Zheng G, Schaefer M, Karplus M. Hemoglobin Bohr Effects: Atomic Origin of the Histidine Residue Contributions. Biochemistry. 2013;52(47):8539-8555.Abstract
The Bohr effect in Hb, which refers to the dependence of the oxygen affinity on the pH, plays an important role in its cooperativity and physiol. function. The dominant contribution to the Bohr effect arises from the difference in the pKa values of His residues of the unliganded (deoxy) and liganded (carbonmonoxy) structures. Using recent high resoln. structures, the residue pKa values corresponding to the two structures are calcd. The method is based on detg. the electrostatic interactions between residues in the protein, relative to those of the residue in soln., by use of the linearized finite difference Poisson-​Boltzmann equation and Monte Carlo sampling of protonation states. Given that good agreement is obtained with the available exptl. values for the contribution of His residues in HbA to the Bohr effect, the calcd. results are used to det. the at. origin of the pKa shift between deoxy and carbonmonoxy HbA. The contributions to the pKa shift calcd. by means of the linear response approxn. show that the salt bridge involving His146 plays an important role in the alk. Bohr effect, as suggested by Perutz but that other interactions are significant as well. A corresponding anal. is made for the contribution of His143 to the acid Bohr effect for which there is no proposed explanation. The method used is summarized and the program by which it is implemented is described in the Appendix.
Ovchinnikov V, Cecchini M, Karplus M. A Simplified Confinement Method for Calculating Absolute Free Energies and Free Energy and Entropy Differences. J. Phys. Chem. B. 2013;117(3):750-762.Abstract
A simple and robust formulation of the path-​independent confinement method for the calcn. of free energies is presented. The simplified confinement method (SCM) does not require matrix diagonalization or switching off the mol. force field, and has a simple convergence criterion. The method can be readily implemented in mol. dynamics programs with minimal or no code modifications. Because the confinement method is a special case of thermodn. integration, it is trivially parallel over the integration variable. The accuracy of the method is demonstrated using a model diat. mol., for which exact results can be computed anal. The method is then applied to the alanine dipeptide in vacuum, and to the α-​helix ↔ β-​sheet transition in a 16-​residue peptide modeled in implicit solvent. The SCM requires less effort for the calcn. of free energy differences than previous formulations because it does not require computing normal modes. The SCM has a diminished advantage for detg. abs. free energy values, because it requires decreasing the MD integration step to obtain accurate results. An approx. confinement procedure is introduced, which can be used to est. directly the configurational entropy difference between two macrostates, without the need for addnl. computation of the difference in the free energy or enthalpy. The approxn. has convergence properties similar to those of the std. confinement method for the calcn. of free energies. The use of the approxn. requires about 5 times less wall-​clock simulation time than that needed to compute enthalpy differences to similar precision from an MD trajectory. For the biomol. systems considered in this study, the errors in the entropy approxn. are under 10​%. Practical applications of the methods to proteins are currently limited to implicit solvent simulations.
Calimet N, Simoes M, Changeux J-P, Karplus M, Taly A, Cecchini M. A Gating Mechanism of Pentameric Ligand-​gated Ion Channels. Proceedings of the National Academy of Sciences of the United States of America. 2013;110(42):E3987-E3996.Abstract
Pentameric ligand-​gated ion channels (pLGICs) play a central role in intercellular communication in the nervous system and are involved in fundamental processes such as attention, learning, and memory. They are oligomeric protein assemblies that convert a chem. signal into an ion flux through the postsynaptic membrane, but the mol. mechanism of gating ions has remained elusive. Here, we present atomistic mol. dynamics simulations of the prokaryotic channels from Gloeobacter violaceus (GLIC) and Erwinia chrysanthemi (ELIC)​, whose crystal structures are thought to represent the active and the resting states of pLGICs, resp., and of the eukaryotic glutamate-​gated chloride channel from Caenorhabditis elegans (GluCI)​, whose openchannel structure was detd. complexed with the pos. allosteric modulator ivermectin. Structural observables extd. from the trajectories of GLIC and ELIC are used as progress variables to analyze the time evolution of GluCI, which was simulated in the absence of ivermectin starting from the structure with bound ivermectin. The trajectory of GluCI with ivermectin removed shows a sequence of structural events that couple agonist unbinding from the extracellular domain to ion-​pore closing in the transmembrane domain. Based on these results, we propose a structural mechanism for the allosteric communication leading to deactivation​/activation of the GluCI channel. This model of gating emphasizes the coupling between the quaternary twisting and the opening​/closing of the ion pore and is likely to apply to other members of the pLGIC family.
Kalgin IV, Caflisch A, Chekmarev SF, Karplus M. New Insights into the Folding of a β-​Sheet Miniprotein in a Reduced Space of Collective Hydrogen Bond Variables: Application to a Hydrodynamic Analysis of the Folding Flow. J. Phys. Chem. B. 2013;117(20):6092-6105.Abstract
A new anal. of the 20 μs equil. folding​/unfolding mol. dynamics simulations of the three-​stranded antiparallel β-​sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted principal component anal. (PCA)​; i.e., to make structured conformations more pronounced, only the formed bonds are included in detg. the principal components. A three-​dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin)​, is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed, and it is complemented by a hydrodynamic anal. The latter, making use of passive tracers in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortexes which correspond to repeated local rearrangement, not only around min. of the free energy surface but also in flat regions between min. The vortexes revealed by the hydrodynamic anal. are apparently not evident in folding pathways generated by transition-​path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is detd. The transition rates show an approx. exponential correlation with distance in the hydrogen bond subspace. Comparison with the many published studies shows good agreement with the present anal. for the parts that can be compared, supporting the robust character of the authors' understanding of this hydrogen atom of protein folding.
Qi Y, Nam K, Spong MC, Banerjee A, Sung R-J, Zhang M, Karplus M, Verdine GL. Strandwise translocation of a DNA glycosylase on undamaged DNA. Proceedings of the National Academy of Sciences of the United States of America. 2012;109(4):1086-1091.Abstract
Base excision repair of genotoxic nucleobase lesions in the genome is critically dependent upon the ability of DNA glycosylases to locate rare sites of damage embedded in a vast excess of undamaged DNA, using only thermal energy to fuel the search process. Considerable interest surrounds the question of how DNA glycosylases translocate efficiently along DNA while maintaining their vigilance for target damaged sites. Here, we report the observation of strandwise translocation of 8-​oxoguanine DNA glycosylase, MutM, along undamaged DNA. In these complexes, the protein is obsd. to translocate by one nucleotide on one strand while remaining untranslocated on the complementary strand. We further report that alterations of single base-​pairs or a single amino acid substitution (R112A) can induce strandwise translocation. Mol. dynamics simulations confirm that MutM can translocate along DNA in a strandwise fashion. These observations reveal a previously unobserved mode of movement for a DNA-​binding protein along the surface of DNA.
Ovchinnikov V, Karplus M. Analysis and Elimination of a Bias in Targeted Molecular Dynamics Simulations of Conformational Transitions: Application to Calmodulin. J. Phys. Chem. B. 2012;116(29):8584-8603.Abstract
The popular targeted mol. dynamics (TMD) method for generating transition paths in complex biomol. systems is revisited. In a typical TMD transition path, the large-​scale changes occur early and the small-​scale changes tend to occur later. As a result, the order of events in the computed paths depends on the direction in which the simulations are performed. To identify the origin of this bias, and to propose a method in which the bias is absent, variants of TMD in the restraint formulation are introduced and applied to the complex open ↔ closed transition in the protein calmodulin. Due to the global best-​fit rotation that is typically part of the TMD method, the simulated system is guided implicitly along the lowest-​frequency normal modes, until the large spatial scales assocd. with these modes are near the target conformation. The remaining portion of the transition is described progressively by higher-​frequency modes, which correspond to smaller-​scale rearrangements. A straightforward modification of TMD that avoids the global best-​fit rotation is the locally restrained TMD (LRTMD) method, in which the biasing potential is constructed from a no. of TMD potentials, each acting on a small connected portion of the protein sequence. With a uniform distribution of these elements, transition paths that lack the length-​scale bias are obtained. Trajectories generated by steered MD in dihedral angle space (DSMD)​, a method that avoids best-​fit rotations altogether, also lack the length-​scale bias. To examine the importance of the paths generated by TMD, LRTMD, and DSMD in the actual transition, we use the finite-​temp. string method to compute the free energy profile assocd. with a transition tube around a path generated by each algorithm. The free energy barriers assocd. with the paths are comparable, suggesting that transitions can occur along each route with similar probabilities. This result indicates that a broad ensemble of paths needs to be calcd. to obtain a full description of conformational changes in biomols. The breadth of the contributing ensemble suggests that energetic barriers for conformational transitions in proteins are offset by entropic contributions that arise from a large no. of possible paths.
Karthikeyan G, Zambaldo C, Barluenga S, Zoete V, Karplus M, Winssinger N. Asymmetric Synthesis of Pochonin E and F, Revision of Their Proposed Structure, and Their Conversion to Potent Hsp90 Inhibitors. Chemistry - A European Journal. 2012;18(29):8978-8986.Abstract
A concise and modular synthesis of pochonin E and F, and their epimers at C-​6 established the correct stereochem. of these two natural products to be (6R)​. Several members of the pochonin family have been shown to bind the heat shock protein 90 (Hsp90)​, which has been the focus of intense drug discovery efforts. Pochonin E and F as well as their epimers were derivatized into the corresponding pochoximes and further modified at the C-​6 position. Mol. dynamics simulations, docking studies, and Hsp90 affinity measurements were performed to evaluate the impact of these modifications.
Crenshaw CM, Nam K, Oo K, Kutchukian PS, Bowman BR, Karplus M, Verdine GL. Enforced Presentation of an Extrahelical Guanine to the Lesion Recognition Pocket of Human 8-​Oxoguanine Glycosylase, hOGG1. Journal of Biological Chemistry. 2012;287(30):24916-24928.Abstract
A poorly understood aspect of DNA repair proteins is their ability to identify exceedingly rare sites of damage embedded in a large excess of nearly identical undamaged DNA, while catalyzing repair only at the damaged sites. Progress toward understanding this problem has been made by comparing the structures and biochem. behavior of these enzymes when they are presented with either a target lesion or a corresponding undamaged nucleobase. Trapping and analyzing such DNA-​protein complexes is particularly difficult in the case of base extrusion DNA repair proteins because of the complexity of the repair reaction, which involves extrusion of the target base from DNA followed by its insertion into the active site where glycosidic bond cleavage is catalyzed. Here we report the structure of a human 8-​oxoguanine (oxoG) DNA glycosylase, hOGG1, in which a normal guanine from DNA has been forcibly inserted into the enzyme active site. Although the interactions of the nucleobase with the active site are only subtly different for G vs. oxoG, hOGG1 fails to catalyze excision of the normal nucleobase. This study demonstrates that even if hOGG1 mistakenly inserts a normal base into its active site, the enzyme can still reject it on the basis of catalytic incompatibility.
Ovchinnikov V, Karplus M, Vanden-Eijnden E. Free energy of conformational transition paths in biomolecules: The string method and its application to myosin VI. J. Chem. Phys. 2011;134(8):085103/1-085103/25.Abstract
A set of techniques developed under the umbrella of the string method is used in combination with all-​atom mol. dynamics simulations to analyze the conformation change between the prepowerstroke (PPS) and rigor (R) structures of the converter domain of myosin VI. The challenges specific to the application of these techniques to such a large and complex biomol. are addressed in detail. These challenges include (i) identifying a proper set of collective variables to apply the string method, (ii) finding a suitable initial string, (iii) obtaining converged profiles of the free energy along the transition path, (iv) validating and interpreting the free energy profiles, and (v) computing the mean first passage time of the transition. A detailed description of the PPS↔R transition in the converter domain of myosin VI is obtained, including the transition path, the free energy along the path, and the rates of interconversion. The methodol. developed here is expected to be useful more generally in studies of conformational transitions in complex biomols. (c) 2011 American Institute of Physics.
Fischer S, Olsen KW, Nam K, Karplus M. Unsuspected pathway of the allosteric transition in hemoglobin. Proceedings of the National Academy of Sciences of the United States of America. 2011;108(14):5608-5613.Abstract
Large conformational transitions play an essential role in the function of many proteins, but expts. do not provide the at. details of the path followed in going from one end structure to the other. For the Hb tetramer, the transition path between the unliganded (T) and tetraoxygenated (R) structures is not known, which limits our understanding of the cooperative mechanism in this classic allosteric system, where both tertiary and quaternary changes are involved. The conjugate peak refinement algorithm is used to compute an unbiased min. energy path at at. detail between the two end states. Although the results confirm some of the proposals of Perutz, the subunit motions do not follow the textbook description of a simple rotation of one αβ-​dimer relative to the other. Instead, the path consists of two sequential quaternary rotations, each involving different subdomains and axes. The quaternary transitions are preceded and followed by phases of tertiary structural changes. The results explain the recent photodissocn. measurements, which suggest that the quaternary transition has a fast (2 μs) as well as a slow (20 μs) component and provide a testable model for single mol. FRET expts.
Luo G-B, Karplus M. Determining the Conformational Change that Accompanies Donor-​Acceptor Distance Fluctuations: An Umbrella Sampling Analysis. J. Phys. Chem. B. 2011;115(24):7991-7995.Abstract
The response of a protein to variation of a specific coordinate can provide insights into the role of the overall architecture in the structural change. Given that the calcd. potential of mean force governing the fluctuation of an electron transfer donor-​acceptor distance in the NAD(P)​H:flavin oxidoreductase (Fre)​/FAD complex was shown to agree with expt., an anal. of the structural response of the rest of the protein to that distance change was made. Significant displacements are found throughout much of the protein, and the coupling pathway resulting in the structural changes was detd. A covariance anal. based on the quasiharmonic modes of the unperturbed protein was used to provide information concerning how the residue motions are correlated. It is found that of the three regions identified as moving together in an NMR study, two undergo significant structural changes when the electron donor-​acceptor distance is varied, and the third does not.
Karplus M. Behind the folding funnel diagram. Nature Chemical Biology. 2011;7(7):401-404.Abstract
A review. This Commentary clarifies the meaning of the funnel diagram, which has been widely cited in papers on protein folding. To aid in the anal. of the funnel diagram, this Commentary reviews historical approaches to understanding the mechanism of protein folding. The primary role of free energy in protein folding is discussed, and it is pointed out that the increase in the configurational entropy as the native state is approached hinders folding, rather than guiding it. Diagrams are introduced that provide a less ambiguous representation of the factors governing the protein folding reaction than the funnel diagram.
Zheng G, Niklasson AMN, Karplus M. Lagrangian formulation with dissipation of Born-​Oppenheimer molecular dynamics using the density-​functional tight-​binding method. J. Chem. Phys. 2011;135(4):044122/1-044122/17.Abstract
An important element detg. the time requirements of Born-​Oppenheimer mol. dynamics (BOMD) is the convergence rate of the self-​consistent soln. of Roothaan equations (SCF)​. We show here that improved convergence and dynamics stability can be achieved by use of a Lagrangian formalism of BOMD with dissipation (DXL-​BOMD)​. In the DXL-​BOMD algorithm, an auxiliary electronic variable (e.g., the electron d. or Fock matrix) is propagated and a dissipative force is added in the propagation to maintain the stability of the dynamics. Implementation of the approach in the self-​consistent charge d. functional tight-​binding method makes possible simulations that are several hundred picoseconds in lengths, in contrast to earlier DFT-​based BOMD calcns., which have been limited to tens of picoseconds or less. The increase in the simulation time results in a more meaningful evaluation of the DXL-​BOMD method. A comparison is made of the no. of iterations (and time) required for convergence of the SCF with DXL-​BOMD and a std. method (starting with a zero charge guess for all atoms at each step)​, which gives accurate propagation with reasonable SCF convergence criteria. From tests using NVE simulations of C2F4 and 20 neutral amino acid mols. in the gas phase, it is found that DXL-​BOMD can improve SCF convergence by up to a factor of two over the std. method. Corresponding results are obtained in simulations of 32 water mols. in a periodic box. Linear response theory is used to analyze the relationship between the energy drift and the correlation of geometry propagation errors.
Ovchinnikov V, Cecchini M, Vanden-Eijnden E, Karplus M. A Conformational Transition in the Myosin VI Converter Contributes to the Variable Step Size. Biophysical Journal. 2011;101(10):2436-2444.Abstract
Myosin VI (MVI) is a dimeric mol. motor that translocates backwards on actin filaments with a surprisingly large and variable step size, given its short lever arm. A recent x-​ray structure of MVI indicates that the large step size can be explained in part by a novel conformation of the converter subdomain in the prepowerstroke state, in which a 53-​residue insert, unique to MVI, reorients the lever arm nearly parallel to the actin filament. To det. whether the existence of the novel converter conformation could contribute to the step-​size variability, we used a path-​based free-​energy simulation tool, the string method, to show that there is a small free-​energy difference between the novel converter conformation and the conventional conformation found in other myosins. This result suggests that MVI can bind to actin with the converter in either conformation. Models of MVI​/MV chimeric dimers show that the variability in the tilting angle of the lever arm that results from the two converter conformations can lead to step-​size variations of ∼12 nm. These variations, in combination with other proposed mechanisms, could explain the exptl. detd. step-​size variability of ∼25 nm for wild-​type MVI. Mutations to test the findings by expt. are suggested.
Qi Y, Spong MC, Nam K, Karplus M, Verdine GL. Entrapment and Structure of an Extrahelical Guanine Attempting to Enter the Active Site of a Bacterial DNA Glycosylase, MutM. Journal of Biological Chemistry. 2010;285(2):1468-1478.Abstract
MutM, a bacterial DNA glycosylase, protects genome integrity by catalyzing glycosidic bond cleavage of 8-​oxoguanine (oxoG) lesions, thereby initiating base excision DNA repair. The process of searching for and locating oxoG lesions is esp. challenging, because of the close structural resemblance of oxoG to its million-​fold more abundant progenitor, G. Extrusion of the target nucleobase from the DNA double helix to an extrahelical position is an essential step in lesion recognition and catalysis by MutM. Although the interactions between the extruded oxoG and the active site of MutM have been well characterized, little is known in structural detail regarding the interrogation of extruded normal DNA bases by MutM. Here we report the capture and structural elucidation of a complex in which MutM is attempting to present an undamaged G to its active site. The structure of this MutM-​extrahelical G complex provides insights into the mechanism MutM employs to discriminate against extrahelical normal DNA bases and into the base extrusion process in general.
Golosov AA, Warren JJ, Beese LS, Karplus M. The Mechanism of the Translocation Step in DNA Replication by DNA Polymerase I: A Computer Simulation Analysis. Structure. 2010;18(1):83-93.Abstract
High-​fidelity DNA polymerases copy DNA rapidly and accurately by adding correct deoxynucleotide triphosphates to a growing primer strand of DNA. Following nucleotide incorporation, a series of conformational changes translocate the DNA substrate by one base pair step, readying the polymerase for the next round of incorporation. Mol. dynamics simulations indicate that the translocation consists globally of a polymerase fingers-​opening transition, followed by the DNA displacement and the insertion of the template base into the preinsertion site. They also show that the pyrophosphate release facilitates the opening transition and that the universally conserved Y714 plays a key role in coupling polymerase opening to DNA translocation. The transition involves several metastable intermediates in one of which the O helix is bent in the vicinity of G711. Completion of the translocation appears to require a gating motion of the O1 helix, perhaps facilitated by the presence of G715. These roles are consistent with the high level of conservation of Y714 and the two glycine residues at these positions. It is likely that a corresponding mechanism is applicable to other polymerases.
Ovchinnikov V, Trout BL, Karplus M. Mechanical Coupling in Myosin V: A Simulation Study. Journal of Molecular Biology. 2010;395(4):815-833.Abstract
Myosin motor function depends on the interaction between different domains that transmit information from one part of the mol. to another. The interdomain coupling in myosin V is studied with restrained targeted mol. dynamics (MD) using an all-​atom representation in explicit solvent. To elucidate the origin of the conformational change due to the binding of ATP, targeting forces are applied to small sets of atoms (the forcing sets, FSs) in the direction of their displacement from the rigor conformation, which has a closed actin-​binding cleft, to the post-​rigor conformation, in which the cleft is open. The "minimal" FS that results in extensive structural changes in the overall myosin conformation is composed of ATP, switch 1, and the nearby HF, HG, and HH helixes. Addn. of switch 2 to the FS is required to achieve a complete opening of the actin-​binding cleft. The restrained targeted mol. dynamics simulations reveal the mech. coupling pathways between (i) the nucleotide-​binding pocket (NBP) and the actin-​binding cleft, (ii) the NBP and the converter, and (iii) the actin-​binding cleft and the converter. Closing of the NBP due to ATP binding is tightly coupled to the opening of the cleft and leads to the rupture of a key hydrogen bond (F441N​/A684O) between switch 2 and the SH1 helix. The actin-​binding cleft may mediate the rupture of this bond via a connection between the HW helix, the relay helix, and switch 2. The findings are consistent with exptl. studies and a recent normal mode anal. The present method is expected to be useful more generally in studies of interdomain coupling in proteins.
Karplus M. Dynamical aspects of molecular recognition. Journal of Molecular Recognition. 2010;23(2):102-104.
Grinthal A, Adamovic I, Weiner B, Karplus M, Kleckner N. PR65, the HEAT-​repeat scaffold of phosphatase PP2A, is an elastic connector that links force and catalysis. Proceedings of the National Academy of Sciences of the United States of America. 2010;107(6):2467-2472.Abstract
PR65 is the two-​layered (α-​α solenoid) HEAT-​repeat scaffold of protein phosphatase PP2A. Mol. dynamics (MD) simulations predict that at forces expected in living systems, PR65 undergoes (visco-​)​elastic deformations in response to pulling​/pushing on its ends. At lower forces, smooth global flexural and torsional changes occur via even redistribution of stress along the hydrophobic core of the mol. At intermediate forces, helix-​helix sepn. along one layer ("fracturing") leads to global relaxation plus loss of contact in the other layer to unstack the affected units. Fracture sites are detd. by unusual sequences in contiguous interhelix turns. Normal mode anal. of the heterotrimeric PP2A enzyme reveals that its ambient conformational fluctuations are dominated by elastic deformations of PR65, which introduce a mech. linkage between the sep. bound regulatory and catalytic subunits. PR65-​dominated fluctuations of PP2A have the effect of opening and closing the enzyme's substrate binding​/catalysis interface, as well as altering the positions of certain catalytic residues. These results suggest that substrate binding​/catalysis are sensitive to mech. force. Force could be imposed from the outside (e.g., in PP2A's response to spindle tension) or arise spontaneously (e.g., in PP2A's interaction with unstructured proteins such as Tau, a microtubule-​assocd. Alzheimer's-​implicated protein)​. The present example supports the view that conformation and function of protein complexes can be modulated by mech. energy inputs, as well as by chem. energy inputs from ligand binding. Given that helical-​repeat proteins are involved in many cellular processes, the findings also encourage the view that mech. forces may be of widespread importance.
Cecchini M, Alexeev Y, Karplus M. Pi release from myosin: A simulation analysis of possible pathways. Structure. 2010;18(4):458-470.Abstract
The release of inorg. phosphate (Pi) is an important element in actomyosin function and has been shown to be accelerated by the binding of myosin to actin. To provide information about the structural elements important for Pi release, possible escape pathways from various isolated myosin II structures were detd. by mol. dynamics simulations designed for studying such slow processes. The residues forming the pathways were identified and their role was evaluated by mutant simulations. Pi release was slow in the pre-​powerstroke structure, an important element in preventing the powerstroke prior to actin binding, and was much more rapid for Pi modeled into the post-​rigor and rigor-​like structures. The previously proposed backdoor route was dominant in the pre-​powerstroke and post-​rigor states, whereas a different path was most important in the rigor-​like state. This finding suggested a mechanism for the actin-​activated acceleration of Pi release.