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Towards a mathematical framework for modelling cell fate dynamics.

Sean T Vittadello1,2,3, Léo Diaz1,2, Yujing Liu1

  • 1School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia.

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|September 24, 2025
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Summary
This summary is machine-generated.

This study introduces random dynamical systems as a new framework for modeling cell fate during development. This approach offers a more flexible and assumption-free alternative to existing models like Waddington's epigenetic landscape.

Keywords:
37N2553Z1092C3792C42

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Area of Science:

  • Developmental Biology
  • Mathematical Biology
  • Computational Biology

Background:

  • Cellular development involves complex interactions between cells and their environment.
  • Existing models of cell fate, such as Waddington's epigenetic landscape, offer simplifications but may overlook environmental influences.
  • There is a lack of consistent definitions for fundamental concepts like 'cell type' and 'cell state' in developmental biology literature.

Purpose of the Study:

  • To critically evaluate existing theoretical and mathematical models of cell fate.
  • To introduce and explore random dynamical systems as a novel framework for modeling cell development.
  • To provide a more flexible and assumption-free approach to understanding cell fate dynamics.

Main Methods:

  • Review and critique of existing cell fate modeling approaches (trees, networks, landscapes).
  • Introduction of random dynamical systems as a conceptual and mathematical framework.
  • Development of basic concepts within the random dynamical systems framework.

Main Results:

  • Existing models often oversimplify complex developmental processes.
  • Random dynamical systems offer a flexible framework for modeling cell fate.
  • This new approach can be discussed in relation to classical models like Waddington's landscape.

Conclusions:

  • A more comprehensive approach to modeling cell fate is needed, explicitly including environmental influences.
  • Random dynamical systems provide a promising alternative for future research in developmental biology.
  • This framework allows for a more nuanced understanding of cell fate determination and differentiation.