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

An improved structural characterisation of reduced French bean plastocyanin based on NMR data and local-elevation molecular dynamics simulation

Deriving structural information about a protein from NMR experimental data is still a non-trivial challenge to computational biochemistry. This is because of the low ratio of the number of independent observables to the number of molecular degrees of freedom, the approximations involved in the different relationships between particular observable quantities and molecular conformation, and the averaged character of the experimental data. For example, protein 3 J-coupling data are seldom used for structure refinement because of the multiple-valuedness and limited accuracy of the Karplus relationship linking a 3 J-coupling to a torsional angle. Moreover, sampling of the large conformational space is still problematic. Using the 99-residue protein plastocyanin as an example we investigated whether use of a thermodynamically calibrated force field, inclusion of solvent degrees of freedom, and application of adaptive local-elevation sampling that accounts for conformational averaging produces a more realistic representation of the ensemble of protein conformations than standard single-structure refinement in a non-explicit solvent using restraints that do not account for averaging and are partly based on non-observed data. Yielding better agreement with observed experimental data, the protein conformational ensemble is less restricted than when using standard single-structure refinement techniques, which are likely to yield a picture of the protein which is too rigi

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

Solvating atomic level fine-grained proteins in supra-molecular level coarse-grained water for molecular dynamics simulations

Simulation of the dynamics of a protein in aqueous solution using an atomic model for both the protein and the many water molecules is still computationally extremely demanding considering the time scale of protein motions. The use of supra-atomic or supra-molecular coarse-grained (CG) models may enhance the computational efficiency, but inevitably at the cost of reduced accuracy. Coarse-graining solvent degrees of freedom is likely to yield a favourable balance between reduced accuracy and enhanced computational speed. Here, the use of a supra-molecular coarse-grained water model that largely preserves the thermodynamic and dielectric properties of atomic level fine-grained (FG) water in molecular dynamics simulations of an atomic model for four proteins is investigated. The results of using an FG, a CG, an implicit, or a vacuum solvent environment of the four proteins are compared, and for hen egg-white lysozyme a comparison to NMR data is made. The mixed-grained simulations do not show large differences compared to the FG atomic level simulations, apart from an increased tendency to form hydrogen bonds between long side chains, which is due to the reduced ability of the supra-molecular CG beads that represent five FG water molecules to make solvent-protein hydrogen bonds. But, the mixed-grained simulations are at least an order of magnitude faster than the atomic level one

On using time-averaging restraints in molecular dynamics simulation

Introducing experimental values as restraints into molecular dynamics (MD) simulations to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, 3J coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. To account for the averaging of experimentally derived quantities inherent in the experimental techniques, time-averaging restraining methods may be used. In the case of structure refinement using 3J coupling constants from NMR experiments, time-averaging methods previously proposed can suffer from large artificially induced structural fluctuations. A modified time-averaged restraining potential energy function is proposed which overcomes this problem. The different possible approaches are compared using stochastic dynamics simulations of antamanide, a cyclic peptide of ten residue

Structure of hen egg-white lysozyme solvated in TFE/water: a molecular dynamics simulation study based on NMR data

Various experimental studies of hen egg white lysozyme (HEWL) in water and TFE/water clearly indicate structural differences between the native state and TFE state of HEWL, e.g. the helical content of the protein in the TFE state is much higher than in the native state. However, the available detailed NMR studies were not sufficient to determine fully a structure of HEWL in the TFE state. Different molecular dynamics (MD) simulations, i.e. at room temperature, at increased temperature and using proton-proton distance restraints derived from NMR NOE data, have been used to generate configurational ensembles corresponding to the TFE state of HEWL. The configurational ensemble obtained at room temperature using atom-atom distance restraints measured for HEWL in TFE/water solution satisfies the experimental data and has the lowest protein energy. In this ensemble residues 50-58, which are part of the β-sheet in native HEWL, adopt fluctuating α-helical secondary structur

Biomolecular structure refinement based on adaptive restraints using local-elevation simulation

Introducing experimental values as restraints into molecular dynamics (MD) simulation to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, dipolar couplings, 3 J-coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. Because multiple torsion angle values ϕ correspond to the same 3 J-coupling constant and high-energy barriers are separating those, restraining 3 J-coupling constants remains difficult. A method to adaptively enforce restraints using a local elevation (LE) potential energy function is presented and applied to 3 J-coupling constant restraining in an MD simulation of hen egg-white lysozyme (HEWL). The method succesfully enhances sampling of the restrained torsion angles until the 37 experimental 3 J-coupling constant values are reached, thereby also improving the agreement with the 1,630 experimental NOE atom-atom distance upper bounds. Afterwards the torsional angles ϕ are kept restrained by the built-up local-elevation potential energie

Quantitative Protein Dynamics from Dominant Folding Pathways

We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem are removed and simulating the entire reaction in atomistic details using existing computers becomes feasible. In addition, this formalism provides a natural framework to investigate the relationships between thermodynamical and kinetic aspects of the folding. For example, it is possible to show that, in order to have a large probability to remain unchanged under Langevin diffusion, the native state has to be characterized by a small conformational entropy. We discuss how to determine the most probable folding pathway, to identify configurations representative of the transition state and to compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine di-peptide, within an all-atom model based on the empiric GROMOS96 force field.Comment: 4 pages, 1 figur

Calculation of NMR-relaxation parameters for flexible molecules from molecular dynamics simulations

Comparatively small molecules such as peptides can show a high internal mobility with transitions between several conformational minima and sometimes coupling between rotational and internal degrees of freedom. In those cases the interpretation of NMR relaxation data is difficult and the use of standard methods for structure determination is questionable. On the other hand, in the case of those system sizes, the timescale of both rotational and internal motions is accessible by molecular dynamics (MD) simulations using explicit solvent. Thus a comparison of distance averages (〈r −6〉−1/6 or 〈r −3〉1/3) over the MD trajectory with NOE (or ROE) derived distances is no longer necessary, the (back)calculation of the complete spectra becomes possible. In the present study we use two 200ns trajectories of a heptapeptide of β-amino acids in methanol at two different temperatures to obtain theoretical ROESY spectra by calculating the exact spectral densities for the interproton vectors and the full relaxation matrix. Those data are then compared with the experimental ones. This analysis permits to test some of the assumptions and approximations that generally have to be made to interpret NMR spectra, and to make a more reliable prediction of the conformational equilibrium that leads to the experimental spectru