The Monte Carlo simulation of pearl chain formation

Summary The phenomenon of pearl chain formation (PCF) is investigated by means of a statistical model using the Monte Carlo method. Fifteen particles (cells) interacting with simple dipole-dipole potential are shown to form chains under the influence of an external field with a threshold potential significantly lower than the two particle estimate. A possible overlap between PCF and the thermal effects of an electric field is suggested.     

Monte Carlo simulation study of thermal fluctuations and conformational energy surface of a small protein, basic pancreatic trypsin inhibitor

The conformation energy surface of a small protein, basic pancreatic trypsin inhibitor, is studied to characterize small-amplitude thermal fluctuations in the protein molecule. In order to see the shape of the conformational energy surface near the energy minimum point, the thermal equilibrium of the molecule is stimulated by the Monte Carlo method of Metropolis et al. From the sample of the equilibrium population, which reflects the shape of the energy surface, orthogonal directions are generated in the conformational space, and the conformational energy is actually calculated along these directions. All energy profiles along these directions are found to be approximately a parabola within the range of thermal fluctuations, which suggests the possibility of harmonic approximation to the conformational energy surface of the globular protein.     

Monte Carlo simulation of biospecific interactions

Numerical simulations of the stochastic time evolution of biospecific interactions are described and show that when molecular populations are large, time course predictions match those obtained using a deterministic expression. When population size is decreased the effects of stochastic noise become apparent. The significance of stochastic noise in sensitive binding-based assay systems suggests an immediate need for models of this type.     

Monte Carlo generation of polypeptide random coil conformations; the persistence vector and the chain vector distribution

Polypeptide random coil conformations of various chain lenghts (N = 5, 10, 20, 40, 80 peptide units) are generated by a Monte Carlo procedure. The characteristic ratio obtained for the sets of generated conformations is identical with the exact value calculated with the average transformation matrix procedure, indicating the equivalence of the two treatments. On the basic of the generated sets of conformations the length and direction of the persistence vector (the averaged chain vector expressed in the reference frame of the first two skeletal bonds) are investigated for various chain lengths. The radial distribution function for the chain vector shows the length of the chain vector for small polypeptides (N = 5, 10) not to deviate far from its most probable value. Also for larger chains up to chains of 80 peptide units very significant deviations from a gaussian distribution are observed.The distribution of the length of the vector connecting the remote end of the chain with the end of the persistence vector exhibited behavior much doser to the gaussian approximation, an improvement especially significant for the short chains.     

Monte Carlo simulation program for ecosystems

A Monte Carlo computer simulation program is designed in orderto describe the spatial and time evolution of a population ofliving individuals under preassigned environmental conditionsof energy. The simulation is inspired by previous techniquesdeveloped in physics — in particular, in molecular dynamicsand simulations of liquids — and it already provides somenew insights regarding macroscopic deterministic models in ecologyand concerning eventual control of artificial biomass productionplants. Received on July 15, 1986; accepted on October 9, 1986     

Monte Carlo simulation of intercalated carbon nanotubes

Monte Carlo simulations of the single- and double-walled carbon nanotubes (CNT) intercalated with different metals have been carried out. The interrelation between the length of a CNT, the number and type of metal atoms has also been established. This research is aimed at studying intercalated systems based on CNTs and d-metals such as Fe and Co. Factors influencing the stability of these composites have been determined theoretically by the Monte Carlo method with the Tersoff potential. The modeling of CNTs intercalated with metals by the Monte Carlo method has proved that there is a correlation between the length of a CNT and the number of endo-atoms of specific type. Thus, in the case of a metallic CNT (9,0) with length 17 bands (3.60 nm), in contrast to Co atoms, Fe atoms are extruded out of the CNT if the number of atoms in the CNT is not less than eight. Thus, this paper shows that a CNT of a certain size can be intercalated with no more than eight Fe atoms. The systems investigated are stabilized by coordination of 3d-atoms close to the CNT wall with a radius-vector of (0.18–0.20) nm. Another characteristic feature is that, within the temperature range of (400–700) K, small systems exhibit ground-state stabilization which is not characteristic of the higher ones. The behavior of Fe and Co endo-atoms between the walls of a double-walled carbon nanotube (DW CNT) is explained by a dominating van der Waals interaction between the Co atoms themselves, which is not true for the Fe atoms.     

A Monte Carlo simulation of chemical reactions

A computer-based algorithm to solve complex chemical rate equations is introduced. A simple Monte Carlo sampling method is used to generate chemical reactions in numbers proportional to reaction probabilities, and a second-order Runge-Kutta method is used to calculate time. The method is compared with a closed form mathematical solution for a simple chemical system, and it is compared with a numerical integration of the rate equations for a more complicated system.     

A Monte Carlo simulation of Auger cascades

The energy imparted to biological tissue after the decay of incorporated Auger emitters stems from two sources: (a) energy deposition by the Auger and Coster-Kronig electrons and (b) the charge potential which remains on the multiple ionized atom after the end of the cascade. For the numerical assessment of both the kinetic energy of the released electrons and the charge potential, a new and--for purposes of microdosimetry--precise method is presented. Based on relativistic Dirac-Fock calculations and a rigorous bookkeeping, this method provides a perfect energy balance of the considered atomic system when applied to Monte Carlo simulations of Auger cascades. By comparing the results for charge distribution for krypton and iodine with experimental data and the electron spectrum of 125I with theoretical data, it can be shown that the approach followed in this work is reasonable and appropriate for the determination of the energy deposited by incorporated Auger emitters in small volumes of condensed matter. The total energy deposited by 125I in a volume of 20-nm diameter is 2.03 keV which is made up by multiple ionization (1.07 keV) and energy deposition by the emitted Auger electrons (0.96 keV).     

A Monte Carlo study of the amylosic chain conformation

Monte Carlo studies of the unperturbed amylosic chain conformation have been carried out in the approximation of separable chain configuration energies. Sample chains of arbitrary chain length have been generated so as to be distributed consistent with refined estimates of the configuration energy and thus suitable for evaluation of averages of the desired configuration-dependent properties. Perspective drawings of representative chains from the Monte Carlo sample have been made for comparison with standard idealizations of amylosic chain conformation. He molecular model employed generates a randomly coiling chain possessing perceptible regions of left-handed pseudohelical backbone trajectory. Distribution functions for the end-to-end distance of short amylosic chains disclose some propensity for the chain to suffer self-intersections at sort range in the chain sequence, which may vitiate the usual amylosic chain models based on the assumed independence of sets of glycosidic linkage torsion angles. The amylosic persistence vector and persistence length have been calculated as a function of chain length for the chain model employed.     

Practical aspects of Monte Carlo simulation of charged particle transport: Mixed algorithms and variance reduction techniques

This paper is concerned with the practical implementation of Monte Carlo simulation methods for charged particle transport. The emphasis is on light particles (electrons and positrons) because of the larger scattering and energy straggling effects. Differential cross sections (DCS) for the various interaction mechanisms are described. As the average number of interactions along the particle track increases with the initial energy, detailed simulation becomes unfeasible at high energies. We can then rely on mixed simulation algorithms: hard events (i.e. individual interactions with angular deflection or energy loss larger than given cutoff values) are sampled from the DCS whereas soft events are simulated by means of a multiple scattering approach. Too frequently, the statistical uncertainty of analogue simulation (i.e. strict simulation of the physical interaction process) is found to be so large that results are meaningless. This problem can be partially solved by applying simple variance reduction techniques. Received: 10 September 1998 / Accepted in revised form: 10 November 1998     

Monte Carlo simulation of the enzymatic lysis of yeast

The overall reaction in the enzymatic lysis of yeast takes place in three major steps: (i) the two-layer wall is digested, (ii) the cell bursts under the osmotic pressure difference to release its intracellular material, and (iii) the intracellular material is digested by the enzymes still present in the solution. The first and third steps are continuous processes, adequately described by Michaelis-Menten kinetic models. The second step is a discrete event, statistical in nature. A model of engineering value should effectively bridge the gap between the two continuous processes (first and third steps). In this work, Monte Carlo simulations are used to identify a suitable function that captures the statistical nature of cell rupture and represents the rate of release of intracellular material. It is shown that the two-parameter beta distribution function serves this purpose most effectively. Comparisons with experimental results indicate that the cell rupture ratio is a widely distributed statistical function. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 290-295, 1997.     

Applicability of broken-rodlike chain model to conformational analysis of polypeptide chain

In order to check the applicability of the broken-rodlike (BR) chain model, consisting of several rods alternatively joined by flexible random coils, to the conformational analysis of a polypeptide chain in the helix-to-coil transition regions, two relations predicted by the Zimm and Bragg theory and the method with the BR chain model are compared. It is shown that, despite a clear difference between the models employed in the two methods, they give substantially identical results in both probability P(j) that a helical residue is in a helical sequence j units long and averaged helical fraction dependence of the mean-squared radius of gyration. Thus the use of the method with the BR chain model in the conformational analysis of a polypeptide chain could be rationalized, at least, with the same degree of approximation as is assumed in the Zimm and Bragg theory. Using the scattering function for the BR chain model, averaged helical-sequence lengths are evaluated for partially ionized poly(L-glutamic acid) (PGA) in added-salt aqueous solution and nonionized PGA in N-methylacetamide, both in a helical state. As a result, it is shown that the length in the latter molecule is approximately tenfold longer than that in the former one.     

The influence of the simulation box geometry in solid-state molecular simulations: phase behaviour of lithium iodide in a dynamic Monte Carlo simulation

In thermodynamic computer simulations, it is common to use cubic simulation boxes, which are then regarded as unit cells of an infinitely large cubic lattice. While this approach is adequate for gases and liquids at low densities, for dense liquids and solid cuboid boxes forming an orthorhombic lattice or parallelepiped boxes forming a triclinic lattice are shown to be advantageous, because they do not predetermine the structure of the simulated system. In this work, an extension of the Ewald summation formalism towards a parallelepiped lattice symmetry is given. Monte Carlo simulations of lithium iodide with cubic, cuboid and parallelepiped box geometries are reported; the latter is found to offer little improvement over the cuboid geometry. The existence of two hexagonal solid phases is discussed.     

Monte Carlo simulation of the water in a channel with charges.

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.     

Monte Carlo simulation of diffusion of adsorbed proteins

We present the results of three-dimensional lattice Monte Carlo simulations of protein diffusion on the liquid-solid interface in a wide temperature range including the most interesting temperatures (from slightly below T(f) and up to T(c), where T(f) and T(c) are the folding and collapse temperatures). For the model under consideration (27 monomers of two types), the temperature dependence of the diffusion coefficient is found to obey the Arrhenius law with the normal value (approximately 10(-2)-10(-3) cm(2)/s) of the preexponential factor. Proteins 2000;39:76-81.     

All-atom Monte Carlo simulation of GCAA RNA folding

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.     

Hydration of uracil and thymine methylderivatives: a Monte Carlo simulation

The simulation performed shows that under methylation of uracil and thymine NH-groups the interaction energy between a base and water (Uwb) is increased. It is also detected that the increase in this energy was observed in the 1st and the 3rd sectors. These conclusions do not confirm the assumption made in the literature on the character of an interaction between methylated bases and water. According to this assumption, when the NH-groups are methylated, the energy of Uwb in these sectors decreases as a result of the van der Waals interactions between a methyl group and water, whose energy compensates the increase in the Uwb energy due to the breaking of an H-bond. Regularity of water molecules near a hydrophobic group under the hydration of polar molecules is detected for the first time.     

Monte Carlo simulation of hydration of the nucleic acid fragments

Systems containing a base or a base pair and 25 water molecules, as well as a helical stack and 30 water molecules per base pair, have been simulated. Changes in the base hydration shell structure, after the bases have been included into the pair and then into the base pair stack, are discussed. Hydration shells of several configurations of the base pair stacks are discussed. Probabilities of formation of the hydrogen-bonded bridges of 1, 2 and 3 water molecules between hydrophilic centres have been estimated. The hydration shell structure was shown to depend on the nature of the base pair and on the stack configuration, while dependence of the global hydration shell characteristics on the stack configuration has been proved to be rather slight. The most typical structural elements of hydration shells, in the glycosidic (minor in B-like conformation) and non-glycosidic (major) grooves, for different configurations of AU and GC stacks, have been found and discussed. The number of hydrogen bonds between water molecules and bases per water molecule was shown to change upon transformation of the stack from A to B configuration. This result is discussed in connection with the reasons for B to A conformational transition and the concept of "water economy". Hydration shell patterns of NH2-groups of AU and GC helical stacks differ significantly.