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A stochastic model for predator-prey systems: basic properties, stability and computer simulation.

A simple stochastic description of a model of a predator-prey system is given. The evolution of the system is described by means of Itô's stochastic differential equations (SDEs), which are the natural stochastic generalization of the Lotka-Volterra deterministic differential equations. Since these SDEs do not satisfy the usual conditions for the existence and uniqueness of the solution, we state a theorem of existence; moreover we study the stability of the equilibrium point and perform a computer simulation to study the behaviour of the trajectories of solutions with given initial data and to estimate first and second moments.

Animals↗

Computational simulation of the docking of Prochlorothrix hollandica plastocyanin to potosystem I: modeling the electron transfer complex.

We have used several docking algorithms (GRAMM, FTDOCK, DOT, AUTODOCK) to examine protein-protein interactions between plastocyanin (Pc)/photosystem I (PSI) in the electron transfer reaction. Because of the large size and complexity of this system, it is faster and easier to use computer simulations than conduct x-ray crystallography or nuclear magnetic resonance experiments. The main criterion for complex selection was the distance between the copper ion of Pc and the P700 chlorophyll special pair. Additionally, the unique tyrosine residue (Tyr(12)) of the hydrophobic docking surface of Prochlorothrix hollandica Pc yields a specific interaction with the lumenal surface of PSI, thus providing the second constraint for the complex. The structure that corresponded best to our criteria was obtained by the GRAMM algorithm. In this structure, the solvent-exposed histidine that coordinates copper in Pc is at the van der Waals distance from the pair of stacked tryptophans that separate the chlorophylls from the solvent, yielding the shortest possible metal-to-metal distance. The unique tyrosine on the surface of the Prochlorothrix Pc hydrophobic patch also participates in a hydrogen bond with the conserved Asn(633) of the PSI PsaB polypeptide (numbering from the Synechococcus elongatus crystal structure). Free energy calculations for complex formation with wild-type Pc, as well as the hydrophobic patch Tyr(12)Gly and Pro(14)Leu Pc mutants, were carried out using a molecular mechanics Poisson-Boltzman, surface area approach (MM/PBSA). The results are in reasonable agreement with our experimental studies, suggesting that the obtained structure can serve as an adequate model for P. hollandica Pc-PSI complex that can be extended for the study of other cyanobacterial Pc/PSI reaction pairs.

Algorithms↗

VNTR allele frequency distributions under the stepwise mutation model: a computer simulation approach.

Variable numbers of tandem repeats (VNTRs) are a class of highly informative and widely dispersed genetic markers. Despite their wide application in biological science, little is known about their mutational mechanisms or population dynamics. The objective of this work was to investigate four summary measures of VNTR allele frequency distributions: number of alleles, number of modes, range in allele size and heterozygosity, using computer simulations of the one-step stepwise mutation model (SMM). We estimated these measures and their probability distributions for a wide range of mutation rates and compared the simulation results with predictions from analytical formulations of the one-step SMM. The average heterozygosity from the simulations agreed with the analytical expectation under the SMM. The average number of alleles, however, was larger in the simulations than the analytical expectation of the SMM. We then compared our simulation expectations with actual data reported in the literature. We used the sample size and observed heterozygosity to determine the expected value, 5th and 95th percentiles for the other three summary measures, allelic size range, number of modes and number of alleles. The loci analyzed were classified into three groups based on the size of the repeat unit: microsatellites (1-2 base pair (bp) repeat unit), short tandem repeats [(STR) 3-5 bp repeat unit], and minisatellites (15-70 bp repeat unit). In general, STR loci were most similar to the simulation results under the SMM for the three summary measures (number of alleles, number of modes and range in allele size), followed by the microsatellite loci and then by the minisatellite loci, which showed deviations in the direction of the infinite allele model (IAM). Based on these differences, we hypothesize that these three classes of loci are subject to different mutational forces.

Alleles↗

Effect of blood flow, tumour and cold stress in a female breast: a novel time-accurate computer simulation.

Breast cancer is a dreadful disease among women and early detection helps in achieving a cure. The mammogram is presently the standard tool for detecting breast abnormality, but its sensitivity is lower for women with dense breasts. It has been found that women with an abnormal thermogram are at a higher risk and have a poorer prognosis. However, performing and interpreting thermograms requires meticulous training. Computer simulations can be an additional tool to help the clinician in the interpretation. In this paper, a novel and flexible finite element model of a female breast is developed. Both steady state and time-dependent solutions are obtained. Steady state solutions globally match experimental thermographic results with the proper choice of blood perfusion source terms, tissue thickness and geometric scaling factor. Although the simulations may not be useful in providing a unique solution (i.e. exact size and location of the tumour owing to the complex physiological relationship between the tumour and the breast surface temperature), it would nevertheless help in the 'analysis by elimination'. An example of this type of analysis is also presented.

Body Temperature↗

Cross-correlation analysis of intracellularly recorded synaptic activities: an evaluation of the method through computer simulation.

Cross-correlation of 'spontaneous' synaptic activities intracellularly recorded from pairs of neurons may be used to detect shared synaptic input, which could remain hidden in the raw data by the non-synchronized postsynaptic potentials (PSPs); besides, if a normalized cross-correlation function is adopted, the fraction of synchronized activity may be quantitatively estimated. To evaluate power and limits of this method, computer-simulated synaptic activities of pairs of neurons, in which a given percentage of PSPs were simultaneous, were subjected to this type of analysis. It was shown that percentages of shared activities as low as 4% and in some cases 2% could be revealed, with a conspicuity which was influenced by the types of associated PSPs.

Action Potentials↗

Computer simulations of liquid silica: equation of state and liquid-liquid phase transition.

We conduct extensive molecular dynamics computer simulations of two models for liquid silica [the model of Woodcock, Angell and Cheeseman, J. Phys. Chem. 65, 1565 (1976); and that of van Beest, Kramer, and van Santen, Phys. Rev. Lett. 64, 1955 (1990)] to determine their thermodynamic properties at low temperature T across a wide density range. We find for both models a wide range of states in which isochores of the potential energy U are a linear function of T(3/5), as recently proposed for simple liquids [Rosenfeld and P. Tarazona, Mol. Phys. 95, 141 (1998)]. We exploit this behavior to fit an accurate equation of state to our thermodynamic data. Extrapolation of this equation of state to low T predicts the occurrence of a liquid-liquid phase transition for both models. We conduct simulations in the region of the predicted phase transition, and confirm its existence by direct observation of phase separating droplets of atoms with distinct local density and coordination environments.

Journal Article↗

Middle cerebral artery anatomy and characteristics of embolic signals: a dual gate computer simulation study.

In terms of microembolic signal (MES) detection, the anatomy of the middle cerebral artery (MCA) mainstem has only scarcely been considered. The vessel itself, however, could be at least partly responsible for the enormous variation when calculating the essential time difference (deltat) values of MES using the dual-gate technique. Therefore, we studied the time characteristics of MES in a computer simulation applying an anatomically realistic vessel and a dual-gate TCD approach. Three different MCA anatomies and two MES to blood intensities were simulated as well as two different sample volume settings. The MES length (proximal sample volume t1; distal sample volume t2) and deltat were calculated for different angles of insonation and sample volume depths. The calculations of the time characteristics of MES showed extreme variation, with only modest changes of the insonation angle (t1 4-34 ms; deltat 9-27 ms) or the sample volume depth (t1 7-27 ms; deltat 6-32 ms). The variation could be considerably reduced with modified TCD settings i.e., a shorter gate separation combined with a shorter receiver gate time in the distal sample volume (deltat with changing insonation angles 6-19 ms; deltat with changing insonation depths 13-17 ms). These results not only urge us to a cautious interpretation of the properties of single MES, but also contribute to an understanding of the marked deltat variation using the dual-gate technique.

Cerebral Arteries↗

The initiator titration model: computer simulation of chromosome and minichromosome control.

The initiator titration model was formulated to explain the initiation control of the bacterial chromosome. In particular, features concerning the replication behaviour of minichromosomes, such as their high copy number and Escherichia coli's ability to coinitiate chromosome and many minichromosome origins, were considered during the formulation of the model. The model is based on the initiator protein DnaA and its binding sites, DnaA boxes, in oriC, in the dnaA promoter and at other positions on the chromosome. Another important factor in the model is the eclipse period created by the hemimethylation of a new oriC which makes it refractory to initiation. The model was analysed by computer simulations using a stochastic approach varying the different input parameters, and the resulting computer cells were compared with data on living E. coli cells. Here we present the outcome of a few of these simulations concerning the eclipse period, in silico-shift experiments blocking initiation or elongation of replication, and introduction of minichromosomes into the computer cells. We also discuss the synthesis of DnaA protein in the computer cells. From our simulations, we conclude that, whether true or not, the model can mimic the in vivo initiation control of E. coli.

Bacterial Proteins↗

Protein-protein interaction: an analysis by computer simulation.

A survey of protein-protein interactions in structures derived by X-ray crystallography of protease-inhibitor and antigen-antibody complexes shows that they form close-packed interfaces from which water is excluded. The interfaces are of almost constant size, and they contain about ten hydrogen bonds. These features account for the stability of the complexes. To test whether they also account for specificity, we designed a computer simulation that searches for complementary surfaces on two protein molecules. In all cases tested, the simulation finds a number of complexes having interfaces and hydrogen bonds equivalent to those of the native complexes. These artificial complexes might represent secondary specificities, which can be detected when normal association is prevented by mutation or other means.

Computer Simulation↗

[The computer simulation of orthodontic tooth movements].

A personal computer programme is presented which allows the prediction of orthodontic tooth movement under the influence of any given force and moment. The changes in position of the front teeth caused by the chosen forces appear on the monitor as a three-dimensional diagram and as a movie-like picture sequence.

Computer Simulation↗

Computer simulation of counterlungs.

We have developed a computer model of chest-mounted counterlungs, which accounts for counterlung shape, effective volume, and pressure centroid. The model has been validated and the principles are applicable to other counterlung systems. The highly non-linear and discontinuous behavior of a counterlung is predicted by use of a sophisticated numerical integration method that computes variables such as pressure and volume in the time domain. Three separate stiffness (reciprocal of compliance) terms have been used which contribute to the diver's work of breathing: material elastic stiffness, "gas" stiffness, and "hydrostatic" stiffness. The model provides a significant advance in the understanding of counterlung behavior, allowing the performance of practical equipment to be predicted.

Computer Simulation↗

Adaptive constraints and the phylogenetic comparative method: a computer simulation test.

Recently, the utility of modern phylogenetic comparative methods (PCMs) has been questioned because of the seemingly restrictive assumptions required by these methods. Although most comparative analyses involve traits thought to be undergoing natural or sexual selection, most PCMs require an assumption that the traits be evolving by less directed random processes, such as Brownian motion (BM). In this study, we use computer simulation to generate data under more realistic evolutionary scenarios and consider the statistical abilities of a variety of PCMs to estimate correlation coefficients from these data. We found that correlations estimated without taking phylogeny into account were often quite poor and never substantially better than those produced by the other tested methods. In contrast, most PCMs performed quite well even when their assumptions were violated. Felsenstein's independent contrasts (FIC) method gave the best performance in many cases, even when weak constraints had been acting throughout phenotypic evolution. When strong constraints acted in opposition to variance-generating (i.e., BM) forces, however, FIC correlation coefficients were biased in the direction of those BM forces. In most cases, all other PCMs tested (phylogenetic generalized least squares, phylogenetic mixed model, spatial autoregression, and phylogenetic eigenvector regression) yielded good statistical performance, regardless of the details of the evolutionary model used to generate the data. Actual parameter estimates given by different PCMs for each dataset, however, were occasionally very different from one another, suggesting that the choice among them should depend on the types of traits and evolutionary processes being considered.

Adaptation, Physiological↗

Restoring unassisted natural gait to paraplegics via functional neuromuscular stimulation: a computer simulation study.

Functional neuromuscular stimulation (FNS) of paralyzed muscles has enabled spinal-cord-injured patients to regain a semblance of lower-extremity control, for example to ambulate while relying heavily on the use of walkers. Given the limitations of FNS, specifically low muscle strengths, high rates of fatigue, and a limited ability to modulate muscle excitations, it remains unclear, however, whether FNS can be developed as a practical means to control the lower extremity musculature to restore aesthetic, unsupported gait to paraplegics. A computer simulation of FNS-assisted bipedal gait shows that it is difficult, but possible to attain undisturbed, level gait at normal speeds provided the electrically-stimulated ankle plantarflexors exhibit either near-normal strengths or are augmented by an orthosis, and at least seven muscle-groups in each leg are stimulated. A combination of dynamic programming and an open-loop, trial-and-error adjustment process was used to find a suboptimal set of discretely-varying muscle stimulation patterns needed for a 3-D, 8 degree-of-freedom dynamic model to sustain a step. An ankle-foot orthosis was found to be especially useful, as it helped to stabilize the stance leg and simplified the task of controlling the foot during swing. It is believed that the process of simulating natural gait with this model will serve to highlight difficulties to be expected during laboratory and clinical trials.

Computer Simulation↗

Movement compatibility for rotary control and circular display--Computer Simulated Test and real Hardware Test.

This experiment studied strength and reversibility of direction-of-motion stereotypes and response times for different configurations of circular displays and rotary knobs. The effect of pointer position, instruction of turn direction, and control plane on movement compatibility was analyzed with precise quantitative measures of strength and reversibility index of stereotype. A comparison of results was made between a Computer Simulated Test and a Hardware Test with real rotary controls. There was consensus in the results of the two tests that strong and significantly reversible clockwise-for-clockwise (CC) and anticlockwise-for-anticlockwise (AA) stereotypes were obtained at the 12 o'clock position. Subjects' response times were found to be generally longer when there were no clear movement stereotypes. Nevertheless, differences of results were observed that while the CC and AA preferences were found to be dominant and reversible at all the planes and pointer positions in the Hardware Test, there was variation in the strength and reversibility of the two stereotypes amongst different testing configurations in the Simulated Test. This phenomenon was explained by the operating of the clockwise-for-right and anticlockwise-for-left principles, as shown in the analysis of contributions of component principles to the overall stereotype. The differences of results from the two tests were discussed with regard to simulation fidelity and it was suggested that a real Hardware Test should be used whenever possible for determination of design parameters of control panels in consideration of movement compatibility. Based on the Hardware Test, a pointer is recommended to be positioned at 12 o'clock position for check reading or resetting purpose, and the frontal plane is the best plane for positioning a rotary control with circular display. The results of this study provided significant implications for the industrial design of control panels used in man-machine interfaces for improved human performance.

Adult↗

A computer simulation of conduction block: effects produced by actual block versus interphase cancellation.

A reduction in compound muscle action potential (CMAP) amplitude and area following proximal versus distal stimulation is the accepted clinical hallmark of conduction block; however, quantitative criteria for determining conduction block remain ambiguous. In this study, digitized records of individual motor unit action potentials (MUAPs) elicited by incremental stimulation in vivo were arithmetically combined in a computer simulation of CMAP generation. Through simulation of possible phase interaction patterns of individual MUAPs, we have shown that abnormal temporal dispersion alone can produce reductions in CMAP area of up to 50%, values that are commonly thought to represent conduction block. Furthermore, by simulating conduction block without excessive temporal dispersion in defined subpopulations of axons, we have demonstrated the importance of the fastest conducting (largest MUAP) axons in determining CMAP amplitude and area. In conclusion, measurements of CMAP amplitude and area in determining conduction block may be misleading if there is significant abnormal temporal dispersion, and quantitation of the degree of conduction block is difficult without knowledge of which subpopulations of axons are affected.

Action Potentials↗

Experiments on movement of DNA regions in Escherichia coli evaluated by computer simulation.

During the cell cycle of Escherichia coli DNA is replicated and segregated over two prospective daughter cells. Nucleoids as a whole separate gradually in line with cell elongation, but sub-nucleoid DNA regions may behave differently, separating non-gradually. We tested the ability of three models to predict the outcome of a fluorescent in situ hybridisation (FISH) experiment. We did this by comparing computer-simulated data with experimental data. The first model predicts gradual separation in line with cell elongation. The second model predicts that origins stick together for some time after duplication before one copy jumps to the other side of the cell (non-gradual separation). The simulated data of these models are very similar, indicating that FISH is not a suitable method to distinguish between these two models. The third model predicts that origins may be anywhere within the nucleoid(s). We found that simulated data using the third model resemble the experimental data most. However, DNA regions are not randomly localised in the cell, although their localisation is fuzzy. We propose that movement of DNA regions is the result of a combination of factors. Nucleoid segregation (or the forces behind it) dictates the overall direction of movement. Other factors, of which we show that diffusion could be an important one, move DNA in other directions giving rise to non-gradual movement in individual cells and contributing to variation in intracellular position per cell length in a population of cells.

Cell Cycle↗

Peripheral binding mode and penetration depth of cobra cardiotoxin on phospholipid membranes as studied by a combined FTIR and computer simulation approach.

Cobra cardiotoxin, a cytotoxic beta-sheet basic polypeptide, is known to cause membrane leakage in many cells including human erythrocytes. Herein, we demonstrate that the major cobra cardiotoxin from Naja atra, CTX A3, can cause leakage of vesicle contents in phosphatidylglycerol (PG) and phosphatidylserine containing, but not in pure phosphatidylcholine (PC), membrane bilayers. By the combined polarized attenuated total reflection infrared spectroscopy and computer simulation studies, CTX A3 is shown to peripherally bind to both zwitterionic and anionic monolayers in a similar edgewise manner with a tilted angle of approximately 48 +/- 20 degrees between the beta-sheet plane of the CTX molecule and the normal of the membrane surface. The average surface area expansion induced by CTX A3 binding to the PG monolayer, however, is two times larger than that of the PC monolayer as determined by the Langmuir minitrough method. Interaction energy considerations of CTX A3 on neutral and negatively charged membrane surfaces suggests that the electrostatic interaction between anionic lipid and cationic CTXs plays a role in modulating the penetration depth of CTX molecules on the initial peripheral binding mode and reveals a pathway leading to the formation of an inserted mode in negatively charged membrane bilayers.

Animals↗