TY  - GEN
Y1  - 2004///
ID  - heidok4549
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/4549/
N2  - New receptor-based models for pattern formation and regulation in multicellular biological systems are proposed. The test organism for the mathematical modelling is a fresh-water polyp, hydra. Another model is applied to describe the growth of  tumour along linear or tubular structure. Models are defined in the form of reaction-diffusion equations with zero flux boundary conditions coupled with ordinary differential equations.   Two mechanisms of pattern formation: diffusion driven instability and hysteresis-driven mechanism are studied and their possibilities and constraints in explanation of different aspects of pattern formation and regulation are demonstrated. Three-variable (describing the dynamics of ligands, free and bound receptors) and four-variable models (including also an enzyme cleaving the ligand) are analysed and compared. It is shown under which conditions they can involve diffusion driven instability mechanism for pattern formation. It is shown that gradient in the density of bound receptors occurs if there is also a second diffusible substance, an enzyme, which degrades ligands. The four-variable model is able to capture results from cutting experiments and reflects {\it{de novo}} pattern formation from dissociated cells.  To explain the grafting experiments a new model including memory-based relation is proposed. Production of the diffusible biochemical molecules has a hysteretic dependence on the density of these molecules and is modelled by additional ordinary differential equations. The stationary and oscillatory patterns, resulting from multiple steady states and switches in the production rates, are found. Finally, a receptor-based approach is applied to a model of the growth of a tumour. Mathematical model describing the population of cells distributed over a linear or tubular structure and the diffusing growth factor which regulates the proliferation is derived and analysed. 
A1  - Marciniak-Czochra, Anna
KW  - Rezeptor-basierte Modelle 
KW  -  Reaktions-Diffusions Gleichungen 
KW  -  Instabilität durch Diffusion 
KW  -  Modellierungpattern formation 
KW  -  receptor-based model 
KW  -  reaction-diffusion equations 
KW  -  hysteresis 
KW  -  diffusion driven instabilities
AV  - public
TI  - Developmental models with cell surface receptor densities defining morphological position
ER  -