Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Stochastic dynamic programming for election timing: A game theory approach

In this paper, we consider dynamic programming for the election timing in the majoritarian parliamentary system such as in Australia, where the government has a constitutional right to call an early election. This right can give the government an advantage to remain in power for as long as possible by calling an election, when its popularity is high. On the other hand, the opposition's natural objective is to gain power, and it will apply controls termed as "boosts" to reduce the chance of the government being re-elected by introducing policy and economic responses. In this paper, we explore equilibrium solutions to the government, and the opposition strategies in a political game using stochastic dynamic programming. Results are given in terms of the expected remaining life in power, call and boost probabilities at each time at any level of popularity.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

The effect of grain refinement and cooling rate on the hot tearing of wrought aluminium alloys

Using modifications to the Rappaz-Drezet-Gremaud hot tearing model, and using empirical equations developed for grain size and dendrite arm spacing (DAS) on the addition of grain refiner for a range of cooling rates, the effect of grain refinement and cooling rate on hot tearing susceptibility has been analysed. It was found that grain refinement decreased the grain size and made the grain morphology more globular. Therefore refining the grain size of an equiaxed dendritic grain decreased the hot tearing susceptibility. However, when the alloy was grain refined such that globular grain morphologies where obtained, further grain refinement increased the hot tearing susceptibility. Increasing the cooling decreased the grain size and made the grain morphology more dendritic and therefore increased the likelihood of hot tearing. The effect was particularly strong for equiaxed dendritic grain morphologies; hence grain refinement is increasingly important at high cooling rates to obtain more globular grain morphologies to reduce the hot tearing susceptibility.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Stochastic modelling of the invasion process of nematodes in fly larvae

Stochastic models based on Markov birth processes are constructed to describe the process of invasion of a fly larva by entomopathogenic nematodes. Various forms for the birth (invasion) rates are proposed. These models are then fitted to data sets describing the observed numbers of nematodes that have invaded a fly larval after a fixed period of time. Non-linear birthrates are required to achieve good fits to these data, with their precise form leading to different patterns of invasion being identified for three populations of nematodes considered. One of these (Nemasys) showed the greatest propensity for invasion. This form of modelling may be useful more generally for analysing data that show variation which is different from that expected from a binomial distribution.

Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

Quantification of geological uncertainty and risk using stochastic simulation and applications in the coal mining industry

Stochastic simulation is a recognised tool for quantifying the spatial distribution of geological uncertainty and risk in earth science and engineering. Metals mining is an area where simulation technologies are extensively used; however, applications in the coal mining industry have been limited. This is particularly due to the lack of a systematic demonstration illustrating the capabilities these techniques have in problem solving in coal mining. This paper presents two broad and technically distinct areas of applications in coal mining. The first deals with the use of simulation in the quantification of uncertainty in coal seam attributes and risk assessment to assist coal resource classification, and drillhole spacing optimisation to meet pre-specified risk levels at a required confidence. The second application presents the use of stochastic simulation in the quantification of fault risk, an area of particular interest to underground coal mining, and documents the performance of the approach. The examples presented demonstrate the advantages and positive contribution stochastic simulation approaches bring to the coal mining industry

Effectiveness of evaporative cooling of beef cattle housed in confinement

Eighteen Angus steers exposed to high heat load conditions were used to assess the effectiveness of four spray cooling systems, on reducing the effects of heat load, the impact on microclimate and water usage. The steers were housed in groups of nine in a fully enclosed shed and were exposed to high heat load conditions for four days. The cooling systems used were water applied via a hose, via overhead sprinklers, via sprinklers at leg height and via misters. The water used was approximately 31 oC and contained 3% NaCl. Fans were used to ensure adequate air movement over the cattle. The animal parameters measured were feed intake, respiration rate, panting score and behaviour. Climatic factors were ambient temperature and wet bulb temperature. Ammonia levels were also measured. The hose, overhead sprinklers and misting were successful in reducing heat load on the cattle. The leg wetting system did not work because the dominant cattle blocked access to the sprinklers. The misting system used the most water (5483 L) and the hose the least (845 L). The application of water had minor impacts on wet bulb temperature, but resulted in significant reductions in dry bulb temperatures.