A conformational transition in the myosin VI converter contributes to the variable step size.

Myosin VI (MVI) is a dimeric molecular 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 determine 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 experimentally determined step-size variability of ∼25 nm for wild-type MVI. Mutations to test the findings by experiment are suggested.

CHARMM: the biomolecular simulation program.

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

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

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

Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin.

A molecular dynamics simulation of myoglobin provides the first direct demonstration that the potential energy surface of a protein is characterized by a large number of thermally accessible minima in the neighborhood of the native structure (for example, approximately 2000 minima were sampled in a 300-picosecond trajectory). This is expected to have important consequences for the interpretation of the activity of transport proteins and enzymes. Different minima correspond to changes in the relative orientation of the helices coupled with side-chain rearrangements that preserve the close packing of the protein interior. The conformational space sampled by the simulation is similar to that found in the evolutionary development of the globins. Glasslike behavior is expected at low temperatures. The minima obtained from the trajectory do not satisfy certain criteria for ultrametricity.

Effective coupling in biological electron transfer: exponential or complex distance dependence?

Calculations for a simple model electron transfer system and tuna cytochrome c demonstrate a dichotomy in the distance dependence of the effective coupling. In one regime, the effective coupling varies exponentially with distance and depends primarily on the average properties of the bridging material; in the other regime, the effective coupling has a complex distance dependence and is more sensitive to the details of the bridging material. Experiments and theory indicate that both regimes may occur in biological systems, providing a perspective on a recent controversy over the nature of the distance dependence.

Crystallographic R factor refinement by molecular dynamics.

Molecular dynamics was used to refine macromolecular structures by incorporating the difference between the observed crystallographic structure factor amplitude and that calculated from an assumed atomic model into the total energy of the system. The method has a radius of convergence that is larger than that of conventional restrained least-squares refinement. Test cases showed that the need for manual corrections during refinement of macromolecular crystal structures is reduced. In crambin, the dynamics calculation moved residues that were misplaced by more than 3 angstroms into the correct positions without human intervention.

Anatomy of a conformational change: hinged "lid" motion of the triosephosphate isomerase loop.

Triosephosphate isomerase (TIM) is used as a model system for the study of how a localized conformational change in a protein structure is produced and related to enzyme reactivity. An 11-residue loop region moves more than 7 angstroms and closes over the active site when substrate binds. The loop acts like a "lid" in that it moves rigidly and is attached by two hinges to the remainder of the protein. The nature of the motion appears to be built into the loop by conserved residues; the hinge regions, in contrast, are not conserved. Results of molecular dynamics calculations confirm the structural analysis and suggest a possible ligand-induced mechanism for loop closure.

Hidden thermodynamics of mutant proteins: a molecular dynamics analysis.

A molecular dynamics simulation method is used to determine the contributions of individual amino acid residues and solvent molecules to free energy changes in proteins. Its application to the hemoglobin interface mutant Asp G1(99) beta----Ala shows that some of the contributions to the difference in the free energy of cooperativity are as large as 60 kilocalories (kcal) per mole. Since the overall free energy change is only -5.5 kcal/mole (versus the experimental value of -3.4 kcal/mole), essential elements of the thermodynamics are hidden in the measured results. By exposing the individual contributions, the free energy simulation provides new insights into the origin of thermodynamic changes in mutant proteins and demonstrates the role of effects beyond those usually considered in structural analyses.

Transition from B to Z DNA: contribution of internal fluctuations to the configurational entropy difference.

The internal motions of the double-stranded DNA oligomer (dCdG)3 (dC, deoxycytidylate; dG, deoxyguanylate) in the B and Z forms have been calculated in the harmonic approximation. A complete vibrational analysis has been made, and the resulting normal mode frequencies have been used to evaluate the vibrational entropy of B and Z DNA. The greater flexibility of the B DNA hexamer leads to an entropic stabilization relative to the stiffer Z DNA hexamer of 22 calories per mole per kelvin at 300 K. The calculated value is of the same order as that (21 to 27 calories per mole per kelvin) obtained from nuclear magnetic resonance measurements on the methylated duplexes (m5dCdG)3 and (dCdGm5dCdGdCdG). This result demonstrates the importance of internal motions, which have been neglected in earlier studies of the transition from B to Z DNA, in the stability of different nucleic acid conformers.

Solution structure of FKBP, a rotamase enzyme and receptor for FK506 and rapamycin.

Immunophilins, when complexed to immunosuppressive ligands, appear to inhibit signal transduction pathways that result in exocytosis and transcription. The solution structure of one of these, the human FK506 and rapamycin binding protein (FKBP), has been determined by nuclear magnetic resonance (NMR). FKBP has a previously unobserved antiparallel beta-sheet folding topology that results in a novel loop crossing and produces a large cavity lined by a conserved array of aromatic residues; this cavity serves as the rotamase active site and drug-binding pocket. There are other significant structural features (such as a protruding positively charged loop and an apparently flexible loop) that may be involved in the biological activity of FKBP.

Solution of a protein crystal structure with a model obtained from NMR interproton distance restraints.

Model calculations were performed to test the possibility of solving crystal structures of proteins by Patterson search techniques with three-dimensional structures obtained from nuclear magnetic resonance (NMR) interproton distance restraints. Structures for crambin obtained from simulated NMR data were used as the test system; the root-mean-square deviations of the NMR structures from the x-ray structure were 1.5 to 2.2 A for backbone atoms and 2.0 to 2.8 A for side-chain atoms. Patterson searches were made to determine the orientation and position of the NMR structures in the unit cell. The correct solution was obtained by comparing the rotation function results of several of the NMR structures and the average structure derived from them. Conventional refinement techniques reduced the R factor from 0.43 at 4 A resolution to 0.27 at 2 A resolution without inclusion of water molecules. The partially refined structure has root-mean-square backbone and side-chain atom deviations from the x-ray structure of 0.5 and 1.3 A, respectively.

Calculation of free-energy differences by confinement simulations. Application to peptide conformers.

Conformational free-energy differences are key quantities for understanding important phenomena in molecular biology that involve large structural changes of macromolecules. In this paper, an improved version of the confinement approach, which is based on earlier developments, is used to determine the free energy of individual molecular states by progressively restraining the corresponding molecular structures to pure harmonic basins, whose absolute free energy can be computed by normal-mode analysis. The method is used to calculate the free-energy difference between two conformational states of the alanine dipeptide in vacuo, and of the beta-hairpin from protein G with an implicit solvation model. In all cases, the confinement results are in excellent agreement with the ones obtained from converged equilibrium molecular dynamics simulations, which have a much larger computational cost. The systematic and statistical errors of the results are evaluated and the origin of the errors is identified. The sensitivity of the calculated free-energy differences to structure-based definitions of the molecular states is discussed. A variant of the method, which closes the thermodynamic cycle by a quasi-harmonic rather than harmonic analysis, is introduced. The latter is proposed for possible use with explicit solvent simulations.

Allosteric communication in myosin V: from small conformational changes to large directed movements.

The rigor to post-rigor transition in myosin, a consequence of ATP binding, plays an essential role in the Lymn-Taylor functional cycle because it results in the dissociation of the actomyosin complex after the powerstroke. On the basis of the X-ray structures of myosin V, we have developed a new normal mode superposition model for the transition path between the two states. Rigid-body motions of the various subdomains and specific residues at the subdomain interfaces are key elements in the transition. The allosteric communication between the nucleotide binding site and the U50/L50 cleft is shown to result from local changes due to ATP binding, which induce large amplitude motions that are encoded in the structure of the protein. The triggering event is the change in the interaction of switch I and the P-loop, which is stabilized by ATP binding. The motion of switch I, which is a relatively rigid element of the U50 subdomain, leads directly to a partial opening of the U50/L50 cleft; the latter is expected to weaken the binding of myosin to actin. The calculated transition path demonstrates the nature of the subdomain coupling and offers an explanation for the mutual exclusion of ATP and actin binding. The mechanism of the uncoupling of the converter from the motor head, an essential part of the transition, is elucidated. The origin of the partial untwisting of the central beta-sheet in the rigor to post-rigor transition is described.

Understanding protein folding via free-energy surfaces from theory and experiment.

The ability of protein molecules to fold into their highly structured functional states is one of the most remarkable evolutionary achievements of biology. In recent years, our understanding of the way in which this complex self-assembly process takes place has increased dramatically. Much of the reason for this advance has been the development of energy surfaces (landscapes), which allow the folding reaction to be described and visualized in a meaningful manner. Analysis of these surfaces, derived from the constructive interplay between theory and experiment, has led to the development of a unified mechanism for folding and a recognition of the underlying factors that control the rates and products of the folding process.

Effective energy functions for protein structure prediction.

Protein structure prediction, fold recognition, homology modeling and design rely mainly on statistical effective energy functions. Although the theoretical foundation of such functions is not clear, their usefulness has been demonstrated in many applications. Molecular mechanics force fields, particularly when augmented by implicit solvation models, provide physical effective energy functions that are beginning to play a role in this area.

Theoretical studies of protein folding and unfolding.

The mechanism of protein folding is being investigated theoretically by the use of both simplified and all-atom models of the polypeptide chain. Lattice heteropolymer simulations of the folding process have led to proposals for the folding mechanism and for the resolution of the Levinthal paradox. Both stability and rapid folding have been shown in model studies to result from the presence of a pronounced global energy minimum corresponding to the native state. Concomitantly, molecular dynamics simulations with detailed atomic models have been used to analyze the initial stages of protein unfolding. Results concerning possible folding intermediates and the role of water in the unfolding process have been obtained. The two types of theoretical approaches are providing information essential for an understanding of the mechanism of protein folding and are useful for the design of experiments to study the mechanism in different proteins.

The fundamentals of protein folding: bringing together theory and experiment.

Experimental and theoretical studies together are providing insights into the mechanism by which proteins fold. Our present knowledge of the essential aspects of the folding reaction is outlined and some approaches, both theoretical and experimental, that are being developed to obtain a more detailed understanding of this complex process are described.

Structural details of urea binding to barnase: a molecular dynamics analysis.

BACKGROUND: The molecular mechanism of urea-induced protein unfolding has not been established. It is generally thought that denaturation results from the stabilizing interactions of urea with portions of the protein that are buried in the native state and become exposed upon unfolding of the protein. RESULTS: We have performed molecular dynamics simulations of barnase (a 110 amino acid RNase from Bacillus amyloliquefaciens) with explicit water and urea molecules at 300 K and 360 K. The native conformation was unaffected in the 300 K simulations at neutral and low pH. Two of the three runs at 360 K and low pH showed some denaturation, with partial unfolding of the hydrophobic core 2. The first solvation shell has a much higher density of urea molecules (water/urea ratio ranging from 2.07 to 2.73) than the bulk (water/urea ratio of 4.56). About one half of the first-shell urea molecules are involved in hydrogen bonds with polar or charged groups on the barnase surface, and between 15% and 18% of the first-shell urea molecules participate in multiple hydrogen bonds with barnase. The more stably bound urea molecules tend to be in crevices or pockets on the barnase surface. CONCLUSIONS: The simulation results indicate that an aqueous urea solution solvates the surface of a polypeptide chain more favorably than pure water. Urea molecules interact more favorably with nonpolar groups of the protein than water does, and the presence of urea improves the interactions of water molecules with the hydrophilic groups of the protein. The results suggest that urea denaturation involves effects on both nonpolar and polar groups of proteins.

Glycogen phosphorylase inhibitors: a free energy perturbation analysis of glucopyranose spirohydantoin analogues.

GP catalyzes the phosphorylation of glycogen to Glc-1-P. Because of its fundamental role in the metabolism of glycogen, GP has been the target for a systematic structure-assisted design of inhibitory compounds, which could be of value in the therapeutic treatment of type 2 diabetes mellitus. The most potent catalytic-site inhibitor of GP identified to date is spirohydantoin of glucopyranose (hydan). In this work, we employ MD free energy simulations to calculate the relative binding affinities for GP of hydan and two spirohydantoin analogues, methyl-hydan and n-hydan, in which a hydrogen atom is replaced by a methyl- or amino group, respectively. The results are compared with the experimental relative affinities of these ligands, estimated by kinetic measurements of the ligand inhibition constants. The calculated binding affinity for methyl-hydan (relative to hydan) is 3.75 +/- 1.4 kcal/mol, in excellent agreement with the experimental value (3.6 +/- 0.2 kcal/mol). For n-hydan, the calculated value is 1.0 +/- 1.1 kcal/mol, somewhat smaller than the experimental result (2.3 +/- 0.1 kcal/mol). A free energy decomposition analysis shows that hydan makes optimum interactions with protein residues and specific water molecules in the catalytic site. In the other two ligands, structural perturbations of the active site by the additional methyl- or amino group reduce the corresponding binding affinities. The computed binding free energies are sensitive to the preference of a specific water molecule for two well-defined positions in the catalytic site. The behavior of this water is analyzed in detail, and the free energy profile for the translocation of the water between the two positions is evaluated. The results provide insights into the role of water molecules in modulating ligand binding affinities. A comparison of the interactions between a set of ligands and their surrounding groups in X-ray structures is often used in the interpretation of binding free energy differences and in guiding the design of new ligands. For the systems in this work, such an approach fails to estimate the order of relative binding strengths, in contrast to the rigorous free energy treatment.

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

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