Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description

3D model of amphioxus steroid receptor complexed with estradiol

The origins of signaling by vertebrate steroids are not fully understood. An important advance was the report that an estrogen-binding steroid receptor [SR] is present in amphioxus, a basal chordate with a similar body plan as vertebrates. To investigate the evolution of estrogen binding to steroid receptors, we constructed a 3D model of amphioxus SR complexed with estradiol. This 3D model indicates that although the SR is activated by estradiol, some interactions between estradiol and human ER[alpha] are not conserved in the SR, which can explain the low affinity of estradiol for the SR. These differences between the SR and ER[alpha] in the steroid-binding domain are sufficient to suggest that another steroid is the physiological regulator of the SR. The 3D model predicts that mutation of Glu-346 to Gln will increase the affinity of testosterone for amphioxus SR and elucidate the evolution of steroid binding to nuclear receptors

Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation & travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape

Effect of Correlation on Multi-Engine Rocket Propulsion Systems

A matter of great concern in the design and operation of multi-engine rocket propulsion systems is the effect of the premature shutdown of one engine on the vehicle. This probability that a premature shutdown will cause a vehicle loss is termed correlation. Based on airbreathing experiences as well as rocket engine data the best estimate of this correlation is made and then applied to the overall multi-engine reliability problem to demonstrate its potential effect. At this point, follow-on analyses are pointed out that illustrate how any potential failures that may cause a correlatable event can be eliminated; thus bringing this correlation to almost 0

Gravitational waves from black hole collisions via an eclectic approach

We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular, we address the problem of combining the close-limit approximation describing ringing black holes and full numerical relativity, required for essentially nonlinear interactions. We demonstrate the effectiveness of our approach using general methods for a model problem, the head-on collision of black holes. Our method allows a more direct physical understanding of these collisions indicating clearly when non-linear methods are important. The success of this method supports our expectation that this unified approach will be able to provide astrophysically relevant results for black hole binaries in time to assist gravitational wave observations.Comment: 4 pages, 3 eps figures, Revte

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealisations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with MATLAB implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community

Centrifuge mounted motion simulator Patent

Centrifuge mounted motion simulator with elevator mechanis

Including the urban heat island in spatial heat health risk assessment strategies: a case study for Birmingham, UK

Background Heatwaves present a significant health risk and the hazard is likely to escalate with the increased future temperatures presently predicted by climate change models. The impact of heatwaves is often felt strongest in towns and cities where populations are concentrated and where the climate is often unintentionally modified to produce an urban heat island effect; where urban areas can be significantly warmer than surrounding rural areas. The purpose of this interdisciplinary study is to integrate remotely sensed urban heat island data alongside commercial social segmentation data via a spatial risk assessment methodology in order to highlight potential heat health risk areas and build the foundations for a climate change risk assessment. This paper uses the city of Birmingham, UK as a case study area. Results When looking at vulnerable sections of the population, the analysis identifies a concentration of "very high" risk areas within the city centre, and a number of pockets of "high risk" areas scattered throughout the conurbation. Further analysis looks at household level data which yields a complicated picture with a considerable range of vulnerabilities at a neighbourhood scale. Conclusions The results illustrate that a concentration of "very high" risk people live within the urban heat island, and this should be taken into account by urban planners and city centre environmental managers when considering climate change adaptation strategies or heatwave alert schemes. The methodology has been designed to be transparent and to make use of powerful and readily available datasets so that it can be easily replicated in other urban areas

Modelling delta-notch perturbations during zebrafish somitogenesis

The discovery over the last 15 years of molecular clocks and gradients in the pre-somitic mesoderm of numerous vertebrate species has added significant weight to Cooke and Zeeman's ‘clock and wavefront’ model of somitogenesis, in which a travelling wavefront determines the spatial position of somite formation and the somitogenesis clock controls periodicity (Cooke and Zeeman, 1976). However, recent high-throughput measurements of spatiotemporal patterns of gene expression in different zebrafish mutant backgrounds allow further quantitative evaluation of the clock and wavefront hypothesis. In this study we describe how our recently proposed model, in which oscillator coupling drives the propagation of an emergent wavefront, can be used to provide mechanistic and testable explanations for the following observed phenomena in zebrafish embryos: (a) the variation in somite measurements across a number of zebrafish mutants; (b) the delayed formation of somites and the formation of ‘salt and pepper’ patterns of gene expression upon disruption of oscillator coupling; and (c) spatial correlations in the ‘salt and pepper’ patterns in Delta-Notch mutants. In light of our results, we propose a number of plausible experiments that could be used to further test the model