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A bimolecular synthetic reaction (imine synthesis) was performed compartmentalized in micrometer-diameter emulsion droplets. The apparent equilibrium constant (Keq) and apparent forward rate constant (k1) were both inversely proportional to the droplet radius. The results are explained by a noncatalytic reaction-adsorption model in which reactants adsorb to the droplet interface with relatively low binding energies of a few kBT, react and diffuse back to the bulk. Reaction thermodynamics is therefore modified by compartmentalization at the mesoscale--without confinement on the molecular scale--leading to a universal mechanism for improving unfavorable reactions.

This Commentary clarifies the meaning of the funnel diagram, which has been widely cited in papers on protein folding. To aid in the analysis 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 decrease [corrected] 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.

Large conformational transitions play an essential role in the function of many proteins, but experiments do not provide the atomic details of the path followed in going from one end structure to the other. For the hemoglobin 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 minimum energy path at atomic detail between the two end states. Although the results confirm some of the proposals of Perutz [Perutz MF (1970) Stereochemistry of cooperative effects in haemoglobin. Nature 228:726-734], 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 photodissociation 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 molecule FRET experiments.

Discrete molecular dynamics has been used to study the folding of a SH3 domain with a Calpha-based Go-model at a temperature within the native state stability region. A standard analysis of the folding process, based on consideration of the mean-force (free energy) surfaces, contact maps and folding time distributions, is complemented by a "hydrodynamic" description of folding flows (Chekmarev et al., PRL, 2008, 018107) using two and three collective variables. Two types of folding trajectories (fast and slow) follow essentially different routes in the final stage of folding. The hydrodynamic description makes possible the calculation of folding flows corresponding to these routes. The results show that the probability flows do not correspond to the free energy surface and that vortex formation is involved in the slow trajectories. Comparison of the simulation results with the experimental data suggests that the two-state kinetics observed for Fyn and Src SH3 domain folding are associated with the slow trajectories, in which a partly formed N- and C-terminal beta sheet hinders the RT-loop from attaching to the protein core; the fast trajectories are not observed because they are in the dead time (1 ms) of the experiments.

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., (Copyright 2009 Wiley Periodicals, Inc.)

Each step of the kinesin motor involves a force-generating molecular rearrangement. Although significant progress has been made in elucidating the broad features of the kinesin mechanochemical cycle, molecular details of the force generation mechanism remain a mystery. Recent molecular dynamics simulations have suggested a mechanism in which the forward drive is produced when the N-terminal cover strand forms a beta-sheet with the neck linker to yield the cover-neck bundle. We tested this proposal by comparing optical trapping motility measurements of cover strand mutants with the wild-type. Motility data, as well as kinetic analyses, revealed impairment of the force-generating capacity accompanied by a greater load dependence in the mechanochemical cycle. In particular, a mutant with the cover strand deleted functioned only marginally, despite the fact that the cover strand, the N-terminal "dangling end," unlike the neck linker and nucleotide-binding pocket, is not involved with any previously considered energy transduction pathway. Furthermore, a constant assisting load, likely in lieu of a power stroke, was shown to rescue forward motility in the cover strand deletion mutant. Our results support a stepping mechanism driven by dynamic cover-neck bundle formation. They also suggest a strategy to generate motors with altered mechanical characteristics by targeting the force-generating element.

The elastic properties (stretching and bending moduli) of myosin are expected to play an important role in its function. Of particular interest is the extended alpha-helical coiled-coil portion of the molecule. Since there is no high resolution structure for the entire coiled-coil, a study is made of the scallop myosin II S2 subdomain for which an x-ray structure is available (Protein Data Bank 1nkn). We estimate the stretching and bending moduli of the S2 subdomain with an atomic level model by use of molecular simulations. Results were obtained from nonequilibrium molecular dynamics simulations in the presence of an external force, from the fluctuations in equilibrium molecular dynamics simulations and from normal modes. In addition, a poly-Ala (78 amino acid residues) alpha-helix model was examined to test the methodology and because of its interest as part of the lever arm. As expected, both the alpha-helix and coiled-coil S2 subdomain are very stiff for stretching along the main axis, with the stretching stiffness constant in the range 60-80 pN/nm (scaled to the 60 nm long S2). Both molecules are much more flexible for bending with a lateral stiffness of approximately 0.010 pN/nm for the S2 and 0.0055 pN/nm for the alpha-helix (scaled to 60 nm). These results are expected to be useful in estimating cross-bridge elasticity, which is required for understanding the strain-dependent transitions in the actomyosin cycle and for the development of three-dimensional models of muscle contraction.

A hydrodynamic description of protein folding is proposed and illustrated with a lattice protein model, which has a free energy surface (FES) typical of proteins with two-state folding kinetics. The flows from the unfolded to the native state are concentrated in a limited region of the FES. The rest is occupied by a flow "vortex", which does not lead to the native state. In contrast with intermediates that are associated with local minima, the vortex is not visible on the FES. The hydrodynamic interpretation thus provides new insights into the mechanism of protein folding and can be a useful complement to standard analyses.

The signal-transduction mechanism of rhodopsin was studied by molecular dynamics (MD) simulations of the high-resolution, inactive structure in an explicit membrane environment. The simulations were employed to calculate equal-time correlations of the fluctuating interaction energy of residue pairs. The resulting interaction-correlation matrix was used to determine a network that couples retinal to the cytoplasmic interface, where transducin binds. Two highly conserved motifs, D(E)RY and NPxxY, were found to have strong interaction correlation with retinal. MD simulations with restraints on each transmembrane helix indicated that the major signal-transduction pathway involves the interdigitating side chains of helices VI and VII. The functional roles of specific residues were elucidated by the calculated effect of retinal isomerization from 11-cis to all-trans on the residue-residue interaction pattern. It is suggested that Glu134 may act as a "signal amplifier" and that Asp83 may introduce a threshold to prevent background noise from activating rhodopsin.

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.

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.

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.

A general method for alchemical free energy simulations using QM, MM, and QM/MM potential is developed by introducing "chaperones" to restrain the structures, particularly near the end points. A calculation of the free energy difference between two triazole tautomers in aqueous solution is used to illustrate the method., ((c) 2004 American Institute of Physics.)

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

There has recently been considerable interest in using NMR spectroscopy to identify ligand binding sites of macromolecules. In particular, a modular approach has been put forward by Fesik et al. (Shuker, S. B.; Hajduk, P. J.; Meadows, R. P.; Fesik, S. W. Science 1996, 274, 1531-1534) in which small ligands that bind to a particular target are identified in a first round of screening and subsequently linked together to form ligands of higher affinity. Similar strategies have also been proposed for in silico drug design, where the binding sites of small chemical groups are identified, and complete ligands are subsequently assembled from different groups that have favorable interactions with the macromolecular target. In this paper, we compare experimental and computational results on a selected target (FKBP12). The binding sites of three small ligands ((2S)1-acetylprolinemethylester, 1-formylpiperidine, 1-piperidinecarboxamide) in FKBP12 were identified independently by NMR and by computational methods. The subsequent comparison of the experimental and computational data showed that the computational method identified and ranked favorably ligand positions that satisfy the experimental NOE constraints.

A simple approach for the efficient exploration of the potential energy surface of a many-body system is presented. The method uses Langevin dynamics trajectories that are successively confined in the various basins of the potential energy surface. The approach is illustrated by determining the potential energy surface, and the thermodynamic and kinetic properties of a solvated model for the alanine tetrapeptide, the shortest peptide that can form an alpha-helical turn. All possible cis isomers are sampled, even though the barriers separating them are as high as 25 kcal/mole. Comparisons with conventional Langevin dynamics confirm the greater efficacy of the approach.

Calculations of the ensemble of solution conformations and thermodynamics of an analogue of the C-terminal helix of ribonuclease A (RN24) and of a synthetic, beta-hairpin forming peptide (BH8) are presented. For efficient sampling of conformation space, molecular dynamics simulations with an implicit solvent potential and umbrella sampling of the potential energy are performed. Starting from the fully extended chains, the simulations yield several folding and unfolding transitions between disordered (coil) conformations of the peptides and the "native" state (RN24, helix; BH8, hairpin); the simulations also lead to the occurrence of "misfolded" conformations (RN24, hairpin; BH8, helix). In agreement with experiment, the calculations predict 58% helix for RN24 at 275 K and an antiparallel-beta content of 38% at 275 K for BH8; the calculated probabilities for the misfolded species are 2% or smaller at all temperatures considered (250-1100 K). Good agreement is also shown between the calculated 3JHNalpha spin-spin coupling constants of RN24 and BH8 at 275 K, and those obtained from NMR experiments at the same temperature. From the calculated probabilities of helix (h), beta-hairpin (b), and coil (c), the free energy differences between the structured substates are DeltaGch=Gc-Gh approximately 1 kcal/mol and DeltaGbh>/=1.8 kcal/mol for RN24, and DeltaGcb approximately 0.7 kcal/mol and DeltaGhb>/=2.7 kcal/mol for BH8. The free energy difference between "correctly" folded and misfolded secondary structures are of interest for understanding the alpha to beta transition that is thought to play a role in amyloid fibril formation., (Copyright 1998 Academic Press)

Molecular dynamics simulations were used to study the structure and dynamics of the Escherichia coli OmpF porin, which is composed of three identical 16-stranded beta-barrels. Simulations of the full trimer in the absence of water and the membrane led to significant contraction of the channel in the interior of each beta-barrel. With very weak harmonic constraints (0.005 kcal/mol A2/atom) applied to the main-chain C alpha atoms of the beta-barrel, the structure was stabilized without alteration of the average fluctuations. The resulting distribution of the fluctuations (small for beta-strands, large for loops and turns) is in good agreement with the x-ray B factors. Dynamic cross-correlation functions showed the importance of coupling between the loop motions and barrel flexibility. This was confirmed by the application of constraints corresponding to the observed temperature factors to the barrel C alpha atoms. With these constraints, the beta-barrel fluctuations were much smaller than the experimental values because of the intrinsic restrictions on the atomic motions, and the loop motions were reduced significantly. This result indicates that considerable care is required in introducing constraints to keep proteins close to the experimental structure during simulations, as has been done in several recent studies. Loop 3, which is thought to be important in gating the pore, undergoes a displacement that shifts it away from the x-ray structure. Analysis shows that this arises from the breakdown of a hydrogen bond network, which appears to result more from the absence of solvent that from the use of standard ionization states for the side chains of certain beta-barrel residues.

A theoretical analysis is made of the decomposition into contributions from individual interactions of the free energy calculated by thermodynamic integration. It is demonstrated that such a decomposition, often referred to as "component analysis," is meaningful, even though it is a function of the integration path. Moreover, it is shown that the path dependence can be used to determine the relation of the contribution of a given interaction to the state of the system. To illustrate these conclusions, a simple transformation (Cl- to Br- in aqueous solution) is analyzed by use of the Reference Interaction Site Model-Hypernetted Chain Closure integral equation approach; it avoids the calculational difficulties of macromolecular simulation while retaining their conceptual complexity. The difference in the solvation free energy between chloride and bromide is calculated, and the contributions of the Lennard-Jones and electrostatic terms in the potential function are analyzed by the use of suitably chosen integration paths. The model is also used to examine the path dependence of individual contributions to the double free energy differences (delta delta G or delta delta A) that are often employed in free energy simulations of biological systems. The alchemical path, as contrasted with the experimental path, is shown to be appropriate for interpreting the effects of mutations on ligand binding and protein stability. The formulation is used to obtain a better understanding of the success of the Poisson-Boltzmann continuum approach for determining the solvation properties of polar and ionic systems.

The diffusion-collision model of protein folding is assessed. A description is given of the qualitative aspects and quantitative results of the diffusion-collision model and their relation to available experimental data. We consider alternative mechanisms for folding and point out their relationship to the diffusion-collision model. We show that the diffusion-collision model is supported by a growing body of experimental and theoretical evidence, and we outline future directions for developing the model and its applications.

A theoretical approach is employed to study the catalysis of the dihydroxyacetone phosphate (DHAP) to D-glyceraldehyde 3-phosphate (GAP) reaction by the enzyme triose phosphate isomerase (TIM). The conformational change in a loop involved in protecting the active site from solvent is examined by use of X-ray data and molecular dynamics simulations. A mixed quantum-mechanics and molecular mechanics potential is used to determine the energy surface along the reaction path. The calculations address the role of the enzyme in lowering the barrier to reaction and provide a decomposition into specific residue contributions. To obtain a clearer understanding of the electronic effects, the polarization of the substrate carbonyl group by the active site residues is examined and compared with FTIR measurements on the wild-type and mutant forms of the enzyme.

A macroscopic electrostatic model is used to calculate the pKa values of the titratable groups in lysozyme. The model makes use of detailed structural information and treats solvation self-energies and interactions arising from permanent partial charges and titratable charges. Both the tetragonal and triclinic crystal structures are analyzed. Half of the experimentally observed pKa shifts (11 out of 21) are well reproduced by calculations for both structures; this includes the unusually high pKa of Glu 35 in the active site. For more than half the pKa's (13 out of 21), there is a large difference (1-3.3 pK units) between the results from the two structures. Many of these correspond to the titrating groups for which the calculations are in error. Since for an ionic strength of 0.1 M the Debye screening between titratable groups leads to a very high effective dielectric constant (the average value for all pairs of titrating groups is approximately 900), near-neighbor interactions dominate the pKa perturbations. Thus, the pKa values are very sensitive to the details of the local protein conformation, and it is likely that side-chain mobility has an important role in determining the observed pKa shifts.

The binding region of immunoglobulins, which includes the portion of the molecule having the most variability in its amino acid sequence, is shown to have a surprisingly constant structure that can be characterized in terms of a simple, well-defined model. The binding region is composed of the antigen combining site plus its immediate vicinity and arises by noncovalent association of the light and heavy chain variable domains (VL and VH, respectively). The antigen combining site itself consists of six polypeptide chain segments ("hypervariable loops") which comprise some 80 amino acid residues and are attached to a framework of VL and VH beta-sheet bilayers. Having analyzed refined x-ray crystallographic coordinates for three antigen-binding fragments (Fab KOL (Marquart, M., Deisenhofer, J., and Huber, R. (1980) J. Mol. Biol. 141, 369-391), MCPC 603 (Segal, D., Padlan, E. A., Cohen, G. H., Rudikoff, S., Potter, M., and Davies, D. R. (1974) Proc. Natl. Acad. Sci. U. S. A. 71, 4298-4302), and NEW (Saul, F. A., Amzel, L. M., and Poljak, R. J. (1978) J. Biol. Chem. 253, 585-597] we use the results to introduce a general model for the VL-VH interface forming the binding region. The region consists of two closely packed beta-sheets, and its geometry corresponds to a 9-stranded, cylindrical barrel of average radius 0.84 nm with an average angle of -53 degrees between its two constituent beta-sheets. The barrel forms the bottom and sides of the antigen combining site. The model demonstrates that the structural variability of the binding region is considerably less than was thought previously. Amino acid residues which are part of the domain-domain interface and appear not to be accessible to solvent or antigen contribute to antibody specificity.