+44 (0)1509 263171
Please use this identifier to cite or link to this item:
|Title: ||Oscillations and patterns in spatially discrete models for developmental intercellular signalling|
|Authors: ||Webb, Steven D.|
Owen, Markus R.
|Issue Date: ||2003|
|Abstract: ||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 many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances.
Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations—this depends crucially on the
production terms and on the relationship between the decay rates of ligand and
Our approach allows for a detailed comparison with the model for Delta-Notch
interactions of Collier et al. , and we find that a formal reduction may be made
only when the ligand receptor binding kinetics are very slow. Without such very
slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal
cellular arrays requires significant activation of receptor production, a feature that
is not apparent from previous analyses.|
|Description: ||This pre-print has been submitted, and accepted, to the journal, Journal of Mathematical Biology [© Springer]. The definitive version: WEBB, S.D. and OWEN, M.R., 2004. Oscillations and patterns in spatially discrete models for developmental intercellular signalling. Journal of Mathematical Biology, 48(4), pp. 444-476, is available at: http://www.springerlink.com/openurl.asp?genre=journal&eissn=1432-1416.|
|Appears in Collections:||Pre-prints (Maths)|
Files associated with this item:
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.