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Coherent modelling switch between pointwise and distributed representations of cell aggregates.

A Colombi1, M Scianna2, L Preziosi1

  • 1Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy.

Journal of Mathematical Biology
|July 18, 2016
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Summary
This summary is machine-generated.

This study introduces a flexible mathematical model for biological systems, allowing cells to switch between particle and mass representations. This framework captures cell differentiation and dynamics for applications like tumor growth and zebrafish development.

Keywords:
Cell differentiationCell phenotypic transitionHybrid systemsMultiscale dynamicsMultiscale modeling

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Area of Science:

  • Mathematical Biology
  • Computational Biology
  • Biophysics

Background:

  • Biological systems comprise diverse cell phenotypes with distinct properties.
  • Cells undergo differentiation and phenotypic transitions in response to stimuli.
  • Existing models may not fully capture these dynamic cellular changes.

Purpose of the Study:

  • To propose a unified modeling framework for biological systems that accounts for cell phenotypic transitions.
  • To integrate cell dynamics, including migration, proliferation, and apoptosis, with chemical kinetics.
  • To provide a versatile tool for simulating complex biological phenomena.

Main Methods:

  • Development of a modeling framework allowing cells to be represented as pointwise particles or distributed masses.
  • Implementation of rules for coherent switching between mathematical representations.
  • Inclusion of cell migratory dynamics, duplication/apoptotic processes, and diffusing chemical kinetics.
  • Numerical simulations of biological systems involving cell phenotypic transition.

Main Results:

  • The proposed model successfully integrates diverse cellular behaviors and transitions.
  • Simulations demonstrated the framework's applicability to tumor spheroid growth.
  • The model accurately represented initial differentiation stages in zebrafish posterior lateral line formation.

Conclusions:

  • The developed modeling framework offers a robust approach to studying biological systems with dynamic cell phenotypes.
  • This approach enhances the understanding of phenomena driven by cell differentiation and behavior.
  • The model provides a valuable tool for investigating complex biological processes in development and disease.