Force fields for protein simulations.
Explore the source record for details and available documents.
Computer Simulation↗
Biomedical subjects
David A Case
Publications and source records attributed to David A Case.
Pseudo-atomic models of swollen CCMV from cryo-electron microscopy data.
The capsid of cowpea chlorotic mottle virus (CCMV) can reversibly switch between two forms that are contingent on the charge of acidic residues that are clustered at the quasi-threefold axes of the T=3 icosahedral particle. The quaternary structure conformations are dependent on divalent metal ions and pH and were previously analyzed by crystallography in the native, compact form, and by cryo-electron microscopy in the compact and swollen forms (Speir et al., 1995). In this report we use the atomic models of the three structurally unique viral subunits determined by crystallography for a detailed interpretation of the 28-A-resolution electron density of the swollen form and the production of a pseudo-atomic model of this particle. The model of the quaternary structure conforms with high fidelity to conventional geometric constraints, quasi-equivalence, intersubunit association energies, and the electron density. It was derived by conserving the pentamers and hexamers of subunits whose associated electron densities are strikingly similar in the two forms of the particles. Treating these as rigid units in the modeling implies that the particle flexibility is accommodated primarily by changes in dimer interactions, an observation that is consistent with the flexible C-terminal polypeptide extensions that stabilize this contact in the crystal structure. Because the hexamers and pentamers were incrementally translated and rotated in a screw motion, with energy minimization at each of 28 steps, a path for the expansion is also implied.
Bromovirus↗
A novel method for finding tRNA genes.
We describe a novel procedure for generating and optimizing pattern descriptors that can be used to find structural motifs in DNA or RNA sequences. This combines a pattern-description language (based primarily on secondary structure alignment and conservation of some key nucleotides) with a scoring function that relies heavily on estimated folding free energies for the secondary structure of interest. For the cloverleaf secondary structure characteristic of tRNA, we show that a fairly simple pattern descriptor can find almost all known tRNA genes in both bacterial and eukaryotic genomes, and that false positives (sequences that match the pattern but that are probably not tRNAs) can be recognized by their high estimated folding free energies. A general procedure for optimizing descriptors (and hence for finding new structural motifs) is also described. For six bacterial, four eukaryotic, and four archaea genome sequences, our results compare favorably with those of the more complex and specialized tRNAscan-SE algorithm. Prospects for using this general approach to find other RNA structural motifs are discussed.
Algorithms↗
Rules and problem solving: another look.
College students were trained on problems similar to the water jar problems developed by Luchins (1942). Some students were instructed that a particular rule would solve all the problems, others had the same problems but were not instructed about the rule, and a third set of students had a series of novel problems in which no single rule operated throughout. In two experiments students in the instructed rule group not only performed best in training but also performed best when transferred to a condition in which a single novel rule was appropriate. Although results from the set of conditions most similar to those of Luchins suggested that students sometimes inappropriately persisted in rule usage, the overall results suggest that rigidity is not a necessary outcome of instructed problem solving. Indeed, many of the results were consistent with the notion that instructed problem solving is flexible problem solving.
Adult↗
Probing multiple effects on 15N, 13C alpha, 13C beta, and 13C' chemical shifts in peptides using density functional theory.
We have used density functional calculations on model peptides to study conformational effects on (15)N, (13)C alpha, (13)C beta, and (13)C' chemical shifts, associated with hydrogen bonding, backbone conformation, and side-chain orientation. The results show a significant dependence on the backbone torsion angles of the nearest three residues. Contributions to (15)N chemical shifts from hydrogen bonding (up to 8 ppm), backbone conformation (up to 13 ppm), side-chain orientation and neighborhood residue effects (up to 22 ppm) are significant, and a unified theory will be required to account for their behavior in proteins. In contrast to this, the dependence on sequence and hydrogen bonding is much less for (13)C alpha and (13)C beta chemical shifts (<0.5 ppm), and moderate for carbonyl carbon shifts (<2 ppm). The effects of side-chain orientation are mainly limited to the residue itself for both nitrogen and carbon, but the chi(1) effect is also significant for the nitrogen shift of the following residue and for the (13)C' shift of the preceding residue. The calculated results are used, in conjunction with an additive model of chemical shift contributions, to create an algorithm for prediction of (15)N and (13)C shifts in proteins from their structure; this includes a model to extrapolate results to regions of torsion angle space that have not been explicitly studied by density functional theory (DFT) calculations. Crystal structures of 20 proteins with measured shifts have been used to test the prediction scheme. Root mean square deviations between calculated and experimental shifts 2.71, 1.22, 1.31, and 1.28 ppm for N, C alpha, C beta, and C', respectively. This prediction algorithm should be helpful in NMR assignment, crystal and solution structure comparison, and structure refinement.
Carbon Isotopes↗
Effective Born radii in the generalized Born approximation: the importance of being perfect.
Generalized Born (GB) models provide, for many applications, an accurate and computationally facile estimate of the electrostatic contribution to aqueous solvation. The GB models involve two main types of approximations relative to the Poisson equation (PE) theory on which they are based. First, the self-energy contributions of individual atoms are estimated and expressed as "effective Born radii." Next, the atom-pair contributions are estimated by an analytical function f(GB) that depends upon the effective Born radii and interatomic distance of the atom pairs. Here, the relative impacts of these approximations are investigated by calculating "perfect" effective Born radii from PE theory, and enquiring as to how well the atom-pairwise energy terms from a GB model using these perfect radii in the standard f(GB) function duplicate the equivalent terms from PE theory. In tests on several biological macromolecules, the use of these perfect radii greatly increases the accuracy of the atom-pair terms; that is, the standard form of f(GB) performs quite well. The remaining small error has a systematic and a random component. The latter cannot be removed without significantly increasing the complexity of the GB model, but an alternative choice of f(GB) can reduce the systematic part. A molecular dynamics simulation using a perfect-radii GB model compares favorably with simulations using conventional GB, even though the radii remain fixed in the former. These results quantify, for the GB field, the importance of getting the effective Born radii right; indeed, with perfect radii, the GB model gives a very good approximation to the underlying PE theory for a variety of biomacromolecular types and conformations.
Macromolecular Substances↗
Metal substitution in the active site of nitrogenase MFe(7)S(9) (M = Mo(4+), V(3+), Fe(3+)).
The unifying view that molybdenum is the essential component in nitrogenase has changed over the past few years with the discovery of a vanadium-containing nitrogenase and an iron-only nitrogenase. The principal question that has arisen for the alternative nitrogenases concerns the structures of their corresponding cofactors and their metal-ion valence assignments and whether there are significant differences with that of the more widely known molybdenum-iron cofactor (FeMoco). Spin-polarized broken-symmetry (BS) density functional theory (DFT) calculations are used to assess which of the two possible metal-ion valence assignments (4Fe(2+)4Fe(3+) or 6Fe(2+)2Fe(3+)) for the iron-only cofactor (FeFeco) best represents the resting state. For the 6Fe(2+)2Fe(3+) oxidation state, the spin coupling pattern for several spin state alignments compatible with S = 0 were generated and assessed by energy criteria. The most likely BS spin state is composed of a 4Fe cluster with spin S(a) = (7)/(2) antiferromagnetically coupled to a 4Fe' cluster with spin S(b) = (7)/(2). This state has the lowest DFT energy for the isolated FeFeco cluster and displays calculated Mössbauer isomer shifts consistent with experiment. Although the S = 0 resting state of FeFeco has recently been proposed to have metal-ion valencies of 4Fe(2+)4Fe(3+) (derived from experimental Mössbauer isomer shifts), our isomer shift calculations for the 4Fe(2+)4Fe(3+) oxidation state are in poorer agreement with experiment. Using the Mo(4+)6Fe(2+)Fe(3+) oxidation level of the cofactor as a starting point, the structural consequences of replacement of molybdenum (Mo(4+)) with vanadium (V(3+)) or iron (Fe(3+)) in the cofactor have been investigated. The size of the cofactor cluster shows a dependency on the nature of the heterometal and increases in the order FeMoco < FeVco < FeFeco.
Absorptiometry, Photon↗
Binding modes for the first coupled electron and proton addition to FeMoco of nitrogenase.
A combined broken-symmetry density functional and electrostatics approach has been used to model the one-electron reduced and protonated state of the iron-molybdenum cofactor active site of nitrogenase. The active site of the protein contains Fe, Mo, S, N, and O atoms, and many possible sites for protonation have been examined. A novel hydridic proton asymmetrically located in the central cavity created by six Fe sites is most favored from the calculations. Under physiological turnover conditions of low electron flux, the formation of this iron-hydride intermediate may represent a first step towards cofactor liberation of dihydrogen in the absence of dinitrogen.
Binding Sites↗
FeMo cofactor of nitrogenase: energetics and local interactions in the protein environment.
A combined broken-symmetry density functional and continuum electrostatics approach has been applied to the iron-molybdenum center (FeMoco) of nitrogenase to evaluate the energetic effects of the local amino acid environment for several spin alignments of FeMoco. The protein environment preferentially stabilizes certain spin coupling patterns. The lowest energy spin alignment pattern in the protein displays calculated properties that match the experimental data better than any of the alternative possibilities. The total interaction energy of the protein with FeMoco has been evaluated and the contribution of each amino acid residue has been broken down into sidechain and backbone components. Arginine, lysine, aspartate and glutamate sidechains exert the largest electrostatic influence on FeMoco; specific residues are highlighted and their interaction with FeMoco discussed in the context of the available X-ray data from Azotobacter vinelandii (Av). Observed data for the M(N)(resting state)-->M(OX)(one-electron oxidized state) and M(N)-->M(R)(one-electron reduced state) or M(I)(alternative one-electron reduced state) redox couples are compared with those calculated for Av. The calculated redox potentials are fairly insensitive to the spin state of the oxidized or reduced states and the predicted qualitative trend of a more negative redox potential for the more reduced M(N)-->M(R) or M(I) couple is in accord with the available redox data. These calculations represent a first step towards the development of a microscopic model of electron and proton transfer events at the nitrogenase active site.
Azotobacter vinelandii↗
Density functional calculation of p K(a) values and redox potentials in the bovine Rieske iron-sulfur protein.
The redox potential of the Rieske iron-sulfur protein depends on pH. It has been proposed that the histidines coordinating one of the irons are responsible for this pH dependence, but an experimental proof for this proposal is still lacking. In this work, we present a density functional/continuum electrostatics calculation of the p K(a) values of the histidines in the Rieske iron-sulfur center. The calculated apparent p K(a) values are 6.9 and 8.8 in the oxidized state, which are in good agreement with the corresponding experimental values of 7.5 and 9.2 and the measured pH dependence of the redox potential. Neither of these two p K(a) values can, however, be assigned to only one of the histidines. We find that both histidines titrate over a wide pH range in the oxidized state. Reduction of the iron-sulfur center shifts the p K(a) values to 11.3 and 12.8, thus above 10.0 as found experimentally. The results provide a complete picture of the coupling of proton and electron binding, showing strongly cooperative binding of protons at electrode potentials near the redox midpoint potential of the cluster. The potential biological function of the low p K(a) value of the histidines and the shift upon reduction are briefly discussed.
Animals↗
Molecular dynamics and NMR spin relaxation in proteins.
Molecular dynamics simulations often play a central role in the analysis of biomolecular NMR data. The focus here is on NMR spin-relaxation, which can provide unique insights into the time-dependence of conformational fluctuations, especially on picosecond to nanosecond time scales which can be directly probed by simulations. A great deal has been learned from such simulations about the general nature of such motions and their impact on NMR observables. In principle, relaxation measurements should also provide valuable benchmarks for judging the quantitative accuracy of simulations, but there are a variety of experimental and computational obstacles to making useful direct comparisons. It seems likely that simulations on time scales that are just now becoming generally feasible may provide important new information on internal motions, overall rotational diffusion, and the coupling between internal and rotational motion. Such information could provide a sound foundation for a new generation of detailed interpretation of NMR spin-relaxation results.
Computer Simulation↗
Comparison of protein solution structures refined by molecular dynamics simulation in vacuum, with a generalized Born model, and with explicit water.
The inclusion of explicit solvent water in molecular dynamics refinement of NMR structures ought to provide the most physically meaningful accounting for the effects of solvent on structure, but is computationally expensive. In order to evaluate the validity of commonly used vacuum refinements and of recently developed continuum solvent model methods, we have used three different methods to refine a set of NMR solution structures of a medium sized protein, Escherichia coli glutaredoxin 2, from starting structures calculated using the program DYANA. The three different refinement protocols used molecular dynamics simulated annealing with the program AMBER in vacuum (VAC), including a generalized Born (GB) solvent model, and a full calculation including explicit solvent water (WAT). The structures obtained using the three methods of refinements were very similar, a reflection of their generally well-determined nature. However, the structures refined with the generalized Born model were more similar to those from explicit water refinement than those refined in vacuum. Significant improvement was seen in the percentage of backbone dihedral angles in the most favored regions of phi, psi space and in hydrogen bond pattern for structures refined with the GB and WAT models, compared with the structures refined in vacuum. The explicit water calculation took an average of 200 h of CPU time per structure on an SGI cluster, compared to 15-90 h for the GB calculation (depending on the parameters used) and 2 h for the vacuum calculation. The generalized Born solvent model proved to be an excellent compromise between the vacuum and explicit water refinements, giving results comparable to those of the explicit water calculation. Some improvement for phi and psi angle distribution and hydrogen bond pattern can also be achieved by energy minimizing the vacuum structures with the GB model, which takes a much shorter time than MD simulations with the GB model.
Computer Simulation↗