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.

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.

Cytokine secretion via cholesterol-rich lipid raft-associated SNAREs at the phagocytic cup

Lipopolysaccharide-activated macrophages rapidly synthesize and secrete tumor necrosis factor α (TNFα) to prime the immune system. Surface delivery of membrane carrying newly synthesized TNFα is controlled and limited by the level of soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins syntaxin 4 and SNAP-23. Many functions in immune cells are coordinated from lipid rafts in the plasmamembrane, and we investigated a possible role for lipid rafts in TNFα trafficking and secretion. TNFα surface delivery and secretion were found to be cholesterol- dependent. Upon macrophage activation, syntaxin 4 was recruited to cholesterol-dependent lipid rafts, whereas its regulatory protein, Munc18c, was excluded from the rafts. Syntaxin 4 in activated macrophages localized to discrete cholesterol-dependent puncta on the plasmamembrane, particularly on filopodia. Imaging the early stages of TNFα surface distribution revealed these puncta to be the initial points of TNFα delivery. During the early stages of phagocytosis, syntaxin 4 was recruited to the phagocytic cup in a cholesterol dependent manner. Insertion of VAMP3-positive recycling endosome membrane is required for efficient ingestion of a pathogen. Without this recruitment of syntaxin 4, it is not incorporated into the plasma membrane, and phagocytosis is greatly reduced. Thus, relocation of syntaxin 4 into lipid rafts in macrophages is a critical and rate-limiting step in initiating an effective immune response.

Biomimetic tubular nanofiber mesh and platelet rich plasma-mediated delivery of BMP-7 for large bone defect regeneration.

There is a growing need for successful bone tissue engineering strategies and advanced biomaterials that mimic the structure and function of native tissues carry great promise. Successful bone repair approaches may include an osteoconductive scaffold, osteoinductive growth factors, cells with an osteogenic potential and capacity for graft vascularisation. To increase osteoinductivity of biomaterials, the local combination and delivery of growth factors has been developed. In the present study we investigated the osteogenic effects of calcium phosphate (CaP)-coated nanofiber mesh tube-mediated delivery of BMP-7 from a PRP matrix for the regeneration of critical sized segmental bone defects in a small animal model. Bilateral full-thickness diaphyseal segmental defects were created in twelve male Lewis rats and nanofiber mesh tubes were placed around the defect. Defects received either treatment with a CaP-coated nanofiber mesh tube (n = 6), an un-coated nanofiber mesh tube (n=6) a CaP-coated nanofiber mesh tube with PRP (n=6) or a CaP-coated nanofiber mesh tube in combination with 5 μg BMP-7 and PRP (n = 6). After 12 weeks, bone volume and biomechanical properties were evaluated using radiography, microCT, biomechanical testing and histology. The results demonstrated significantly higher biomechanical properties and bone volume for the BMP group compared to the control groups. These results were supported by the histological evaluations, where BMP group showed the highest rate of bone regeneration within the defect. In conclusion, BMP-7 delivery via PRP enhanced functional bone defect regeneration, and together these data support the use of BMP-7 in the treatment of critical sized defects.

Australian Learning and Teaching Council, Learning and Teaching Academic Standards Statement for Architecture

The development of the Learning and Teaching Academic Standards Statement for Architecture (the Statement) centred on requirements for the Master of Architecture and proceeded alongside similar developments in the building and construction discipline under the guidance and support of the Australian Deans of Built Environment and Design (ADBED). Through their representation of Australian architecture programs, ADBED have provided high-level leadership for the Learning and Teaching Academic Standards Project in Architecture (LTAS Architecture). The threshold learning outcomes (TLOs), the description of the nature and extent of the discipline, and accompanying notes were developed through wide consultation with the discipline and profession nationally. They have been considered and debated by ADBED on a number of occasions and have, in their fi nal form, been strongly endorsed by the Deans. ADBED formed the core of the Architecture Reference Group (chaired by an ADBED member) that drew together representatives of every peak organisation for the profession and discipline in Australia. The views of the architectural education community and profession have been provided both through individual submissions and the voices of a number of peak bodies. Over two hundred individuals from the practising profession, the academic workforce and the student cohort have worked together to build consensus about the capabilities expected of a graduate of an Australian Master of Architecture degree. It was critical from the outset that the Statement should embrace the wisdom of the greater ‘tribe’, should ensure that graduates of the Australian Master of Architecture were eligible for professional registration and, at the same time, should allow for scope and diversity in the shape of Australian architectural education. A consultation strategy adopted by the Discipline Scholar involved meetings and workshops in Perth, Melbourne, Sydney, Canberra and Brisbane. Stakeholders from all jurisdictions and most universities participated in the early phases of consultation through a series of workshops that concluded late in October 2010. The Draft Architecture Standards Statement was formed from these early meetings and consultation in respect of that document continued through early 2011. This publication represents the outcomes of work to establish an agreed standards statement for the Master of Architecture. Significant further work remains to ensure the alignment of professional accreditation and recognition procedures with emerging regulatory frameworks cascading from the establishment of the Tertiary Education Quality and Standards Agency (TEQSA). The Australian architecture community hopes that mechanisms can be found to integrate TEQSA’s quality assurance purpose with well-established and understood systems of professional accreditation to ensure the good standing of Australian architectural education into the future. The work to build renewed and integrated quality assurance processes and to foster the interests of this project will continue, for at least the next eighteen months, under the auspices of Australian Learning and Teaching Council (ALTC)-funded Architecture Discipline Network (ADN), led by ADBED and Queensland University of Technology. The Discipline Scholar gratefully acknowledges the generous contributions given by those in stakeholder communities to the formulation of the Statement. Professional and academic colleagues have travelled and gathered to shape the Standards Statement. Debate has been vigorous and spirited and the Statement is rich with the purpose, critical thinking and good judgement of the Australian architectural education community. The commitments made to the processes that have produced this Statement reflect a deep and abiding interest by the constituency in architectural education. This commitment bodes well for the vibrancy and productivity of the emergent Architecture Discipline Network (ADN). Endorsement, in writing, was received from the Australian Institute of Architects National Education Committee (AIA NEC): The National Education Committee (NEC) of the Australian Institute of Architects thank you for your work thus far in developing the Learning and Teaching Academic Standards for Architecture In particular, we acknowledge your close consultation with the NEC on the project along with a comprehensive cross-section of the professional and academic communities in architecture. The TLOs with the nuanced levels of capacities – to identify, develop, explain, demonstrate etc – are described at an appropriate level to be understood as minimum expectations for a Master of Architecture graduate. The Architects Accreditation Council of Australia (AACA) has noted: There is a clear correlation between the current processes for accreditation and what may be the procedures in the future following the current review. The requirement of the outcomes as outlined in the draft paper to demonstrate capability is an appropriate way of expressing the measure of whether the learning outcomes have been achieved. The measure of capability as described in the outcome statements is enhanced with explanatory descriptions in the accompanying notes.