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Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling.
In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns canExpand
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Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration
In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult life,Expand
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A cellular automaton model for tumour growth in inhomogeneous environment.
Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In thisExpand
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Mathematical Models of Avascular Tumor Growth
This review will outline a number of illustrative mathematical models describing the growth of avascular tumors. The aim of the review is to provide a relatively comprehensive list of existing modelsExpand
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Inherent noise can facilitate coherence in collective swarm motion
Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directionalExpand
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On the spatial spread of the grey squirrel in Britain
We present a diffusion–competition model to describe the interaction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters fromExpand
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Chaste: A test-driven approach to software development for biological modelling
Chaste (‘Cancer, heart and soft-tissue environment’) is a software library and a set of test suites for computational simulations in the domain of biology. Current functionality has arisen fromExpand
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Reaction and diffusion on growing domains: Scenarios for robust pattern formation
We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion modelsExpand
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Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells.
The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells overExpand
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Enzyme kinetics at high enzyme concentration
We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0Expand
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