Computer simulation of human thoracic skeletal response - volume I, theory.

National Highway Traffic Safety Administration, Washington, D.C.

Distinct conformational properties determined by implicit and explicit representation of protein-solvent interactions. An analytical and computer simulation study

In the protein folding problem, solvent-mediated forces are commonly represented by intra-chain pairwise contact energy. Although this approximation has proven to be useful in several circumstances, it is limited in some other aspects of the problem. Here we show that it is possible to achieve two models to represent the chain-solvent system. one of them with implicit and other with explicit solvent, such that both reproduce the same thermodynamic results. Firstly, lattice models treated by analytical methods, were used to show that the implicit and explicitly representation of solvent effects can be energetically equivalent only if local solvent properties are time and spatially invariant. Following, applying the same reasoning Used for the lattice models, two inter-consistent Monte Carlo off-lattice models for implicit and explicit solvent are constructed, being that now in the latter the solvent properties are allowed to fluctuate. Then, it is shown that the chain configurational evolution as well as the globule equilibrium conformation are significantly distinct for implicit and explicit solvent systems. Actually, strongly contrasting with the implicit solvent version, the explicit solvent model predicts: (i) a malleable globule, in agreement with the estimated large protein-volume fluctuations; (ii) thermal conformational stability, resembling the conformational hear resistance of globular proteins, in which radii of gyration are practically insensitive to thermal effects over a relatively wide range of temperatures; and (iii) smaller radii of gyration at higher temperatures, indicating that the chain conformational entropy in the unfolded state is significantly smaller than that estimated from random coil configurations. Finally, we comment on the meaning of these results with respect to the understanding of the folding process. (C) 2009 Elsevier B.V. All rights reserved.

Study of water and dimethylformamide interaction by computer simulation

Monte Carlo simulations of water-dimethylformamide (DMF) mixtures were performed in the isothermal and isobaric ensemble at 298.15 K and 1 atm. The intermolecular interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term. The TIP4P model was used for simulating water molecules, and a six-site model previously optimised by us was used to represent DMF. The potential energy for the water-DMF interaction was obtained via standard geometric combining rules using the original potential parameters for the pure liquids. The radial distribution functions calculated for water-DMF mixtures show well characterised hydrogen bonds between the oxygen site of DMF and hydrogen of water. A structureless correlation curve was observed for the interaction between the hydrogen site of the carbonyl group and the oxygen site of water. Hydration effects on the stabilisation of the DMF molecule in aqueous solution have been investigated using statistical perturbation theory. The results show that energetic changes involved in the hydration process are not strong enough to stabilise another configuration of DMF than the planar one.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, AbelianU(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev’s toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^

Progress toward chemical accuracy in the computer simulation of condensed phase reactions.

We describe a procedure for the generation of chemically accurate computer-simulation models to study chemical reactions in the condensed phase. The process involves (i) the use of a coupled semiempirical quantum and classical molecular mechanics method to represent solutes and solvent, respectively; (ii) the optimization of semiempirical quantum mechanics (QM) parameters to produce a computationally efficient and chemically accurate QM model; (iii) the calibration of a quantum/classical microsolvation model using ab initio quantum theory; and (iv) the use of statistical mechanical principles and methods to simulate, on massively parallel computers, the thermodynamic properties of chemical reactions in aqueous solution. The utility of this process is demonstrated by the calculation of the enthalpy of reaction in vacuum and free energy change in aqueous solution for a proton transfer involving methanol, methoxide, imidazole, and imidazolium, which are functional groups involved with proton transfers in many biochemical systems. An optimized semiempirical QM model is produced, which results in the calculation of heats of formation of the above chemical species to within 1.0 kcal/mol (1 kcal = 4.18 kJ) of experimental values. The use of the calibrated QM and microsolvation QM/MM (molecular mechanics) models for the simulation of a proton transfer in aqueous solution gives a calculated free energy that is within 1.0 kcal/mol (12.2 calculated vs. 12.8 experimental) of a value estimated from experimental pKa values of the reacting species.

Adsorption of Lennard-Jones fluids in carbon slit pores of a finite length. A computer simulation study

The adsorption of simple Lennard-Jones fluids in a carbon slit pore of finite length was studied with Canonical Ensemble (NVT) and Gibbs Ensemble Monte Carlo Simulations (GEMC). The Canonical Ensemble was a collection of cubic simulation boxes in which a finite pore resides, while the Gibbs Ensemble was that of the pore space of the finite pore. Argon was used as a model for Lennard-Jones fluids, while the adsorbent was modelled as a finite carbon slit pore whose two walls were composed of three graphene layers with carbon atoms arranged in a hexagonal pattern. The Lennard-Jones (LJ) 12-6 potential model was used to compute the interaction energy between two fluid particles, and also between a fluid particle and a carbon atom. Argon adsorption isotherms were obtained at 87.3 K for pore widths of 1.0, 1.5 and 2.0 nm using both Canonical and Gibbs Ensembles. These results were compared with isotherms obtained with corresponding infinite pores using Grand Canonical Ensembles. The effects of the number of cycles necessary to reach equilibrium, the initial allocation of particles, the displacement step and the simulation box size were particularly investigated in the Monte Carlo simulation with Canonical Ensembles. Of these parameters, the displacement step had the most significant effect on the performance of the Monte Carlo simulation. The simulation box size was also important, especially at low pressures at which the size must be sufficiently large to have a statistically acceptable number of particles in the bulk phase. Finally, it was found that the Canonical Ensemble and the Gibbs Ensemble both yielded the same isotherm (within statistical error); however, the computation time for GEMC was shorter than that for canonical ensemble simulation. However, the latter method described the proper interface between the reservoir and the adsorbed phase (and hence the meniscus).

Studies of Protein-Protein and Protein-Water Interactions by Small Angle X-Ray Scattering, Terahertz Spectroscopy, ASMOS, And Computer Simulation

The protein folding problem has been one of the most challenging subjects in biological physics due to its complexity. Energy landscape theory based on statistical mechanics provides a thermodynamic interpretation of the protein folding process. We have been working to answer fundamental questions about protein-protein and protein-water interactions, which are very important for describing the energy landscape surface of proteins correctly. At first, we present a new method for computing protein-protein interaction potentials of solvated proteins directly from SAXS data. An ensemble of proteins was modeled by Metropolis Monte Carlo and Molecular Dynamics simulations, and the global X-ray scattering of the whole model ensemble was computed at each snapshot of the simulation. The interaction potential model was optimized and iterated by a Levenberg-Marquardt algorithm. Secondly, we report that terahertz spectroscopy directly probes hydration dynamics around proteins and determines the size of the dynamical hydration shell. We also present the sequence and pH-dependence of the hydration shell and the effect of the hydrophobicity. On the other hand, kinetic terahertz absorption (KITA) spectroscopy is introduced to study the refolding kinetics of ubiquitin and its mutants. KITA results are compared to small angle X-ray scattering, tryptophan fluorescence, and circular dichroism results. We propose that KITA monitors the rearrangement of hydrogen bonding during secondary structure formation. Finally, we present development of the automated single molecule operating system (ASMOS) for a high throughput single molecule detector, which levitates a single protein molecule in a 10 µm diameter droplet by the laser guidance. I also have performed supporting calculations and simulations with my own program codes.

XSophe-Sophe-XeprView (R). A computer simulation software suite (v. 1.1.3) for the analysis of continuous wave EPR spectra

The XSophe-Sophe-XeprView((R)) computer simulation software suite enables scientists to easily determine spin Hamiltonian parameters from isotropic, randomly oriented and single crystal continuous wave electron paramagnetic resonance (CW EPR) spectra from radicals and isolated paramagnetic metal ion centers or clusters found in metalloproteins, chemical systems and materials science. XSophe provides an X-windows graphical user interface to the Sophe programme and allows: creation of multiple input files, local and remote execution of Sophe, the display of sophelog (output from Sophe) and input parameters/files. Sophe is a sophisticated computer simulation software programme employing a number of innovative technologies including; the Sydney OPera HousE (SOPHE) partition and interpolation schemes, a field segmentation algorithm, the mosaic misorientation linewidth model, parallelization and spectral optimisation. In conjunction with the SOPHE partition scheme and the field segmentation algorithm, the SOPHE interpolation scheme and the mosaic misorientation linewidth model greatly increase the speed of simulations for most spin systems. Employing brute force matrix diagonalization in the simulation of an EPR spectrum from a high spin Cr(III) complex with the spin Hamiltonian parameters g(e) = 2.00, D = 0.10 cm(-1), E/D = 0.25, A(x) = 120.0, A(y) = 120.0, A(z) = 240.0 x 10(-4) cm(-1) requires a SOPHE grid size of N = 400 (to produce a good signal to noise ratio) and takes 229.47 s. In contrast the use of either the SOPHE interpolation scheme or the mosaic misorientation linewidth model requires a SOPHE grid size of only N = 18 and takes 44.08 and 0.79 s, respectively. Results from Sophe are transferred via the Common Object Request Broker Architecture (CORBA) to XSophe and subsequently to XeprView((R)) where the simulated CW EPR spectra (1D and 2D) can be compared to the experimental spectra. Energy level diagrams, transition roadmaps and transition surfaces aid the interpretation of complicated randomly oriented CW EPR spectra and can be viewed with a web browser and an OpenInventor scene graph viewer.

RWMODEL II: Computer simulation of the Rescorla-Wagner model of Pavlovian conditioning

RWMODEL II simulates the Rescorla-Wagner model of Pavlovian conditioning. It is written in Delphi and runs under Windows 3.1 and Windows 95. The program was designed for novice and expert users and can be employed in teaching, as well as in research. It is user friendly and requires a minimal level of computer literacy but is sufficiently flexible to permit a wide range of simulations. It allows the display of empirical data, against which predictions from the model can be validated.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Molecular dynamics computer simulation of scratch resistance testing of polymers: visualization

Experimental scratch resistance testing provides two numbers: the penetration depth Rp and the healing depth Rh. In molecular dynamics computer simulations, we create a material consisting of N statistical chain segments by polymerization; a reinforcing phase can be included. Then we simulate the movement of an indenter and response of the segments during X time steps. Each segment at each time step has three Cartesian coordinates of position and three of momentum. We describe methods of visualization of results based on a record of 6NX coordinates. We obtain a continuous dependence on time t of positions of each of the segments on the path of the indenter. Scratch resistance at a given location can be connected to spatial structures of individual polymeric chains.