Biomedical subjects

Martin Karplus

Publications and source records attributed to Martin Karplus.

At least 19 recordsLinked to original sources

PubMed2006

Two-metal-ion mechanism for hammerhead-ribozyme catalysis.

The hammerhead ribozyme is one of the best studied ribozymes, but it still presents challenges for our understanding of RNA catalysis. It catalyzes a transesterification reaction that converts a 5',3' diester to a 2',3' cyclic phosphate diester via an S(N)2 mechanism. Thus, the overall reaction corresponds to that catalyzed by bovine pancreatic ribonuclease. However, an essential distinguishing aspect is that metal ions are not involved in RNase catalysis but appear to be important in ribozymes. Although various techniques have been used to assign specific functions to metals in the hammerhead ribozyme, their number and roles in catalysis is not clear. Two recent theoretical studies on RNA catalysis examined the reaction mechanism of a single-metal-ion model. A two-metal-ion model, which is supported by experiment and based on ab initio and density functional theory calculations, is described here. The proposed mechanism of the reaction has four chemical steps with three intermediates and four transition states along the reaction pathway. Reaction profiles are calculated in the gas phase and in solution. The early steps of the reaction are found to be fast (with low activation barriers), and the last step, corresponding to the departure of the leaving group, is rate limiting. This two-metal-ion model differs from the models proposed previously in that the two metal ions function not only as Lewis acids but also as general acids/bases. Comparison with experiment shows good agreement with thermodynamic and kinetic data. A detailed analysis based on natural bond orbitals (NBOs) and natural energy decomposition (NEDA) provides insights into the role of metal ions and other factors important for catalysis.

Catalysis↗

PubMed2005

The allosteric mechanism of yeast chorismate mutase: a dynamic analysis.

The effector-regulated allosteric mechanism of yeast chorismate mutase (YCM) was studied by normal mode analysis and targeted molecular dynamics. The normal mode analysis shows that the conformational change between YCM in the R state and in the T state can be represented by a relatively small number of low-frequency modes. This suggests that the transition is coded in the structure and is likely to have a low energetic barrier. Quantitative comparisons (i.e. frequencies) between the low-frequency modes of YCM with and without effectors (modeled structures) reveal that the binding of Trp increases the global flexibility, whereas Tyr decreases global flexibility. The targeted molecular dynamics simulation of substrate analog release from the YCM active site suggests that a series of residues are critical for orienting and "recruiting" the substrate. The simulation led to the switching of a series of substrate-release-coupled salt-bridge partners in the ligand-binding domain; similar changes occur in the transition between YCM R-state and T-state crystal structures. Thus, the normal mode analysis and targeted molecular dynamics results provide evidence that the effectors regulate YCM activity by influencing the global flexibility. The change in flexibility is coupled to the binding of substrate to the T state and release of the product from the R state, respectively.

Allosteric Regulation↗

PubMed2005

A structure-based model for the synthesis and hydrolysis of ATP by F1-ATPase.

Many essential functions of living cells are performed by nanoscale protein motors. The best characterized of these is F(o)F1-ATP synthase, the smallest rotary motor. This rotary motor catalyzes the synthesis of ATP with high efficiency under conditions where the reactants (ADP, H2PO4(-)) and the product (ATP) are present in the cell at similar concentrations. We present a detailed structure-based kinetic model for the mechanism of action of F1-ATPase and demonstrate the role of different protein conformations for substrate binding during ATP synthesis and ATP hydrolysis. The model shows that the pathway for ATP hydrolysis is not simply the pathway for ATP synthesis in reverse. The findings of the model also explain why the cellular concentration of ATP does not inhibit ATP synthesis.

Adenosine Triphosphate↗

PubMed2005

Study of the insulin dimerization: binding free energy calculations and per-residue free energy decomposition.

A calculation of the binding free energy for the dimerization of insulin has been performed using the molecular mechanics-generalized Born surface area approach. The calculated absolute binding free energy is -11.9 kcal/mol, in approximate agreement with the experimental value of -7.2 kcal/mol. The results show that the dimerization is mainly due to nonpolar interactions. The role of the hydrogen bonds between the 2 monomers appears to give the direction of the interactions. A per-atom decomposition of the binding free energy has been performed to identify the residues contributing most to the self association free energy. Residues B24-B26 are found to make the largest favorable contributions to the dimerization. Other residues situated at the interface between the 2 monomers were found to make favorable but smaller contributions to the dimerization: Tyr B16, Val B12, and Pro B28, and to an even lesser extent, Gly B23. The energy decomposition on a per-residue basis is in agreement with experimental alanine scanning data. The results obtained from a single trajectory (i.e., the dimer trajectory is also used for the monomer analysis) and 2 trajectories (i.e., separate trajectories are used for the monomer and dimer) are similar.

Crystallography, X-Ray↗

PubMed2005

Large amplitude conformational change in proteins explored with a plastic network model: adenylate kinase.

The plastic network model (PNM) is used to generate a conformational change pathway for Escherichia coli adenylate kinase based on two crystal structures, namely that of an open and a closed conformer. In this model, the energy basins corresponding to known conformers are connected at their lowest common energies. The results are used to evaluate and analyze the minimal energy pathways between these basins. The open to closed transition analysis provides an identification of hinges that is in agreement with the existing definitions based on the available X-ray structures. The elastic energy distribution and the C(alpha) pseudo-dihedral variation provide similar information on these hinges. The ensemble of the 45 published structures for this protein and closely related proteins is shown to always be within 3.0 A of the pathway, which corresponds to a conformational change between two end structures that differ by a C(alpha)-atom root-mean-squared deviation of 7.1A.

Adenylate Kinase↗

PubMed2005

Transition state contact orders correlate with protein folding rates.

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.

Kinetics↗

PubMed2005

Design, synthesis, and biological evaluation of HSP90 inhibitors based on conformational analysis of radicicol and its analogues.

The molecular chaperone HSP90 is an attractive target for chemotherapy because its activity is required for the functional maturation of a number of oncogenes. Among the known inhibitors, radicicol, a 14-member macrolide, stands out as the most potent. A molecular dynamics/minimization of radicicol showed that there were three low energy conformers of the macrocycle. The lowest of these is the bioactive conformation observed in the cocrystal structure of radicicol with HSP90. Corresponding conformational analyses of several known analogues gave a good correlation between the bioactivity and the energy of the bioactive conformer, relative to other conformers. Based on this observation, a number of proposed analogues were analyzed for their propensity to adopt the bioactive conformation prior to synthesis. This led to the identification of pochonin D, a recently isolated secondary metabolite of Pochonia chlamydosporia, as a potential inhibitor of HSP90. Pochonin D was synthesized using polymer-bound reagents and shown to be nearly as potent an HSP90 inhibitor as radicicol.

Drug Design↗

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

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↗