Simple combined explicit/implicit water model

A simple combined water model (SCW model) for the calculation of the hydration free energy is presented. In the frame of the model a solute is placed in the centre of the spherical cavity with explicit water molecules, which are considered at the atomistic level. Rigid wall potential at the boundary of the cavity restricts the moving of the explicit water molecules. Water outside the sphere is considered as the conducting continuum (implicit part of the model). Simulation is performed in the frame of the NVT ensemble (constant number of particles, volume and temperature), density of water is fixed and equal to experimental value 1 g/cm³. The energy of electrostatic interaction of atomic point charges of the explicit water molecules with conducting continuum is calculated analytically by means of the image charges method. It provides high computational efficiency of the SCW model. For the averaging of the calculated thermodynamic and structural values over microstates of the system the thermodynamic integration method is used. The possible using of SCW for the docking problem is discussed.     

Free energy surfaces of miniproteins with a betabetaalpha motif: replica exchange molecular dynamics simulation with an implicit solvation model

Designed miniproteins with a betabetaalpha motif, such as BBA5, 1FSD, and 1PSV can serve as a benchmark set to test the validity of all-atom force fields with computer simulation, because they contain all the basic structural elements in protein folding. Unfortunately, it was found that the standard all-atom force fields with the generalized Born (GB) implicit solvation model tend to produce distorted free energy surfaces for the betabetaalpha proteins, not only because energetically those proteins need to be described by more balanced weights of the alpha- and beta-strands, but also because the GB implicit solvation model suffers from overestimated salt bridge effects. In an attempt to resolve these problems, we have modified one of the standard all-atom force fields in conjunction with the GB model, such that each native state of the betabetaalpha proteins is in its free energy minimum state with reasonable energy barriers separating local minima. With this modified energy model, the free energy contour map in each protein was constructed from the replica exchange molecular dynamics REMD simulation. The resulting free energy surfaces are significantly improved in comparison with previous simulation results and consistent with general views on small protein folding behaviors with realistic topology and energetics of all three proteins.     

Partition of protein solvation into group contributions from molecular dynamics simulations

Linear response theory coupled to molecular dynamics simulations with an explicit solvent representation is used to derive fractional contributions of amino acid residues to the solvation of proteins. The new fractional methods developed here are compared with standard approaches based on empirical 1D and 3D statistical potentials, as well as with estimates obtained from the analysis of classical molecular interaction potentials. The new fractional methods, which have a clear physical basis and explicitly account for the effects due to protein structure and flexibility, provide an accurate picture of the contribution to solvation of different regions of the protein.     

Evidences for the action mechanism of angiotensin II and its analogs on Plasmodium sporozoite membranes

Malaria is an infectious disease responsible for approximately one million deaths annually. Oligopeptides such as angiotensin II (AII) and its analogs are known to have antimalarial effects against Plasmodium gallinaceum and Plasmodium falciparum. However, their mechanism of action is still not fully understood at the molecular level. In the work reported here, we investigated this issue by comparing the antimalarial activity of AII with that of (i) its diastereomer formed by only d ‐amino acids; (ii) its isomer with reversed sequence; and (iii) its analogs restricted by lactam bridges, the so‐called VC5 peptides. Data from fluorescence spectroscopy indicated that the antiplasmodial activities of both all‐D‐AII and all‐D‐VC5 were as high as those of the related peptides AII and VC5, respectively. In contrast, retro‐AII had no significant effect against P. gallinaceum. Conformational analysis by circular dichroism suggested that AII and its active analogs usually adopted a β‐turn conformation in different solutions. In the presence of membrane‐mimetic micelles, AII had also a β‐turn conformation, while retro‐AII was random. Molecular dynamics simulations demonstrated that the AII chains were slightly more bent than retro‐AII at the surface of a model membrane. At the hydrophobic membrane interior, however, the retro‐AII chain was severely coiled and rigid. AII was much more flexible and able to experience both straight and coiled conformations. We took it as an indication of the stronger ability of AII to interact with membrane headgroups and promote pore formation. Copyright © 2016 European Peptide Society and John Wiley & Sons, Ltd.     

Sampling efficiency in explicit and implicit membrane environments studied by peptide folding simulations

Efficient exploration of the conformational space of peptides embedded in biological membranes is vital to extract converged thermodynamic and kinetic data from simulation studies. Recently developed implicit membrane models promise vast increases in sampling efficiency compared to explicit membrane simulations, allowing for ab initio structure prediction and functional studies. In this study, a previously developed implicit membrane model, based on the generalized Born method, is compared to an explicit di‐palmitoyl‐phosphatidyl‐choline lipid bilayer and an octane slab membrane mimic. The complete folding process of a synthetic 16‐residue peptide is compared using these three setups. Since the comparison requires the entire folding pathway to be captured, individual simulations ranged up to 3 μs of MD. A quantitative sampling comparison using a wide range of performance metrics reveals that the implicit membrane model is at least 2 orders of magnitude more efficient than the simplest explicit setups. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Modeling of peptides and proteins in a membrane environment: I. A solvation model mimicking a lipid bilayer

A theoretical solvation model of peptides and proteins that mimics the heterogeneous membrane-water system was proposed. Our approach is based on the combined use of atomic parameters of solvation for water and hydrocarbons, which approximates the hydrated polar groups and acyl chains of lipids, respectively. This model was tested in simulations of several peptides: a nonpolar 20-mer polyleucine, a hydrophobic peptide with terminal polar groups, and a strongly amphiphilic peptide. The conformational space of the peptides in the presence of the membrane was studied by the Monte Carlo method. Unlike a polar solvent and vacuum, the membrane-like environment was shown to stabilize the α-helical conformation: low-energy structures have a helicity index of 100% in all cases. At the same time, the energetically most favorable orientations of the peptides relative to the membrane depend on their hydrophobic properties: nonpolar polyleucine is entirely immersed in the bilayer and the hydrophobic peptide with polar groups at the termini adopts a transbilayer orientation, whereas the amphiphilic peptide lies at the interface parallel to the membrane plane. The results of the simulations agree well with the available experimental data for these systems. In the following communications of this series, we plan to describe applications of the solvation model to membrane-bound proteins and peptides with biologically important functional activities.     

Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.     

Monte Carlo simulations of a protein molecule with and without hydration energy calculated by the hydration-shell model

Monte Carlo simulations of a small protein, carmbin, were carried out with and without hydration energy. The methodology presented here is characterized, as compared with the other similar simulations of proteins in solution, by two points: (1) protein conformations are treated in fixed geometry so that dihedral angles are independent variables rather than cartesian coordinates of atoms; and (2) instead of treating water molecules explicitly in the calculation, hydration energy is incorporated in the conformational energy function in the form of g _i A _i, whereA _i is the accessible surface area of an atomic groupi in a given conformation, andg _i is the free energy of hydration per unit surface area of the atomic group (i.e., hydration-shell model). Reality of this model was tested by carrying out Monte Carlo simulations for the two kinds of starting conformations, native and unfolded ones, and in the two kinds of systems,in vacuo and solution. In the simulations starting from the native conformation, the differences between the mean propertiesin vacuo and solution simulations are not very large, but their fluctuations around the mean conformation during the simulation are relatively smaller in solution thanin vacuo. On the other hand, in the simulations starting from the unfolded conformation, the molecule fluctuates much more largely in solution thanin vacuo, and the effects of taking into account the hydration energy are pronounced very much. The results suggest that the method presented in this paper is useful for the simulations of proteins in solution.     

Inclusion of solvation free energy with molecular mechanics energy: alanyl dipeptide as a test case.

A combined force field of molecular mechanics and solvation free energy is tested by carrying out energy minimization and molecular dynamics on several conformations of the alanyl dipeptide. Our results are qualitatively consistent with previous experimental and computational studies, in that the addition of solvation energy stabilizes the C5 conformation of the alanyl dipeptide relative to the C7.     

Monte Carlo Study of Structural and Thermodynamic Properties of Liquid Chloroform Using a Five Site Model

A five site potential model combining Lennard–Jones plus Coulomb potential functions has been developed for chloroform molecule. The partial charges needed for Coulombic interactions were derived using the chelpg procedure implemented in the gaussian 92 program. These calculations were performed at the MP2 level with MC-311G* basis set for Cl and 6-311G** for C and H atoms. The parameters for the Lennard–Jones potentials were optimized to reproduce experimental values for the density and enthalpy of vaporization of the pure liquid at 298 K and 1 atm. The statistical mechanics calculations were performed with the Monte Carlo method in the isothermic and isobaric (NpT) ensemble. Besides the values obtained for density, ρ, and molar enthalpy of vaporization at constant pressure, Δ H_V, for liquid chloroform, results for molar volume, V_m, molar heat capacity, C_p, isobaric thermal expansivity, α_p, and isothermal compressibility, κ_T, for this pure liquid are also in very good agreement with experimental observations. Size effects on the values of thermodynamic properties were investigated. The potential model was also tested by computing the free energy for solvating one chloroform molecule into its own liquid at 298 K using a statistical perturbation approach. The result obtained compares well with the experimental value. Site–site pair correlation functions were calculated and are in good accordance with theoretical results available in the literature. Dipole–dipole correlation functions for the present five site model were also calculated at different carbon–carbon distances. These correlations were compared to those obtained using the four site model reported in the literature. An investigation of the solvent dependence of the relative free energy for cis/trans conversion of a hypothetical solute in TIP4P water and chloroform was accomplished. The results show strong interaction of water and chloroform molecules with the gauche conformer. The value obtained for the free energy barrier for cis/trans rotation in TIP4P water is higher than that for chloroform. This result is in agreement with the continuous theory for solvation as the conformer with higher dipole moment is more favoured by the solvent with higher dieletric constant. The results also show an increase in entropy as the solute goes from the cis to the trans geometry and this result is more appreciable in the aqueous solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Application of molecular dynamics and free energy perturbation methods to metalloporphyrin-ligand systems II: CO and dioxygen binding to myoglobin.

The protein contribution to the relative binding affinity of the ligands CO and O2 toward myoglobin (Mb) has been simulated using free energy perturbation calculations. The tautomers of the His E7 residue are different for the oxymyoglobin (MbO2) and carboxymyoglobin (MbCO) systems. This was modeled by performing two-step calculations that mutate the ligand and mutate the His E7 tautomers in separate steps. Differences in hydrogen bonding to the O2 and CO ligands were incorporated into the model. The O2 complex was calculated to be 2-3 kcal/mol more stable than the corresponding CO complex when compared to the same difference in an isolated heme control. This value agrees well with the experimental value of 2.0 kcal/mol. In qualitative agreement with experiments, the Fe-C-O bond is found to be bent (theta = 159.8 degrees) with a small tilt (theta = 6.2 degrees). The contributions made by each of the 29 residues--within the 9.0-A radius of the iron atom--to the free energy difference are separated into van der Waals and electrostatic contributions; the latter contributions are dominant. Aside from the proximal histidine and the heme group, the residues having the largest difference in free energy in mutating MbO2-->MbCO are His E7, Phe CD1, Phe CD4, Val E11, and Thr E10.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

RASPA: molecular simulation software for adsorption and diffusion in flexible nanoporous materials

A new software package, RASPA, for simulating adsorption and diffusion of molecules in flexible nanoporous materials is presented. The code implements the latest state-of-the-art algorithms for molecular dynamics and Monte Carlo (MC) in various ensembles including symplectic/measure-preserving integrators, Ewald summation, configurational-bias MC, continuous fractional component MC, reactive MC and Baker's minimisation. We show example applications of RASPA in computing coexistence properties, adsorption isotherms for single and multiple components, self- and collective diffusivities, reaction systems and visualisation. The software is released under the GNU General Public License.     

The Influence of Starting Coordinates in Free Energy Simulations of Ligand Binding to Dihydrofolate Reductase

Abstract

Molecular dynamics (MD) simulation combined with free energy perturbation (FEP) methods have been used to study the key structural differences and relative free energies for the binding of 6-methyl-N5-deazapterin (N8 protonated) and the 8-substituted compound, 6,8-dimethyl-N5-deazapterin (N3 protonated), to dihydrofolate reductase (DHFR). The free energy changes have been calculated using a variety of initial X-ray coordinates derived from bacterial and vertebrate (including human) DHFRs, and both with and without the reduced cofactor nicotinamide adenine dinucleotide (NADPH) bound. Given a sufficiently long simulation time for the FEP calculations (ca. 200 ps), all structures obtained after mutating 6,8-methyl-N5-deazapterin to 6-methyl-N5-deazapterin exhibited hydrogen bond formation between a backbone carbonyl group of DHFR and H(N8) of 6-methyl-N5-deazapterin, analogous to that found in the X-ray crystal structure of N5-deazafolate(N8 protonated) bound to human DHFR. However, both simulation and experiment suggest this additional H-bonding does not greatly enhance thermodynamic stability, with experiment indicating at most a factor of 2 difference in the relative affinities of the two ligand cations for vertebrate DHFR. Moreover, a binding differential of 10 in favour of the protonated 8-substituted compound is found experimentally for bacterial DHFR. The MD/FEP calculations suggest that the relative cost of ligand desolvation may largely cancel the lowering of free energy obtained in the active site, resulting in predicted binding differences within the range indicated by the vertebrate and bacterial DHFR experiments. However, the theoretical free energy changes could not be obtained with the accuracy required for the rationalization of the observed species dependence. While sampling difficulties are known to be inherent in MD simulation methodologies, these studies with several initial coordinate sets have demonstrated the contribution of coordinate choice to this problem. The results indicate that for demanding protein-ligand binding problems such as this one, the accuracy of the method may be no better than ± 2 kcal/mol.     

Increased dithiothreitol-insensitive,type 2 angiotensin II receptors in selected brain areas of young rats

1. Angiotensin II receptors have been studied by quantitative autoradiography in selected brain areas of young (2-week-old) and adult (8-week-old) rats. 2. In young rats, angiotensin II receptors were present in brain areas which did not express receptors in the adult brain, such as thalamic nuclei, cortical areas, and the cerebellum. 3. Young rats had more angiotensin II receptors in the subfornical organ than adult rats. In the inferior olive, the number of angiotensin receptors in young animals was 10 times higher than that in adult rats. Angiotensin II binding in the inferior olive was insensitive to incubation in the presence of dithiothreitol. 4. Conversely, the number of angiotensin II receptors in the nucleus of the solitary tract was lower in young rats compared to adults. Incubation in the presence of dithiothreitol resulted in a more than 90% inhibition of angiotensin II binding in the nucleus of the solitary tract. 5. Our results indicate the presence of two types of angiotensin II receptor in brain, one sensitive (type 1) and one insensitive (type 2) to the reducing agent dithiothreitol. 6. The expression of type 2 angiotensin II receptors, insensitive to dithiothreitol, is more marked in young rats, indicating a role for this type of angiotensin receptors in brain development.     

Decreased plasma levels of nitric oxide metabolites, angiotensin II, and aldosterone in spontaneously hypertensive rats exposed to 5 mT static magnetic field

Previously, we found that whole body exposure to static magnetic fields (SMF) at 10 mT (B(max)) and 25 mT (B(max)) for 2-9 weeks suppressed and delayed blood pressure (BP) elevation in young, stroke resistant, spontaneously hypertensive rats (SHR). In this study, we investigated the interrelated antipressor effects of lower field strengths and nitric oxide (NO) metabolites (NO(x) = NO(2)(-) + NO(3)(-)) in SHR. Seven-week-old male rats were exposed to two different ranges of SMF intensity, 0.3-1.0 mT or 1.5-5.0 mT, for 12 weeks. Three experimental groups of 20 animals each were examined: (1) no exposure with intraperitoneal (ip) saline injection (sham-exposed control); (2) 1 mT SMF exposure with ip saline injection (1 mT); (3) 5 mT SMF exposure with ip saline injection (5 mT). Arterial BP, heart rate (HR), skin blood flow (SBF), plasma NO metabolites (NO(x)), and plasma catecholamine levels were monitored. SMF at 5 mT, but not 1 mT, significantly suppressed and retarded the early stage development of hypertension for several weeks, compared with the age matched, unexposed (sham exposed) control. Exposure to 5 mT resulted in reduced plasma NO(x) concentrations together with lower levels of angiotensin II and aldosterone in SHR. These results suggest that SMF may suppress and delay BP elevation via the NO pathways and hormonal regulatory systems.     

Quantum simulation for muoniated and deuterated methyl radicals in implicit water solvent: combined ab initio path integral molecular dynamics and the polarizable continuum model simulation study

We have combined ab initio path integral molecular dynamics (PIMD) simulation and the polarizable continuum model (PCM) method to efficiently incorporate solvent effects into nuclear quantum fluctuation of molecular systems. Our combined ab initio PIMD–PCM simulation was applied to muoniated and deuterated methyl radical immersed in implicit water solvent to gain information on solvent and isotope effects from one simulation run. We found that solvent effects lead to the bond elongation and a decrease in the magnitude of isotropic hyperfine coupling constants. These are consistent with the trends in conventional static calculations and experiments. In addition, the performance of cavity models (universal force field, united atom specified for Kohn–Sham and these hybrid models) and the conservation of the PIMD–PCM Hamiltonian were accessed. We confirmed that solvent effects on nuclear quantum fluctuation are efficiently computed using our combined simulation of quantum solute in implicit solvent.     

Ab initio simulation of a 57-residue protein in explicit solvent reproduces the native conformation in the lowest free-energy cluster

An enhanced conformational sampling method, multicanonical molecular dynamics (McMD), was applied to the ab intio folding of the 57-residue first repeat of human glutamyl- prolyl-tRNA synthetase (EPRS-R1) in explicit solvent. The simulation started from a fully extended structure of EPRS-R1 and did not utilize prior structural knowledge. A canonical ensemble, which is a conformational ensemble thermodynamically probable at an arbitrary temperature, was constructed by reweighting the sampled structures. Conformational clusters were obtained from the canonical ensemble at 300 K, and the largest cluster (i.e., the lowest free-energy cluster), which contained 34% of the structures in the ensemble, was characterized by the highest similarity to the NMR structure relative to all alternative clusters. This lowest free-energy cluster included native-like structures composed of two anti-parallel α-helices. The canonical ensemble at 300 K also showed that a short Gly-containing segment, which adopts an α-helix in the native structure, has a tendency to be structurally disordered. Atomic-level analyses demonstrated clearly that inter-residue hydrophobic interactions drive the helix formation of the Gly-containing segment, and that increasing the hydrophobic contacts accompanies exclusion of water molecules from the vicinity of this segment. This study has shown, for the first time, that the free-energy landscape of a structurally well-ordered protein of about 60 residues is obtainable with an all atom model in explicit water without prior structural knowledge.     

Conformational space exploration of Met- and Leu-enkephalin using the MOLS method, molecular dynamics, and Monte Carlo simulation--a comparative study

We report here a comparative study of the molecular conformational energy landscape generated using the mutually orthogonal Latin squares (MOLS) method, molecular dynamics (MD), and Monte Carlo (MC) simulation. The MOLS method, as described earlier from our laboratory, uses an experimental design technique to rapidly and exhaustively sample the low energy conformations of a molecule. MD and MC simulations have been used to perform similar tasks. In the comparison reported here, the three methods were applied to a pair of neuropeptides, namely Met- and Leu-enkephalin. A set of 1500 conformations of these enkephalins were generated using these methods with CHARMM22 force field, and the resulting samples were analyzed to determine the extent and nature of coverage of the conformational space. The results indicate that the MOLS method samples a larger number of possible conformations and identifies conformations closer to the experimental structures than the MD and MC simulations.