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A system of nonlinear partial differential equations is proposed as a model for the growth of an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living or dead, and, depending on the concentration of a generic nutrient, the live cells may reproduce (expanding the tumour) or die (causing contraction). These volume changes(More)
We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe(More)
OBJECTIVES The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal(More)
We build on our earlier mathematical model (Ward & King, 1997, IMA J. Appl. Math Appl. Med. Biol., 14, 39-69) by incorporating two necrotic depletion mechanisms, which results in a model that can predict all the main phases of avascular-tumour growth and heterogeneity. The model assumes a continuum of live cells which, depending on the concentration of a(More)
Aquaporins are membrane channels that facilitate water movement across cell membranes. In plants, aquaporins contribute to water relations. Here, we establish a new link between aquaporin-dependent tissue hydraulics and auxin-regulated root development in Arabidopsis thaliana. We report that most aquaporin genes are repressed during lateral root formation(More)
Cell wall apposition (CWA) formation is one of the first lines of defence used by plants to halt invading fungi such as powdery mildew. Lignin is a complex polymer of hydroxylated and methoxylated phenylpropane units (monolignols) and lignification renders the cell wall more resistant to pathogen attack. The role of monolignol biosynthesis in CWA-mediated(More)
We analyzed the expression pattern of various terpene synthase (TPS) genes in response to a wounding injury applied to the apical leader of Sitka spruce (Picea sitchensis Bong. Carr.) genotypes known to be resistant (R) or susceptible (S) to white pine weevil (Pissodes strobi Peck.) attack. The purpose was to test if differences in constitutive or(More)
Many solid tumour growth models are formulated as systems of parabolic and/or hyperbolic equations. Here an alternative, two-phase theory is developed to describe solid tumour growth. Versions of earlier models are recovered when suitable limits of the new model are taken. We contend that the multi-phase approach represents a more general, and natural,(More)
Gravity profoundly influences plant growth and development. Plants respond to changes in orientation by using gravitropic responses to modify their growth. Cholodny and Went hypothesized over 80 years ago that plants bend in response to a gravity stimulus by generating a lateral gradient of a growth regulator at an organ's apex, later found to be auxin.(More)
This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue(More)