Space as the final frontier in stochastic simulations of biological systems

Recent technological and theoretical advances are only now allowing the simulation of detailed kinetic models of biological systems that reflect the stochastic movement and reactivity of individual molecules within cellular compartments. The behavior of many systems could not be properly understood without this level of resolution, opening up new perspectives of using computer simulations to accelerate biological research. We review the modeling methodology applied to stochastic spatial models, also to the attention of non-expert potential users. Modeling choices, current limitations and perspectives of improvement of current general-purpose modeling/simulation platforms for biological systems are discussed.     

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches

Computer simulations have become an invaluable tool to studythe sometimes counterintuitive temporal dynamics of (bio-)chemicalsystems. In particular, stochastic simulation methods have attractedincreasing interest recently. In contrast to the well-knowndeterministic approach based on ordinary differential equations,they can capture effects that occur due to the underlying discretenessof the systems and random fluctuations in molecular numbers.Numerous stochastic, approximate stochastic and hybrid simulationmethods have been proposed in the literature. In this article,they are systematically reviewed in order to guide the researcherand help her find the appropriate method for a specific problem.      

Use of the Gibbs Sampler to Obtain Conditional Tests, with Applications

A random sample is drawn from a distribution which admits aminimal sufficient statistic for the parameters. The Gibbs sampleris proposed to generate samples, called conditionally sufficientor co-sufficient samples, from the conditional distributionof the sample given its value of the sufficient statistic. Theprocedure is illustrated for the gamma distribution. Co-sufficientsamples may be used to give exact tests of fit; for the gammadistribution these are compared for size and power with approximatetests based on the parametric bootstrap.     

The stochastic community and the logistic-J distribution

A new formal model called the multispecies logistical (MSL) system produces species/abundance distributions that are compared statistically with those found in natural communities. The system, which is able to handle thousands of individuals from hundreds of species, iteratively selects random pairs of individuals and transfers a unit of biomass (or energy) between the respective species. Several elaborations of the model, including those with trophic compartments, appear to produce the same distribution. The theoretical distribution underlying the MSL system is a hyperbolic section, here called the logistic-J distribution. In the study reported here, the logistic-J distribution has been fitted to the species-abundance histograms of 125 randomly selected taxocoenoses. Since the overall chi square score of the logistic-J achieved near-optimality in this study, it cannot be distinguished statistically from the J-curves observed by field biologists. For comparison, the log-series distribution was given the same test and scored significantly higher (more poorly) than the mean logistic-J score. If there is a single, major distribution underlying natural communities, it is not the log-series distribution. Nor, owing to a mathematical error in its formulation, can it be the lognormal distribution. In the MSL system each species follows a “stochastic orbit” about the mean abundance producing, in consequence, the logistic-J distribution. Such orbits are produced by any system in which the probabilities of reproduction and death are approximately equal. Accordingly, the “stochastic communities hypothesis” is proposed here as the overall mechanism governing abundances in all natural communities. It is not a single mechanism, per se, but the net effect of all environmental influences.     

Normal Approximation of a Discrete Distribution on Exact Test of Uniform Association in a 2 × 3 Table

For the analysis of 2 × 3 tables, TOMIZAWA (1993) considered an exact test of uniform association, which is an extension of independence, and then derived a discrete distribution. This paper gives a normal approximation of the discrete distribution and describes that the normalized statistic can test a one-sided hypothesis on the uniform association. Also it points out that the square of the normalized test statistic is equal to the Pearson's chi-squared statistic for testing the uniform association.     

The spikes trains probability distributions: A stochastic calculus approach

We discuss the statistics of spikes trains for different types of integrate-and-fire neurons and different types of synaptic noise models. In contrast with the usual approaches in neuroscience, mainly based on statistical physics methods such as the Fokker-Planck equation or the mean-field theory, we chose the point of the view of the stochastic calculus theory to characterize neurons in noisy environments. We present four stochastic calculus techniques that can be used to find the probability distributions attached to the spikes trains. We illustrate the power of these techniques for four types of widely used neuron models. Despite the fact that these techniques are mathematically intricate we believe that they can be useful for answering questions in neuroscience that naturally arise from the variability of neuronal activity. For each technique we indicate its range of applicability and its limitations.     

Numerical simulation of a stochastic model for cancerous cells submitted to chemotherapy

A stochastic model is proposed to study the problem of inherent resistance by cell populations when chemotherapeutic agents are used to control tumor growth. Stochastic differential equations are introduced and numerically integrated to simulate expected response to the chemotherapeutic strategies as a function of different parameters. Satisfactory demonstration runs of the model indicate that it could represent a useful tool in verifying the results of experimental and clinical chemotherapy courses and planning treatment strategies. Some types of behaviour are illustrated graphically.Work supported by the C.N.R. Grants: 85.02652.01; 86.02116.01     

A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks

Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.     

A stochastic analysis of actin polymerization in the presence of twinfilin and gelsolin

We develop an efficient stochastic simulation algorithm for analyzing actin filament growth and decay in the presence of various actin-binding proteins. The evolution of nucleotide profiles of filaments can be tracked and the resulting feedback to actin-binding proteins is incorporated. The computational efficiency of the new method enables us to focus on experimentally realistic problems, and as one example we use it to analyze the experimental data of Helfer et al. [(2006). Mammalian twinfilin sequesters ADP-G-actin and caps filament barbed ends: implications in motility. EMBO J. 25, 1184-1195] on the capping and G-actin sequestering activity of twinfilin. We show that the binding specificity of twinfilin for ADP-G-actin is crucial for the observed biphasic evolution of the filament length distribution in the presence of twinfilin, and we demonstrate that twinfilin can be an essential part of the molecular machinery for regulating filament lengths after a short burst of polymerization. Significantly, our simulations indicate that the pyrenyl-actin fluorescence experiments would fail to report the emergence of large filaments under certain experimental conditions.