Anja Voss-Böhme (TU Dresden): Interacting particle systems for analyzing emergent collective cell behavior
Thursday, 19.01.2012 14:15 im Raum 229/230
Interacting particle systems (IPSs) are stochastic models for the temporal
evolution of spatially extended systems. While they were developed initially
to analyze numerically equilibrium behavior in statistical physics, it has
become clear in the meantime that IPSs are valuable non-equilibrium models
in their own right. In particular, they prove more and more to be
appropriate in another field of application: biological systems which are
by nature open, non-equilibrium systems where noise is ubiquitous.
Considering the field of developmental biology, an important application
area for IPSs is the analysis of the emergent collective behavior that
results from local interactions of biological cells. When cells react to
their surrounding, neighboring cells as well as extracellular matrix and
other environmental influences, with type-specific differences, what are the
emergent properties for the whole tissue?
For exemplary problems, IPS models are proposed and studied which describe
the major details of the respective intercellular interaction. Several
results concerning the long-time behavior and the emergence of structure at
the tissue scale are presented and interpreted in biological terms.
Mathematical challenges that require further theoretical developments are