Multiscale mathematical modelling of dynamics of structure formation in biological systems

• Applicant: Professorin Dr. Anna Marciniak-Czochra
• Subject Area: Mathematics
• Term: from 2008 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 78498494

The aim of this interdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations and asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales (spatial and temporal), geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. The ground-breaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in developmental process, in the context of recently discovered signalling pathways; (ii) By providing models involving signalling and cell transformation, the project will contribute to the field theory of carcinogenesis. (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools

• DFG Programme: Independent Junior Research Groups