A Monte Carlo simulation model for studying evolution in age-structured populations

This model provides for any number of genotypes defined by age-specific survival and fecundity rates in a population with completely overlapping generations and growing under the control of density-governing functions affecting survival or fecundity. It is tested in situations involving two alleles at one locus. Nonselection populations at Hardy–Weinberg equilibrium obey the ecogenetic law; i.e., each genotype follows Lotka's law regarding rate of increase and stable age distribution as if it were an independent true-breeding population. Populations experiencing age- and density-independent selection approximate this situation, and the changes in gene frequency are predicted by relative fitnesses bases on λ, the finite rate of increase of the genotypes. Polymorphic gene equilibria occurring at steady-state population sizes are determined by fitnesses based on R, the net reproductive rate. In examples involving differences in generation time produced by age-dependent differences in fecundity, the allele associated with longer generation time may be favored or opposed by selection, depending on whether the density-governing factor controlling population size affects survival or fecundity. If such genotypes have similar R's, a genetic equilibrium may be established if the population is governed by a density function acting upon fecundity. Received: August 23, 1999 / Accepted: July 13, 2000     

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.     

Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme

Monte Carlo (MC) molecular simulation describes fluid systems with rich information, and it is capable of predicting many fluid properties of engineering interest. In general, it is more accurate and representative than equations of state. On the other hand, it requires much more computational effort and simulation time. For that purpose, several techniques have been developed in order to speed up MC molecular simulations while preserving their precision. In particular, early rejection schemes are capable of reducing computational cost by reaching the rejection decision for the undesired MC trials at an earlier stage in comparison to the conventional scheme. In a recent work, we have introduced a ‘conservative’ early rejection scheme as a method to accelerate MC simulations while producing exactly the same results as the conventional algorithm. In this paper, we introduce a ‘non-conservative’ early rejection scheme, which is much faster than the conservative scheme, yet it preserves the precision of the method. The proposed scheme is tested for systems of structureless Lennard-Jones particles in both canonical and NVT-Gibbs ensembles. Numerical experiments were conducted at several thermodynamic conditions for different number of particles. Results show that at certain thermodynamic conditions, the non-conservative method is capable of doubling the speed of the MC molecular simulations in both canonical and NVT-Gibbs ensembles.     

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.     

A Monte Carlo method for the simulation of kinetie models

The purpose of this note is to illustrate the feasibility of simulating kinetic systems, such as commonly encountered in photosynthesis research, using the Monte Carlo (MC) method. In this approach, chemical events are considered at the molecular level where they occur randomly and the macroscopic kinetic evolution results from averaging a large number of such events. Their repeated simulation is easily accomplished using digital computing. It is shown that the MC approach is well suited to the capabilities and resources of modern microcomputers. A software package is briefly described and discussed, allowing a simple programming of any kinetic model system and its resolution. The execution is reasonably fast and accurate; it is not subject to such instabilities as found with the conventional analytical approach.Abbreviations MC Monte Carlo - RN random number - PSU photosynthetic unit Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.     

Monte Carlo kilovoltage X-ray tube simulation: A statistical analysis and compact simulation method

IntroductionMonte Carlo (MC) simulations are a powerful tool for improving image quality in X-ray based imaging modalities. An accurate X-ray source model is essential to MC modeling for CBCT but can be difficult to implement on a GPU while maintaining efficiency and memory limitations. A statistical analysis of the photon distribution from a MC X-ray tube simulation is conducted in hopes of building a compact source model.Materials & methodsMC simulations of an X-ray tube were carried out using BEAMnrc. The resulting photons were sorted into four categories: primary, scatter, off-focal radiation (OFR), and both (scatter and OFR). A statistical analysis of the photon components (energy, position, direction) was completed. A novel method for a compact (memory efficient) representation of the PHSP data was implemented and tested using different statistical based linear transformations (PCA, ZCA, ICA), as well as a geometrical transformation.ResultsThe statistical analysis showed all photon groupings had strong correlations between position and direction, with the largest correlation in the primary data. The novel method was successful in compactly representing the primary (error < 2%) and scatter (error < 6%) photon groupings by reducing the component correlations.Discussion & conclusionStatistical linear transforms provide a method of reducing the memory required to accurately simulate an X-ray source in a GPU MC system. If all photon types are required, the proposed method reduces the memory requirements by 3.8 times. When only primary and scatter data is needed, the memory requirement is reduced from gigabytes to kilobytes.     

Simulating proteins at constant pH: An approach combining molecular dynamics and Monte Carlo simulation

For the structure and function of proteins, the pH of the solution is one of the determining parameters. Current molecular dynamics (MD) simulations account for the solution pH only in a limited way by keeping each titratable site in a chosen protonation state. We present an algorithm that generates trajectories at a Boltzmann distributed ensemble of protonation states by a combination of MD and Monte Carlo (MC) simulation. The algorithm is useful for pH-dependent structural studies and to investigate in detail the titration behavior of proteins. The method is tested on the acidic residues of the protein hen egg white lysozyme. It is shown that small structural changes may have a big effect on the pK(A) values of titratable residues.     

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.     

Monte Carlo simulation of denaturation of adsorbed proteins

Denaturation of model proteinlike molecules at the liquid–solid interface is simulated over a wide temperature range by employing the lattice Monte Carlo technique. Initially, the molecule containing 27 monomers of two types (A and B) is assumed to be adsorbed in the native folded state (a 3 × 3 × 3 cube) so that one of its sides is in contact with the surface. The details of the denaturation kinetics are found to be slightly dependent on the choice of the side, but the main qualitative conclusions hold for all the sides. In particular, the kinetics obey approximately the conventional first-order law at T > T_c (T_c is the collapse temperature for solution). With decreasing temperature, below T_c but above T_f (T_f is the folding temperature for solution), deviations appear from the first-order kinetics. For the most interesting temperatures, that is, below T_f, the denaturation kinetics are shown to be qualitatively different from the conventional ones. In particular, the denaturation process occurs via several intermediate steps due to trapping in metastable states. Mathematically, this means that (i) the transition to the denatured state of a given molecule is nonexponential, and (ii) the denaturation process cannot be described by a single rate constant k_r. One should rather introduce a distribution of values of this rate constant (different values of k_r correspond to the transitions to the altered state via different metastable states). Proteins 30:168–176, 1998. © 1998 Wiley-Liss, Inc.     

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.     

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.