On the dependence of molecular conformation on the type of solvent environment: a molecular dynamics study of cyclosporin A

The dependence of the conformation of cyclosporin A (CPA), a cyclic undecapeptide with potent immunosuppressive activity, on the type of solvent environment is examined using the computer simulation method of molecular dynamics (MD). Conformational and dynamic properties of CPA in aqueous solution are obtained from MD simulations of a CPA molecule dissolved in a box with water molecules. Corresponding properties of CPA in apolar solution are obtained from MD simulations of CPA in a box with carbontetrachloride. The results of these simulations in H2O and in CCl4 are compared to each other and to those of previous simulations of crystalline CPA and of an isolated CPA molecule. The conformation of the backbone of the cyclic polypeptide is basically independent of the type of solvent. In aqueous solution the beta-pleated sheet is slightly weaker and the gamma-turn is a bit less pronounced than in apolar solution. Side chains may adopt different conformations in different solvents. In apolar solution the hydrophobic side chain of the MeBmt residue is in an extended conformation with its hydroxyl group hydrogen bonded to the backbone carbonyl group. In aqueous solution this hydrophobic side chain folds over the core of the molecule and the mentioned hydrogen bond is broken in favor of hydrogen bonding to water molecules. The conformation obtained from the MD simulation in CCl4 nicely agrees with experimental atom-atom distance data as obtained from nmr experiments in chloroform. In aqueous solution the relaxation of atomic motion tends to be slower than in apolar solution.     

Solvent reorganization contribution to the transfer thermodynamics of small nonpolar molecules.

The experimental thermodynamic data for the dissolution of five simple hydrocarbon molecules in water were combined with the solute-solvent interaction energy from a computer simulation study to yield data on the enthalpy change of solvent reorganization. Similar data were generated for dissolving these same solute molecules in their respective neat solvents using the equilibrium vapor pressure and the heat of vaporization data for the pure liquid. The enthalpy and the free energy changes upon cavity formation were also estimated using the temperature dependence of the solute-solvent interaction energy. Both the enthalpy and T delta S for cavity formation rapidly increase with temperature in both solvent types, and the free energy of cavity formation can be reproduced accurately by the scaled particle theory over the entire temperature range in all cases. These results indicate that the characteristic structure formation around an inert solute molecule in water produces compensating changes in enthalpy and entropy, and that the hydrophobicity arises mainly from the difference in the excluded volume effect.     

Hybrid approaches to molecular simulation

Molecular dynamics (MD) simulation is an established method for studying the conformational changes that are important for protein function. Recent advances in hardware and software have allowed MD simulations over the same timescales as experiment, improving the agreement between theory and experiment to a large extent. However, running such simulations are costly, in terms of resources, storage, and trajectory analysis. There is still a place for techniques that involve short MD simulations. In order to overcome the sampling paucity of short time-scales, hybrid methods that include some form of MD simulation can exploit certain features of the system of interest, often combining experimental information in surprising ways. Here, we review some recent hybrid approaches to the simulation of proteins.     

Combined monte carlo and molecular dynamics simulation of fully hydrated dioleyl and palmitoyl-oleyl phosphatidylcholine lipid bilayers

We have applied a new equilibration procedure for the atomic level simulation of a hydrated lipid bilayer to hydrated bilayers of dioleyl-phosphatidylcholine (DOPC) and palmitoyl-oleyl phosphatidylcholine (POPC). The procedure consists of alternating molecular dynamics trajectory calculations in a constant surface tension and temperature ensemble with configurational bias Monte Carlo moves to different regions of the configuration space of the bilayer in a constant volume and temperature ensemble. The procedure is applied to bilayers of 128 molecules of POPC with 4628 water molecules, and 128 molecules of DOPC with 4825 water molecules. Progress toward equilibration is almost three times as fast in central processing unit (CPU) time compared with a purely molecular dynamics (MD) simulation. Equilibration is complete, as judged by the lack of energy drift in 200-ps runs of continuous MD. After the equilibrium state was reached, as determined by agreement between the simulation volume per lipid molecule with experiment, continuous MD was run in an ensemble in which the lateral area was restrained to fluctuate about a mean value and a pressure of 1 atm applied normal to the bilayer surface. Three separate continuous MD runs, 200 ps in duration each, separated by 10,000 CBMC steps, were carried out for each system. Properties of the systems were calculated and averaged over the three separate runs. Results of the simulations are presented and compared with experimental data and with other recent simulations of POPC and DOPC. Analysis of the hydration environment in the headgroups supports a mechanism by which unsaturation contributes to reduced transition temperatures. In this view, the relatively horizontal orientation of the unsaturated bond increases the area per lipid, resulting in increased water penetration between the headgroups. As a result the headgroup-headgroup interactions are attenuated and shielded, and this contributes to the lowered transition temperature.     

Finite-size effects of Kirkwood–Buff integrals from molecular simulations

The modelling of thermodynamic properties of liquids from local density fluctuations is relevant to many chemical and biological processes. The Kirkwood–Buff (KB) theory connects the microscopic structure of isotropic liquids with macroscopic properties such as partial derivatives of activity coefficients, partial molar volumes and compressibilities. Originally, KB integrals were formulated for open and infinite systems which are difficult to access with standard Molecular Dynamics (MD) simulations. Recently, KB integrals for finite and open systems were formulated (J Phys Chem Lett. 2013;4:235). From the scaling of KB integrals for finite subvolumes, embedded in larger reservoirs, with the inverse of the size of these subvolumes, estimates for KB integrals in the thermodynamic limit are obtained. Two system size effects are observed in MD simulations: (1) effects due to the size of the simulation box and the size of the finite subvolume embedded in the simulation box, and (2) effects due to computing radial distribution functions (RDF) from a closed and finite system. In this study, we investigate the two effects in detail by computing KB integrals using the following methods: (1) Monte Carlo simulations of finite subvolumes of a liquid with an analytic RDF and (2) MD simulations of a WCA mixture for various simulation box sizes, but at the same thermodynamic state. We investigate the effect of the size of the simulation box and quantify the differences compared to KB integrals computed in the thermodynamic limit. We demonstrate that calculations of KB integrals should not be extended beyond half the size of the simulation box. For finite-size effects related to the RDF, we find that the Van der Vegt correction (J Chem Theory Comput. 2013;9:1347) yields the most accurate results.     

Description of hydration free energy density as a function of molecular physical properties

A method to calculate the solvation free energy density (SFED) at any point in the cavity surface or solvent volume surrounding a solute is proposed. In the special case in which the solvent is water, the SFED is referred to as the hydration free energy density (HFED). The HFED is described as a function of some physical properties of the molecules. These properties are represented by simple basis functions. The hydration free energy of a solute was obtained by integrating the HFED over the solvent volume surrounding the solute, using a grid model. Of 34 basis functions that were introduced to describe the HFED, only six contribute significantly to the HFED. These functions are representations of the surface area and volume of the solute, of the polarization and dispersion of the solute, and of two types of electrostatic interactions between the solute and its environment. The HFED is described as a linear combination of these basis functions, evaluated by summing the interaction energy between each atom of the solute with a grid point in the solvent, where each grid point is a representation of a finite volume of the solvent. The linear combination coefficients were determined by minimizing the error between the calculated and experimental hydration free energies of 81 neutral organic molecules that have a variety of functional groups. The calculated hydration free energies agree well with the experimental results. The hydration free energy of any other solute molecule can then be calculated by summing the product of the linear combination coefficients and the basis functions for the solute.     

Mass-weighted molecular dynamics simulation of cyclic polypeptides.

A modified molecular dynamics (MD) method in which atomic masses are weighted was developed previously for studying the conformational flexibility of neuroregulating tetrapeptide Phe-Met-Arg-Phe-amide (FMRF-amide). The method has now been applied to longer and constrained molecules, namely a disulfide-linked cyclic hexapeptide, c[CYFQNC], and its linear and "pseudo-cyclic" analogues. The sampling of dehedral conformational space of teh linear hexapeptide in mass-weighted MD simulations was found to be improved significantly over conventional MD simulations, as in the case of the shorter FMRF-amide molecule studied previously. In the cyclic hexapeptide, the internal constraint of the molecule due to the intramolecular disulfide bond (hence the absence of free terminals in the molecule) does not adversely affect the significant improvement of conformational sampling in mass-weighted MD simulations over normal MD simulations. The pseudo-cyclic polypeptide is identical to the linear CYFQNC molecule in amino acid sequence (i.e., side chains of the cysteine residues are reduced), but the positions of its two terminal heavy atoms were held fixed in space such that the molecule has a nearly cyclic conformation. For this molecule, the mass-weighted MD simulation generated a wide range of polypeptide backbone conformations covering the internal dihedral degrees of freedom; moreover, the physical space of the pseudo-cyclic structure was also sampled in a complete revolution of the entire molecular fragment about the two fixed termini during the simulation. These characteristics suggest that mass-weighted MD can also be an extremely useful method for conformational analyses of constrained molecules and, in particular, for modeling loops on protein surfaces.     

The captured volume of multilamellar vesicles

Characterization of classical 'hand-shaken' multilamellar lipid vesicles (MLVs) confirmed that these systems exclude solute during formation thus confounding previous captured volume measurements which typically have utilized solute as a merker of the occluded aqueous space. We used solvent rather than solute to determine the captured volume of these systems and obtained values at least twice those previously reported. We present here a captured volume and lamellarity profile of 'hand-shaken' MLVs and suggest that these parameters are dependent on the lipid concentration present during hydration.     

Principles of quantitative analysis of two-dimensional spectra of nuclear Overhauser effect in evaluation of protein and peptide conformation

To elucidate potentialities of two-dimensional homonuclear Overhauser effect (NOESY) spectra of peptides and proteins for their spatial structure determination, impact of experimental parameters and intrinsic properties of the investigated molecule on proton cross-peak volumes in NOESY spectra was analysed. Recommendations which could increase accuracy of cross-peak volume measurements were suggested. Influence of intrinsic properties of a molecule (spin-lattice relaxation times T1, correlation time tau C and surrounding protons) on the volume of cross-peak for particular protons was analyzed using a complete relaxation matrix of the (formula; see text) helix of gramicidin A. Nonselective relaxation time T1 of the protons was found to affect only slightly the results of cross-peak volumes computer simulation, whereas correlation time tau C and surrounding protons seriously influenced cross-peak volumes. Nevertheless, cross-peak volumes between NH, C alpha H and C beta H protons of a dipeptide fragment of the entire molecule could be accurately simulated using the relaxation matrix of the individual dipeptide. Thus local conformations (torsion angles phi, psi and chi 1) of amino acid residues could be deduced independently of one another and prior to the complete analysis of a molecular structure. The result can be obtained even in the presence of spin-diffusion at mixing times providing maximal volumes of cross-peaks in NOESY spectra.     

Volumetric effects of ionization of amino and carboxyl termini of alpha,omega-aminocarboxylic acids

We have determined the partial molar volumes and adiabatic compressibilities of a homologous series of six alpha,omega-aminocarboxylic acids over a broad pH range at 25 degrees C. We interpret the resulting data in terms of the changes in hydration associated with neutralization of amino and carboxyl termini. By combining our volumetric results with pH-dependent data on 1-anilinonaphthalene-8-sulfonic acid fluorescence we propose the following explanation to the long-standing observation that changes in volume and compressibility accompanying neutralization of a carboxyl group depend on the type of the solute in contrast to solute-independent changes in these parameters accompanying neutralization of an amino group. Unlike amino groups, neutralized carboxyl groups are capable of forming hydrogen-bonded structures stabilized by hydrogen bonds between the carbonyl oxygen of one solute molecule and the hydroxyl group of another molecule. Formation of such hydrogen-bonded structures causes an additional decrease in solute hydration with concomitant increases in volume and compressibility. Furthermore, solutes with large aliphatic moieties may form larger associates stabilized, in addition to intermolecular hydrogen bonds, by hydrophobic interactions which will result in further increases in volume and compressibility. In the aggregate, our results emphasize the need for further studies focused on developing an understanding of the role of electrostatic interactions in stabilizing/destabilizing proteins and protein complexes.     

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.     

Construction, MD Simulation, and Hydrodynamic Validation of an All-Atom Model of a Monoclonal IgG Antibody

At 150 kDa, antibodies of the IgG class are too large for their structure to be determined with current NMR methodologies. Because of hinge-region flexibility, it is difficult to obtain atomic-level structural information from the crystal, and questions regarding antibody structure and dynamics in solution remain unaddressed. Here we describe the construction of a model of a human IgG1 monoclonal antibody (trastuzumab) from the crystal structures of fragments. We use a combination of molecular-dynamics (MD) simulation, continuum hydrodynamics modeling, and experimental diffusion measurements to explore antibody behavior in aqueous solution. Hydrodynamic modeling provides a link between the atomic-level details of MD simulation and the size- and shape-dependent data provided by hydrodynamic measurements. Eight independent 40 ns MD trajectories were obtained with the AMBER program suite. The ensemble average of the computed transport properties over all of the MD trajectories agrees remarkably well with the value of the translational diffusion coefficient obtained with dynamic light scattering at 20°C and 27°C, and the intrinsic viscosity measured at 20°C. Therefore, our MD results likely represent a realistic sampling of the conformational space that an antibody explores in aqueous solution.     

Structural and energetic properties of canonical and oxidized telomeric complexes studied by molecular dynamics simulations

The structural and energetic properties of native and oxidized telomeric complexes were defined by means of molecular dynamic (MD) simulations. As a starting point, the experimental conformation of B-DNA d(GpTpTpApGpGpGpTpTpApGpGpG) oligomer bound to human protein telomeric repeat binding factor 1 (TRF1) was used. The influence on the stability of the telomeric complex of the presence of 8-oxoguanine (8oxoG) in the central telomeric triad (CTT) was estimated based on trajectories collected during 130 ns MD runs. The data obtained indicate that the system analyzed is highly sensitive to the presence of oxidative damage in the CTT of the B-DNA telomeric sequence. The most important changes were observed in the immediate vicinity of the 8-oxoguanine molecule. The significantly higher mobility of arginine 425 interacting directly with the oxidized guanine molecule has a large influence on the structural, dynamic and energetic properties of neighboring amino acids. Local changes observed for individual hydrogen bonded interactions localized in the major groove of B-DNA also have significant impact on the properties of hydrophobic clusters, which are the second type of force responsible for stability of the studied bio-system. All the changes reported in detail here unambiguously indicate a significant decrease in telomer binding affinity after oxidation.     

All-atom molecular dynamics simulations using orientational constraints from anisotropic NMR samples

Orientational constraints obtained from solid state NMR experiments on anisotropic samples are used here in molecular dynamics (MD) simulations for determining the structure and dynamics of several different membrane-bound molecules. The new MD technique is based on the inclusion of orientation dependent pseudo-forces in the COSMOS-NMR force field. These forces drive molecular rotations and re-orientations in the simulation, such that the motional time-averages of the tensorial NMR properties approach the experimentally measured parameters. The orientational-constraint-driven MD simulations are universally applicable to all NMR interaction tensors, such as chemical shifts, dipolar couplings and quadrupolar interactions. The strategy does not depend on the initial choice of coordinates, and is in principle suitable for any flexible molecule. To test the method on three systems of increasing complexity, we used as constraints some deuterium quadrupolar couplings from the literature on pyrene, cholesterol and an antimicrobial peptide embedded in oriented lipid bilayers. The MD simulations were able to reproduce the NMR parameters within experimental error. The alignment of the three membrane-bound molecules and some aspects of their conformation were thus derived from the NMR data, in good agreement with previous analyses. Furthermore, the new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of all three systems.     

A molecular simulation picture of DNA hydration around A- and B-DNA

Recent results from molecular dynamics (MD) simulations on hydration of DNA with respect to conformation are reviewed and compared with experimental data. MD simulations of explicit solvent around DNA can now give a detailed model of DNA that not only matches well with the experimental data but provides additional insight beyond current experimental limitations. Such simulation results are analyzed with a focus on differential hydration properties between A- and B-DNA and between C/G and A/T base pairs. The extent of hydration is determined from the number of waters in the primary shell and compared to experimental numbers from different measurements. High-resolution hydration patterns around the whole DNA are shown and correlated with the conformations. The role of ions associating with DNA is discussed with respect to changes in the hydration structure correlating with DNA conformation.     

A systematic molecular dynamics simulation study of temperature dependent bilayer structural properties

Although lipid force fields (FFs) used in molecular dynamics (MD) simulations have proved to be accurate, there has not been a systematic study on their accuracy over a range of temperatures. Motivated by the X-ray and neutron scattering measurements of common phosphatidylcholine (PC) bilayers (Ku?erka et al. BBA. 1808: 2761, 2011), the CHARMM36 (C36) FF accuracy is tested in this work with MD simulations of six common PC lipid bilayers over a wide range of temperatures. The calculated scattering form factors and deuterium order parameters from the C36 MD simulations agree well with the X-ray, neutron, and NMR experimental data. There is excellent agreement between MD simulations and experimental estimates for the surface area per lipid, bilayer thickness (D_B), hydrophobic thickness (D_C), and lipid volume (V_L). The only minor discrepancy between simulation and experiment is a measure of (D_B − D_HH) / 2 where D_HH is the distance between the maxima in the electron density profile along the bilayer normal. Additional MD simulations with pure water and heptane over a range of temperatures provide explanations of possible reasons causing the minor deviation. Overall, the C36 FF is accurate for use with liquid crystalline PC bilayers of varying chain types and over biologically relevant temperatures.     

Combining optimal control theory and molecular dynamics for protein folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the Cα atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the Cα atoms. In turn, MD simulation provides an all-atom conformation whose Cα positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the Cα atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization-MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages.     

Effects of interaction with sulphur compounds and free volume in imidazolium-based ionic liquid on desulphurisation: a molecular dynamics study

Interaction energy with sulphur compounds and free volume in imidazolium-based ionic liquid were calculated by molecular dynamics (MD) simulations to examine their effects on desulphurisation. From microstructure analysis and energy contribution calculation, it is found that an increasing fractional free volume in ionic liquid and an enhancement of interaction with solute by tuning the structure of ionic liquid or oxidising sulphur compounds are favourable for desulphurisation, which allows more efficient packing of sulphur compounds in ionic liquids and more easily extraction of sulphur compounds from fuel. The MD results are in good agreement with experimental desulphurisation performance.     

Hydrogen bonding-assisted interaction between amitriptyline hydrochloride and hemoglobin: spectroscopic and molecular dynamics studies

Herein, we have explored the interaction between amitriptyline hydrochloride (AMT) and hemoglobin (Hb), using steady-state and time-resolved fluorescence spectroscopy, UV–visible spectroscopy, and circular dichroism spectroscopy, in combination with molecular docking and molecular dynamic (MD) simulation methods. The steady-state fluorescence reveals the static quenching mechanism in the interaction system, which was further confirmed by UV–visible and time-resolved fluorescence spectroscopy. The binding constant, number of binding sites, and thermodynamic parameters viz. ΔG, ΔH, ΔS are also considered; result confirms that the binding of the AMT with Hb is a spontaneous process, involving hydrogen bonding and van der Waals interactions with a single binding site, as also confirmed by molecular docking study. Synchronous fluorescence, CD data, and MD simulation results contribute toward understanding the effect of AMT on Hb to interpret the conformational change in Hb upon binding in aqueous solution.