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.

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.

Influences on student learning in engineering : some results from case study fieldwork

This paper closely examines factors affecting students’ progression in their engineering programs through fieldwork conducted at three Australian universities. To extract clues on how specific teaching methods can be used to maximize learning, the investigation considered factors such as understanding how students take in, process and present information. A number of focus groups were conducted with students and the data gathered was combined with survey results of students’ and academics’ learning styles. The paper reports on the process followed, and provides some analysis of the gathered data, as part of an Australian Learning and Teaching Council, ALTC, Associate Fellowship program.

Finitude (Mallee:Time)

An interactive installation with full body interface, digital projection, multi-touch sensitive screen surfaces, interactive 3D gaming software, motorised dioramas, 4.1 spatial sound & new furniture forms - investigating the cultural dimensions of sustainability through the lens of 'time'. “Time is change, time is finitude. Humans are a finite species. Every decision we make today brings that end closer, or alternatively pushes it further away. Nothing can be neutral”. Tony Fry DETAILS: Finitude (Mallee:Time) is a major new media/sculptural hybrid work premiered in 2011 in version 1 at the Ka-rama Motel for the Mildura Palimpsest #8 ('Collaborators and Saboteurs'). Each participant/viewer lies comfortably on their back on the double bed of Room 22. Directly above them, supported by a wooden structure, not unlike a house frame, is a semi-transparent Perspex screen that displays projected 3D imagery and is simultaneously sensitive to the lightest of finger touches. Depending upon the ever changing qualities of the projected image on this screen the participant can see through its surface to a series of physical dioramas suspended above, lit by subtle LED spotlighting. This diorama consists of a slowly rotating series of physical environments, which also include several animatronic components, allowing the realtime composition of whimsical ‘landscapes’ of both 'real' and 'virtual' media. Through subtle, non-didactic touch-sensitive interactivity the participant then has influence over both the 3D graphic imagery, the physical movements of the diorama and the 4.1 immersive soundscape, creating an uncanny blend of physical and virtual media. Five speakers positioned around the room deliver a rich interactive soundscape that responds both audibly and physically to interactions. VERSION 1, CONTEXT/THEORY: Finitude (Mallee: Time) is Version 1 of a series of presentations during 2012-14. This version has been inspired through a series of recent visits and residencies in the SW Victoria Mallee country. Further drawing on recent writings by post colonial author Paul Carter, the work is envisaged as an evolving ‘personal topography’ of place-discovery. By contrasting and melding readily available generalisations of the Mallee regions’ rational surfaces, climatic maps and ecological systems with what Carter calls “a fine capillary system of interconnected words, places, memories and sensations” generated through my own idiosyncratic research processes, Finitude (Mallee Time) invokes a “dark writing” of place through outside eyes - an approach that avoids concentration upon what 'everyone else knows', to instead imagine and develop a sense how things might be. This basis in re-imagining and re-invention becomes the vehicle for the work’s more fundamental intention - as a meditative re-imagination of 'time' (and region) as finite resources: Towards this end, every object, process and idea in the work is re-thought as having its own ‘time component’ or ‘residue’ that becomes deposited into our 'collective future'. Thought this way Finitude (Mallee Time) suggests the poverty of predominant images of time as ‘mechanism’ to instead envisage time as a plastic cyclical medium that we can each choose to ‘give to’ or ‘take away from’ our future. Put another way - time has become finitude.

Seasonality of suicide in Shandong China, 1991–2009 : associations with gender, age, area and methods of suicide

Backgrounds Whether suicide in China has significant seasonal variations is unclear. The aim of this study is to examine the seasonality of suicide in Shandong China and to assess the associations of suicide seasonality with gender, residence, age and methods of suicide. Methods Three types of tests (Chi-square, Edwards' T and Roger's Log method) were used to detect the seasonality of the suicide data extracted from the official mortality data of Shandong Disease Surveillance Point (DSP) system. Peak/low ratios (PLRs) and 95% confidence intervals (CIs) were calculated to indicate the magnitude of seasonality. Results A statistically significant seasonality with a single peak in suicide rates in spring and early summer, and a dip in winter was observed, which remained relatively consistent over years. Regardless of gender, suicide seasonality was more pronounced in rural areas, younger age groups and for non-violent methods, in particular, self-poisoning by pesticide. Conclusions There are statistically significant seasonal variations of completed suicide for both men and women in Shandong, China. Differences exist between residence (urban/rural), age groups and suicide methods. Results appear to support a sociological explanation of suicide seasonality.

Reduced sampling efficiency causes degraded Vernier hyperacuity with normal aging: Vernier acuity in position noise

Vernier acuity, a form of visual hyperacuity, is amongst the most precise forms of spatial vision. Under optimal conditions Vernier thresholds are much finer than the inter-photoreceptor distance. Achievement of such high precision is based substantially on cortical computations, most likely in the primary visual cortex. Using stimuli with added positional noise, we show that Vernier processing is reduced with advancing age across a wide range of noise levels. Using an ideal observer model, we are able to characterize the mechanisms underlying age-related loss, and show that the reduction in Vernier acuity can be mainly attributed to the reduction in efficiency of sampling, with no significant change in the level of internal position noise, or spatial distortion, in the visual system.

Land fraud and inappropriate dealings in an electronic environment : An Australian and New Zealand perspective

The thesis presented in this paper is that the land fraud committed by Matthew Perrin in Queensland and inflicted upon Roger Mildenhall in Western Australia demonstrates the need for urgent procedural reform to the conveyancing process. Should this not occur, then calls to reform the substantive principles of the Torrens system will be heard throughout the jurisdictions that adopt title by registration, particularly in those places where immediate indefeasibility is still the norm. This paper closely examines the factual matrix behind both of these frauds, and asks what steps should have been taken to prevent them occurring. With 2012 bringing us Australian legislation embedding a national e-conveyancing system and a new Land Transfer Act for New Zealand we ask what legislative measures should be introduced to minimise the potential for such fraud. In undertaking this study, we reflect on whether the activities of Perrin and the criminals responsible for stealing Mildenhall's land would have succeeded under the present system for automated registration utilised in New Zealand.