Biomedical subjects

Martin Karplus

Publications and source records attributed to Martin Karplus.

At least 19 recordsLinked to original sources

PubMed2006

Implications of alternative substrate binding modes for catalysis by uracil-DNA glycosylase: an apparent discrepancy resolved.

A theoretical study showed that the base excision repair enzyme uracil-DNA glycosylase (UDG) exploits electrostatic interactions with backbone phosphate groups in the substrate for catalysis. Although experiments performed to test the calculated results confirmed the predicted importance of the -2, -1, and +1 phosphate groups, there was an apparent disagreement with regard to the +2 phosphate group. The calculations indicated that it made an important contribution, while experimentally, the effect of its deletion or neutralization was small. The +2 phosphate group interacts directly with an active site histidine (H148 in humans) in the crystal structure of UDG in complex with double-stranded (ds) DNA. We previously calculated that H148 has a strong anticatalytic effect due to its protonation, and here we use alchemical free energy simulations to estimate its site-specific pKa. We find that it is positively charged over the entire experimental pH range (4-10), so its deprotonation cannot compensate for deletion or neutralization of the +2 phosphate group. The free energy simulations are facilitated by an efficient charge-scaling procedure that allows quantitative correction for the implicit treatment of solvent far from the active site; improvements are made to that method to account carefully for differences in the truncation of electrostatic interactions in the contributing molecular-mechanical and continuum-electrostatic approaches. Additional simulations are used to demonstrate that the +2 phosphate group is fully solvent exposed in complexes with single-stranded DNA substrates like those used in the experiments. In contrast, it is well-structured and buried in the dsDNA complex used in the original simulations. Differences in solvent shielding thus account for the apparent lack of an effect observed experimentally upon neutralization or deletion of this group.

Catalysis↗

PubMed2006

Implications of the quaternary twist allosteric model for the physiology and pathology of nicotinic acetylcholine receptors.

Nicotinic acetylcholine receptors (nAChR) are pentameric ligand-gated ion channels composed of subunits that consist of an extracellular domain that carries the ligand-binding site and a distinct ion-pore domain. Signal transduction results from the allosteric coupling between the two domains: the distance from the binding site to the gate of the pore domain is 50 A. Normal mode analysis with a C(alpha) Gaussian network of a new structural model of the neuronal alpha7 nAChR showed that the lowest mode involves a global quaternary twist motion that opens the ion pore. A molecular probe analysis, in which the network is modified at each individual amino acid residue, demonstrated that the major effect is to change the frequency, but not the form, of the twist mode. The largest effects were observed for the ligand-binding site and the Cys-loop. Most (24/27) of spontaneous mutations known to cause congenital myasthenia and autosomal dominant nocturnal frontal lobe epilepsy are located either at the interface between subunits or, within a given subunit, at the interface between rigid blocks. These interfaces are modified significantly by the twist mode. The present analysis, thus, supports the quaternary twist model of the nAChR allosteric transition and provides a qualitative interpretation of the effect of the mutations responsible for several receptor pathologies.

Allosteric Regulation↗

PubMed2006

One-dimensional free-energy profiles of complex systems: progress variables that preserve the barriers.

We show that the balanced minimum-cut procedure introduced in PNAS 2004, 101, 14766 can be reinterpreted as a method for solving the constrained optimization problem of finding the minimum cut among the cuts with a particular value of an additive function of the nodes on either side of the cut. Such an additive function (e.g., the partition function of the reactant region) can be used as a progress coordinate to determine a one-dimensional profile (FEP) of the free-energy surface of the protein-folding reaction as well as other complex reactions. The algorithm is based on the network (obtained from an equilibrium molecular dynamics simulation) that represents the calculated reaction behavior. The resulting FEP gives the exact values of the free energy as a function of the progress coordinate; i.e., at each value of the progress coordinate, the profile is obtained from the surface with the minimal partition function among the surfaces that divide the full free-energy surface between two chosen end points. In many cases, the balanced minimum-cut procedure gives results for only a limited set of points. An approximate method based on p(fold) is shown to provide the profile for a more complete set of values of the progress coordinate. Applications of the approach to model problems and to realistic systems (beta-hairpin of protein G, LJ38 cluster) are presented.

Algorithms↗

PubMed2006

Nucleophilic attack on phosphate diesters: a density functional study of in-line reactivity in dianionic, monoanionic, and neutral systems.

A density functional study of the hydrolysis reaction of phosphodiesters with a series of attacking nucleophiles in the gas phase and in solution is presented. The nucleophiles HOH, HO-, CH3OH, and CH3O- were studied in reactions with ethylene phosphate, 2'3'-ribose cyclic phosphate and in their neutral (protonated) and monoanionic forms. Stationary-point geometries for the reactions were determined at the density functional B3LYP/6-31++G(d,p) level followed by energy refinement at the B3LYP/6-311++G(3df,2p) level. Solvation effects were estimated by using a dielectric approximation with the polarizable continuum model (PCM) at the gas-phase optimized geometries. This series of reactions characterizes factors that influence the intrinsic reactivity of the model phosphate compounds, including the effect of nucleophile, protonation state, cyclic structure, and solvent. The present study of the in-line mechanism for phosphodiester hydrolysis, a reaction of considerable biological importance, has implications for enzymatic mechanisms. The analysis generally supports the associative mechanism for phosphate ester hydrolysis. The results highlight the importance for the reaction barrier of charge neutralization resulting from the protonation of the nonbridging phosphoryl oxygens and the role of internal hydrogen transfer in the gas-phase mechanism. It also shows that solvent stabilization has a profound influence on the relative barrier heights for the dianionic, monoanionic, and neutral reactions. The calculations provide a comprehensive data set for the in-line hydrolysis mechanisms that can be used for the development of improved semiempirical quantum models for phosphate hydrolysis reactions.

Anions↗

PubMed2006

Dynamic distance disorder in proteins is caused by trapping.

Dynamic disorder in proteins, as demonstrated by variations in single-molecule electron transfer rates, is investigated by molecular dynamics simulations. The potential of mean force for the fluctuating donor-acceptor distance is calculated for the NAD(P)H:flavin oxidoreductase (Fre) complex with flavin adenine dinucleotide (FAD) and is found to be in agreement with that estimated from electron transfer experiments. The calculated autocorrelation function of the distance fluctuations has a simple exponential behavior at low temperatures and stretched exponential behavior at higher temperatures on femtosecond to nanosecond time scales. This indicates that the calculated dynamic disorder arises from a wide range of trapping times in potential wells on the protein energy landscape and suggests a corresponding origin for the stretched exponential behavior observed experimentally on longer time scales.

Algorithms↗

PubMed2006

Conformational sampling via a self-regulating effective energy surface.

The difficulty of efficiently sampling the phase space of complex systems with rough energy surfaces is well known. Typical solutions to the problem involve accelerating the crossing of barriers, but such methods often have the secondary problem that the low-energy states of interest are inadequately sampled, unless the parameters of the search algorithm are modified as the system evolves. A method is presented to improve the sampling with particular emphasis on the low-energy conformations, which make the most important contributions to the thermodynamics of the system. The algorithm proposed here samples the details of the minima, while easily surmounting barriers. This is achieved by introducing a self-regulating sampling variable which depends on the current state of the system. Two replicas of the system are introduced and the sampling variable is treated as a particle coupled to the physical system. The method is illustrated with a simple model system and is applied to the realistic example of barrier crossing in a protein-ligand complex.

Algorithms↗

PubMed2006

Folding of ubiquitin: a simple model describes the strange kinetics.

The ubiquitin mutant UbG folding experiments of Sabelko et al., in which "strange kinetics" were observed, are interpreted in terms of a simple kinetic model. A minimal set of states consisting of a semicompact globule, two off-pathway traps, and the native state are included; the fully unfolded state is not considered because folding to the semicompact globule is fast. Both the low- and the high-temperature experiments of Sabelko et al. are fitted by a system of kinetic equations determining the transitions between these states. It is possible that cold- and heat-denaturated states of UbG are the basis of the off-pathway traps. The fits of the kinetic model to the experimental results provides an estimate of the rate constants for the various reaction channels and show how their contributions vary with temperature. Introduction of an on-pathway intermediate instead of one of the off-pathway traps does not lead to agreement with the experiments.

Kinetics↗

PubMed2006

A Src-like inactive conformation in the abl tyrosine kinase domain.

The improper activation of the Abl tyrosine kinase results in chronic myeloid leukemia (CML). The recognition of an inactive conformation of Abl, in which a catalytically important Asp-Phe-Gly (DFG) motif is flipped by approximately 180 degrees with respect to the active conformation, underlies the specificity of the cancer drug imatinib, which is used to treat CML. The DFG motif is not flipped in crystal structures of inactive forms of the closely related Src kinases, and imatinib does not inhibit c-Src. We present a structure of the kinase domain of Abl, determined in complex with an ATP-peptide conjugate, in which the protein adopts an inactive conformation that resembles closely that of the Src kinases. An interesting aspect of the Src-like inactive structure, suggested by molecular dynamics simulations and additional crystal structures, is the presence of features that might facilitate the flip of the DFG motif by providing room for the phenylalanine to move and by coordinating the aspartate side chain as it leaves the active site. One class of mutations in BCR-Abl that confers resistance to imatinib appears more likely to destabilize the inactive Src-like conformation than the active or imatinib-bound conformations. Our results suggest that interconversion between distinctly different inactive conformations is a characteristic feature of the Abl kinase domain.

Amino Acid Motifs↗

PubMed2006

Optimal estimates of free energies from multistate nonequilibrium work data.

We derive the optimal estimates of the free energies of an arbitrary number of thermodynamic states from nonequilibrium work measurements; the work data are collected from forward and reverse switching processes and obey a fluctuation theorem. The maximum likelihood formulation properly reweights all pathways contributing to a free energy difference and is directly applicable to simulations and experiments. We demonstrate dramatic gains in efficiency by combining the analysis with parallel tempering simulations for alchemical mutations of model amino acids.

Amino Acids↗

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↗

PubMed2006

Spinach on the ceiling: a theoretical chemist's return to biology.

I was born in Vienna and came to the United States as a refugee in October 1938. This experience played an important role in my view of the world and my approach to science: It contributed to my realization that it was safe to stop working in fields that I felt I understood and to focus on different areas of research by asking questions that would teach me and others something new. I describe my experiences that led me from chemistry and physics back to my first love, biology, and outline some of the contributions I have made as part of my ongoing learning experience.

Austria↗

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

Potential energy surface and molecular dynamics of MbNO: existence of an unsuspected FeON minimum.

Ligands such as CO, O(2), or NO are involved in the biological function of myoglobin. Here we investigate the energetics and dynamics of NO interacting with the Fe(II) heme group in native myoglobin using ab initio and molecular dynamics simulations. At the global minimum of the ab initio potential energy surface (PES), the binding energy of 23.4 kcal/mol and the Fe-NO structure compare well with the experimental results. Interestingly, the PES is found to exhibit two minima: There exists a metastable, linear Fe-O-N minimum in addition to the known, bent Fe-N-O global minimum conformation. Moreover, the T-shaped configuration is found to be a saddle point, in contrast to the corresponding minimum for NO interacting with Fe(III). To use the ab initio results for finite temperature molecular dynamics simulations, an analytical function was fitted to represent the Fe-NO interaction. The simulations show that the secondary minimum is dynamically stable up to 250 K and has a lifetime of several hundred picoseconds at 300 K. The difference in the topology of the heme-NO PES from that assumed previously (one deep, single Fe-NO minimum) suggests that it is important to use the full PES for a quantitative understanding of this system. Why the metastable state has not been observed in the many spectroscopic studies of myoglobin interacting with NO is discussed, and possible approaches to finding it are outlined.

Iron↗

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↗