Mathematical Modelling of Juxtacrine Cell Signalling
AUTHORS:
Markus R. Owen (1,3) & Jonathan A. Sherratt (2,3)
1: Department of Mathematics, University of Utah,
Salt Lake City, Utah 84112, USA.
2: Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK.
3: Mathematics Institute,
University of Warwick, Coventry CV4 7AL, UK.
ABSTRACT:
Juxtacrine signalling is emerging as an important means of cellular
communication, in which signalling molecules anchored in the cell
membrane bind to and activate receptors on the surface of immediately
neighbouring cells. We develop a mathematical model to describe this
process, consisting of a coupled system of ordinary differential
equations, with one identical set of equations for each cell. We use
a generic representation of ligand--receptor binding, and assume that
binding exerts a positive feedback on the secretion of new receptors
and ligand. By linearising the model equations about a homogeneous
equilibrium, we categorise the range and extent of signal patterns as
a function of parameters. We show in particular that the signal decay
rate depends crucially on the form of the feedback functions, and can
be made arbitrarily small by appropriate choice of feedback, for any
set of kinetic parameters. As a specific example, we consider the
application of our model to juxtacrine signalling by TGF-alpha in
response to epidermal wounding. We demonstrate that all the
predictions of our linear analysis are confirmed in numerical
simulations of the nonlinear system, and discuss the implications for
the healing response.
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