Project B05

Mathematical modeling of spatio-temporal dynamics of Wnt signaling and its function in development and regeneration

Project leader: Anna Marciniak-Czochra

Abstract

The focus of this project is mathematical modeling of spatial dynamics of Wnt signaling and of its function in development and regeneration. In particular, we will investigate the role of different components of the complex spatio-temporal signaling in symmetry breaking and pattern formation of gene expression and the function of Wnt signaling in tissue self-renewal and differentiation. Since the underlying processes are determined by multiple signals quantitatively integrated in a dynamical and self-organized way, mathematical modeling is indispensable as support and guidance of experimental research. Integration of experimental research with mathematical methods is needed for model derivation, reduction and analysis, accurate numerical methods of model simulation and statistical methods of data analysis and model identification. The current project is based on our recently established comprehensive computational framework for modeling pattern formation in Hydra (collaboration with T. Holstein/M. Tanaka (A05), and I. Sinning/S. Özbek, (B07) projects). Coupling a model of Wnt signaling with a realistic tissue geometry allows simulating small mechanical tissue deformations and, therefore, linking key signaling factors and their interactions with experimentally observed phenotypes. The aim of this project is to provide mechanistic modeling of the underlying processes that are still not well understood at the molecular level. To this end, we propose a new approach to model identification. It will combine modern statistical methods of parameter estimation with singular perturbation analysis of the hypothetical mechanisms. We will investigate pattern formation capability of experimentally identified molecular interactions such as Wnt-Dkk signaling and the role of multiple Wnts in coordination of robust tissue patterning. Furthermore, we will extend our mathematical models of tissue development and regeneration to account for the function of Wnt signaling in stem cell activation, self-renewal and differentiation. We will focus on the example of stem cell dynamics in adult neurogenesis with A. Martin-Villalba (B06). Motivated by our preliminary results, we will investigate the process of switching between canonical and non-canonical Wnt signaling in neuronal stem cell activation as a function of biological time (age) and in cancer. Mathematical models will be developed and validated iteratively, based on data provided by collaborating experimentalists. In summary, this project will not only contribute to a better understanding of the underlying molecular mechanisms but will also allow comparing them in a range of systems in the course of systems evolution.

Project-related publications

  • Ziegler, B., I. Yiallouros, B. Trageser, S. Kumar, M. Mercker, S. Kling, M. Fath, U. Warnken, M. Schnölzer, T.W. Holstein, M. Hartl, A. Marciniak-Czochra, J. Stetefeld, W. Stöcker, and S. Özbek. 2021. The Wnt-specific astacin proteinase controls head formation in Hydra. BMC Biol., 19(1):120. PMID: 34107975
  • Köthe, A., A. Marciniak-Czochra, and I. Takagi8. 2020. Hysteresis-driven mechanism of pattern formation in a basic reaction-diffusion-ODE model. Disc. Cont. Dyn. Systems. A. 40: 3595.
  • Kowall, C., A. Marciniak-Czochra, and A. Mikelic. 2020. Long-time shadow limit for a reaction–diffusion-ODE system. Applied Mathematics Letters. 106790.
  • Kalamakis, G., D. Brüne, 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. Malm, B. Berninger, A. Del Sol, A. Marciniak-Czochra, and A.Martin-Villalba. 2019. Control of quiescence modulates the maintenance and regenerative capacity of neural stem cells in the aging brain. Cell. 176: 1407-1419. e14. PMID: 30827680
  • Brinkmann, F., M. Mercker, T. Richter and A. Marciniak-Czochra. 2018 Post-Turing tissue pattern formation: Advent of Mechanochemistry. PLoS Comp. Biol. 14: e1006259. PMID:29969460
  • Marciniak-Czochra, A., S. Härting, G. Karch and K. Suzuki. 2018. Dynamical spike solutions in a nonlocal model of pattern formation. Nonlinearity. 31: 1757.
  • Ziebell, F., S. Dehler, A. Martin-Villalba, and A. Marciniak-Czochra. 2018. Revealing age related changes of adult hippocampal neurogenesis using mathematical models. Development. 45: dev153544. PMID: 29229768
  • Härting, S., A. Marciniak-Czochra, and I. Takagi. 2017. Stable patterns with jump discontinuity in systems with Turing instability and hysteresis. Disc. Cont. Dyn. Systems A. 37: 757-800.
  • Mercker, M., A. Köthe and A. Marciniak-Czochra. 2015. Mechanochemical symmetry breaking in Hydra aggregates. Biophysical J. 108: 23962407. PMID:25954896.
  • Mercker, M., D. Hartman and A. Marciniak-Czochra. 2013. A mechanochemical model for embryonic pattern formation: Coupling tissue mechanics and morphogen expression. PLoS One. 8:e82617. PMID: 24376555