by Steffen Härting
by Moritz Mercker
by Moritz Mercker
by Steffen Härting
Welcome to
by Steffen Härting
by Steffen Härting
by Alexandra Köthe

Research Group

Applied Analysis and Modelling in Biosciences

Prof. Dr. Anna Marciniak-Czochra

Institute of Mathematics,
Interdisciplinary Center of Scientific Computing (IWR)
and BIOQUANT Center, Heidelberg University.

Research focus: The interdisciplinary expertise of our research group lies in the areas of applied mathematics and mathematical and computational biosciences. Specifically, our field of focus is the dynamics of self-organisation and structure formation in developmental and regeneration processes and in cancer. The aim of our research is to develop and analyse mathematical models of the dynamics of structure formation in multicellular systems and to develop new mathematical methods of modelling of such complex processes. We collaborate closely with experimentalists and clinicians, and pursue mathematical problems arising in modelling of biological processes, both analytically and computationally.
Mathematical areas of interest are partial differential equations, dynamical systems, and multiscale and singular perturbation analysis. Methods of mathematical analysis are used to formulate the models and to study the spatio-temporal behaviour of solutions, such as stability and dependence on characteristic scales, geometry, and sensitivity to initial data and key parameters.

Our analytical research includes:
(1) Analysis of nonlinear structured population models; linking continuous and discrete structures;
(2) Analysis of pattern formation mechanisms in the systems of reaction-diffusion type;
(3) Derivation of effective models from first-principles to describe transport of cells and molecules through heterogeneous media such as biological tissues.
One area of focus is related to models of growth, transport and transformation processes in spaces reflecting within-population heterogeneity. Another area of focus involves new mathematical models of symmetry breaking and pattern formation in multicellular systems and analysis of a variety of pattern formation mechanisms.  Particular attention is paid to methods of model upscaling and reduction allowing derivation and analysis of tractable models of complex processes.

Applications in biology and medicine: Mathematical models and methods developed by the group are applied to specific problems of developmental and cell biology.

(1) Stem cell dynamics in development, regeneration and cancer
The first area of focus is mathematical modeling, analysis, and simulation of dynamics of stem cell self-renewal, differentiation, and clonal evolution in different contexts. Our interdisciplinary research is part of the Collaborative Research Center (SFB 873) “Maintenance and Differentiation of Stem Cells in Development and Disease’’.

Our current research is devoted to:
- mathematical modelling the plant meristem development providing mechanistic understanding of meristem regulation and mutant phenotypes (collaboration with the group of Jan Lohmann, COS, Heidelberg University);
- mathematical modelling of stem cell-based development of the fish respiratory organ (collaboration with the group of Lazaro Centanin, COS, Heidelberg University);
- mathematical modelling of aging and regeneration in adult neurogenesis (collaboration with the laboratories of Ana Martin-Villalba, DKFZ, Heidelberg and Francois Guillemot, Francis Crick Institute, London);
- modelling of healthy and cancerous hematopoiesis, including blood regeneration, development of acute leukemias, clonal selection and resulting therapy resistance in blood cancers (collaboration with hematologists Anthony D. Ho, Carsten Müller-Tidow and Christoph Lutz, Heidelberg Medical Clinic);
Our research in mathematical hematology became part of the newly established interdisciplinary Thematic Research Network “Integrative Blood Biology Network (iBLOOD): From Basic Molecular Mechanisms to Advanced Cellular Therapies” (Heidelberg University and German Cancer Research Center).

(2) Pattern formation
The second, related, line of our research is modelling, analysis and simulation of symmetry breaking and pattern formation in developmental biology. The related applications oriented research is part of the Collaborative Research Center (SFB) 1324 “Mechanisms and functions of Wnt signaling”.
The focus of our current project is: -mathematical modelling of symmetry breaking and pattern formation in Hydra; in parcticular mechanisms and fuction of spatio-temporal Wnt signalling and of mechano-chemical interactions (collabration with experimental groups of Thomas Holstein and Suat Özbek, COS, Heidelberg University).