Corrections of the periodic boundary conditions with rectangular simulation boxes on the diffusion coefficient,general aspects

It is generally known that the effect of the periodic boundary conditions using cubic boxes manifests itself as the underestimation for the self-diffusion coefficient and the difference between the experimental value and the simulation is proportional to the reciprocal of system size. Rather than the cubic boxes, the effect of the rectangular boxes, which has been normally ignored, however, exhibits some distinct features, according to the hydrodynamics theory on molecular diffusion. In particular, the diffusion coefficient along the direction of the short side length of the box is always larger than that along the larger side length. What’s unusual is that some components or even all three components of the diffusion coefficient may exceed that of an infinite system. Through the comparisons of the flow patterns excited by the diffusing particles, we find that the positive and negative corrections are linked to the local and global vortex of fluid, respectively. It appears that the box shape affects the diffusion by modifying the flow pattern. The theoretical predictions are further tested by molecular dynamics simulations.     

Multiscale computer simulation of the immature HIV-1 virion

Multiscale computer simulations, employing a combination of experimental data and coarse-graining methods, are used to explore the structure of the immature HIV-1 virion. A coarse-grained (CG) representation is developed for the virion membrane shell and Gag polypeptides using molecular level information. Building on the results from electron cryotomography experiments, the simulations under certain conditions reveal the existence of an incomplete p6 hexameric lattice formed from hexameric bundles of the Gag CA domains. In particular, the formation and stability of the immature Gag lattice at the CG level requires enhanced interfacial interactions of the CA protein C-terminal domains (CTDs). An exact mapping of the CG representation back to the molecular level then allows for detailed atomistic molecular dynamics studies to confirm the existence of these enhanced CA_CTD interactions and to probe their possible origin. The multiscale simulations further provide insight into potential CA_CTD mutations that may disrupt or modify the Gag immature lattice assembly process in the immature HIV-1 virion.     

Contact interactions method: a new algorithm for protein folding simulations.

Computer simulations of simple exact lattice models are an aid in the study of protein folding process; they have sometimes resulted in predictions experimentally proved. The contact interactions (CI) method is here proposed as a new algorithm for the conformational search in the low-energy regions of protein chains modeled as copolymers of hydrophobic and polar monomers configured as self-avoiding walks on square or cubic lattices. It may be regarded as an extension of the standard Monte Carlo method improved by the concept of cooperativity deriving from nonlocal contact interactions. A major difference with respect to other algorithms is that criteria for the acceptance of new conformations generated during the simulations are not based on the energy of the entire molecule, but cooling factors associated with each residue define regions of the model protein with higher or lower mobility. Nine sequences of length ranging from 20 to 64 residues were used on the square lattice and 15 sequences of length ranging from 46 to 136 residues were used on the cubic lattice. The CI algorithm proved very efficient both in two and three dimensions, and allowed us to localize energy minima not localized by other searching algorithms described in the literature. Use of this algorithm is not limited to the conformational search, because it allows the exploration of thermodynamic and kinetic behavior of model protein chains.     

A computer simulation study of the hierarchical assembly behaviour of triblock patchy particles

We study the hierarchical self-assembly behaviour of ACB triblock patchy particles via Brownian dynamics (BD) simulations, where the product of the first stage is set as the initial structure for the second stage. We offer a promising design rule to investigate the assembly mechanism of ACB triblock patchy particles in selective solvent conditions by two-stage optimisation. At the first stage, the attractive hydrophobic interactions only exist between patches A at low concentration in order to generate subunits. At the second stage, the attractions also exist between patches B for studying the assembly process from subunits to target structures by heating/cooling method. By regulating the interactions between patches B as well as the concentrations of patchy particles, the ordered structures that determined by various influence factors are studied. Via properly designing the assembly models and routes, we can observe the formation process of simple cubic lattice and kagome lattice structures, respectively. The results reveal that the concentration and attractive strength play the critical roles in the whole process of hierarchical self-assembly.     

Protein folding. Effect of packing density on chain conformation

Recent lattice polymer simulations by Chan & Dill suggest that compactness may be a significant driving force in the formation of secondary structure. We have addressed the robustness of this conclusion for non-lattice polymers using a rotational isomeric model of proteins. Boundary conditions are used to enforce compactness and excluded volume effects are explicitly incorporated. As in the cubic lattice studies, compactness is seen to influence secondary structure content. This effect is modest for densities comparable to native proteins but dramatic for chains that are approximately 30% more dense than native proteins. alpha-Helical structure is common but beta-sheet structure is rare. It appears that lattices impart to compact chains an organizational bias that favors beta-sheet structure. The strengths and weakness of various simplified representations of polypeptide chains are also discussed.     

Explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide duplex: lattice-sum versus reaction-field electrostatics

Five long-timescale (10 ns) explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide dimer are performed using the GROMOS 45A4 force field and the simple-point-charge water model, in order to investigate the effect of the treatment of long-range electrostatic interactions as well as of the box shape and size on the structure and dynamics of the molecule (starting from an idealised B-DNA conformation). Long-range electrostatic interactions are handled using either a lattice-sum (LS) method (particle–particle–particle–mesh; one simulation performed within a cubic box) or a cutoff-based reaction-field (RF) method (four simulations, with long-range cutoff distances of 1.4 or 2.0 nm and performed within cubic or truncated octahedral periodic boxes). The overall double-helical structure, including Watson–Crick (WC) base-pairing, is well conserved in the simulation employing the LS scheme. In contrast, the WC base-pairing is nearly completely disrupted in the four simulations employing the RF scheme. These four simulations result in highly distorted compact (cutoff distance of 1.4 nm) or extended (cutoff distance of 2 nm) structures, irrespective of the shape and size of the computational box. These differences observed between the two schemes seem correlated with large differences in the radial distribution function between charged entities (backbone phosphate groups and sodium counterions) within the system.     

Protein dynamics: From the native to the unfolded state and back again

Simulations to study protein unfolding and folding were performed. The unfolding simulations make use of molecular dynamics and treat an atomic model of barnase in aqueous solvent. The cooperative nature of the unfolding transition and the important role of water are described. The folding simulations are based on a bead model of the protein on a cubic lattice. It is shown for the 27-mer model that a large energy gap between the lowest energy (native) state and the excited states is a necessary and sufficient condition for fast folding.     

Periodic boundary conditions for the simulation of uniaxial extensional flow of arbitrary duration

It is very common with molecular dynamics and other simulation techniques to apply Lees–Edwards periodic boundary conditions (PBCs) for the simulation of shear flow. However, the behaviour of a complex liquid can be quite different under extensional flow. Simple deformation of a simulation cell and its periodic images only allows for simulations of these flows with short duration. For the simulation of planar extensional flow, it was recognised that the PBCs of Kraynik and Reinelt [Int. J. Multiphase Flow 1992;18:1045] could be used to perform simulations of this flow with arbitrary duration. However, a very common extensional flow in industrial applications and experiment is uniaxial extensional flow. Kraynik and Reinelt found that their method could not be directly generalised to this flow because of the lack of a lattice which reproduces itself during uniaxial extension. PBCs are presented in this article, which avoid this problem by finding a lattice which is compatible with the flow, finding the reduced basis to the lattice at all times and using this basis when calculating the position and separation of particles. Using these new PBCs, we perform nonequilibrium molecular dynamics simulations of a simple liquid and show that the technique gives results which agree with those from simulations using simply deforming PBCs.     

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56?Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.     

Computer simulation of surface-induced aggregation of ferritin.

Models are presented describing the transient mass-transport limited adsorption and cluster growth of ferritin at a solid surface. Computer simulations are carried out on a hexagonal lattice using a computer model that can be characterized as a two-dimensional stochastic cellular automaton allowing different rules regarding association, lateral interaction and dissociation to be incorporated in the model. The fractal dimensions of individual clusters were extracted from simulated aggregates and for similar rules found to be consistent with literature values on reversible diffusion-limited aggregation in two dimensions. The distribution of clusters versus free surface were shown to be affected by neighbor-dependent association probability. Low fractal dimension clusters were generated by a combination of strong lateral cohesion and neighbor-dependent dissociation to the bulk. By comparing computer simulated aggregation to experimental electron micrographs of adsorbed ferritin layers it is suggested that neighbor-dependent association, neighbor-dependent dissociation and lateral interactions are important factors in the complex dynamics of adsorbed protein layers.     

Molecular dynamics simulation of the size-dependent morphological stability of cubic shape silver nanoparticles

The morphological stability of sharp-edged silver nanoparticles is examined by the classical molecular dynamics (MD) simulations. The crystalline structure and the perfect fcc atom packing of a series of silver nanocubes (AgNC) of different sizes varying from 63 up to 1099 atoms are compared against quasi-spherical nanoparticles of the same sizes at temperature 303 K. Our MD simulations demonstrate that starting from the preformed perfect crystalline structures the cubic shape is preserved for AgNCs composed of 365–1099 atoms. Surprisingly, the rapid loss of the cubic shape morphology and transformation into the non-fcc-structure are found for smaller AgNCs composed of less than ~256 atoms. No such loss of the preformed crystalline structure is seen for quasi-spherical nanoparticles composed of 38–1007 atoms. The analysis of the temperature dependence and the binding energy of outermost Ag surface atoms suggests that the loss of the perfect cubic shape, rounding and smoothing of sharp edges and corners are driven by the tendency towards the increase in their coordination number. In addition, we revealed that AgNC₁₀₉₉ partially loses its sharp edges and corners in the aqueous environment; however, the polymer coating with poly(vinyl alcohol) (PVA) was able to preserve the well-defined cubic morphology. Finally, these results help improve the understanding of the role of surface capping agents in solution phase synthesis of Ag nanocubes.     

The thermal properties of binary structure sI clathrate hydrate from molecular dynamics simulation

In this work, we present temperature dependence of lattice parameter and normalised lattice parameter in the atmospheric pressure and 120 bar and also pressure dependence of unit cell volume and normalised unit cell volume at 150 and 250?K for variety guests with different size, polarity and guest–host hydrogen bonding capability such as trimethylene oxide (TMO), ethylene oxide (EO), formaldehyde (FA), cyclobutane (CB), cyclopropane (CP) and ethane (Et) in the large cages with CH₄ in small cages of sI clathrate hydrates by molecular dynamics simulations. The obtained values of lattice parameters for the guest species are compatible with the experimental values. These clathrate hydrates are simulated with TIP4P/ice four-site water potential. Herein, isobaric thermal expansivity and isothermal compressibility are calculated at a temperature range of 50–250?K and a wide pressure range. These structural properties have been compared for guests which they are isoelectronic and have similar masses but with different size and polarity. We use molecular dynamics simulations to relate microscopic guest properties, like guest–host hydrogen bonding to macroscopic sI clathrate hydrate properties. The temperature dependence of thermodynamic properties such as constant-volume and constant-pressure heat capacity is presented in the atmospheric pressure for these guest species.     

Observation of inverted cubic phase in hydrated dioleoylphosphatidylethanolamine membranes

We report the observation of an inverted cubic phase in aqueous dispersions of 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) by small-angle X-ray diffraction. DOPE is a paradigm in the study of nonlamellar phases in biological systems: it exhibits a well-known phase transition from the lamellar (L alpha) to the inverted hexagonal phase (HII) as the temperature is raised. The transition is observed to occur rapidly when a DOPE dispersion is heated from 2 degrees C, where the L alpha phase is stable, to 15 degrees C, where the HII phase is stable. We report on the induction of a crystallographically well-defined cubic lattice that is slowly formed when the lipid dispersion is rapidly cycled between -5 and 15 degrees C hundreds of times. Once formed, the cubic lattice is stable at 4 degrees C for several weeks and exhibits the same remarkable metastability that characterizes other cubic phases in lipid-water systems. X-ray diffraction indicates that the cubic lattice is most consistent with either the Pn3m or Pn3 space group. Tests of lipid purity after induction of the cubic indicate the lipid is at least 98% pure. The cubic lattice can be destroyed and the system reset by cycling the specimen several times between -30 and 2 degrees C. The kinetics of the formation of the cubic are dependent on the thermal history of the sample, overall water concentration, and the extreme temperatures of the cycle.(ABSTRACT TRUNCATED AT 250 WORDS)     

Fitting protein chains to cubic lattice is NP-complete

It is known that folding a protein chain into a cubic lattice is an NP-complete problem. We consider a seemingly easier problem: given a three-dimensional (3D) fold of a protein chain (coordinates of its C(alpha) atoms), we want to find the closest lattice approximation of this fold. This problem has been studied under names such as "lattice approximation of a protein chain", "the protein chain fitting problem", and "building of protein lattice models". We show that this problem is NP-complete for the cubic lattice with side close to 3.8 A and coordinate root mean square deviation.     

Lattice and non-lattice models of tumour angiogenesis

In order to progress from the relatively harmless avascular state to the potentially lethal vascular state, solid tumours must induce the growth of new blood vessels from existing ones, a process called angiogenesis. The capillary growth centres around endothelial cells: there are several cell-based models of this process in the literature and these have reproduced some of the key microscopic features of capillary growth. The most common approach is to simulate the movement of leading endothelial cells on a regular lattice. Here, we apply a circular random walk model to the process of angiogenesis, and thus allow the cells to move independently of a lattice; the results display good agreement with empirical observations. We also run simulations of two lattice-based models in order to make a critical comparison of the different modelling approaches. Finally, non-lattice simulations are carried out in the context of a realistic model of tumour angiogenesis, and potential anti-angiogenic strategies are evaluated.     

Conformational entropy of a polymer chain grafted to rough surfaces

A polymer molecule (represented by a statistical chain) end-grafted to a topologically rough surface was studied by static MC simulations. A modified self-avoiding walk on a cubic lattice was used to model the polymer in an athermal solution. Different statistical models of surface roughness were applied. Conformational entropies of chains attached to uncorrelated Gaussian, Brownian, and fractional Brownian surfaces were calculated. Results were compared with the predictions of a simple analytical model of a macromolecule end-grafted to a fractal surface.

Folding protein alpha-carbon chains into compact forms by Monte Carlo methods.

A method is presented for generating folded chains of specific amino acid sequences on a simple cubic lattice. Monte Carlo simulations are used to transform extended geometries of simplified alpha-carbon chains for eight small monomeric globular proteins into folded states. Permitted chain transitions are limited to a few types of moves, all restricted to occur on the lattice. Crude residue-residue potentials derived from statistical structure data are used to describe the energies for each conformer. The low resolution structures obtained by this procedure contain many of the correct gross features of the native folded architectures with respect to average residue energy per nonbonded contact, segment density, and location of surface loops and disulfide pairs. Rms deviations between these and the native X-ray structures and percentage of native long-range contacts found in these final folded structures are 7.6 +/- 0.7 A and 48 +/- 3%, respectively. This procedure can be useful for predicting approximate tertiary interactions from amino acid sequence.     

Virtual Igor: an analytical phantom for the simulation of the Saint Petersburg brick phantom in arbitrary layouts in MCNP

A computer code called Virtual Igor is presented. The code generates an analytical representation of the Saint Petersburg brick phantom family (Igor, Olga, Irina), which is frequently used for the calibration of whole-body counters, in arbitrary user-defined layouts for the use in the Monte-Carlo radiation transport code MCNP. The computer code reads a file in the ldraw format, which can easily be produced by simple freeware software with graphical user interfaces and which contains the types and coordinates of the bricks. Ldraw files with the canonical layouts of the brick phantom are provided with Virtual Igor. The code determines the positions of (2.75 cm)³ segments of the bricks, where 2.75 cm is the smallest length in the layout and, therefore, represents the spacing of the segment lattice. Each segment contains the exact geometry of the respective part of the brick, using cuboid and cylindrical surfaces. The user can define which rod source drill holes of which bricks contain the rod-type radionuclide sources. The method facilitates the comparison of different layouts of the Saint Petersburg brick phantom with each other and with anthropomorphic computational phantoms.

     

A First-Passage Time Approach to Diffusion in Liquids and Superionic Conductors

Abstract

As a new tool to investigate single-particle motion in condensed matter, a first-passage time (FPT) approach to diffusion is developed and applied to the molecular dynamics simulations of simple liquids and superionic conductor CaF₂. It is shown that a continuous diffusion model reproduces the observed FPT distribution quite well for both liquids and CaF₂, which enables us to evaluate diffusion constants with good accuracy by our method. On a length scale as small as a lattice constant, however, the effect of hopping appears in the FPT distribution of F^? ions, which can not be described by a continuous diffusion model. A simple hopping diffusion model is proposed and examined from the FPT viewpoint.