research partners    
Ph.D. students    
consortium members    

Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
phone: +48 22 5544551
fax: +48 22 5544700

Spatio-temporal dynamics of structured populations - the growth of epidermis
Ryszard Rudnicki (IMPAN) and Anna Marciniak-Czochra (IWR, University of Heidelberg)
The project is carried out by Przemysław Paździorek at IM PAN
The aim of this project is to develop mathematical tools for modelling of the spatio-temporal dynamics of structured populations. The models will be applied to specific problems of growth and differentiation of epithelial cells.

The epidermal physiology results from a complex regulated homeostasis of keratinocyte proliferation, differentiation and death and is tightly regulated by a specific protein expression during cellular maturation. Mathematical and computational models are considered a promising and inevitable tool for the understanding of this complex system.

Structured population approach is of special interest for modelling of processes in polymer chemistry and ecology. Our team has been already involved in development of new structured population models of biological processes and mathematical methods for studying this type of equations. In particular, coagulation-fragmentation equations earlier used in modelling such physical processes, have been applied by us to study dynamics of phytoplankton aggregates [1], [2]. In [3] model equations for diffusion and growth of polymers with linear structure were derived. Modelling growth and regeneration of heterogeneous tissues consisting of cells of different differentiation stages and different biochemical and morphological properties requires new models of structured populations.

The main aim of this project is to derive and analyse mathematical models of the normal and pathological development of epidermis. The project will be handled in close collaboration with the group of Dr. Ing. Niels Grabe, Tissue Imaging and Analysis Center, BIOQUANT. The models will be validated based on the quantitative data obtained using automated tissue slide scanning (Hamamatsu NanoZoomer Digital Pathology system). We will address the questions of the role of cell-to-cell communication, interactions with environment and replicative senescence in the growth and regeneration of epidermis. Rigorous model derivation will help to understand influence of different scales of these processes on the macroscopic dynamics of the tissue.

[1] O. Arino and R. Rudnicki (2004), Comptes Rendus Biologies, 327: 961-969.
[2] R. Rudnicki and R. Wieczorek (2008), in: Russo R (Ed) Aquaculture I. Dynamic Biochemistry, Process Biotechnology and Molecular Biology, 2: 55-63.
[3] F. Guias (2001) Stochastic Anal. Appl., 19: 245-278.