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We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of(More)
A key problem in developmental biology is how pattern and planar polarity are transmitted in epithelial structures. Examples include Drosophila neuronal differentiation, ommatidia formation in the compound eye, and wing hair polarization. A key component for the generation of such patterns is direct cell-cell signalling by transmembrane ligands, called(More)
Techniques for determining the long-term dynamics of host-parasite systems are well established for mixed populations. The field of spatial modelling in ecology is more recent but a number of key advances have been made. In this paper, we use state-of-the-art approximation techniques, supported by simulations, in order to investigate the role of recovery(More)
One proposed mechanism of tumour escape from immune surveillance is tumour up-regulation of the cell surface ligand FasL, which can lead to apoptosis of Fas receptor (Fas) positive lymphocytes. Based upon this 'counterattack', we have developed a mathematical model involving tumour cell-lymphocyte interaction, cell surface expression of Fas/FasL, and their(More)
The CD28 superagonist (CD28SA) TGN1412 was administered to humans as an agent that can selectively activate and expand regulatory T cells but resulted in uncontrolled T cell activation accompanied by cytokine storm. The molecular mechanisms that underlie this uncontrolled T cell activation are unclear. Physiological activation of T cells leads to(More)
Gabapentin is used in the treatment of epilepsy and neuropathic pain. Gabapentin has high and saturable permeability across the BBB, but no mechanistic studies underpinning this process have been reported. The aim of the current study was to investigate the transport of gabapentin in a model of the BBB, identify the important drug transporter(s) and to use(More)
The assumption that populations are completely mixed is reasonable for many populations, but there is likely to be some degree of local interaction whether spatially or socially in many systems. An important question is therefore how strong these local interactions need to be before there are significant effects on the dynamics of the system. Here, our(More)
Tumour hypoxia is associated with poor drug delivery and low rates of cell proliferation, factors that limit the efficacy of therapies that target proliferating cells. Since macrophages localise within hypoxic regions, a promising way to target hypoxic tumour cells involves engineering macrophages to express therapeutic genes under hypoxia. In this paper we(More)
It is clear that the evolution of infectious disease may be influenced by population spatial structure and transmission networks but we lack an understanding of the role of acquired immunity. Here we examine theoretically the role of spatial structure in the evolution of infectious disease described by the classic Susceptible, Infected, Recovered (SIR)(More)
The rich theory of infectious disease modelling using the Susceptible-Infectious-Recovered (SIR) framework is mainly based on the assumption of a well-mixed population, under which evolutionary behaviours (typically derived using adaptive dynamics) are shown to depend critically on the qualitative features of a virulence-transmission trade-off. Spatial(More)