Multi-scale hybrid and agent-based modeling of cell differentiation

2023;
: pp. 617–624
https://doi.org/10.23939/mmc2023.03.617
Received: February 16, 2023
Revised: July 12, 2023
Accepted: July 13, 2023

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 617–624 (2023)

1
Fundamental and Applied Mathematics Laboratory, Ain Chock Faculty of Sciences, Hassan II University
2
Fundamental and Applied Mathematics Laboratory, Ain Chock Faculty of Sciences, Hassan II University
3
Fundamental and Applied Mathematics Laboratory, Ain Chock Faculty of Sciences, Hassan II University
4
Camille Jordan Institute, UMR 5208 CNRS, University Lyon 1

In this work we propose a hybrid model of cell population dynamics, where cells are considered as discrete elements whose dynamics depending on the intracellular and extracellular regulation. The model takes into account different cell types which include undifferentiated cells and two types of differentiated cells. We use a simulation algorithm based on the dynamical systems approach on the one hand, and the multi-agent approach on the other hand.  Both approaches have been implemented using NetLogo and Python. We discuss cell choice between two types of differentiated cells and analyze the coexistence of cell lineages.

  1. Benmir M., Bessonov N., Boujena S., Volpert V.  Travelling Waves of Cell Differentiation.  Acta biotheoretica.  63 (4), 381–395 (2015).
  2. Anderson A., Rejniak K.  Single-cell-based models in biology and medicine.  Springer Science & Business Media (2007).
  3. Bernard S.  Modélisation multi-échelles en biologie. HAL. Vol. 2013 (2013).
  4. Osborne J. M., Walter A., Kershaw S., Mirams G., Fletcher A., Pathmanathan P., Gavaghan D., Jensen O., Maini P., Byrne H.  A hybrid approach to multi-scale modelling of cancer.  Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.  368 (1930), 5013–5028 (2010).
  5. Volpert V.  Elliptic partial differential equations.  Vol. 2, Springer (2014).
  6. Deutsch A., Dormann S.  Mathematical modeling of biological pattern formation. Springer (2005).
  7. Karttunen M., Vattulainen I., Lukkarinen A.  Novel methods in soft matter simulations. Vol. 640, Springer Science & Business Media (2004).
  8. Patel A. A., Gawlinski E. T., Lemieux S. K., Gatenby R. A.  A cellular automaton model of early tumor growth and invasion: the effects of native tissue vascularity and increased anaerobic tumor metabolism.  Journal of Theoretical Biology.  213 (3), 315–331 (2001).
  9. Satoh A.  Introduction to Practice of Molecular Simulation Molecular Dynamics, Monte Carlo, Brownian Dynamics, Lattice Boltzmann and Dissipative Particle Dynamics.  Elsevier (2010).
  10. Bessonov N., Eymard N., Kurbatova P., Volpert V.  Mathematical modeling of erythropoiesis in vivo with multiple erythroblastic islands.  Applied Mathematics Letters.  25 (9), 1217–1221 (2012).
  11. Demin I., Crauste F., Gandrillon O., Volpert V.  A multi-scale model of erythropoiesis.  Journal of biological dynamics.  4 (1), 59–70 (2010).
  12. Kurbatova P., Eymard N., Volpert V.  Hybrid model of erythropoiesis.  Acta Biotheoretica.  61 (3), 305–315 (2013).
  13. Bessonov N., Demin I., Pujo-Menjouet L., Volpert V.  A multi-agent model describing self-renewal of differentiation effects on the blood cell population.  Mathematical and Computer Modelling.  49 (11–12), 2116–2127 (2009).
  14. Wilensky U., Rand W.  An Introduction to Agent-Based Modeling: Modeling Natural, Social, and Engineered Complex Systems with NetLogo.  The MIT Press (2015).
  15. Dalle Nogare D., Chitnis A. B.  NetLogo agent-based models as tools for understanding the self-organization of cell fate, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium.  Seminars in Cell & Developmental Biology.  100, 186–198 (2020).
  16. Vieira L. S., Laubenbacher R. C.  Computational models in systems biology: standards, dissemination, and best practices.  Current Opinion in Biotechnology.  75, 102702 (2022).