Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

Monte Carlo simulation of protein folding in the presence of residue-specific binding sites

Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residue-specific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.     

Application of kinetic Monte Carlo method to the vapour–liquid equilibria of associating fluids and their mixtures

Canonical kinetic Monte Carlo (C-kMC) simulations have been carried out to assess their feasibility and potential for calculating the vapour–liquid equilibria of various pure components with increasingly strong electrostatic interactions (carbon dioxide, methanol, ammonia and water) over a wide range of temperatures and for methanol/water mixtures at 298 K. The simulation results show that C-kMC is successful as a method for studying phase equilibria and thermodynamic properties. For all the examples investigated, the performance of the C-kMC method is at least as good as that of the conventional Monte Carlo (MC) methods and is efficient at low temperature where these fail. It also provides a route that is superior to the Widom method for the calculation of chemical potential. We recommend this method for this purpose and as an alternative to conventional MC for simulations of strongly associating fluids and at low temperatures.     

Analysis of conjugated bile acids by packed-column supercritical fluid chromatography

A rapid method has been developed for the simultaneous separation of the polar glycine- and taurine-conjugated bile acids by packed-column supercritical fluid chromatography. Samples were analysed on a cyanopropyl-bonded silica column with ultraviolet detection at 210 nm and carbon dioxide modified with methanol as the mobile phase. The influence of the stationary phase, modifier concentration, temperature, column pressure and modifier identity on retention was also studied. This new chromatographic method is applicable to the assay of conjugated bile acids in duodenal bile samples from patients with hepatobiliary diseases.     

A simple model of the hydrophobic effect for molecular simulation of interfacial phenomena

A coarse-grained model for simulation of interfacial phenomena in aqueous systems has been developed. The model captures the hydrophobic effect by only considering the structure and cohesiveness of water. Monte Carlo (MC) simulations of water-oil mixtures show that low concentrations of oil are solvated with little perturbation of the hydrogen bonding network structure of the water, while high concentrations of oil are excluded altogether. Analysis of the water structure in the simulations indicates that the water molecules maintain close to four coordination in the presence of solutes and the distribution of bond angles is not markedly affected by the presence of solutes. MC simulations of an alkane oligomer in water and a poly(ethylene oxide) (PEO) oligomer in water indicate that the chains are quite flexible and also do not perturb the network structure of the water phase.     

Pulling-speed-dependent force-extension profiles for semiflexible chains

We present theory and simulations to describe nonequilibrium stretching of semiflexible chains that serve as models of DNA molecules. Using a self-consistent dynamical variational approach, we calculate the force-extension curves for worm-like chains as a function of the pulling speed, v(0). Due to nonequilibrium effects the stretching force, which increases with v(0), shows nonmonotonic variations as the persistence length increases. To complement the theoretical calculations we also present Langevin simulation results for extensible worm-like chain models for the dynamics of stretching. The theoretical force-extension predictions compare well with the simulation results. The simulations show that, at high enough pulling speeds, the propagation of tension along the chain conformations transverse to the applied force occurs by the Brochard-Wyart's stem-flower mechanism. The predicted nonequilibrium effects can only be observed in double-stranded DNA at large ( approximately 100 microm/s) pulling speeds.     

Ab initio computational modeling of loops in G-protein-coupled receptors: lessons from the crystal structure of rhodopsin

With the help of the crystal structure of rhodopsin an ab initio method has been developed to calculate the three-dimensional structure of the loops that connect the transmembrane helices (TMHs). The goal of this procedure is to calculate the loop structures in other G-protein coupled receptors (GPCRs) for which only model coordinates of the TMHs are available. To mimic this situation a construct of rhodopsin was used that only includes the experimental coordinates of the TMHs while the rest of the structure, including the terminal domains, has been removed. To calculate the structure of the loops a method was designed based on Monte Carlo (MC) simulations which use a temperature annealing protocol, and a scaled collective variables (SCV) technique with proper structural constraints. Because only part of the protein is used in the calculations the usual approach of modeling loops, which consists of finding a single, lowest energy conformation of the system, is abandoned because such a single structure may not be a representative member of the native ensemble. Instead, the method was designed to generate structural ensembles from which the single lowest free energy ensemble is identified as representative of the native folding of the loop. To find the native ensemble a successive series of SCV-MC simulations are carried out to allow the loops to undergo structural changes in a controlled manner. To increase the chances of finding the native funnel for the loop, some of the SCV-MC simulations are carried out at elevated temperatures. The native ensemble can be identified by an MC search starting from any conformation already in the native funnel. The hypothesis is that native structures are trapped in the conformational space because of the high-energy barriers that surround the native funnel. The existence of such ensembles is demonstrated by generating multiple copies of the loops from their crystal structures in rhodopsin and carrying out an extended SCV-MC search. For the extracellular loops e1 and e3, and the intracellular loop i1 that were used in this work, the procedure resulted in dense clusters of structures with Calpha-RMSD approximately 0.5 angstroms. To test the predictive power of the method the crystal structure of each loop was replaced by its extended conformations. For e1 and i1 the procedure identifies native clusters with Calpha-RMSD approximately 0.5 angstroms and good structural overlap of the side chains; for e3, two clusters were found with Calpha-RMSD approximately 1.1 angstroms each, but with poor overlap of the side chains. Further searching led to a single cluster with lower Calpha-RMSD but higher energy than the two previous clusters. This discrepancy was found to be due to the missing elements in the constructs available from experiment for use in the calculations. Because this problem will likely appear whenever parts of the structural information are missing, possible solutions are discussed.     

Free-energy landscape of glycerol permeation through aquaglyceroporin GlpF determined from steered molecular dynamics simulations

The free-energy landscape of glycerol permeation through the aquaglyceroporin GlpF has been estimated in the literature by the nonequilibrium method of steered molecular dynamics (SMD) simulations and by the equilibrium method of adaptive biasing force (ABF) simulations. However, the ABF results qualitatively disagree with the SMD results that were based on the Jarzynski equality (JE) relating the equilibrium free-energy difference to the nonequilibrium work of the irreversible pulling experiments. In this paper, I present a new SMD study of the glycerol permeation through GlpF to explore the free-energy profile of glycerol along the permeation channel. Instead of the JE in terms of thermodynamic work, I use the fluctuation-dissipation theorem (FDT) of Brownian dynamics (BD), in terms of mechanical work, for extracting the free-energy difference from the nonequilibrium work of irreversible pulling experiments. The results of this new SMD-BD-FDT study are in agreement with the experimental data and with the ABF results.     

Membrane adsorption,folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

Prediction of conformation of rat galanin in the presence and absence of water with the use of monte Carlo methods and the ECEPP/3 force field

The conformation of the 29-residue rat galanin neuropeptide was studied using the Monte Carlo with energy minimization (MCM) and electrostatically driven Monte Carlo (EDMC) methods. According to a previously elaborated procedure, the polypeptide chain was first treated in a united-residue approximation, in order to enable extensive exploration of the conformational space to be carried out (with the use of MCM), Then the low-energy united-residue conformations were converted to the all-atom representations, and EDMC simulations were carried out for the all-atom polypeptide chains, using the ECEPP/3 force field with hydration included. In order to estimate the effect of environment on galanin conformation, the low-energy conformations obtained as a result of these simulations were taken as starting structures for further EDMC runs that did not include hydration. The lowest-energy conformation obtained in aqueous solution calculations had a nonhelical N-terminal part packed against the nonpolar face of a residual helix that extended from Pro¹³ toward the C-terminus. One next lowest-energy structure was a nearly-all-helical conformation, but with a markedly higher energy. In contrast, all of the low-energy conformations in the absence of water were all-helical differing only by the extent to which the helix was kinked around Pro¹³. These results are in qualitative agreement with the available NMR and CD data of galanin in aqueous and nonaqueous solvents.     

Prediction of protein conformation on the basis of a search for compact structures: test on avian pancreatic polypeptide.

Based on the concept that hydrophobic interactions cause a polypeptide chain to adopt a compact structure, a method is proposed to predict the structure of a protein. The procedure is carried out in four stages: (1) use of a virtual-bond united-residue approximation with the side chains represented by spheres to search conformational space extensively using specially designed interactions to lead to a collapsed structure, (2) conversion of the lowest-energy virtual-bond united-residue chain to one with a real polypeptide backbone, with optimization of the hydrogen-bond network among the backbone groups, (3) perturbation of the latter structure by the electrostatically driven Monte Carlo (EDMC) procedure, and (4) conversion of the spherical representation of the side chains to real groups and perturbation of the whole molecule by the EDMC procedure using the empirical conformational energy program for peptides (ECEPP/2) energy function plus hydration. Application of this procedure to the 36-residue avian pancreatic polypeptide led to a structure that resembled the one determined by X-ray crystallography; it had an alpha-helix starting at residue 13, with the N-terminal portion of the chain in an extended conformation packed against the alpha-helix. Similar structures with slightly higher energies, but looser packing, were also obtained.     

Atomistic simulations of the effects of polyglutamine chain length and solvent quality on conformational equilibria and spontaneous homodimerization

Aggregation of expanded polyglutamine tracts is associated with nine different neurodegenerative diseases, including Huntington's disease. Experiments and computer simulations have demonstrated that monomeric forms of polyglutamine molecules sample heterogeneous sets of collapsed structures in water. The current work focuses on a mechanistic characterization of polyglutamine homodimerization as a function of chain length and temperature. These studies were carried out using molecular simulations based on a recently developed continuum solvation model that was designed for studying conformational and binding equilibria of intrinsically disordered molecules such as polyglutamine systems. The main results are as follows: Polyglutamine molecules form disordered, collapsed globules in aqueous solution. These molecules spontaneously associate at conditions approaching those of typical in vitro experiments for chains of length N ≥ 15. The spontaneity of these homotypic associations increases with increasing chain length and decreases with increasing temperature. Similar and generic driving forces govern both collapse and spontaneous homodimerization of polyglutamine in aqueous milieus. Collapse and dimerization maximize self-interactions and reduce the interface between polyglutamine molecules and the surrounding solvent. Other than these generic considerations, there do not appear to be any specific structural requirements for either chain collapse or chain dimerization; that is, both collapse and dimerization are nonspecific in that disordered globules form disordered dimers. In fact, it is shown that the driving force for intermolecular associations is governed by spontaneous conformational fluctuations within monomeric polyglutamine. These results suggest that polyglutamine aggregation is unlikely to follow a homogeneous nucleation mechanism with the monomer as the critical nucleus. Instead, the results support the formation of disordered, non-β-sheet-like soluble molten oligomers as early intermediates—a proposal that is congruent with recent experimental data.     

Solution Microstructure of Confined Fluids with Directional Interactions under the Influence of an External Field: Mean Field Considerations

Lattice density functional theory (DFT) and Monte Carlo simulations are used to probe the phase behavior and equilibrium structure of molecules with directional interactions with and without the influence of body forces. It is found that the application of a position-specific external field can be used to control the microstructure of confined fluids. In the absence of an external field, a condensation transition can take place within the pore at sufficiently high densities. This phase transition results in a solution microstructure made up of chains of monomers oriented parallel to the pore walls. With the application of a weak field, it is possible to disrupt this solution microstructure. This type of effect could allow controlled mixing at a local level. Upon application of a stronger field, chains reform in a direction perpendicular to the walls.     

New version of Monte Carlo expanded ensemble method for precise calculations of free energy difference

A new version of Monte Carlo (MC) expanded ensemble (EE) method is proposed for the calculations of free energy difference (FED) between two different systems with close values of the free energy. In order to check the method the FED between simple model systems (fluid of hard spheres and freely jointed polymer chain of hard spheres) was calculated. The free energy of the mentioned above systems was also calculated by a standard MC EE method in order to compare the results of two simulations. It was shown that the accuracy of a new algorithm is the same as of a standard one. At the same time new version of EE allows us to obtain FED between two systems having quite different structures, but similar free energies, during one simulation run.     

Development of a deformable phantom for experimental verification of 4D Monte Carlo simulations in a deforming anatomy

PurposeTo verify the accuracy of 4D Monte Carlo (MC) simulations, using the 4DdefDOSXYZnrc user code, in a deforming anatomy. We developed a tissue-equivalent and reproducible deformable lung phantom and evaluated 4D simulations of delivered dose to the phantom by comparing calculations against measurements.MethodsA novel deformable phantom consisting of flexible foam, emulating lung tissue, inside a Lucite external body was constructed. A removable plug, containing an elastic tumor that can hold film and other dosimeters, was inserted in the phantom. Point dose and position measurements were performed inside and outside the tumor using RADPOS 4D dosimetry system. The phantom was irradiated on an Elekta Infinity linac in both stationary and moving states. The dose delivery was simulated using delivery log files and the phantom motion recorded with RADPOS.ResultsReproducibility of the phantom motion was determined to be within 1 mm. The phantom motion presented realistic features like hysteresis. MC calculations and measurements agreed within 2% at the center of tumor. Outside the tumor agreements were better than 5% which were within the positional/dose reading uncertainties at the measurement points. More than 94% of dose points from MC simulations agreed within 2%/2 mm compared to film measurements.ConclusionThe deformable lung phantom presented realistic and reproducible motion characteristics and its use for verification of 4D dose calculations was demonstrated. Our 4DMC method is capable of accurate calculations of the realistic dose delivered to a moving and deforming anatomy during static and dynamic beam delivery techniques.     

A New Potential Model for Carbon Dioxide from AB Initio Calculations

Abstract

Ab initio quantum chemical calculations have been carried out for carbon dioxide dimer and the results have been used to establish potential functions usable in molecular simulations. Since the intermolecular interaction in carbon dioxide is fairly weak, careful treatment is required: this study uses 6–31G* basis set and takes electron correlations by the 2nd order Møller-Plesset theory into account. The potential energy surface is elucidated using the four representative relative configurations of the dimer. A new potential function model has been proposed on the basis of these ab initio data. In the super-critical region, this model is used to calculate the PVT relation of carbon dioxide fluid by the Monte Carlo simulations and confirmed to reproduce reasonably well the experimental isotherms.     

Evaluating adsorbed-phase activity coefficient models using a 2D-lattice model

Despite the wide use of the real adsorbed solution theory to predict multicomponent adsorption equilibrium, the models used for the adsorbed phase activity coefficients are usually borrowed from the gas–liquid phase equilibria. In this work, the accuracy of the Wilson and NRTL models for evaluating adsorbed phase activity coefficients is tested using a 2D-lattice model. An accurate model for adsorbed-phase activity coefficients should have no problem in fitting adsorption data obtained using this simple lattice model. The results, however, show that the commonly used Wilson and NRTL models cannot describe the adsorbed phase activity coefficients for slightly non-ideal to strong non-ideal mixtures. Therefore, until new models for adsorbed phase activity coefficients are developed, we should use existing models for liquids with care. In the second part of this work, the use of Monte Carlo simulations on a segregated 2D-lattice model, for predicting adsorption of mixtures is investigated. The segregated model assumes that the competition for adsorption occurs at isolated adsorption sites, and that the molecules from each adsorption site interact with the bulk phase independently. Two binary mixtures in two adsorbent materials were used as case studies for testing the predictions of the segregated 2D-lattice model: the binary system CO₂–N₂ in the hypothetical pure silica zeolite PCOD8200029, with isolated adsorption sites and normal preference for adsorption, and the binary system CO₂–C₃H₈ in pure silica mordenite (MOR), with isolated adsorption sites and inverse site preference. The segregated 2D-lattice model provides accurate predictions for the system CO₂–N₂ in PCOD8200029 but fails in predicting the adsorption behaviour of CO₂–C₃H₈ in pure silica MOR. The predictions of the segregated ideal adsorbed solution theory model are superior to those of the 2D-lattice model.     

An overview of recent developments in FLUKA PET tools

The new developments of the FLUKA Positron-Emission-Tomography (PET) tools are detailed. FLUKA is a fully integrated Monte Carlo (MC) particle transport code, used for an extended range of applications, including Medical Physics. Recently, it provided the medical community with dedicated simulation tools for clinical applications, including the PET simulation package. PET is a well-established imaging technique in nuclear medicine, and a promising method for clinical in vivo treatment verification in hadrontherapy. The application of clinically established PET scanners to new irradiation environments such as hadrontherapy requires further experimental and theoretical research to which MC simulations could be applied. The FLUKA PET tools, besides featuring PET scanner models in its library, allow the configuration of new PET prototypes via the FLUKA Graphical User Interface (GUI) Flair. Both the beam time structure and scan time can be specified by the user, reproducing PET acquisitions in time, in a particle therapy scenario. Furthermore, different scoring routines allow the analysis of single and coincident events, and identification of parent isotopes generating annihilation events. Two reconstruction codes are currently supported: the Filtered Back–Projection (FBP) and Maximum–Likelihood Expectation Maximization (MLEM), the latter embedded in the tools. Compatibility with other reconstruction frameworks is also possible. The FLUKA PET tools package has been successfully tested for different detectors and scenarios, including conventional functional PET applications and in beam PET, either using radioactive sources, or simulating hadron beam irradiations. The results obtained so far confirm the FLUKA PET tools suitability to perform PET simulations in R&D environment.     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.