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.

Look before you leap : a confidence-based method for selecting species criticality while avoiding negative populations in τ-leaping

The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes “significantly” during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

Drinking and driving in Vietnam : perceptions and risk

Road traffic injuries are a major global public health problem but continue to receive inadequate attention. Alcohol influences both risk and consequence of road traffic injury but the scale of the problem is not well understood in many countries. In Vietnam, economic development has brought a substantial increase in the number of registered motorcycles as well as alcohol consumption. Traffic injury is among the leading causes of death in Vietnam but there is little local information regarding alcohol related traffic injuries. The primary goal of this study is to explore the drinking and driving patterns of males and their perceptions towards drink-driving and to determine the relationship between alcohol consumption and road traffic injuries. Furthermore, this thesis aims to present the situation analysis for choosing priority actions to reduce drinking and driving in Vietnam. The study is a combination of two cross-sectional surveys and a pilot study. The pilot study, involving 224 traffic injured patients, was conducted to test the tools and the feasibility of approach methods. In the first survey, male patrons (n=464) were randomly selected at seven restaurants. Face-to-face interviews were conducted when patrons just arrived and breath tests were collected when they were about to leave the restaurant. In the second survey, male patients admitted to hospital following a traffic injury (n=480, of which 414 were motorcycle or bicycle riders) were interviewed and their blood alcohol concentration (BAC) measured by breathalyzer. The results show broadly similar patterns of drinking and driving among male patrons and male traffic injured patients with a high frequency of drinking and drink-driving reported among the majority of the two groups. A high proportion of male patrons were leaving restaurants with a BAC over the legal limit. Factors that significantly associate with the number of drinks and BAC were age, hazardous drinking, frequency of drink-driving in the past year, self-estimated number of drinks consumed to drive legally, perceived family’s disapproval of drink-driving, and perceived legal risk and physical risk. The proportion of patrons and patients with BAC above the legal limit of 0.05 were 86.7% and 60.4% respectively, which was much higher than found in previous studies. In addition, both groups had a high prevalence of BAC over 0.15g/100ml (39.7% of patrons and 45.6% patients), a level that can seriously affect driving capacity. Results from the case-crossover analysis for patients indicate a dose-response relationship between alcohol consumption and the risk of traffic injury. The risk of traffic injury increased when alcohol was consumed before driving and there was a more than 13 fold increase when six or more drinks were consumed. Regarding perceptions towards drinking and driving, findings corroborate the low awareness among males in Vietnam, with a majority of respondents holding a low knowledge of safe and legally permissible alcohol use, and a low perceived risk of drinking and driving. The results also indicate a huge gap in prevention skills in terms of planning ahead or using alternative transport to avoid drink-driving and a perception by patrons and patients of a low rate of disapproval of drink-driving from peers and family. Findings in this study have considerable implications for national policy, injury prevention, clinical practice, reporting systems, and for further research. The low rate of compliance with existing laws and a generally low perceived legal risk toward drink-driving in this study call for the strengthening of enforcement along with mass media campaigns and news coverage in order to decrease the widespread perception of impunity and thereby, to reduce the level of drink-driving. In addition, no significant difference was found in this study on risk of traffic injuries between car drivers and motorcycle drivers. The current inconsistency between legal BAC for drivers of motorcycles, compared to cars, thus needs addressing. Furthermore, as drinking was found to be very common, rather than solely targeting drink-driving, it is important to call for a more strategic and comprehensive approach to alcohol policy in Viet Nam. This study also has considerable implications for clinical practice in terms of screening and brief interventions. Our study suggests that the short form of the AUDIT (AUDIT-C) screening tool is appropriate for use in busy emergency departments. The high proportion of traffic injured patients with evidence of alcohol abuse or hazardous drinking suggests that brief interventions by alcohol and drug counselors in emergency departments are a sensible option to addressing this important problem. The significance of this study is in the combination of the systematic collection of breath test and use of case-crossover design to estimate the risk of traffic injuries after alcohol consumption. The results provide convincing evidence to policy makers, health authorities and the media to help raise community awareness and policy advocacy toward the drinkdriving problem in Vietnam. The findings suggest an urgent need for a multi-sectoral approach to curtail drink-driving in Vietnam, especially programs to raise community awareness and effective legal enforcement. Furthermore, serving as a situation analysis, the thesis should inform the formulation of interventions designed to curtail drinking and driving in Vietnam and other developing countries.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes