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Martin Karplus

Publications and source records attributed to Martin Karplus.

At least 55 records · Page 3Linked to original sources
PubMed2004

The role of carbon-donor hydrogen bonds in stabilizing tryptophan conformations.

Although most side-chain torsion angles correspond to low-energy rotameric positions, deviations occur with significant frequency. One striking example arises in Trp residues, which have an important role in stabilizing protein structures because of their size and mixed hydrophobic/hydrophilic character. Ten percent of Trp side-chains have unexplained conformations with chi(2) near 0 degrees instead of the expected 90 degrees. The current work is a structural and energetic analysis of these conformations. It is shown that many Trp residues with these orientations are stabilized by three-center carbon-donor hydrogen bonds of the form C-H...X...H-C, where X is a polar hydrogen-bond acceptor in the environment of the side-chain. The bridging hydrogen bonds occur both within the Trp side-chain and between the side-chain and the local protein backbone. Free energy maps of an isolated Trp residue in an explicit water environment show a minimum corresponding to the off-rotamer peak observed in the crystallographic data. Bridging carbon-donor hydrogen bonds are also shown to stabilize on-rotamer Trp conformations, and similar bridging hydrogen bonds also stabilize some off-rotamer Asp conformations. The present results suggest a previously unrecognized role for three-center carbon-donor hydrogen bonds in protein structures and support the view that the off-rotamer Trp side-chain orientations are real rather than artifacts of crystallographic refinements. Certain of the off-rotamer Trp conformations appear to have a functional role.

Aspartic Acid↗
PubMed2004

Comparison of the transition state ensembles for folding of Im7 and Im9 determined using all-atom molecular dynamics simulations with phi value restraints.

Delineation of the structural properties of transition states is key to deriving models for protein folding. Here we describe the structures of the transition states of the bacterial immunity proteins Im7 and Im9 obtained by all-atom molecular dynamics simulations with phi value restraints derived from protein engineering experiments. This pair of proteins is of special interest because, at pH 7 and 10 degrees C, Im7 folds via an intermediate while Im9 folds with a two-state transition. The structures of the transition states for Im7 and Im9, together with their radii of gyration and distances from the native state, are similar. The typical distance between any two members of the transition state ensemble of both proteins is large, with that of Im9 nearly twice that of Im7. Thus, a broad range of structures make up the transition state ensembles of these proteins. The ensembles satisfy the set of rather low phi values and yet are consistent with high beta(T) values (> 0.85 for both proteins). For both Im7 and Im9 the inter-helical angles are highly variable in the transition state ensembles, although the native contacts between helices I and IV are well conserved. By measuring the distribution of the accessible surface area for each residue we show that the hydrophobic residues that are buried in the native state remain buried in the transition state, corresponding to a hydrophobic collapse to a relatively ordered globule. The data provide new insights into the structural properties of the transition states of these proteins at an atomic level of detail and show that molecular dynamics simulations with phi value restraints can significantly enhance the knowledge of the transition state ensembles (TSE) provided by the experimental phi values alone.

Bacterial Proteins↗
PubMed2004

Free energy simulations: use of reverse cumulative averaging to determine the equilibrated region and the time required for convergence.

A method is proposed for improving the accuracy and efficiency of free energy simulations. The essential idea is that the convergence of the relevant measure (e.g., the free energy derivative in thermodynamic integration) is monitored in the reverse direction starting from the last frame of the trajectory, instead of the usual approach, which begins with the first frame and goes in the forward direction. This simple change in the use of the simulation data makes it straightforward to eliminate the contamination of the averages by contributions from the equilibrating region. A statistical criterion is introduced for distinguishing the equilibrated (production) region from the equilibrating region. The proposed method, called reverse cumulative averaging, is illustrated by its application to the well-studied case of the alchemical free energy simulation of ethane to methanol.

Computer Simulation↗
PubMed2004

How enzymes work: analysis by modern rate theory and computer simulations.

Advances in transition state theory and computer simulations are providing new insights into the sources of enzyme catalysis. Both lowering of the activation free energy and changes in the generalized transmission coefficient (recrossing of the transition state, tunneling, and nonequilibrium contributions) can play a role. A framework for understanding these effects is presented, and the contributions of the different factors, as illustrated by specific enzymes, are identified and quantified by computer simulations. The resulting understanding of enzyme catalysis is used to comment on alternative proposals of how enzymes work.

Catalysis↗
PubMed2004

Biomolecular motors: the F1-ATPase paradigm.

The realization that many essential functions of living cells are performed by nanoscale motors consisting of protein complexes has given rise to an intense effort to understand their mechanisms. Considerable progress has been made in the past two years by a combination of biophysical techniques and theoretical analysis. Single-molecule studies have played a spectacular role for a variety of motors including kinesin, myosin, and polymerases. The understanding of F(1)-ATPase, the smallest biomolecular rotary motor, has made particular progress by the interplay of experimental and theoretical studies; the latter have provided information not available from experiment.

Animals↗
PubMed2004

The role of sequence and structure in protein folding kinetics; the diffusion-collision model applied to proteins L and G.

The diffusion-collision model (DCM) is applied to the folding kinetics of protein L and protein G. In the DCM, the two proteins are treated as consisting of two beta-hairpins and one alpha-helix, so that they are isomorphous with the three-helix bundle DCM model. In the absence of sequence dependent factors, both proteins would fold in the same way in the DCM, with the coalescence of the N-terminal hairpin and the helix slightly favored over the C-terminal hairpin and the helix because the former are closer together than the latter. However, sequence dependent factors make the N-terminal hairpin of protein L and the C-terminal hairpin of protein G more stable in the ensemble of unfolded conformations. This difference in the stabilities gives rise to the difference in the calculated folding behavior, in agreement with experiment.

Amino Acid Sequence↗
PubMed2004

Theoretical investigations on Azotobacter vinelandii ferredoxin I: effects of electron transfer on protein dynamics.

Structural, energetic, and dynamical studies of Azotobacter vinelandii ferredoxin I are presented for native and mutant forms. The protein contains two iron-sulfur clusters, one of which ([3Fe-4S]) is believed to play a central role in the electron-coupled proton transfer. Different charge sets for the [3Fe-4S] cluster in its reduced and oxidized state are calculated with broken symmetry ab initio density functional theory methods and used in molecular dynamics (MD) simulations. The validity of the ab initio calculations is assessed by comparing partially optimized structures of the [3Fe-4S] clusters with x-ray structures. Possible proton transfer pathways between the protein and the iron-sulfur cluster are examined by both MD simulations and ab initio calculations. The MD simulations identify three main-chain hydrogen atoms--HN(13), HN(14), and HN(16)--that are within H-bonding distance of the [3Fe-4S] cluster throughout the MD simulations. They could thus play a role in the proton transfer from the protein to the iron-sulfur cluster. By contrast, the HD2(15) atom of the Asp-15 is seldom close enough to the [3Fe-4S] cluster to transfer a proton. Poisson-Boltzmann calculations indicate that there is a low, but nonzero probability, that Asp-15 is protonated at pH 7; this is a requirement for it to serve as a proton donor. Ab initio calculations with a fragment model for the protein find similar behavior for the transfer of a proton from the OH of the protonated side chain and the main-chain NH of Asp-15. The existence of a stable salt bridge between Asp-15 and Lys-84 in the D15E mutant, versus its absence in the wild-type, has been suggested as the cause of the difference in the rate of proton transfer. Extensive MD simulations were done to test this idea; the results do not support the proposal. The present findings, together with the available data, serve as the basis for an alternative proposal for the mechanism of the coupled electron-proton transfer reaction in ferredoxin I.

Azotobacter vinelandii↗
PubMed2004

The unfolding action of GroEL on a protein substrate.

A molecular dynamics simulation of the active unfolding of denatured rhodanese by the chaperone GroEL is presented. The compact denatured protein is bound initially to the cis cavity and forms stable contacts with several of the subunits. As the cis ring apical domains of GroEL undergo the transition from the closed to the more open (ATP-bound) state, they exert a force on rhodanese that leads to the increased unfolding of certain loops. The contacts between GroEL and rhodanese are analyzed and their variation during the GroEL transition is shown. The major contacts, which give rise to the stretching force, are found to be similar to those observed in crystal structures of peptides bound to the apical domains. The results of the simulation show that multidomain interactions play an essential role, in accord with experiments. Implications of the results for mutation experiments and for the action of GroEL are discussed.

Binding Sites↗
PubMed2004

Dependence of DNA polymerase replication rate on external forces: a model based on molecular dynamics simulations.

Molecular dynamics simulations are presented for a Thermus aquaticus (Taq) DNA polymerase I complex (consisting of the protein, the primer-template DNA strands, and the incoming nucleotide) subjected to external forces. The results obtained with a force applied to the DNA template strand provide insights into the effect of the tension on the activity of the enzyme. At forces below 30 pN a local model based on the parameters determined from the simulations, including the restricted motion of the DNA bases at the active site, yields a replication rate dependence on force in agreement with experiment. Simulations above 40 pN reveal large conformational changes in the enzyme-bound DNA that may have a role in the force-induced exonucleolysis observed experimentally.

Binding Sites↗
PubMed2003

Rare fluctuations of native proteins sampled by equilibrium hydrogen exchange.

We present a method for determining the ensembles of native protein structures that result from the large fluctuations of low probability revealed by hydrogen-exchange experiments. The measured protection factors are used to bias Monte Carlo simulations to sample the structures of the exchange competent species. The approach is illustrated by its application to the case of alpha-lactalbumin.

Humans↗
PubMed2003

Structures and relative free energies of partially folded states of proteins.

The ability of proteins to fold to well defined compact structures is one of the most remarkable examples of the effect of natural selection on biological molecules. To understand their properties, including the stability, the mechanism of folding, and the possibilities of misfolding and association, it is necessary to know the protein free energy landscape. We use NMR data as restraints in a Monte Carlo sampling procedure to determine the ensemble of structures populated by human alpha-lactalbumin in the presence of increasing concentrations of urea. The ensembles of structures that represent the partially folded states of the protein show that two structural cores, corresponding to portions of the alpha and beta domains of the native protein, are preserved even when the native-like interactions that define their existence are substantially weakened. Analysis of the network of residual contacts reveals the presence of a complex interface region between the two structural cores and indicates that the development of specific interactions within this interface is the key step in achieving the native structure. The relative probabilities of the conformations determined from the NMR data are used to construct a coarse-grained free energy landscape for alpha-lactalbumin in the absence of urea. The form of the landscape, together with the existence of distinct cores, supports the concept that robustness and modularity are the properties that make possible the folding of complex proteins.

Humans↗
PubMed2003

A model for the cooperative free energy transduction and kinetics of ATP hydrolysis by F1-ATPase.

Although the binding change mechanism of rotary catalysis by which F1-ATPase hydrolyzes ATP has been supported by equilibrium, kinetic, and structural observations, many questions concerning the function remain unanswered. Because of the importance of this enzyme, the search for a full understanding of its mechanism is a key problem in structural biology. Making use of the results of free energy simulations and experimental binding constant measurements, a model is developed for the free energy change during the hydrolysis cycle. This model makes possible the development of a kinetic scheme for ATP hydrolysis by F1-ATPase, in which the rate constants are associated with specific configurations of the beta subunits. An essential new element is that the strong binding site for ADP,Pi is shown to be the betaDP site, in contrast to the strong binding site for ATP, which is betaTP. This result provides a rationale for the rotation of the gamma subunit, which induces the cooperativity required for a tri-site binding change mechanism. The model explains a series of experimental data, including the ATP concentration dependence of the rate of hydrolysis and catalytic site occupation for both the Escherichia coli F1-ATPase (EcF1) and Thermophilic Bacillus PS3 F1-ATPase (TF1), which have different behavior.

Adenosine Triphosphate↗
PubMed2003

Modeling zinc in biomolecules with the self consistent charge-density functional tight binding (SCC-DFTB) method: applications to structural and energetic analysis.

Parameters for the zinc ion have been developed in the self-consistent charge density functional tight-binding (SCC-DFTB) framework. The approach was tested against B3LYP calculations for a range of systems, including small molecules that contain the typical coordination environment of zinc in biological systems (cysteine, histidine, glutamic/aspartic acids, and water) and active site models for a number of enzymes such as alcohol dehydrogenase, carbonic anhydrase, and aminopeptidase. The SCC-DFTB approach reproduces structural and energetic properties rather reliably (e.g., total and relative ligand binding energies and deprotonation energies of ligands and barriers for zinc-assisted proton transfers), as compared with B3LYP/6-311+G** or MP2/6-311+G** calculations.

Alcohol Dehydrogenase↗
PubMed2003

Cooperativity in Scapharca dimeric hemoglobin: simulation of binding intermediates and elucidation of the role of interfacial water.

Cooperative binding of ligands to proteins can serve to increase their efficiency and to regulate their activity. Thus, understanding of the mechanism of cooperativity is one of the central concerns of molecular biology. For the tetrameric human hemoglobin (HbA), the cooperative mechanism involves a reasonably well understood combination of tertiary and quaternary changes that occur during the binding process. The dimeric hemoglobin of Scapharca (HbI), which is composed of subunits with the same fold as in HbA, is also highly cooperative but the structural changes on ligand binding are small. A re-orientation of Phe97 in the binding pocket and changes in the number of interfacial water molecules have been implicated in the cooperative mechanism. To explore the role of these factors, we have investigated models of partially liganded intermediate states of HbI with molecular dynamics simulation methods. Since, unlike HbA, no structures for intermediates are available, they were constructed by combining subunits from the unliganded and liganded dimers. Two structurally distinct intermediates were examined, and it was shown that the transition between the two intermediates is directly coupled to the number of interfacial water molecules. Further, it was found that there is a well-defined water channel that connects the interface between the subunits to bulk water. The bottleneck (gate) of the channel, which can be open or closed, is made of hydrophilic residues. The implication of the present results for the cooperative mechanism of HbI is discussed.

Allosteric Regulation↗
PubMed2003

An improved method for nonbonded list generation: rapid determination of near-neighbor pairs.

Generation of the list of near-neighbor pairs of atoms not bonded to each other is a key feature of many programs for calculating the energy and energy derivatives for large molecules. Because this step can take a significant amount of CPU time, more efficient nonbonded list generation can speed up the energy calculations. In this article, a novel nonbonded list generation algorithm, BYCC, is introduced. It combines certain features of other algorithms and achieves more rapid nonbonded list generation; a factor of approximately 2.5 for a molecule of 5000 atoms with a cutoff in the 10 A range is obtained on Hewlett-Packard (HP) and Alpha processors, without greatly increasing memory requirements.

Algorithms↗
PubMed2003

Self-consistent determination of the transition state for protein folding: application to a fibronectin type III domain.

We present a general approach in which theory and experiments are combined in an iterative manner to provide a detailed description of the transition state ensemble (TSE) for folding. The method is illustrated by applying it to TNfn3, a fibronectin type III domain protein. In the first iteration, a coarse-grained determination of the TSE is carried out by using a limited set of experimental phi values as constraints in a molecular dynamics sampling simulation. The resulting model of the TSE is used to determine the additional residues whose phi value measurement would provide the most information for refining the TSE. Successive iterations with an increasing number of phi value measurements are carried out until no further changes in the properties of the TSE are detected or there are no additional residues whose phi values can be measured. In the study of TNfn3 three iterations were necessary to achieve self-consistency. A retrospective application of the method can be used to determine the accuracy of the TSE results and to find "key residues" for folding, i.e., those that are most important for the formation of the TSE. The approach reported here is an efficient method for finding the structures that make up the TSEs for protein folding. Its use will improve future efforts for their experimental determination and refinement.

Fibronectins↗
PubMed2003

Molecular dynamics of biological macromolecules: a brief history and perspective.

A description of the origin of my interest in and the development of molecular dynamics simulations of biomolecules is presented with a historical overview, including the role of my interactions with Shneior Lifson and his group in Israel. Some early applications of the methodology by members of my group are summarized, followed by a description of examples of recent applications and some discussion of possible future directions.

Biopolymers↗