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 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.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

The theories of reasoned action and planned behaviour applied to business decision : a selective annotated bibliography

Purpose: This paper provides a selective annotated bibliography that summarises journal articles which have employed either the theory of reasoned action or the theory of planned behaviour to circumstances which are relevant to business activities. Design/methodology/approach: Searches were conducted on the EBSCO Host and ProQuest databases to identify papers that had used either the theory of reasoned action or theory of planned behaviour in their methodology. The bibliography was separated into three categories- financial decision making, strategic decision making, and professional decision making. Implications: The information presented in this paper is intended to assist and facilitate further research by broadening the awareness of the literature and providing examples of the application of the theory as it has been employed in prior research.

Charting the system : the integrated master schedule as a multi-level and poly-temporal boundary object in complex projects

This paper investigates the use of visual artifacts to represent a complex adaptive system (CAS). The integrated master schedule (IMS) is one of those visuals widely used in complex projects for scheduling, budgeting, and project management. In this paper, we discuss how the IMS outperforms the traditional timelines and acts as a ‘multi-level and poly-temporal boundary object’ that visually represents the CAS. We report the findings of a case study project on the way the IMS mapped interactions, interdependencies, constraints and fractal patterns in a complex project. Finally, we discuss how the IMS was utilised as a complex boundary object by eliciting commitment and development of shared mental models, and facilitating negotiation through the layers of multiple interpretations from stakeholders.

Predictors of young people’s charitable intentions to donate money : an extended theory of planned behavior perspective

An extended theory of planned behavior (TPB) was used to predict young people’s intentions to donate money to charities in the future. Students (N = 210; 18-24 years) completed a questionnaire assessing their attitude, subjective norm, perceived behavioral control [PBC], moral obligation, past behavior and intentions toward donating money. Regression analyses revealed the extended TPB explained 61% of the variance in intentions to donate money. Attitude, PBC, moral norm, and past behavior predicted intentions, representing future targets for charitable giving interventions.

Testing a model of physical activity among mothers and fathers of young children: integrating self-determined motivation, planning, and the theory of planned behavior

Parents are at risk for inactivity; however, research into understanding parental physical activity (PA) is scarce. We integrated self-determined motivation, planning, and the theory of planned behavior (TPB) to better understand parental PA. Parents (252 mothers, 206 fathers) completed a main questionnaire assessing measures underpinning these constructs and a 1-week follow-up of PA behavior to examine whether self-determined motivation indirectly influenced intention via the TPB variables (i.e., attitude, subjective norm, and perceived behavioral control) and intention indirectly influenced behavior via planning. We found self-determined motivation on intention was fully mediated by the TPB variables and intention on behavior was partially mediated by the planning variables. In addition, slight differences in the model’s paths between the sexes were revealed. The results illustrate the range of important determinants of parental PA and provide support for the integrated model in explaining PA decision making as well as the importance of examining sex differences.

Investigating mothers' decisions about their child's sun-protective behaviour using the Theory of Planned Behaviour

This study tested the utility of the Theory of Planned Behaviour (TPB) to predict mothers’ decisions to ensure their child engages in sun-protective behaviours. Mothers (N = 162) of children aged four or five years completed standard TPB items (attitude, subjective norm, perceived behavioural control, intention) and additional variables of role construction, mothers’ own sun safe behaviour, planning and past behaviour. One week later, participants (N = 116) reported their behaviour. Results found support for the TPB constructs, role construction, past behaviour and the mediating role of planning. These findings can inform strategies to prevent skin cancer.

Temporal boundary objects in megaprojects : mapping the system with the integrated master schedule

Recently, a stream of project management research has recognized the critical role of boundary objects in the organization of projects. In this paper, we investigate how one advanced scheduling tool, the Integrated Master Schedule (IMS), is used as a temporal boundary object at various stages of complex projects. The IMS is critical to megaprojects which typically span long periods of time and face a high degree of complexity and uncertainty. In this paper, we conceptualize projects of this type as complex adaptive systems (CAS). We report the findings of four case projects on how the IMS mapped interactions, interdependencies, constraints, and fractal patterns of these emerging projects, and how the process of IMS visualization enabled communication and negotiation of project realities. This paper highlights that this advanced timeline tool acts as a boundary object and elicits shared understanding of complex projects from their stakeholders.

Towards an integration of the theory of planned behaviour and cognitive behavioural strategies : an example from a school-based injury prevention programme

Adolescent risk-taking behavior has potentially serious injury consequences and school-based behavior change programs provide potential for reducing such harm. A well-designed program is likely to be theory-based and ecologically valid however it is rare that the operationalisation process of theories is described. The aim of this paper is to outline how the Theory of Planned Behavior and Cognitive Behavioral Therapy informed intervention design in a school setting. Teacher interviews provided insights into strategies that might be implemented within the curriculum and provided detail used to operationalise theory constructs. Benefits and challenges in applying both theories are described with examples from an injury prevention program, Skills for Preventing Injury in Youth.

Vitronectin – master controller or micromanager?

The concept of the cellular glycoprotein vitronectin acts as a biological ‘glue’ and key controller of mammalian tissue repair and remodelling activity is emerging from nearly 50 years of experimental in vitro and in vivo data. Unexpectedly, the vitronectin-knock-out mouse was found to be viable and to have largely normal phenotype. However, diligent observation revealed that the VN-KO animal exhibits delayed coagulation and poor wound healing. This is interpreted to indicate that vitronectin occupies a role in the earliest events of thrombogenesis and tissue repair. That role is as a foundation upon which the thrombus grows in an organised structure. In addition to closing the wound, the thrombus also serves to protect the underlying tissue from oxidation, is a reservoir of mitogens and tissue repair mediators and provides a provisional scaffold for the repairing tissue. In the absence of vitronectin (e.g. VN-KO animal) this cascade is disrupted before it begins. Our data demonstrates that a wide variety of biologically active species associate with VN. While initial studies were focused on mitogens, other classes of bioactives (e.g. glycosaminoglycans, metalloproteinases) are now also known to specifically interact with VN. Many of these interactions are long-lived, often resulting in multi-protein complexes, while others are stable for prolonged periods. Multiprotein complexes provide several advantages: prolonging molecular interaction; sustaining local concentrations, facilitating co-stimulation of cell surface receptors and thereby enhancing cellular / biological responses. We contend that these, or equivalent, multi-protein complexes mediate vitronectin functionality in vivo. It is also likely that many of the species demonstrated to associate with vitronectin in vitro, also associate with vitronectin in vivo in similar multi-protein complexes. Thus the predominant biological function of vitronectin is that of a master controller of the extracellular environment; informing, and possibly instructing cells ‘where’ to behave, ‘when’ to behave, and ‘how’ to behave (i.e. appropriately for the current circumstance).