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 new mechanism of model membrane fusion determined from Monte Carlo simulation

We have carried out extensive Monte Carlo simulations of the fusion of tense apposed bilayers formed by amphiphilic molecules within the framework of a coarse-grained lattice model. The fusion pathway differs from the usual stalk mechanism. Stalks do form between the apposed bilayers, but rather than expand radially to form an axial-symmetric hemifusion diaphragm of the trans leaves of both bilayers, they promote in their vicinity the nucleation of small holes in the bilayers. Two subsequent paths are observed. 1) The stalk encircles a hole in one bilayer creating a diaphragm comprised of both leaves of the other intact bilayer, which ruptures to complete the fusion pore. 2) Before the stalk can encircle a hole in one bilayer, a second hole forms in the other bilayer, and the stalk aligns and encircles them both to complete the fusion pore. Both pathways give rise to mixing between the cis and trans leaves of the bilayer and allow for transient leakage.     

Monte Carlo simulation of early molecular evolution in the RNA World

The origin of life remains a highly speculative field, mainly due to the shortage of our knowledge on prebiotic chemistry and basic understanding on the essence of life. In this context, computer simulation is expected to play an important role. For instance, the scenario concerning the genesis of the widely accepted RNA World remains blurry, though we have gathered some circumstantial evidence and fragmented knowledge on several supposed stages, including formation of polynucleotides from a prebiotic nucleotide pool, emergence of RNA replicases (RNA molecules catalyzing their own replication), and evolution of RNA replicases. It is highly valuable to simulate the stages as a continuous process to evaluate the plausibility of the supposition and study the rules involved. Here we construct a computer simulation on the process using Monte Carlo method. It demonstrates that primordial RNA replicases may appear and spread in a nucleotide pool provided they could recognize their own sequence and their complements as catalytic targets, and then may evolve to more efficient RNA replicases. Apart from its indication on the genesis of the RNA World, the vivid simulation of emergence of the “first replicative molecules” and their subsequent evolution is impressive and may help to get insight into “how could self-replication and Darwinian evolution, two key features of life, emerge in a non-life background?” thus improve our understanding of “what is life” when studying origins of life.     

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 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     

A Monte Carlo code for positive ion track simulation

An ion interaction model has been described for simulating positive ion tracks in a variety of media with the capability of interfacing with several secondary electron transport codes. Data are presented for single- and double-differential cross-sections, binding energies, probability density distribution for delocalisation parameters for conductors and tissue, branching ratios and ionisation efficiencies for water vapour and liquid water. Received: 20 September 1998 / Accepted in revised form: 15 February 1999     

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.     

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.     

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.     

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.     

Combined Monte Carlo and molecular dynamics simulation of hydrated lipid-cholesterol lipid bilayers at low cholesterol concentration

We have applied a hybrid equilibration and sampling procedure for the atomic level simulation of a hydrated lipid bilayer to systems consisting of dipalmitoyl phosphatidylcholine (DPPC) and cholesterol, and palmitoyl-oleyl phosphatidylcholine (POPC) at low (approximately 6%) cholesterol concentration. The procedure is applied to bilayers of 94 molecules of DPPC, 6 molecules of cholesterol, and 3205 water molecules, and to bilayers of 120 molecules of POPC, 8 molecules of cholesterol, and 4268 water molecules, at a temperature of 325 K. After equilibration, three separate 400-ps continuous molecular dynamics runs, separated by 10,000 configurational bias Monte Carlo steps, were carried out for each system. Properties of the systems were calculated and averaged over the three separate runs. Results of the simulations are presented and compared with experimental data and with other recent simulations of DPPC and cholesterol, and of pure DPPC, and pure POPC. Certain properties of the bilayers are indistinguishable from cholesterol-free bilayers, including lateral diffusion and electron density. Other properties, most notably the order parameter profile, show the effect of cholesterol even at low concentrations.     

A Monte Carlo simulation of hydration of xanthine-derivatives and their stacked forms.

Results on a Monte Carlo simulation of the hydration of monomer and possible stacked dimer forms of a purine alkaloid series in 200- and 400-water molecule clusters are presented. Investigation of different purine stacked dimers in a 200-water molecule cluster reveals that for caffeine there exists one, for theophylline two and for theobromine four dimers are energetically favorable. For caffeine, the same energetically favored stacked dimer form is observed in both the 200- and 400-water molecule cluster. The main factor stabilizing the preferred dimer stacks is the change in the interaction between water molecules of the monomer cluster and those water molecules in the dimer cluster.     

A Monte Carlo simulation of plasmid replication during the bacterial division cycle

Plasmids have cell cycle replication patterns that need to be considered in models of their replication dynamics. To compare current theories for control of plasmid replication with experimental data for timing of plasmid replication with the cell cycle, a Monte Carlo simulation of plasmid replication and partition was developed. High-copy plasmid replication was simulated by incorporating equations previously developed from the known molecular biology of ColE1-type plasmids into the cell-cycle simulation. Two types of molecular mechanisms for low-copy plasmid replication were tested: accumulation of an initiator protein in proportion to cell mass and binding of the plasmid origin to the cell membrane. The low-copy plasmids were partitioned actively, with a specific mechanism to mediate the transfer from mother to daughter cells, whereas the high-copy plasmids were partitioned passively with cell mass.The simulation results and experimental data demonstrate cell-cycle-specific replication for the low-copy F plasmid and cell-cycle-independent replication for the high-copy pBR322, ColBM, and R6K plasmids. The simulation results indicate that synchronous replication at multiple plasmid origins is critical for the cell-cycle-specific pattern observed in rapidly growing cells. Variability in the synchrony of initiation of multiple plasmid origins give rise to a cell-cycle-independent pattern and is offered as a plausible explanation for the controversy surrounding the replication pattern of the low-copy plasmids. A comparison of experimental data and simulation results for the low-copy F plasmid at several growth rates indicates that either initiation mechanism would be sufficient to explain the timing of replication with the cell cycle. The simulation results also demonstrate that, although cell-cycle-specific and cell-cycle independent replication patterns give rise to very different gene-expression patterns during short induction periods in age-selected populations, long-term expression of genes encoded on low-copy and high-copy plasmids in exponentially growing cells have nearly the same patterns. These results may be important for the future use of low-copy plasmids as expression vectors and validate the use of simpler models for high-copy plasmids that do not consider cell-cycle phenomena. (c) 1996 John Wiley & Sons, Inc.     

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.     

A Monte Carlo code for the simulation of heavy-ion tracks in water

TILDA, a new Monte Carlo track structure code for ions in gaseous water that is valid for both high-LET (approximately 10(4) keV/microm) and low-LET ions, is presented. It is specially designed for a comparison of the patterns of energy deposited by a large range of ions. Low-LET ions are described in a perturbative frame, whereas heavy ions with a very high stopping power are treated using the Lindhard local density approximation and the Russek and Meli statistical method. Ionization cross sections singly differential with energy compare well with the experiment. As an illustration of the non-perturbative interaction of high-LET ions, a comparison between the ion tracks of light and heavy ions with the same specific energy is presented (1.4 MeV/nucleon helium and uranium ions). The mean energy for ejected electrons was found to be approximately four times larger for uranium than for helium, leading to a much larger track radius in the first case. For electrons, except for the excitation cross sections that are deduced from experimental fits, cross sections are derived analytically. For any orientation of the target molecule, the code calculates multiple differential cross sections as a function of the ejection and scattering angles and of the energy transfer. The corresponding singly differential and total ionization cross sections are in good agreement with experimental data. The angular distribution of secondary electrons is shown to depend strongly on the orientation of the water molecule.     

Monte Carlo simulation of photoselective cyclization of azobenzene-containing oligosarcosines

Conformations of (Sar)_n? Azo? (Sar)_n oligomers [Sar = sarcosine (N-methylglycine) unit. Azo = p-aminoazobenzene unit] were computer-simulated for trans and cis states of the azobenzene group. Each part of the oligosarcosine chain was assumed to behave independently and the ring-closure probability, i.e., the probability that the end-to-end distance of the above oligomer is shorter than 4 Å, was evaluated from an overlap integral of the two three-dimensional distribution functions for the left and right halves of the oligosarcosine chain. The ring-closure probability for the cis azobenzene unit was larger than that for trans, indicating the preference of cyclization reaction to the corresponding intermolecular reactions. The prediction agrees qualitatively with the experimental observation reported by us in our companion paper, but the calculated ring-closure probability for the cis state was substantially larger than the experimental value. The difference was explained as a result of intramolecular overlappings of the two halves of the oligosarcosine chain, which is facilitated when the azobenzene group is in the cis state.