The Lennard-Jones Fluid Revisited: Computer Simulation Results

Abstract

Pseudoexperimental data of high accuracy on the pressure and the internal energy of the Lennard-Jones fluid have been generated both by the Monte Carlo and molecular dynamics methods for five subcritical and three supercritical isotherms. Values of the chemical potential of the Lennard-Jones fluid computed by a new version of the gradual insertion particle method for two isotherms up to very high densities are also reported and discussed, and compared with existing data.     

Folding Lennard-Jones proteins by a contact potential

We studied the possibility to approximate a Lennard-Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by molecular dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are the contact maps associated with these native conformations. We show that such a requirement cannot be satisfied exactly, i.e., no such contact parameters exist. Nevertheless, we found that one can find contact energy parameters for which an energy minimization procedure, acting in the space of contact maps, yields maps whose corresponding structures are close to the native ones. Finally, we show that when these structures are used as the initial point of a molecular dynamics energy minimization process, the correct native folds are recovered with high probability.     

Development of a simple embedding procedure allowing immunocytochemical localization at the ultrastructural level

Immunobed solution A is a water-soluble acrylic compound recently developed for immunocytochemical localization at the light microscopic level. In this study, we combined it with methyl methacrylate (MMA) to achieve sufficient hardness to obtain ultra-thin sections. Samples of platelets were dehydrated and embedded in the water-soluble acrylic mixture (WSAM). The embedding process was carried out at 4 degrees C and final polymerization was induced with either chemical (benzoyl peroxide) or physical (UV light) catalysts. Tubulin was localized at the ultrastructural level in sections embedded according to these two methods. Results were compared with those obtained in platelets processed in Lowicryl. Dehydration and embedding with the WSAM yielded a preservation of antigenicity similar to that obtained in Lowicryl. The new procedure benefits from the low temperature achieved during polymerization, providing good ultrastructural morphology and immunolocalization of protein antigens with the simplicity of a routine embedding procedure for light microscopy.     

Production of fine and speciality chemicals: procedure for the estimation of LCIs

Goal, Scope, Background  To improve the environmental performance of chemical products or services, especially via comparisons of chemical products, LCA is a suitable evaluation method. However, no procedure to obtain comprehensive LCI-data on the production of fine and speciality chemicals is available to date, and information on such production processes is scarce. Thus, a procedure was developed for the estimation of LCIs of chemical production process-steps, which relies on only a small amount of input data. Methods  A generic input-output scheme of chemical production process-steps was set up, and equations to calculate inputs and outputs were established. For most parameters in the resulting estimation procedure, default values were derived from on-site data on chemical production processes and from heuristics. Uncertainties in the estimated default values were reflected as best-case and worst-case scenarios. The procedure was applied to a case study comparing the production of two active ingredients used for crop protection. Verification and a sensitivity analysis were carried out. Results and Discussion  It was found that the impacts from the mass and energy flows estimated by the procedure represent a significant share of the impacts assessed in the case study. In a verification, LCI-data from existing processes yielded results within the range of the estimated best-case and worst-case scenarios. Note that verification data could not be obtained for all process steps. From the verification results, it was inferred that mass and energy flows of existing processes for the production of fine and speciality chemicals correspond more frequently to the estimated best-case than to the worst-case scenario. In the sensitivity analysis, solvent demand was found to be the most crucial parameter in the environmental performance of the chemical production processes assessed. Conclusion  Mass and energy flows in LCIs of production processes for fine and speciality chemicals should not be neglected, even if only little information on a process is available. The estimation procedure described here helps to overcome lacking information in a transparent, consistent way. Recommendations and Outlook  Additional verifications and a more detailed estimation of the default parameters are desirable to learn more about the accuracy of the estimation procedure. The procedure should also be applied to case studies to gain insight into the usefulness of the estimation results in different decision-making contexts.     

Molecular Dynamics Simulations With First Order Coupling to a Bath of Constant Chemical Potential

Abstract

In molecular dynamics simulations the temperature or pressure can be controlled by applying a weak first-order coupling to a bath of constant temperature or pressure. This weak coupling technique to control system properties using a first-order relaxation equation is analyzed from a statistical mechanics point of view. It is shown, how the weak coupling scheme can be generalized and applied to a bath of contstant chemical potential. The presented method, to which in the following will be referred to as chemical potential weak coupling, is applied and tested on a Lennard-Jones fluid. The thermodynamic quantities known from the literature are accuratly reproduced.

The temperature and chemical potential weak coupling methods aim to sample the canonical and grand canonical ensembles respectively. By analyzing the fluctuations in energy and number of particles, the tight relation between the ensembles and the distributions obtained from the weak coupling simulations is demonstrated. The influence of the choice of the coupling parameters on the quality of the approximation of the ensemble distribution is discussed.     

Commercial riboflavin production by recombinant Bacillus subtilis: down-stream processing and comparison of the composition of riboflavin produced by fermentation or chemical synthesis

A novel process for riboflavin production using a recombinant Bacillus subtilis strain has been developed. Here we describe a down-stream processing procedure to obtain riboflavin qualities having a minimal content of 96% (‘feed-grade’) and 98% (‘food/pharma-grade’) riboflavin, respectively. Compared to riboflavin produced by chemical synthesis, products with improved chemical purity were obtained. All compounds representing more than 0.1% of the final products were identified. Feed-grade riboflavin material ex fermentation contained small amounts of amino acids and amino sugars and the biosynthetic riboflavin precursor dimethyl-ribityl-lumazine. All other side products found were derived from riboflavin, resulted from the purification procedure and were also found in riboflavin obtained by chemical synthesis. The Bacillus-produced riboflavin does not contain DNA. The data presented here were used to obtain product approval for the commercial application in the USA, Japan and the UK. Received 22 July 1998/ Accepted in revised form 8 November 1998     

A minimalist's reactive potential for efficient molecular modelling of chemistry

We review a minimalist's reactive force field, reactive state summation (RSS) potential. The essence of RSS potential scheme is to model each reactive state by individual non-reactive force fields, then modulate each term by a reaction-coordinate-dependent weight function, finally sum together to obtain the reactive potential. Compared with existing reactive potentials, RSS potential is easier to formulate and parameterise and is computationally efficient, at the expense of lesser accuracy. Thus, RSS potential can be regarded as a ‘reactive Lennard-Jones’ potential. Three exemplary RSS potentials are described in the context of their respective chemical systems: RSS-nitrogen for modelling detonation, RSS-carbon for modelling pyrolysis of activated carbon and RSS-fuel-catalyst for modelling catalytic chemical reaction.     

Structure-guided forcefield optimization

Accurate modeling of biomolecular systems requires accurate forcefields. Widely used molecular mechanics (MM) forcefields obtain parameters from experimental data and quantum chemistry calculations on small molecules but do not have a clear way to take advantage of the information in high-resolution macromolecular structures. In contrast, knowledge-based methods largely ignore the physical chemistry of interatomic interactions, and instead derive parameters almost exclusively from macromolecular structures. This can involve considerable double counting of the same physical interactions. Here, we describe a method for forcefield improvement that combines the strengths of the two approaches. We use this method to improve the Rosetta all-atom forcefield, in which the total energy is expressed as the sum of terms representing different physical interactions as in MM forcefields and the parameters are tuned to reproduce the properties of macromolecular structures. To resolve inaccuracies resulting from possible double counting of interactions, we compare distribution functions from low-energy modeled structures to those from crystal structures. The structural and physical bases of the deviations between the modeled and reference structures are identified and used to guide forcefield improvements. We describe improvements resolving double counting between backbone hydrogen bond interactions and Lennard-Jones interactions in helices; between sidechain-backbone hydrogen bonds and the backbone torsion potential; and between the sidechain torsion potential and Lennard-Jones interactions. Discrepancies between computed and observed distributions are also used to guide the incorporation of an explicit Cα-hydrogen bond in β sheets. The method can be used generally to integrate different sources of information for forcefield improvement.     

Comparison of simple perturbation-theory estimates for the liquid–solid and the liquid–vapor interfacial free energies of Lennard-Jones systems

The most naive perturbation method to estimate interfacial free energies is based on the assumption that the interface between coexisting phases is infinitely sharp. Although this approximation does not yield particularly accurate estimates for the liquid–vapor surface tension, we find that it works surprisingly well for the interface between a dense liquid and a solid. As an illustration we estimate the liquid–solid interfacial free energy of a Lennard-Jones system with truncated and shifted interactions and compare the results with numerical data that have been reported in the literature. We find that the agreement between theory and simulation is excellent. In contrast, if we apply the same procedure to estimate the variation of the liquid–vapor surface tension, for different variants of the Lennard-Jones potential (truncated/shifted/force-shifted), we find that the agreement with the available simulation data is, at best, fair. The present method makes it possible to obtain quick and easy estimate of the effect on the surface free energy of different potential-truncation schemes used in computer simulations.     

Catalyst free growth of a carbon nanotube-alumina composite structure

Aligned arrays of multiwall carbon tubes (CNTs) were prepared within cylindrical pores of compact porous anodic aluminum oxide (PAOX) by a non-catalytic chemical vapor deposition (CVD) method. Optimum CNT synthesis conditions were determined for two crucial reaction parameters, e.g. the precursor gas flow and the reaction time for a given fixed reaction temperature. Gas phase oxidation followed by a wet chemical dissolution allows selective removal of carbon by-products from the surface of the CNT/PAOX composite without destroying its structure. The developed procedure opens up the way to obtain CNT/alumina composites with open, 2D arranged pores by a selective gas phase and solution chemical etching technique.     

Thermal Properties of Supercritical Carbon Dioxide by Monte Carlo Simulations

We present simulation results for the volume expansivity, isothermal compressibility, isobaric heat capacity, Joule-Thomson coefficient and speed of sound for carbon dioxide (CO 2 ) in the supercritical region, using the fluctuation method based on Monte Carlo simulations in the isothermal-isobaric ensemble. We model CO 2 as a quadrupolar two-center Lennard-Jones fluid with potential parameters reported in the literature, derived from vapor-liquid equilibria (VLE) of CO 2 . We compare simulation results with an equation of state (EOS) for the two-center Lennard-Jones plus point quadrupole (2CLJQ) fluid and with a multiparametric EOS adjusted to represent CO 2 experimental data. It is concluded that the VLE-based parameters used to model CO 2 as a quadrupolar two-center Lennard-Jones fluid (both simulations and EOS) can be used with confidence for the prediction of thermodynamic properties, including those of industrial interest such as the speed of sound or Joule-Thomson coefficient, for CO 2 in the supercritical region, except in the extended critical region.     

The Extrapolation of Vapour–liquid Equilibrium Curves of Pure Fluids in Alternative Gibbs Ensemble Monte Carlo Implementations

Extrapolation schemes based on Taylor series expansion to determine the vapour–liquid equilibrium (VLE) curves of pure molecular fluids are presented for the NpH and μVL versions of the Gibbs ensemble Monte Carlo (GEMC) simulations. The coexistence curves of the various configurational quantities can be expressed as Taylor series around the simulated equilibrium point as a function of pressure in the NpH version and chemical potential in the μVL version. The coefficients of the Taylor series are calculated from single GEMC simulations using Clapeyron-like equations and fluctuation formulas. A Padè approximant is used to widen the range where the extrapolation is accurate. These methods are demonstrated on atomic Lennard-Jones fluid. The procedure is found to be an accurate and useful tool to calculate wide sections of the VLE curves. With this procedure the saturation heat capacity can be directly determined using the calculated derivatives.     

Development and testing of an automated approach to protein docking

A new version of GRAMM was applied to Targets 14, 18, and 19 in CAPRI Round 5. The predictions were generated without manual intervention. Ten top-ranked matches for each target were submitted. The docking was performed by a rigid-body procedure with a smoothed potential function to accommodate conformational changes. The first stage was a global search on a fine grid with a projection of a smoothed Lennard-Jones potential. The top predictions from the first stage were subjected to the conjugate gradient minimization with the same smoothed potential. The resulting local minima were reranked according to the weighted sum of Lennard-Jones potential, pairwise residue-residue statistical preferences, cluster occupancy, and the degree of the evolutionary conservation of the predicted interface. For Targets 14 and 18, the conformation of the complex was predicted with root-mean-square deviation (RMSD) of the ligand interface atoms 0.68 A and 1.88 A correspondingly. For Target 19, the interface areas on both proteins were correctly predicted. The performance of the procedure was also analyzed on the benchmark of bound-unbound protein complexes. The results show that, on average, conformations of only 3 side-chains need to be optimized during docking of unbound structures before the backbone changes become a limiting factor. The GRAMM-X docking server is available for public use at http://www.bioinformatics.ku.edu.     

Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature.

Molecular dynamics simulations of 500 ps were performed on a system consisting of a bilayer of 64 molecules of the lipid dipalmitoylphosphatidylcholine and 23 water molecules per lipid at an isotropic pressure of 1 atm and 50 degrees C. Special attention was devoted to reproduce the correct density of the lipid, because this quantity is known experimentally with a precision better than 1%. For this purpose, the Lennard-Jones parameters of the hydrocarbon chains were adjusted by simulating a system consisting of 128 pentadecane molecules and varying the Lennard-Jones parameters until the experimental density and heat of vaporization were obtained. With these parameters the lipid density resulted in perfect agreement with the experimental density. The orientational order parameter of the hydrocarbon chains agreed perfectly well with the experimental values, which, because of its correlation with the area per lipid, makes it possible to give a proper estimate of the area per lipid of 0.61 +/- 0.01 nm2.     

An improved generalized AMBER force field (GAFF) for urea

We describe an improved force field parameter set for the generalized AMBER force field (GAFF) for urea. Quantum chemical computations were used to obtain geometrical and energetic parameters of urea dimers and larger oligomers using AM1 semiempirical MO theory, density functional theory at the B3LYP/6-31G(d,p) level, MP2 and CCSD ab initio calculations with the 6-311++G(d,p), aug-cc-pVDZ, aug-cc-pVTZ, and aug-cc-pVQZ basis sets, and with the CBS-QB3 and CBS-APNO complete basis set methods. Seven different urea dimer structures were optimized at the MP2/aug-cc-pVDZ level to obtain accurate interaction energies. Atomic partial charges were calculated at the MP2/aug-cc-pVDZ level with the restrained electrostatic potential (RESP) fitting approach. The interaction energies computed with these new RESP charges in the force field are consistent with those obtained from CCSD and MP2 calculations. The linear dimer structure calculated using the force field with modified geometrical parameters and the new RESP charge set agrees well with available experimental data.     

Ab initio parameterization of YFF1, a universal force field for drug-design applications

The YFF1 is a new universal molecular mechanic force field designed for drug discovery purposes. The electrostatic part of YFF1 has already been parameterized to reproduce ab initio calculated dipole and quadrupole moments. Now we report a parameterization of the van der Waals interactions (vdW) for the same atom types that were previously defined. The 6–12 Lennard-Jones potential terms were parameterized against homodimerization energies calculated at the MP2/6-31 G* level of theory. The Boys-Bernardi counterpoise correction was employed to account for the basis-set superposition error. As a source of structural information we used about 2,400 neutral compounds from the ZINC2007 database. About 6,600 homodimeric configurations were generated from this dataset. A special “closure” procedure was designed to accelerate the parameters fitting. As a result, dimerization energies of small organic compounds are reproduced with an average unsigned error of 1.1 kcal mol^-1. Although the primary goal of this work was to parameterize nonbonded interactions, bonded parameters were also derived, by fitting to PM6 semiempirically optimized geometries of approximately 20,000 compounds.     

Monte Carlo Simulations of the Chemical Potential and Free Energy for Trimer and Hexamer Rings

Abstract

The chemical potential of a trimer and hexamer model ring system was determined by computer simulation over a range of temperatures and densities. Such ring molecules are important as model aromatic and naphthenic hydrocarbons. Thermodynamic integration of the pressure along a reversible path, Widom's ghost particle insertion method and Kirkwood's charging parameter method were used over a molecular density range of 0.05 to 0.30. Data were obtained by Monte Carlo simulation of a 96 molecule system that was modelled with a Lennard-Jones 6-12 truncated potential. The original insertion method, which does not take into account the orientation of the molecule when it is inserted, gives results for the chemical potential which deviate from that obtained using the thermodynamic pressure integration. At high density or temperature the deviation is significant. We have modified the Widom insertion technique to account for this short range orientation and find good agreement between this technique and the thermodynamic integration method for the chemical potential. We also calculated the free energy difference between our model ring molecules and ring molecules made up of hard spheres.     

Anaerobic digestion model No. 1-based distributed parameter model of an anaerobic reactor: II. Model validation

In this study, an ADM1-based distributed parameter model was validated using experimental results obtained in a laboratory-scale 10 L UASB reactor. Sensitivity analysis of the model parameters was used to select four parameters for estimation by a numerical procedure while other parameters were accepted from ADM1 benchmark simulations. The parameter estimation procedure used measurements of liquid phase components obtained at different sampling points in the reactor and under different operating conditions. Model verification used real time fluorescence-based measurements of chemical oxygen demand and volatile fatty acids at four sampling locations in the reactor. Overall, the distributed parameter model was able to describe the distribution of liquid phase components in the reactor and adequately simulated the effect of external recirculation on degradation efficiency. The model can be used in the design, analysis and optimization of UASB reactors.     

Comparison of Different Torsion Angle Approaches for NMR Structure Determination

A new procedure for NMR structure determination, based on the Internal Coordinate Molecular Dynamics (ICMD) approach, is presented. The method finds biopolymer conformations that satisfy usual NMR-derived restraints by using high temperature dynamics in torsion angle space. A variable target function algorithm gradually increases the number of NOE-based restraints applied, with the treatment of ambiguous and floating restraints included. This soft procedure allows combining artificially high temperature with a general purpose force-field including Coulombic and Lennard-Jones non-bonded interactions, which improves the quality of the ensemble of conformations obtained in the gas-phase. The new method is compared to existing algorithms by using the structures of eight ribosomal proteins earlier obtained with state-of-the-art procedures and included into the RECOORD database [Nederveen, A., Doreleijers, J., Vranken, W., Miller, Z., Spronk, C., Nabuurs, S., Guntert, P., Livny, M., Markley, M., Nilges, M., Ulrich, E., Kaptein, R. and Bonvin, A.M. (2005) Proteins, 59, 662–672]. For the majority of tested proteins, the ICMD algorithm shows similar convergence and somewhat better quality Z scores for the ϕ, ψ distributions. The new method is more computationally demanding although the overall load is reasonable.