Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Contribution of DEAF1 structural domains to the interaction with the breast cancer oncogene LMO4

The proteins LMO4 and DEAF1 contribute to the proliferation of mammary epithelial cells. During breast cancer LMO4 is upregulated, affecting its interaction with other protein partners. This may set cells on a path to tumour formation. LMO4 and DEAF1 interact, but it is unknown how they cooperate to regulate cell proliferation. In this study, we identify a specific LMO4-binding domain in DEAF1. This domain contains an unstructured region that directly contacts LMO4, and a coiled coil that contains the DEAF1 nuclear export signal (NES). The coiled coil region can form tetramers and has the typical properties of a coiled coil domain. Using a simple cell-based assay, we show that LMO4 modulates the activity of the DEAF NES, causing nuclear accumulation of a construct containing the LMO4-interaction region of DEAF1.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.

Arts practice and disconnected youth in Australia : impact and domains of change

Background: This paper describes research conducted with Big hART, Australia's most awarded participatory arts company. It considers three projects, LUCKY, GOLD and NGAPARTJI NGAPARTJI across separate sites in Tasmania, Western NSW and Northern Territory, respectively, in order to understand project impact from the perspective of project participants, Arts workers, community members and funders. Methods: Semi-structured interviews were conducted with 29 respondents. The data were coded thematically and analysed using the constant comparative method of qualitative data analysis. Results: Seven broad domains of change were identified: psychosocial health; community; agency and behavioural change; the Art; economic effect; learning and identity. Conclusions: Experiences of participatory arts are interrelated in an ecology of practice that is iterative, relational, developmental, temporal and contextually bound. This means that questions of impact are contingent, and there is no one path that participants travel or single measure that can adequately capture the richness and diversity of experience. Consequently, it is the productive tensions between the domains of change that are important and the way they are animated through Arts practice that provides sign posts towards the impact of Big hART projects.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Exterior of old synagogue; Hochberg Synagogues; Exterior

Digital Image

Garden gate to Daijas' father's house Architecture; Residences; Exterior

Verso: Das Gartentor zu Daijas Vaterhaus Georg lebete um die Ecke

Exterior view of Schoenbeck residence; Stadtoldendorf, Germany.

Photo owned by Annette Rochaix, Belmont Switz. Deposited: Archiv Cantonales, Remens, Switz. Copy by T. Krakauer

Exterior of the A. Godshaw Jewelry Store; Welwyn Garden City.

The store moved to larger quarters in the 1990s.

Exterior of the A. Godshaw Jewelry Store; Welwyn Garden City.

The store moved to larger quarters in the 1990s.

Exterior view of Gottschalk residence; Seelhorst Strasse 27, Hannover, Germany.

Fig. 13 in family portrait