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Martin Karplus

Publications and source records attributed to Martin Karplus.

At least 37 records · Page 2Linked to original sources
PubMed2005

Normal mode calculations of icosahedral viruses with full dihedral flexibility by use of molecular symmetry.

The study of the dynamics and thermodynamics of small icosahedral virus capsids is an active field of research. Normal mode analysis is one of the computational tools that can provide important insights into the conformational changes of the virus associated with cell entry or caused by changing of the physicochemical environment. Normal mode analysis of virus capsids has been limited due to the size of these systems, which often exceed 50,000 residues. Here we present the first normal mode calculation with full dihedral flexibility of several virus capsids, including poliovirus, rhinovirus, and cowpea chlorotic mottle virus. The calculations were made possible by applying group theoretical methods, which greatly simplified the calculations without any approximation beyond the all-atom force field representations in general use for smaller protein systems. Since a full Cartesian basis set was too large to be handled by the available computer memory, we used a basis set that includes all internal dihedral angles of the system with the exception of the peptide bonds, which were assumed rigid. The fluctuations of the normal modes are shown to correlate well with crystallographic temperature factors. The motions of the first several normal modes of each symmetry type are described. A hinge bending motion in poliovirus was found that may be involved in the mechanism by which bound small molecules inhibit conformational changes of the capsid. Fully flexible normal mode calculations of virus capsids are expected to increase our understanding of virus dynamics and thermodynamics, and can be useful in the refinement of cryo-electron microscopy structures of viruses.

Bromovirus↗
PubMed2005

Structure of a repair enzyme interrogating undamaged DNA elucidates recognition of damaged DNA.

How DNA repair proteins distinguish between the rare sites of damage and the vast expanse of normal DNA is poorly understood. Recognizing the mutagenic lesion 8-oxoguanine (oxoG) represents an especially formidable challenge, because this oxidized nucleobase differs by only two atoms from its normal counterpart, guanine (G). Here we report the use of a covalent trapping strategy to capture a human oxoG repair protein, 8-oxoguanine DNA glycosylase I (hOGG1), in the act of interrogating normal DNA. The X-ray structure of the trapped complex features a target G nucleobase extruded from the DNA helix but denied insertion into the lesion recognition pocket of the enzyme. Free energy difference calculations show that both attractive and repulsive interactions have an important role in the preferential binding of oxoG compared with G to the active site. The structure reveals a remarkably effective gate-keeping strategy for lesion discrimination and suggests a mechanism for oxoG insertion into the hOGG1 active site.

Base Sequence↗
PubMed2005

Folding time distributions as an approach to protein folding kinetics.

A 27-residue lattice heteropolymer subject to Monte Carlo dynamics on a simple cubic lattice is studied over a range of temperatures. Folding time distributions are used to obtain information concerning the details of folding kinetics. The results are compared with those from methods based on mean force surfaces expressed in terms of a reduced set of variables and on a disconnectivity graph for the same system. A detailed analysis of the folding trajectories is given, and the importance of dead-end traps in determining the folding time is demonstrated. We show that the calculated folding kinetics can be modeled by a system of kinetic equations, with the essential rate constants determined from the Monte Carlo simulations and the resulting folding time distributions. The kinetic equations make possible an analysis of the variation of the importance of different channels with temperature. In particular, we show that the presence of intermediates may be masked in the folding time distributions, with the mean folding time being independent of the height of the barrier between the intermediates and collapsed globule state of the system. This and other results demonstrate that care has to be used in interpreting experimental folding data in terms of the underlying kinetics. Correspondingly, simulations are shown to have to satisfy certain requirements to obtain proper sampling of the dead-end traps.

Kinetics↗
PubMed2005

What contributions to protein side-chain dynamics are probed by NMR experiments? A molecular dynamics simulation analysis.

Molecular dynamics simulations of the structurally homologous proteins TNfn3 and FNfn10 have been used to investigate the contributions to side-chain dynamics measured by NMR relaxation experiments. The results reproduce the variation in core side-chain dynamics observed by NMR and highlight the relevance of anharmonic motion and transitions between local minima for explaining NMR side-chain order parameters. A method is described for calculating converged order parameters by use of replica exchange molecular dynamics in conjunction with an implicit solvent model. These simulations allow the influence of various factors, such as the flexibility of side-chains and their free volume, on the mobility to be tested by perturbing the system. Deletion mutations are found to have the largest effect on the more densely packed FNfn10. Some counterintuitive effects are seen, such as an increase in order parameters close to deletion mutation sites, but these can be rationalized in terms of direct interactions with the modified side-chains. A statistical analysis of published order parameters supports the conclusions drawn from the simulations.

Amino Acids↗
PubMed2005

Role of conformational heterogeneity in domain swapping and adapter function of the Cks proteins.

Cks proteins are adapter molecules that coordinate the assembly of multiprotein complexes. They share the ability to domain swap by exchanging a beta-strand, beta4. Here we use NMR spectroscopy and molecular dynamics simulations to investigate the dynamic properties of human Cks1 and its response on assembly with components of the SCF(Skp2) ubiquitin ligation machinery. In the NMR experiment with the free form of Cks1, a subset of residues displayed elevated R2 values and the cross-peaks of neighboring residues were missing from the spectrum, indicating a substantial conformational exchange contribution on the microsecond to millisecond time scale. Strikingly the region of greatest conformational variability was the beta4-strand that domain swaps to form the dimer. Binding of the ligand common to all Cks proteins, Cdk2, suppressed the conformational heterogeneity. This response was specific to Cdk2 binding; in contrast, binding of Skp2, a ligand unique to human Cks1, did not alter the dynamic behavior. Short time (<5 ns) molecular dynamics simulations indicate that residues of Cks1 that form the binding site for phosphorylated ligands are considerably more flexible in the free form of Cks1 than they are in the Cdk2-Cks1 complex. A cooperative interaction between Cdk2 and Cks1 is suggested, which reduces the configurational entropy of Cks1 and therefore facilitates phosphoprotein binding. Indications of an unusual dynamic behavior of strand beta4 in the free form of Cks1 were obtained from longer time scale (50 ns) dynamics simulations. A spontaneous reversible unzipping of hydrogen bonds between beta4 and beta2 was observed, suggesting an early intermediate structure for unfolding and/or domain swapping. We propose that the dynamic properties of the beta-sheet and its modification upon ligand binding underlie the domain swapping ability and the adapter function of Cks proteins.

Allosteric Site↗
PubMed2005

Simulation of conformational transitions by the restricted perturbation-targeted molecular dynamics method.

A method for the simulation of conformational transitions is presented. The method, based on targeted molecular dynamics (TMD), limits the conformational change at each molecular dynamics step to a fixed size, that minimizes the root mean square deviation from the target. The method is more efficient than standard TMD and yields lower energy pathways, but, like the TMD method, requires only a single molecular dynamics simulation. Test calculations and comparisons with standard TMD calculations for the alanine dipeptide with the analytic continuum electrostatics implicit solvent model are presented.

Journal Article↗
PubMed2005

Protein structural transitions and their functional role.

Living cells are a collection of molecular machines which carry out many of the functions essential for the cell's existence, differentiation and reproduction. Most, though not all, of these machines are made up of proteins. Because of their complexity, an understanding of how they work requires a synergistic combination of experimental and theoretical studies. In this paper we outline our studies of two such protein machines. One is GroEL, the chaperone from Escherichia coli, which aids in protein folding; the other is F(1)-ATPase, a motor protein which synthesizes and hydrolyses ATP.

Chaperonin 60↗
PubMed2005

Electrostatic energies and forces computed without explicit interparticle interactions: a linear time complexity formulation.

A rapid method for the calculation of the electrostatic energy of a system without a cutoff is described in which the computational time grows linearly with the number of particles or charges. The inverse of the distance is approximated as a polynomial, which is then transformed into a function whose terms involve individual particles, instead of particle pairs, by a partitioning of the double sum. In this way, the electrostatic energy that is determined by the interparticle interactions is obtained without explicit calculation of these interactions. For systems of positive charges positioned on a face-centered cubic lattice, the calculation of the energy by the new method is shown to be faster than the calculation of the exact energy, in many cases by an order of magnitude, and to be accurate to within 1-2%. The application of this method to increase the accuracy of conventional truncation-based calculations in condensed-phase systems is also demonstrated by combining the approximated long-range electrostatic interactions with the exact short-range interactions in a "hybrid" calculation. For a 20-A sphere of water molecules, the forces are shown to be six times as accurate using this hybrid method as those calculated with conventional truncation of the electrostatic energy function at 12 A. This is accomplished with a slight increase in speed, and with a sevenfold increase in speed relative to the exact all-pair calculation. Structures minimized with the hybrid function are shown to be closer to structures minimized with an exact all-pair electrostatic energy function than are those minimized with a conventional 13-A cutoff-based electrostatic energy function. Comparison of the energies and forces calculated with the exact method illustrate that the absolute errors obtained with standard truncation can be very large. The extension of the current method to other pairwise functions as well as to multibody functions, is described.

Algorithms↗
PubMed2004

Calculation of the aqueous solvation energy and entropy, as well as free energy, of simple polar solutes.

With the advent of more powerful computers, the question of calculating thermodynamic quantities, such as the energy and the entropy, in solute-solvent systems is revisited. The calculation of these thermodynamic quantitites was limited in the past by their slow convergence relative to the free energy. Using molecular dynamics simulations, the energy, entropy, and free energy of solvation of NMA and CH(3)NH(2), as well as their relative values, have been determined. Three different methods (the thermodynamic perturbation method, the thermodynamic integration method, and a finite-difference method) are compared. The finite difference method gives the best results and accurate values for the entropy and energy were obtained using a reasonable amount to computer time. The results suggest that a meaningful thermodynamic description of biomolecular processes can be realized with present methods and the available computer time.

Journal Article↗
PubMed2004

Hidden complexity of free energy surfaces for peptide (protein) folding.

An understanding of the thermodynamics and kinetics of protein folding requires a knowledge of the free energy surface governing the motion of the polypeptide chain. Because of the many degrees of freedom involved, surfaces projected on only one or two progress variables are generally used in descriptions of the folding reaction. Such projections result in relatively smooth surfaces, but they could mask the complexity of the unprojected surface. Here we introduce an approach to determine the actual (unprojected) free energy surface and apply it to the second beta-hairpin of protein G, which has been used as a model system for protein folding. The surface is represented by a disconnectivity graph calculated from a long equilibrium folding-unfolding trajectory. The denatured state is found to have multiple low free energy basins. Nevertheless, the peptide shows exponential kinetics in folding to the native basin. Projected surfaces obtained from the present analysis have a simple form in agreement with other studies of the beta-hairpin. The hidden complexity found for the beta-hairpin surface suggests that the standard funnel picture of protein folding should be revisited.

Amino Acid Sequence↗
PubMed2004

A comparison of the dynamic behavior of monomeric and dimeric insulin shows structural rearrangements in the active monomer.

Molecular dynamics (MD) simulations (5-10ns in length) and normal mode analyses were performed for the monomer and dimer of native porcine insulin in aqueous solution; both starting structures were obtained from an insulin hexamer. Several simulations were done to confirm that the results obtained are meaningful. The insulin dimer is very stable during the simulation and remains very close to the starting X-ray structure; the RMS fluctuations calculated from the MD simulation agree with the experimental B-factors. Correlated motions were found within each of the two monomers; they can be explained by persistent non-bonded interactions and disulfide bridges. The correlated motions between residues B24 and B26 of the two monomers are due to non-bonded interactions between the side-chains and backbone atoms. For the isolated monomer in solution, the A chain and the helix of the B chain are found to be stable during 5ns and 10ns MD simulations. However, the N-terminal and the C-terminal parts of the B chain are very flexible. The C-terminal part of the B chain moves away from the X-ray conformation after 0.5-2.5ns and exposes the N-terminal residues of the A chain that are thought to be important for the binding of insulin to its receptor. Our results thus support the hypothesis that, when monomeric insulin is released from the hexamer (or the dimer in our study), the C-terminal end of the monomer (residues B25-B30) is rearranged to allow binding to the insulin receptor. The greater flexibility of the C-terminal part of the beta chain in the B24 (Phe-->Gly) mutant is in accord with the NMR results. The details of the backbone and side-chain motions are presented. The transition between the starting conformation and the more dynamic structure of the monomers is characterized by displacements of the backbone of Phe B25 and Tyr B26; of these, Phe B25 has been implicated in insulin activation.

Amino Acid Sequence↗
PubMed2004

Kinetic control of dimer structure formation in amyloid fibrillogenesis.

Amyloid fibril formation involves nonfibrillar oligomeric intermediates, which are important as possible cytotoxic species in neurodegenerative diseases. However, their transient nature and polydispersity have made it difficult to identify their formation mechanism or structure. We have investigated the dimerization process, the first step in aggregate formation, by multiple molecular dynamics simulations of five beta-sheet-forming peptides. Contrary to the regular beta-sheet structure of the amyloid fibril, the dimers exhibit all possible combinations of beta-sheets, with an overall preference for antiparallel arrangements. Through statistical analysis of 1,000 dimerization trajectories, each 1 ns in length, we have demonstrated that the observed distribution of dimer configurations is kinetically determined; hydrophobic interactions orient the peptides so as to minimize the solvent accessible surface area, and the dimer structures become trapped in energetically unfavorable conformations. Once the hydrophobic contacts are present, the backbone hydrogen bonds form rapidly by a zipper-like mechanism. The initial nonequilibrium structures formed are stable during the 1-ns simulation time for all five peptides at room temperature. In contrast, at higher temperatures, where rapid equilibration among different configurations occurs, the distribution follows the global energies. The relaxation time of dimers at room temperature was estimated to be longer than the time for diffusional encounters with other oligomers at typical concentrations. These results suggest that kinetic trapping could play a role in the structural evolution of early aggregates in amyloid fibrillogenesis.

Amyloid beta-Peptides↗
PubMed2004

The crystallographic structure of the aldose reductase-IDD552 complex shows direct proton donation from tyrosine 48.

The X-ray crystal structure of human aldose reductase (ALR2) in complex with the inhibitor IDD552 was determined using crystals obtained from two crystallization conditions with different pH values (pH 5 and 8). In both structures the charged carboxylic head of the inhibitor binds to the active site, making hydrogen-bond interactions with His110 and Tyr48 and electrostatic interactions with NADP+. There is an important difference between the two structures: the observation of a double conformation of the carboxylic acid moiety of the inhibitor at pH 8, with one water molecule interacting with the main configuration. This is the first time that a water molecule has been observed deep inside the ALR2 active site. Furthermore, in the configuration with the lower occupancy factor the difference electron-density map shows a clear peak (2.5sigma) for the H atom in the hydrogen bond between the inhibitor's carboxylic acid and the Tyr48 side-chain O atom. The position of this peak implies that this H atom is shared between both O atoms, indicating possible direct proton transfer from this residue to the inhibitor. This fact agrees with the model of the catalytic mechanism, in which the proton is donated by the Tyr48 hydroxyl to the substrate. These observations are useful both in drug design and in understanding the ALR2 mechanism.

Aldehyde Reductase↗
PubMed2004

A normal mode analysis of structural plasticity in the biomolecular motor F(1)-ATPase.

Normal modes have been used to explore the inherent flexibility of the alpha, beta and gamma subunits of F(1)-ATPase in isolation and as part of the alpha(3)beta(3)gamma complex. It was found that the structural plasticity of the gamma and beta subunits, in particular, correlates with their functions. The N and C-terminal helices forming the coiled-coil domain of the gamma subunit are highly flexible in the isolated subunit, but more rigid in the alpha(3)beta(3)gamma complex due to interactions with other subunits. The globular domain of the gamma subunit is structurally relatively rigid when isolated and in the alpha(3)beta(3)gamma complex; this is important for its functional role in coupling the F(0) and F(1) complex of ATP synthase and in inducing the conformational changes of the beta subunits in synthesis. Most important, the character of the lowest-frequency modes of the beta(E) subunit is highly correlated with the large beta(E) --> beta(TP) transition. This holds for the C-terminal domain and the nucleotide-binding domain, which undergo significant conformational transitions in the functional cycle of F(1)-ATPase. This is most evident in the ligand-free beta(E) subunit; the flexibility in the nucleotide-binding domain is reduced somewhat in the beta(TP) subunit in the presence of Mg(2+).ATP. The low-frequency modes of the alpha(3)beta(3)gamma complex show that the motions of the globular domain of the gamma subunit and of the C-terminal and nucleotide binding domains of the beta(E) subunits are coupled, in accord with their function. Overall, the normal mode analysis reveals that F(1)-ATPase, like other macromolecular assemblies, has the intrinsic structural flexibility required for its function encoded in its sequence and three-dimensional structure. This inherent plasticity is an essential aspect of assuring a small free energy cost for the large-scale conformational transition that occurs in molecular motors.

Models, Molecular↗
PubMed2004

The origin of protein sidechain order parameter distributions.

Previous work by Wand et al. (Nature 2001, 411, 501-504) showed that the NMR order parameters characterizing the amplitude of motion of protein side chains seemed to form a multimodal distribution. At the time, no detailed explanation of this at the molecular level was offered, yet three "classes" of motion were inferred. We have analyzed a larger published data set and found that, although the distribution is multimodal, the evidence for three classes is weak. More significantly, we have been able to provide a simple physical explanation for the distributions based on the results of molecular dynamics simulations. This result will aid in the interpretation of data from NMR dynamics experiments.

Amino Acids↗
PubMed2004

X-ray structural and simulation analysis of a protein mutant: the value of a combined approach.

The effect of the mutation Arg 96 to His on the stability of bacteriophage T4 lysozyme has been previously studied by calorimetric experiments, X-ray crystallography, and free energy simulation techniques. The experimental and calculated values for the difference between the free energy of denaturation of the mutant and the wild type are in reasonable agreement. However, the two approaches led to different explanations for the loss in stability. To analyze the differences, a series of refinements based on the crystallographic data were performed, a number of aspects of the simulations were reexamined, and continuum electrostatic calculations were done to complement the latter. The results of those comparisons provide a better understanding of the origin of the free energy difference in this mutant. Furthermore, they show the importance of the combined use of simulations and crystallography for interpreting the effects of mutations on the energetics of the system.

Bacteriophage T4↗
PubMed2004

Investigation of glucose binding sites on insulin.

Possible insulin binding sites for D-glucose have been investigated theoretically by docking and molecular dynamics (MD) simulations. Two different docking programs for small molecules were used; Multiple Copy Simultaneous Search (MCSS) and Solvation Energy for Exhaustive Docking (SEED) programs. The configurations resulting from the MCSS search were evaluated with a scoring function developed to estimate the binding free energy. SEED calculations were performed using various values for the dielectric constant of the solute. It is found that scores emphasizing non-polar interactions gave a preferential binding site in agreement with that inferred from recent fluorescence and NMR NOESY experiments. The calculated binding affinity of -1.4 to -3.5 kcal/mol is within the measured range of -2.0 +/- 0.5 kcal/mol. The validity of the binding site is suggested by the dynamical stability of the bound glucose when examined with MD simulations with explicit solvent. Alternative binding sites were found in the simulations and their relative stabilities were estimated. The motions of the bound glucose during molecular dynamics simulations are correlated with the motions of the insulin side chains that are in contact with it and with larger scale insulin motions. These results raise the question of whether glucose binding to insulin could play a role in its activity. The results establish the complementarity of molecular dynamics simulations and normal mode analyses with the search for binding sites proposed with small molecule docking programs.

Binding Sites↗