Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

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 models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Car ownership, mileage, and risky driving among young intermediate drivers

Introduction: Young drivers are at greatest risk of injury or death from a car crash in the first six months of independent driving. In Queensland, the graduated driver licensing (GDL) program was extensively modified in July 2007 and aims to minimise this risk. Increased mileage and car ownership have been found to play a role in risky driving, offences and crashes; however GDL programs typically do not consider these variables. The paper explores the mileage and car ownership characteristics of young newly-licensed intermediate (Provisional) drivers and their relation to risky driving, crashes and offences. Methods: Drivers (n = 1032) aged 17-19 years recruited from across Queensland for longitudinal research completed Survey 1 exploring pre-licence and Learner experiences and sociodemographic characteristics. Survey 2 explored the same variables with a subset of these drivers (n = 341) after they had completed their first six months of independent driving. Results: At Survey 2, most young drivers owned their vehicle. Novices who drove more kilometres and who spent more hours each week driving were more likely to report risky driving. These drivers were also more likely to report being detected by Police for a driving-related offence. Conclusions: GDL programs should incorporate education for the parent and novice driver regarding the increased risks associated with increased driving exposure, particularly where the novices own their vehicle. Parents should be encouraged to delay exclusive access to a vehicle for the novice driver.

Mileage, car ownership, experience of punishment avoidance and the risky driving of young drivers

Objective: Young drivers are at greatest risk of injury or death from a car crash in the first six months of independent driving. In Queensland, the graduated driver licensing (GDL) program was extensively modified in July 2007 in order to reduce this risk. Increased mileage and car ownership have been found to play a role in risky driving, offences and crashes; however GDL programs typically do not consider these variables. In addition, young novice drivers’ experiences of punishment avoidance have not previously been examined. The paper explores the mileage (duration and distance), car ownership and punishment avoidance behaviour of young newly-licensed intermediate (Provisional) drivers and their relationship with risky driving, crashes and offences. Methods: Drivers (n = 1032) aged 17-19 years recruited from across Queensland for longitudinal research completed Survey 1 exploring pre-licence and Learner experiences and sociodemographic characteristics. Survey 2 explored the same variables with a subset of these drivers (n = 341) after they had completed their first six months of independent driving. Results: Most young drivers in Survey 2 reported owning a vehicle and paying attention to Police presence. Drivers who had their own car reported significantly greater mileage and more risky driving. Novices who drove more kilometres, spent more hours each week driving, or avoided actual and anticipated Police presence were more likely to report risky driving. These drivers were also more likely to report being detected by Police for a driving-related offence. The media, parents, friends and other drivers play a pivotal role in informing novices of on-road Police enforcement operations. Conclusions: GDL programs should incorporate education for the parent and novice driver regarding the increased risks associated with greater driving particularly where the novices own a vehicle. Parents should be encouraged to delay exclusive access to a vehicle for the novice driver. Parents should also consider whether their young novice will deliberately avoid Police if they tell them their location. This may reinforce not only the risky behaviour but also the young novice’s beliefs that their parents condone this behaviour.