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Mathematical Modeling of Stem Cell Ageing


The regenerative capacity and the functionality of tissues decline with age. These processes are related to changes of stem cell properties. Especially in the context of regenerative medicine or tissue transplantations it is relevant to understand and counteract age-related stem cell impairments. Mathematical models can help to understand and quantify how stem cell properties change with age.

Cooperation partners: F. Ziebell (EMBL Heidelberg), G. Kalamakis (Department of Biosystems Science and Engineering, ETH Zürich), W. Wagner (Helmholtz Institute for Biomedical Engineering), A. Martin-Villalba (German Cancer Research Center dkfz, Heidelberg), A. Marciniak-Czochra (Institute for Applied Mathematics, Heidelberg University)

Multiple processes contribute to age-related tissue changes. We focus on the following.

Replicative senescence: Replicative senescence describes the phenomenon that cells stop to multiply after they have performed a certain number of divisions. It is unclear in how far this also applies to adult stem cells such as hematopoietic stem cells. Mathematical models allow to test this hypothesis. Ordinary differential equation models of blod cell formation suggest that a limit of 50 division per hematopoietic stem cell is not in contradiction to life-long blood cell formation.

Culture-related changes: In vitro multiplication of cells is an important part of regenerative medicine. Depending on the culture conditions the obtained cell population can either have a homogeneous age-structure, i.e., each cell has approximately performed the same number of divisions, or have a heterogeneous age-structure, i.e., some cells have performed significantly more divisions than others. Individual based computational models (cellular automata) are an efficient tool to study how cell culture conditions (e.g., plating density, confluence before replating etc.) impact on the composition of the obtained cell population. Computer simulations suggest that in case of contact-inhibited cells high plating densities in combination with replating at low confluence lead to cell populations with homogeneous age-structure whereas low plating densities in combination with replating at high confluence lead to heterogenous populations.

In vivo aging of neural stem cells: Learning and cognition require formation of new neurons throughout the whole life. Formation of neurons in the adult brain (adult neurogenesis) is driven by a small population of neural stem cells (NSC). In the murine brain NSC are located in the hippocampus and in the subventricular zone. Experiments indicate that the total number of NSC and the number of actively dividing NSC decline with age. However, the decline saturates at old ages and complete extinction of NSC is prevented. Ordinary differential equation models allow to study the mechanisms underlying these changes. The models suggest that an age-related reduction of the rates at which quiescent cells are activated can explain the observed changes. Changes of cell-cycle duration or self-renewal are not in line with the measured dynamics.


MSC culture
simulated culture of mesenchymal stromal cells (MSC).
Yellow - small numberof performed divisions
Purple - high nunber of performed divisions


Key publications

  1. Y. Han, J. Franzen, T. Stiehl, M. Gobs, CC. Kuo, M. Nikolic, J. Hapala, BE. Koop, K. Strathmann, S. Ritz‐Timme, W. Wagner. "New Targeted Approaches for Epigenetic Age Predictions" BMC Biol , 18(1):71, 2020.
  2. G. Kalamakis, D. Brune, S. Ravichandran, J. Bolz, W. Fan, F. Ziebell, T. Stiehl, F. Catala-Martinez, J. Kupke, S. Zhao, E. Llorens-Bobadilla, K. Bauer, S. Limpert, B. Berger, U. Christen, P. Schmezer, J.P. Mallm, B. Berninger, S. Anders, A. Del Sol, A. Marciniak-Czochra, and A. Martin-Villalba. "Quiescence Modulates Stem Cell Maintenance and Regenerative Capacity in the Aging Brain", Cell, 176(6):1407-1419.e14, 2019.
  3. A. Schellenberg, T. Stiehl, P. Horn, S. Joussen, N. Pallua, A. D. Ho, W. Wagner, "Population dynamics of mesenchymal stromal cells during culture expansion", Cytotherapy 14: 401-411, 2012.
  4. D. Cholewa*, T. Stiehl*, G. Bokermann, S. Joussen, C. Koch, T. Walenda, N. Pallua, A. Marciniak-Czochra, C. V. Suschek, W. Wagner, "Expansion of Adipose Mesenchymal Stromal Cells is Affected by Human Platelet Lysate and Plating Density", Cell Transplantation 20: 1409-22, 2011. * shared first authorship
  5. A. Marciniak-Czochra, T. Stiehl, W. Wagner, "Modeling of replicative senescence in hematopoietic development", Aging 1: 723-732, 2009.