Absolute FKBP binding affinities obtained via non-equilibrium unbinding simulations

We compute absolute binding affinities for two ligands bound to the FKBP protein using non-equilibrium unbinding simulations. The methodology is straight-forward, requiring little or no modification to many modern molecular simulation packages. The approach makes use of a physical pathway, eliminating the need for complicated alchemical decoupling schemes. Results of this study are promising. For the ligands studied here the binding affinities are typically estimated within less than 4.0 kJ/mol of the target values; and the target values are within less than 1.0 kJ/mol of experiment. These results suggest that non-equilibrium simulation could provide a simple and robust means to estimate protein-ligand binding affinities.Comment: 9 pages, 3 figures (no necessary color). Changes made to methodology and results between revision

Are polar liquids less simple?

Strong correlation between equilibrium fluctuations of the potential energy, U, and the virial, W, is a characteristic of a liquid that implies the presence of certain dynamic properties, such as density scaling of the relaxation times and isochronal superpositioning of the relaxation function. In this work we employ molecular dynamics simulations (mds) on methanol and two variations, lacking hydrogen bonds and a dipole moment, to assess the connection between the correlation of U and W and these dynamic properties. We show, in accord with prior results of others [T.S. Ingebrigtsen, T.B. Schroder, J.C. Dyre, Phys. Rev. X 2, 011011 (2012).], that simple van der Waals liquids exhibit both strong correlations and the expected dynamic behavior. However, for polar liquids this correspondence breaks down - weaker correlation between U and W is not associated with worse conformance to density scaling or isochronal superpositioning. The reason for this is that strong correlation between U and W only requires their proportionality, whereas the expected dynamic behavior depends primarily on constancy of the proportionality constant for all state points. For hydrogen-bonded liquids, neither strong correlation nor adherence to the dynamic properties is observed; however, this nonconformance is not directly related to the concentration of hydrogen bonds, but rather to the greater deviation of the intermolecular potential from an inverse power law (IPL). Only (hypothetical) liquids having interactions governed strictly by an IPL are perfectly correlating and exhibit the consequent dynamic properties over all thermodynamic conditions.Comment: 14 pages, 8 figure

What stabilizes the 3_14-helix in beta^3-peptides? A conformational analysis using molecular simulation.

Beta-peptides are analogs of natural alpha-peptides and form a variety of remarkably stable structures. Having an additional carbon atom in the backbone of each residue, their folded conformation is not only influenced by the side-chain sequence but also and foremost by their substitution pattern. The precise mechanism by which the side chains interact with the backbone is, however, hitherto not completely known. In order to unravel the various effects by which the side chains influence the backbone conformation, we quantify to which extent the dihedral angles of a beta^3-substited peptide with an additional methyl group on the central C_alpha-atom can be regarded as independent degrees of freedom and analyze the distributions of these dihedral angles. We also selectively capture the steric effect of substituents on the C_alpha- and C_beta-atoms of the central residue by alchemically changing them into dummy atoms, which have no non-bonded interactions. We find that the folded state of the beta^3-peptide is primarily stabilized by a steric exclusion of large parts of the unfolded state (entropic effect) and only subsequently by mutual dependence of the psi-dihedral angles (enthalpic effect). The folded state of beta-peptides is stabilized by a different mechanism than that of alpha-peptides

Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained system arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear response function of constrained quantum-classical systems contains non-trivial additional terms which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic

Validation of the GROMOS force-field parameter set 45A3 against nuclear magnetic resonance data of hen egg lysozyme

The quality of molecular dynamics (MD) simulations of proteins depends critically on the biomolecular force field that is used. Such force fields are defined by force-field parameter sets, which are generally determined and improved through calibration of properties of small molecules against experimental or theoretical data. By application to large molecules such as proteins, a new force-field parameter set can be validated. We report two 3.5ns molecular dynamics simulations of hen egg white lysozyme in water applying the widely used GROMOS force-field parameter set 43A1 and a new set 45A3. The two MD ensembles are evaluated against NMR spectroscopic data NOE atom-atom distance bounds, 3JNH α and 3Jαβ coupling constants, and 15N relaxation data. It is shown that the two sets reproduce structural properties about equally well. The 45A3 ensemble fulfills the atom-atom distance bounds derived from NMR spectroscopy slightly less well than the 43A1 ensemble, with most of the NOE distance violations in both ensembles involving residues located in loops or flexible regions of the protein. Convergence patterns are very similar in both simulations atom-positional root-mean-square differences (RMSD) with respect to the X-ray and NMR model structures and NOE inter-proton distances converge within 1.0-1.5ns while backbone 3JHNα-coupling constants and 1H- 15N order parameters take slightly longer, 1.0-2.0ns. As expected, side-chain 3Jαβ-coupling constants and 1H- 15N order parameters do not reach full convergence for all residues in the time period simulated. This is particularly noticeable for side chains which display rare structural transitions. When comparing each simulation trajectory with an older and a newer set of experimental NOE data on lysozyme, it is found that the newer, larger, set of experimental data agrees as well with each of the simulations. In other words, the experimental data converged towards the theoretical resul

Molecular dynamics simulation of the transport of small molecules across a polymer membrane

The transport of small molecules through a polymer membrane is modeled using the computer simulation technique of molecular dynamics (MD). The transport coefficient is derived from a combination of the excess free energy and the diffusion constant. Both properties are derived from MD simulations, applied to helium and methane in polydimethylsiloxane (PDMS). The diffusional process appears to have the character of a jump diffusion for methane and less so for helium. Jumps are allowed by fluctuations of the size and shape of holes. Experimental diffusion constants are well reproduced. The excess free energies, determined by a particle insertion method, are lower by 5-7 kJ/mol than experimental values. It is shown that, as a result of a higher solubility, methane has a higher permeability constant than helium, despite its lower diffusion constant

SYMBOLIC SOLUTION OF BOUNDARY VALUE PROBLEM VIA MATHEMATICA

Symbolic computation has been applied to Runge-Kutta technique in order to solve a two-point boundary value problem. The unknown boundary values are considered as symbolic variables, therefore they will appear in a system of algebraic equations, after the integration of the ordinary differential equations. Then this algebraic equation system can be solved for the unknown initial values and substituted into the solution. Consequently, only one integration pass is enough to solve the problem instead of using an iteration technique like shooting method. This procedure is illustrated by solving the boundary value problem of the mechanical analysis of a liquid storage tank. Computations were carried out by the MATHEMATICA symbolic system

Polarizable molecular interactions in condensed phase and their equivalent nonpolarizable models

Earlier, using phenomenological approach, we showed that in some cases polarizable models of condensed phase systems can be reduced to nonpolarizable equivalent models with scaled charges. Examples of such systems include ionic liquids, TIPnP-type models of water, protein force fields, and others, where interactions and dynamics of inherently polarizable species can be accurately described by nonpolarizable models. To describe electrostatic interactions, the effective charges of simple ionic liquids are obtained by scaling the actual charges of ions by a factor of 1/sqrt(eps_el), which is due to electronic polarization screening effect; the scaling factor of neutral species is more complicated. Here, using several theoretical models, we examine how exactly the scaling factors appear in theory, and how, and under what conditions, polarizable Hamiltonians are reduced to nonpolarizable ones. These models allow one to trace the origin of the scaling factors, determine their values, and obtain important insights on the nature of polarizable interactions in condensed matter systems.Comment: 43 pages, 3 figure

The effect of force-field parameters on properties of liquids:Parametrization of a simple three-site model for methanol

A simple rigid three-site model for methanol compatible with the simple point charge (SPC) water and the GROMOS96 force field is parametrized and tested. The influence of different force-field parameters, such as the methanol geometry and the charge distribution on several properties calculated by molecular dynamics is investigated. In particular an attempt was made to obtain good agreement with experimental data for the static dielectric constant and the mixing enthalpy with water. The model is compared to other methanol models from the literature in terms of the ability to reproduce a range of experimental properties.<br/