Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

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.

Profluorescent nitroxides as sensitive probes of oxidative change and free radical reactions

This paper presents a review on the use of tethered nitroxide–fluorophore molecules as probes of oxidative change and free radical generation and reaction. The proximity of the nitroxide free radical to the fluorophore suppresses the normal fluorescence emission process. Nitroxide free radical scavenging, metabolism or redox chemistry return the system to its natural fluorescent state and so these tethered nitroxide–fluorophore molecules are described as being profluorescent. A survey of profluorescent nitroxides found in the literature is provided as well as background on the mechanism of action and applications of these compounds as fluorometric probes within the fields of biological, materials and environmental sciences.

Living characteristics of the free-radical ring-closing polymerization of diallyldimethylammonium chloride

In this communication we provide the most recent results on RAFT-mediated ring-closing polymerization of diallyldimethylammonium chloride (DADMAC). The polymerization was carried out in aqueous solution employing 2,2′-azobis(2-methylpropionamidine)-dihydrochloride as the free radical initiator and trithiocarbonate RAFT agent (2-{[(dodecylsulfanyl)carbonothioyl sulfanyl]}propanoic acid, DoPAT) as the controlling RAFT agent. The results show that – while the system is not as completely controlled as previously described – it is nevertheless possible to mediate the polymerization of DADMAC and impart some living characteristics onto the system. The initial study on the RAFT-mediated polymerization of DADMAC may have overestimated the degree of livingness within this reaction. However, it is possible – at low conversions – for some living characteristics to be observed, as the evolution of molecular weight with conversion is linear. In addition, polymers with a reasonably narrow polydispersity can be isolated.

A social marketing approach to value creation in a Well-Women’s health service

Understanding consumer value is imperative in health care as the receipt of value drives the demand for health care services. While there is increasing research into health-care that adopts an economic approach to value, this paper investigates a non-financial exchange context and uses an experiential approach to value, guided by a social marketing approach to behaviour change. An experiential approach is deemed more appropriate for government health-care services that are free and for preventative rather than treatment purposes. Thus instead of using an illness-paradigm to view health services outcomes, we adopt a wellness paradigm. Using qualitative data gathered during 25 depth interviews the authors demonstrate how social marketing thinking has guided the identification of six themes that represent four dimensions of value (functional, emotional, social and altruistic) evident during the health care consumption process of a free government service.

Stochastic regularization method for backward Cauchy problem in Banach spaces

We consider a stochastic regularization method for solving the backward Cauchy problem in Banach spaces. An order of convergence is obtained on sourcewise representative elements.

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.

Complementary use of modeling grammars

Conceptual modeling continues to be an important means for graphically capturing the requirements of an information system. Observations of modeling practice suggest that modelers often use multiple modeling grammars in combination to articulate various aspects of real-world domains. We extend an ontological theory of representation to suggest why and how users employ multiple conceptual modeling grammars in combination. We provide an empirical test of the extended theory using survey data and structured interviews about the use of traditional and structured analysis grammars within an automated tool environment. We find that users of the analyzed tool combine grammars to overcome the ontological incompleteness that exists in each grammar. Users further selected their starting grammar from a predicted subset of grammars only. The qualitative data provides insights as to why some of the predicted deficiencies manifest in practice differently than predicted.

Bending and bundling of metal-free vertically aligned ZnO nanowires due to electrostatic interaction

Bending and bundling was observed from vertically aligned arrays of ZnO nanowires with flat (0001) top surfaces, which were synthesized using a vapor-phase method without metal catalysts. Sufficient evidence was found to exclude electron-beam bombardment during scanning electron microscopy as a cause for bending and bundling. We attribute the bending and bundling to electrostatic interactions due to charged (0001) polar surfaces, and also discussed the threshold surface charge densities for the bending and bundling based on a simple cantilever-bending model. Some growth features were indicative of the operation of electrostatic interactions during the growth.

Catalyst-free growth and optical properties of vertically aligned ZnO Nanorod Arrays on Si substrates covered with thin buffer layers

Vertically aligned ZnO nanorods have been grown on silicon substrates pre-coated with thin, less than 10 nm, textured ZnO seeding layers via a vapor-solid mechanism. The ZnO seeding layers, which were essential for vertical alignment of ZnO nanorods without using any metal catalyst, were prepared by decomposing zinc acetate. The structure and the luminescence properties of the ZnO nanorods synthesized onto ZnO seeding layers were investigated and their morphologies were compared with those of single-crystalline GaN substrates and silicon substrates covered with sputtered ZnO flms. Patterning of ZnO seed layers using photolithography allowed the fabrication of patterned ZnO-nanorod arrays.

The current context of Queensland primary teacher engagement with professional learning through professional associations

Engaging Queensland primary teachers in professional associations can be a challenge, particularly for subject-specific associations. Professional associations are recognised providers of professional learning. By not being involved in professional associations primary teachers are missing potential quality professional learning opportunities that can impact the results of their students. The purpose of the research is twofold: Firstly, to provide a thorough understanding of the current context in order to assist professional associations who wish to change from their current level of primary teacher engagement; and secondly, to contribute to the literature in the area of professional learning for primary teachers within professional associations. Using a three part research design, interviews of primary teachers and focus groups of professional association participants and executives were conducted and themed to examine the current context of engagement. Force field analysis was used to provide the framework to identify the driving and restraining forces for primary teacher engagement in professional learning through professional associations. Communities of practice and professional learning communities were specifically examined as potential models for professional associations to consider. The outcome is a diagrammatic framework outlining the current context of primary teacher engagement, specifically the driving and restraining forces of primary teacher engagement with professional associations. This research also identifies considerations for professional associations wishing to change their level of primary teacher engagement. The results of this research show that there are key themes that provide maximum impact if wishing to increase engagement of primary teachers in professional associations. However the implications of this lies with professional associations and their alignment between intent and practice dedicated to this change.

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

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

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.