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.

Stochastic analysis of the VEGF receptor response curve

Recently, an analysis of the response curve of the vascular endothelial growth factor (VEGF) receptor and its application to cancer therapy was described in [T. Alarcón, and K. Page, J. R. Soc. Lond. Interface 4, 283–304 (2007)]. The analysis is significantly extended here by demonstrating that an alternative computational strategy, namely the Krylov FSP algorithm for the direct solution of the chemical master equation, is feasible for the study of the receptor model. The new method allows us to further investigate the hypothesis of symmetry in the stochastic fluctuations of the response. Also, by augmenting the original model with a single reversible reaction we formulate a plausible mechanism capable of realizing a bimodal response, which is reported experimentally but which is not exhibited by the original model. The significance of these findings for mechanisms of tumour resistance to antiangiogenic therapy is discussed.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

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

Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches.

Understanding business process models : the costs and benefits of structuredness

Previous research has put forward a number of properties of business process models that have an impact on their understandability. Two such properties are compactness and(block-)structuredness. What has not been sufficiently appreciated at this point is that these desirable properties may be at odds with one another. This paper presents the results of a two-pronged study aimed at exploring the trade-off between compactness and structuredness of process models. The first prong of the study is a comparative analysis of the complexity of a set of unstructured process models from industrial practice and of their corresponding structured versions. The second prong is an experiment wherein a cohort of students was exposed to semantically equivalent unstructured and structured process models. The key finding is that structuredness is not an absolute desideratum vis-a-vis for process model understandability. Instead, subtle trade-offs between structuredness and other model properties are at play.

The impact of infrastructure charges on new housing costs : an international comparison

Sourcing funding for the provision of new urban infrastructure has been a policy dilemma for governments around the world for decades. This is particularly relevant in high growth areas where new services are required to support swelling populations. Existing communities resist the introduction of new taxes to fund such infrastructure, hence the introduction of charges to the developer has flourished. The Australian infrastructure funding policy dilemmas are reflective of similar matters to some extent in the United Kingdom, and to a greater extent the United States of America. In these countries, infrastructure cost recovery policies have been in place since the 1940’s and 1970’s respectively. There is an extensive body of theoretical and empirical literature that discusses the passing on (to home buyers) or passing back (to the englobo land seller) of these increased infrastructure charges, and the corresponding impact on housing cost and supply. The purpose of this research is to examine the international evidence that suggests infrastructure charges contribute to increased house prices as well as reduced land supply. The paper concludes that whilst the theoretical work is largely consistent, the empirical research to date is inconclusive and further research is required into these impacts in Australia.

Land buyers likely to foot reform costs

Article in Courier Mail. Friday July 22, 2011.

Legal Profession Act 2007 s 319 - Whether costs agreement made after trial valid and enforceable - whether agreement had retrospective operation

The decision in QCOAL Pty Ltd v Cliffs Australia Coal Pty Ltd [2010] QSC 479 involved an examination of a number of issues relating to the assessment of costs under the Legal Profession Act 2007 (Qld). The decision highlights a range of issues which, in slightly different circumstances, may have deprived the successful party of the right to recover costs by reference to the costs agreement.

Interim bills and costs assessment : was the application in or out of time?

This article examines the decision in Turner v Mitchells Solicitors [2011] QDC 61 and the issue whether an application for assessment of costs under an interim bill at the time of a final bill is subject to the usual 12-month restriction.

The GST Compliance Costs Of Nonprofit Organisations

On 2 December 1998, the Federal Government tabled their policy paper entitled Regulation Impact Statement for the Introduction of a Goods and Services Tax (RIS) in the House of Representatives. The Federal Government predicted that total gross GST compliance costs to Australian businesses in the first year of implementation would be approximately $1,912 million (or $1,195 per firm). Furthermore, it is estimated that the recurrent net compliance costs will be much lower at $131 per firm. Whilst the government made brief references to charitable organisations in their analysis, it stated that the compliance costs faced by nonprofits would, in substance, be no different to the compliance costs faced by businesses or government departments. This paper examines the RIS process in relation to nonprofit organisations in the context of recent taxation legislation affecting nonprofit organisations. It argues that the assumption that nonprofit compliance costs are similar to government and business costs is flawed and makes a case for the RIS process to be reformed to include more appropriate assessments of the impact of legislation on nonprofit enterprises.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

An estimate of road accident costs in Singapore

An earlier study by the Asian Development Bank (ADB) showed that the annual cost of road traffic accidents in 2001 was S$699.36 million which was 0.5% of the annual GDP. This paper attempts to update of the cost estimates of road traffic accidents. More precise methods of computing the human cost, lost output and property damage are adopted which grew in an annual cost of S$610.3 million or 0.338% of the annual GDP in 2003. A more conservative estimate of S$878,000 for fatal accident is also obtained, compared to the earlier figure of S$1.4 million. This study has shown that it is necessary to update the annual traffic accident costs regularly, as the figures vary with the number of accidents which change with time.