMe are in good agreement with the experimental ones; better agreement is achieved with the MD-based method. The titration curves of XAO in methanol and DMSO, calculated using the MD-based approach, trace the shape of the experimental curves, reproducing the pH jump, while those calculated with the EDMC-based approach and the titration curve in water calculated using the MD-based approach have smooth shapes characteristic of the titration of weak multifunctional acids with small differences between the dissociation constants. Nevertheless, quantitative agreement between theoretically predicted and experimental titration curves is not achieved in all three solvents even with the MD-based approach, which is manifested by a smaller pH range of the calculated titration curves with respect to the experimental curves. The poorer agreement obtained for water than for the nonaqueous solvents suggests a significant role of specific solvation in water, which cannot be accounted for by the mean-field solvation models.

Algorithms↗

PubMed2006

A localized specific interaction alters the unfolding pathways of structural homologues.

Reductive unfolding studies of proteins are designed to provide information about intramolecular interactions that govern the formation (and stabilization) of the native state and about folding/unfolding pathways. By mutating Tyr92 to G, A, or L in the model protein, bovine pancreatic ribonuclease A, and through analysis of temperature factors and molecular dynamics simulations of the crystal structures of these mutants, it is demonstrated that the markedly different reductive unfolding rates and pathways of ribonuclease A and its structural homologue onconase can be attributed to a single, localized, ring-stacking interaction between Tyr92 and Pro93 in the bovine variant. The fortuitous location of this specific stabilizing interaction in a disulfide-bond-containing loop region of ribonuclease A results in the localized modulation of protein dynamics that, in turn, enhances the susceptibility of the disulfide bond to reduction leading to an alteration in the reductive unfolding behavior of the homologues. These results have important implications for folding studies involving topological determinants to obtain folding/unfolding rates and pathways, for protein structure-function prediction through fold recognition, and for predicting proteolytic cleavage sites.

Animals↗

PubMed2006

Polyproline II conformation is one of many local conformational states and is not an overall conformation of unfolded peptides and proteins.

The alanine-based peptide Ac-XX(A)7OO-NH2, referred to as XAO (where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively), has recently been proposed to possess a well defined polyproline II (P(II)) conformation at low temperatures. Based on the results of extensive NMR and CD investigations combined with theoretical calculations, reported here, we present evidence that, on the contrary, this peptide does not have any significant amount of organized P(II) structure but exists in an ensemble of conformations with a distorted bend in the N- and C-terminal regions. The conformational ensemble was obtained by molecular dynamics/simulated annealing calculations using the amber suite of programs with time-averaged distance and dihedral-angle restraints obtained from rotating-frame nuclear Overhauser effect (ROE) volumes and vicinal coupling constants 3J(HN Eta alpha), respectively. The computed ensemble-averaged radius of gyration Rg (7.4 +/- 1.0) A is in excellent agreement with that measured by small-angle x-ray scattering (SAXS) whereas, if the XAO peptide were in the P(II) conformation, Rg would be 11.6 A. Depending on the pH, peptide concentration, and temperature, the CD spectra of XAO do or do not possess the maximum with positive ellipticity in the 217-nm region, which is characteristic of the P(II) structure, reflecting a shifting conformational equilibrium rather than an all-or-none transition. The "P(II) conformation" should, therefore, be considered as one of the accessible conformational states of individual amino acid residues in peptides and proteins rather than as a structure of most of the chain in the early stage of folding.

Alanine↗

PubMed2006

Stepwise deamidation of ribonuclease A at five sites determined by top down mass spectrometry.

Although deamidation at asparagine and glutamine has been found in numerous studies of a variety of proteins, in almost all cases the analytical methodology that was used could detect only a single site of deamidation. For the extensively studied case of reduced bovine ribonuclease A (13,689 Da), only Asn67 deamidation has been demonstrated previously, although one study found three monodeamidated fractions. Here top down tandem mass spectrometry shows that Asn67 deamidation is extensive before Asn71 and Asn94 react; these are more than half deamidated before Asn34 reacts, and its deamidation is extensive before that at Gln74 is initiated. Except for the initial Asn67 site, these large reactivity differences correlate poorly with neighboring amino acid identities and instead indicate residual conformational effects despite the strongly denaturing media that were used; deamidation at Asn67 could enhance that at Asn71, and these enhance that at Gln74. This success in the site-specific quantitation of deamidation in a 14 kDa protein mixture, despite the minimal 1 Da (-NH2 --> -OH) change in the molecular mass, is further evidence of the broad applicability of the top down MS/MS methodology for characterization of protein posttranslational modifications.

Amides↗

PubMed2005

Protein structure prediction with the UNRES force-field using Replica-Exchange Monte Carlo-with-Minimization; Comparison with MCM, CSA, and CFMC.

Two current methods of global optimization are coupled to produce the Replica-Exchange method together with Monte Carlo-with-Minimization (REMCM). Its performance is compared with each separate component and with other global optimization techniques. REMCM was applied to search the conformational space of coarse grain protein systems described by the UNRES force field. The method consists of several noninteracting copies of Monte Carlo simulation, and minimization was used after every perturbation to enhance the sampling of low-energy conformations. REMCM was applied to five proteins of different topology, and the results were compared to those from other optimization methods, namely Monte Carlo-with-Minimization (MCM), Conformational Space Annealing (CSA), and Conformational Family Monte Carlo (CFMC). REMCM located global minima for four proteins faster and more consistently than either MCM or CFMC, and it converged faster than CSA for three of the five proteins tested. A performance comparison was also carried out between REMCM and the traditional Replica Exchange method (REM) for one protein, with REMCM showing a significant improvement. Moreover, because of its simplicity, REMCM was easy to implement, thereby offering an alternative to other global optimization methods used in protein structure prediction.

Algorithms↗

PubMed2005

Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains.

Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.

Computer Simulation↗

PubMed2005

Coupling between conformation and proton binding in proteins.

Interest centers here on whether the use of a fixed charge distribution of a protein solute, or a treatment that considers proton-binding equilibria by solving the Poisson equation, is a better approach to discriminate native from non-native conformations of proteins. In this analysis of the charge distribution of 7 proteins, we estimate the solvation free energy contribution to the total free energy by exploring the 2(zeta) possible ionization states of the whole molecule, with zeta being the number of ionizable groups in the amino acid sequence, for every conformation in the ensembles of 7 proteins. As an additional consideration of the role of electrostatic interactions in determining the charge distribution of native folds, we carried out a comparison of alternative charge assignment models for the ionizable residues in a set of 21 native-like proteins. The results of this work indicate that (1) for 6 out of 7 proteins, estimation of solvent polarization based on the Generalized Born model with a fixed charge distribution provides the optimal trade-off between accuracy, with respect to the Poisson equation, and speed when compared to the accessible surface area model; for the seventh protein, consideration of all possible ionization states of the whole molecule appears to be crucial to discriminate the native from non-native conformations; (2) significant differences in the degree of ionization and hence the charge distribution for native folds are found between the different charge models examined; (3) the stability of the native state is determined by a delicate balance of all the energy components, and (4) conformational entropy, and hence the dynamics of folding, may play a crucial role for a successful ab initio protein folding prediction.

Ions↗

PubMed2005

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems.

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.

Algorithms↗

PubMed2005

Molecular dynamics with the united-residue model of polypeptide chains. I. Lagrange equations of motion and tests of numerical stability in the microcanonical mode.

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(alpha)...C(alpha) and C(alpha)...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.

Alanine↗

PubMed2005

The oxidative folding rate of bovine pancreatic ribonuclease is enhanced by a covalently attached oligosaccharide.

Bovine pancreatic ribonuclease B (RNase B) differs from RNase A by the presence of an oligosaccharide moiety covalently attached to Asn 34. Oxidative folding studies of RNase B were carried out at different temperatures using DTT(ox) as the oxidizing agent, and the results were compared with those for RNase A. The oxidative folding rates of RNase B are between 1.7 and 1.3 times faster than those of RNase A at the temperatures that were investigated. The folding pathways of RNase B were determined to be similar to those of RNase A in that two structured intermediates, each lacking one native disulfide bond, were found to populate the regeneration pathways at 25 degrees C and pH 8.3. The thermodynamic stabilities of these two glycosylated intermediates, and their rates of formation from their unstructured precursors in the rate-determining step, were found to be higher than those of their unglycosylated counterparts from RNase A. Thus, the underlying cause for the faster rate of oxidative regeneration of native RNase B appears to be both thermodynamic and kinetic due to the higher stability, and faster rate of formation, of the intermediates of RNase B compared to those of RNase A.

Animals↗