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A free boundary mechanobiological model of epithelial tissues

View ORCID ProfileTamara A. Tambyah, Ryan J. Murphy, Pascal R. Buenzli, View ORCID ProfileMatthew J. Simpson
doi: https://doi.org/10.1101/2020.07.02.185686
Tamara A. Tambyah
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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Ryan J. Murphy
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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Pascal R. Buenzli
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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Matthew J. Simpson
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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  • For correspondence: matthew.simpson@qut.edu.au
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Abstract

In this study, we couple intracellular signalling and cell–based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction–diffusion equations are derived to describe tissue–level outcomes. The free boundary evolves as a result of the underlying biological mechanisms included in the discrete model. To demonstrate the accuracy of the continuum model, we compare numerical solutions of the discrete and continuum models for two different signalling pathways. First, we study the Rac–Rho pathway where cell– and tissue–level mechanics are directly related to intracellular signalling. Second, we study an activator–inhibitor system which gives rise to spatial and temporal patterning related to Turing patterns. In all cases, the continuum model and free boundary condition accurately reflect the cell–level processes included in the discrete model.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • https://github.com/tamaratambyah/Tambyah2020_v2

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted September 29, 2020.
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A free boundary mechanobiological model of epithelial tissues
Tamara A. Tambyah, Ryan J. Murphy, Pascal R. Buenzli, Matthew J. Simpson
bioRxiv 2020.07.02.185686; doi: https://doi.org/10.1101/2020.07.02.185686
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A free boundary mechanobiological model of epithelial tissues
Tamara A. Tambyah, Ryan J. Murphy, Pascal R. Buenzli, Matthew J. Simpson
bioRxiv 2020.07.02.185686; doi: https://doi.org/10.1101/2020.07.02.185686

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