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M Karplus

Publications and source records attributed to M Karplus.

At least 55 records · Page 3Linked to original sources
PubMed1998

A metastable state in folding simulations of a protein model.

The native state of a protein is generally believed to be the global free energy minimum. However, there is increasing evidence that kinetically selected states play a role in the biological function of some proteins. In a recent folding study of a 125-residue heteropolymer model, one of 200 sequences was found to fold repeatedly to a particular local minimum that did not interconvert to the global minimum. The kinetic preference for this 'metastable' state is shown to derive from an entropic barrier associated with inserting a tail segment into the protein interior of the serpin-like global minimum structure. The relation of the present results to the role of metastable states in functioning and pathogenic proteins is discussed.

Computer Simulation↗
PubMed1997

Folding thermodynamics of a model three-helix-bundle protein.

The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-to-ordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single "optimization" parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helix-bundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393-396].

Animals↗
PubMed1997

Three-dimensional quantitative structure-activity relationships from molecular similarity matrices and genetic neural networks. 1. Method and validations.

The utility of genetic neural network (GNN) to obtain quantitative structure-activity relationships (QSAR) from molecular similarity matrices is described. In this application, the corticosteroid-binding globulin (CBG) binding affinity of the well-known steroid data set is examined. Excellent predictivity can be obtained through the use of either electrostatic or shape properties alone. Statistical validation using a standard randomization test indicates that the results are not due to chance correlations. Application of GNN on the combined electrostatic and shape matrix produces a six-descriptor model with a cross-validated r2 value of 0.94. The model is superior to those obtained from partial least-squares and genetic regressions, and it also compares favorably with the results for the same data set from other established 3D QSAR methods. The theoretical basis for the use of molecular similarity in QSAR is discussed.

Algorithms↗
PubMed1997

Three-dimensional quantitative structure-activity relationships from molecular similarity matrices and genetic neural networks. 2. Applications.

Validation of a method that uses a genetic neural network with electrostatic and steric similarity matrices (SM/GNN) to obtain quantitative structure-activity relationships (QSARs) is performed with eight data sets. Biological and physicochemical properties from a broad range of chemical classes are correlated and predicted using this technique. Quantitatively the results compare favorably with the benchmarks obtained by a number of well-established QSAR methods; qualitatively the models are consistent with the published descriptions on the relative contribution of steric and electrostatic factors. The results demonstrate the general utility of this method in deriving QSARs. The implication of the importance of molecular alignment and possible methodological improvements are discussed.

Cholinesterase Inhibitors↗
PubMed1997

"New view" of protein folding reconciled with the old through multiple unfolding simulations.

Twenty-four molecular dynamics trajectories of chymotrypsin inhibitor 2 provide a direct demonstration of the diversity of unfolding pathways. Comparison with experiments suggests that the transition state region for folding and unfolding occurs early with only 25 percent of the native contacts and that the root-mean-square deviations between contributing structures can be as large as 15 angstroms. Nevertheless, a statistically preferred unfolding pathway emerges from the simulations; disruption of tertiary interactions between the helix and a two-stranded portion of the beta sheet is the primary unfolding event. The results suggest a synthesis of the "new" and the classical view of protein folding with a preferred pathway on a funnel-like average energy surface.

Computer Simulation↗
PubMed1997

Ligand-induced conformational changes in ras p21: a normal mode and energy minimization analysis.

A normal mode and energy minimization of ras p21 is used to determine the flexibility of the protein and the origin of the conformational differences between GTP and GDP-bound forms. To preserve the integrity of the structures, a hydration shell of water molecules was included as part of the system. Certain low-frequency modes were found to have high involvement coefficients with the conformational transition between the GTP and GDP-bound structures; the involvement coefficients of some of the modes increase when the gamma-phosphate group is removed. Two unstable modes that appear in the GTP-bound structure upon deletion of the gamma-phosphate group were determined and shown to have dominant contributions in the regions of switch I and switch II; there was also a significant displacement of loop 1. The initial motion in these regions is predicted by the modes to be approximately perpendicular to the direction of the transition from the GTP-bound state to the GDP-bound state. The overall conformational change in the switch I and II regions involves rearrangements of the protein backbone within these regions, rather than rigid body motion. Differences in the low-frequency modes of the GTP and GDP-bound forms appear to play a role in ligand binding. A coupling between the helix alpha3 position and the deletion of the gamma-phosphate group may be involved in the interaction with GAP. The oncogenic mutation G12D leads to a global increase in the rigidity of the protein. Thus, the mutant is likely to have a higher barrier for the conformational change to the inactive form; this would slow the transition and could be related to its oncogenic properties.

Binding Sites↗
PubMed1997

Molecular switch in signal transduction: reaction paths of the conformational changes in ras p21.

Conformational changes in ras p21 triggered by the hydrolysis of GTP play an essential role in the signal transduction pathway. The path for the conformational change is determined by molecular dynamics simulation with a holonomic constraint directing the system from the known GTP-bound structure (with the gamma-phosphate removed) to the GDP-bound structure. The simulation is done with a shell of water molecules surrounding the protein. In the switch I region, the side chain of Tyr-32, which undergoes a large displacement, moves through the space between loop 2 and the rest of the protein, rather than on the outside of the protein. As a result, the charged residues Glu-31 and Asp-33, which interact with Raf in the homologous RafRBD-Raps complex, remain exposed during the transition. In the switch II region, the conformational changes of alpha2 and loop 4 are strongly coupled. A transient hydrogen bonding complex between Arg-68 and Tyr-71 in the switch II region and Glu-37 in switch I region stabilizes the intermediate conformation of alpha2 and facilitates the unwinding of a helical turn of alpha2 (residues 66-69), which in turn permits the larger scale motion of loop 4. Hydrogen bond exchange between the protein and solvent molecules is found to be important in the transition. Possible functional implications of the results are discussed.

Computer Simulation↗
PubMed1997

PDB-based protein loop prediction: parameters for selection and methods for optimization.

An approach to loop prediction that starts with a database search is presented and analyzed. To obtain meaningful statistics, 130 loops from 21 proteins were studied. The correlation between the internal conformation of the loop and the conformation of the neighboring stem residues was examined. Distances between C(alpha) and C(beta) of the immediate neighbor residues at each end select template loops as well as more complex (e.g. three residues on either side) matching criteria. To have a high probability that the best possible loop candidate in the database is included in the set, relatively large cutoffs for matching the interatomic distances of the stem residues have to be used in the template loop selection procedure; for loops of length 5, this results in an average of 1000 loops and for loops of length 9, the number is about 1500. The required number increases only slowly with loop length, in contrast to the exponential time increase involved in direct searches of the conformational space. The best loops among the large number of candidates can be determined by ranking them with the standard CHARMM non-bonded energy function (without electrostatics) applied to the backbone and C(beta) atoms. The same representation (backbone plus C(beta)) can be used to optimize the loop orientations relative to the rest of the protein by constrained energy minimization. Target loops that have many non-bonded contacts with the protein yield better results so that analysis of the non-bonded contacts of the selected template loops is useful in determining the expected accuracy of a prediction. The method for loop selection and optimization predicted eight (out of 18) loops of up to nine residues to an RMSD better than 1.07 A relative to the crystal structure; for 17 of the 18 loops, one of the three lowest energy template loops had an RMSD of less than 1.79 A. The prediction of antibody loops from a database search is more effective than that for non-antibody loops. Provided that they belong to one of the canonical classes, very similar antibody loops are certain to exist in the database. Superposition of the stem residues for antibody loops also results in a better orientation than with arbitrary target loops because the neighboring residues tend to have a more similar beta-strand structure. Two H3 loops (for which no canonical structures have been proposed) were predicted with reasonable accuracy (RMSD of 0.49 A and 1.07 A) even though no corresponding antibody loops were in the database.

Algorithms↗
PubMed1997

Use of the multiple copy simultaneous search (MCSS) method to design a new class of picornavirus capsid binding drugs.

A combinatorial ligand design approach based on the multiple copy simultaneous search (MCSS) method and a simple scheme for joining MCSS functional group sites was applied to the binding pocket of P3/Sabin poliovirus and rhinovirus 14. The MCSS method determines where specific functional (chemical) groups have local potential energy minima in the binding site. Before the virus application, test calculations were run to determine the optimal set of input parameters to be used in evaluating the MCSS results. The MCSS minima are analysed and selected minima are connected with (CH2)n linkers to form candidate ligands, whose structures are optimized in the binding site. Estimates of the binding strength were made for the ligands and compared with those for known drugs. The results indicate that the proposed ligands should bind to P3/Sabin poliovirus at least as well as the best of the existing drugs, and that they should also bind to P1/Mahoney poliovirus and rhinovirus 14. A detailed comparison of the poliovirus and rhinovirus binding pockets and an analysis of drug binding specificity is presented.

Algorithms↗
PubMed1997

Dynamics and unfolding pathways of a hyperthermophilic and a mesophilic rubredoxin.

Molecular dynamics simulations in solution are performed for a rubredoxin from the hyperthermophilic archaeon Pyrococcus furiosus (RdPf) and one from the mesophilic organism Desulfovibrio vulgaris (RdDv). The two proteins are simulated at four temperatures: 300 K, 373 K, 473 K (two sets), and 500 K; the various simulations extended from 200 ps to 1,020 ps. At room temperature, the two proteins are stable, remain close to the crystal structure, and exhibit similar dynamic behavior; the RMS residue fluctuations are slightly smaller in the hyperthermophilic protein. An analysis of the average energy contributions in the two proteins is made; the results suggest that the intraprotein energy stabilizes RdPf relative to RdDv. At 373 K, the mesophilic protein unfolds rapidly (it begins to unfold at 300 ps), whereas the hyperthermophilic does not unfold over the simulation of 600 ps. This is in accord with the expected stability of the two proteins. At 473 K, where both proteins are expected to be unstable, unfolding behavior is observed within 200 ps and the mesophilic protein unfolds faster than the hyperthermophilic one. At 500 K, both proteins unfold; the hyperthermophilic protein does so faster than the mesophilic protein. The unfolding behavior for the two proteins is found to be very similar. Although the exact order of events differs from one trajectory to another, both proteins unfold first by opening of the loop region to expose the hydrophobic core. This is followed by unzipping of the beta-sheet. The results obtained in the simulation are discussed in terms of the factors involved in flexibility and thermostability.

Amino Acid Sequence↗
PubMed1997

Computer simulations of the OmpF porin from the outer membrane of Escherichia coli.

Molecular dynamics simulations were used to study the structure and dynamics of the Escherichia coli OmpF porin, which is composed of three identical 16-stranded beta-barrels. Simulations of the full trimer in the absence of water and the membrane led to significant contraction of the channel in the interior of each beta-barrel. With very weak harmonic constraints (0.005 kcal/mol A2/atom) applied to the main-chain C alpha atoms of the beta-barrel, the structure was stabilized without alteration of the average fluctuations. The resulting distribution of the fluctuations (small for beta-strands, large for loops and turns) is in good agreement with the x-ray B factors. Dynamic cross-correlation functions showed the importance of coupling between the loop motions and barrel flexibility. This was confirmed by the application of constraints corresponding to the observed temperature factors to the barrel C alpha atoms. With these constraints, the beta-barrel fluctuations were much smaller than the experimental values because of the intrinsic restrictions on the atomic motions, and the loop motions were reduced significantly. This result indicates that considerable care is required in introducing constraints to keep proteins close to the experimental structure during simulations, as has been done in several recent studies. Loop 3, which is thought to be important in gating the pore, undergoes a displacement that shifts it away from the x-ray structure. Analysis shows that this arises from the breakdown of a hydrogen bond network, which appears to result more from the absence of solvent that from the use of standard ionization states for the side chains of certain beta-barrel residues.

Amino Acid Sequence↗
PubMed1997

The Levinthal paradox: yesterday and today.

A change in the perception of the protein folding problem has taken place recently. The nature of the change is outlined and the reasons for it are presented. An essential element is the recognition that a bias toward the native state over much of the effective energy surface may govern the folding process. This has replaced the random search paradigm of Levinthal and suggests that there are many ways of reaching the native state in a reasonable time so that a specific pathway does not have to be postulated. The change in perception is due primarily to the application of statistical mechanical models and lattice simulations to protein folding. Examples of lattice model results on protein folding are presented. It is pointed out that the new optimism about the protein folding problem must be complemented by more detailed studies to determine the structural and energetic factors that introduce the biases which make possible the folding of real proteins.

Models, Chemical↗
PubMed1997

A comparison between molecular dynamics and X-ray results for dissociated CO in myoglobin.

The distribution of carbon monoxide after photodissociation in the myoglobin haem pocket has been investigated using molecular dynamics simulations at 300 K. The results show that both intermediates (one close to the haem iron and one further away) observed in recent low temperature X-ray studies of photodissociated CO have a high probability of occurrence, even at ambient temperatures. The fact that the O of CO is oriented toward the haem iron in the closer intermediate provides an explanation for the slow rate of CO geminate rebinding. A refinement against X-ray data generated from the molecular dynamics simulations indicates that the CO has a broader distribution in the haem pocket than is apparent from the experimental electron density. This effect is likely to be general for systems containing highly mobile groups.

Algorithms↗
PubMed1996

Genetic neural networks for quantitative structure-activity relationships: improvements and application of benzodiazepine affinity for benzodiazepine/GABAA receptors.

A novel tool, called a genetic neural network (GNN), has been developed for obtaining quantitative structure-activity relationships (QSAR) for high-dimensional data sets (J. Med. Chem. 1996, 39, 1521-1530). The GNN method uses a neural network to correlate activity with descriptors that are preselected by a genetic algorithm. To provide an extended test of the GNN method, the data on 57 benzodiazepines given by Maddalena and Johnston (MJ; J. Med. Chem. 1995, 38, 715-724) have been examined with an enhanced version of GNN, and the results are compared with the excellent QSAR of MJ. The problematic steepest descent training has been replaced by the scaled conjugate gradient algorithm. This leads to a substantial gain in performance in both robustness of prediction and speed of computation. The cross-validation GNN simulation and the subsequent run based on an unbiased and more efficient protocol led to the discovery of other 10-descriptor QSARs that are superior to the best model of MJ based on backward elimination selection and neural network training. Results from a series of GNNs with a different number of inputs showed that a neural network with fewer inputs can produce QSARs as good as or even better than those with higher dimensions. The top-ranking models from a GNN simulation using only six input descriptors are presented, and the chemical significance of the chosen descriptors is discussed. The statistical significance of these GNN QSARs is validated. The best QSARs are used to provide a graphical tool that aids the design of new drug analogues. By replacing functional groups at the 7- and 2'-positions with ones that have optimal substituent parameters, a number of new benzodiazepines with high potency are predicted.

Algorithms↗
PubMed1996

Comment on a "fluctuation and cross correlation analysis of protein motions observed in nanosecond molecular dynamics simulations".

Long range positive correlations in the internal atomic motions have been observed in molecular dynamics simulations of the bovine pancreatic trypsin inhibitor. Since the results depend on the removal of overall translation and rotation (which is not unique), some care is required. It is pointed out that original use of all of the C atoms as a frame of reference is more appropriate than the selection of a particular subset. The former comes closest to reflecting the zero rotation condition in a normal mode analysis, which also shows the existence of long range correlations.

Animals↗
PubMed1996

The folding mechanism of larger model proteins: role of native structure.

The folding mechanism of a 125-bead heteropolymer model for proteins is investigated with Monte Carlo simulations on a cubic lattice. Sequences that do and do not fold in a reasonable time are compared. The overall folding behavior is found to be more complex than that of models for smaller proteins. Folding begins with a rapid collapse followed by a slow search through the semi-compact globule for a sequence-dependent stable core with about 30 out of 176 native contacts which serves as the transition state for folding to a near-native structure. Efficient search for the core is dependent on structural features of the native state. Sequences that fold have large amounts of stable, cooperative structure that is accessible through short-range initiation sites, such as those in anti-parallel sheets connected by turns. Before folding is completed, the system can encounter a second bottleneck, involving the condensation and rearrangement of surface residues. Overly stable local structure of the surface residues slows this stage of the folding process. The relation of the results from the 125-mer model studies to the folding of real proteins is discussed.

Models, Theoretical↗