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Research

Our projects are devoted to construction and analysis of multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and development of new mathematical methods for modeling of such complex processes. Mathematical models and methods developed by us are applied to specific problems of developmental and cell biology, such as:

role of biomechanics in developmental pattern formation, mechanisms of tissue evagination on the example of budding formation in Hydra (collaboration with Almut Kohler, Developmental Biology and Cell Physiology, University of Karlsruhe, Fernanda Rossetti and Motomu Tanaka, Institute of Physical Chemistry, Heidelberg University, Mihaela Zigman and Thomas Holstein, Zoology Institute, Heidelberg University)
self-organisation and pattern formation during development, with special emphasis on the role of Wnt signalling pathway coordinating of cell differentiation (collaboration with the group of Thomas Holstein, Zoology Institute, Heidelberg University)
differentiation and maintenance of stem cells population, the role of aging and replicative senescence (collaboration with the group of Wolfgang Wagner, University of Aachen and Anthony Ho, Heidelberg Medical Clinic, and Stefan Pfister, DKFZ)
dynamics of medulloblastoma; the role of beta-cathenin signalling (collaboration with Dr. Stefan Pfister, DKFZ)
the growth of early tumours - the influence of growth factor production and cooperation between partially transformed cells (collaboration with Marek Kimmel, Rice University, Houston)
heat shock protein signalling and its influence on neoplastic transformation (collaboration with the group of Maciej Żylicz, International Institute of Molecular and Cell Biology, University of Warsaw)

Mathematical methods and techniques employed in the projects are the analysis of systems of partial differential equations, asymptotic analysis and methods of dynamical systems, as well as computational methods. These techniques are used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales (spatial and temporal), initial data and key parameters. We focus on:

analysis of pattern formation mechanisms in the reaction-diffusion systems coupled with ordinary differential equations (hysteresis-driven and Turing-type patterns)
analysis of structured population equations (collaboration with the group of Benoit Perthame, Laboratoire J.-L. Lions and Univ. P. et M. Curie, Paris and Piotr Gwiazda, University of Warsaw)