A Cell Growth Model Adapted for the Minimum Cell Size Division

Brunt, Bruce van; Gul, Sheraz; Wake, G. C.

doi:10.1017/s1446181115000218

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…Returning to the basic cell division model there have been at least three distinct generalizations apart from choices of variable growth and division rates such as found in [22,40]. These generalizations are:…”

Section: Some Generalizationsmentioning

confidence: 99%

Cell Division And The Pantograph Equation

2018

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Simple models for size structured cell populations undergoing growth and division produce a class of functional ordinary differential equations, called pantograph equations, that describe the long time asymptotics of the cell number density. Pantograph equations arise in a number of applications outside this model and, as a result, have been studied heavily over the last five decades. In this paper we review and survey the rôle of the pantograph equation in the context of cell division. In addition, for a simple case we present a method of solution based on the Mellin transform and establish uniqueness directly from the transform equation.Article published online by EDP Sciences and available at https://www.esaim-proc.org or https://doi.

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Section: Some Generalizationsmentioning

confidence: 99%

Cell Division And The Pantograph Equation

2018

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Multicellular mechanochemical hybrid cellular Potts model of tissue formation during epithelial‐mesenchymal transition

2021

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Epithelial-mesenchymal transition (EMT) is the transdifferentiation of epithelial cells to a mesenchymal phenotype, in which cells lose epithelial-like cell-cell adhesions and gain mesenchymal-like enhanced contractility and mobility. EMT is crucial for tissue regeneration and is also implicated in pathological conditions, such as cancer metastasis. Prior work has shown that transforming growth factor-β1 (TGF-β1) is a potent inducer of this biological process. In this study, we develop a computational model coupling mechanical and biochemical signaling in a multicellular tissue undergoing EMT. Specifically, we utilize a recently developed formulation that integrates a multicellular cellular Potts model (CPM), a lattice-based stochastic model governing cell movement; a first moment of area model, governing cellular traction and junctional forces; a finite element model, which defines extracellular matrix (ECM) substrate strains; an intracellular signaling TGF-β1-mediated EMT model that governs cellular phenotype; and an extracellular signaling component governing ECM and TGF-β1 signaling. In this study, we modeled the spatial cellular patterns that occur in tissue and the ECM during EMT. Our model predicts that EMT often initially occurs at a tissue boundary due to mechanochemical coupling, which results in transdifferentiation to progress inwards toward the center. Variation in model parameters demonstrated conditions enhancing and suppressing EMT, especially to drive EMT in the absence of TGF-β1 and inhibit EMT in the presence of TGF-β1. Specifically, enhancing the mechanochemical feedback typically promoted EMT, whereas greater assembled ECM degradation suppressed EMT. Simulated scratch test experiments illustrate that ECM composition can impact closure directly through EMT signaling. In conclusion, we integrated mechanical, biochemical, and extracellular signaling networks in a novel hybrid computational model to reproduce tissue formation dynamics of EMT.

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