Travelling waves in a free boundary mechanobiological model of an epithelial tissue

Murphy, Ryan J; Buenzli, Pascal R.; Baker, Ruth E.; Simpson, Matthew J.

doi:10.1016/j.aml.2020.106636

Cited by 10 publications

(10 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The mathematical framework that we develop here, and in related studies [30, 31, 32, 35, 36], is well-suited to incorporate additional biological mechanisms and explore different modelling assumptions. One modelling assumption we could change would be to allow the EMT-inducing chemical to diffuse across the boundary at the rear of the tissue, which may prevent a build up of chemical.…”

Section: Discussionmentioning

confidence: 99%

“…We consider a one-dimensional chain of cells to represent the cross-section of an epithelial tissue (Figure 1). Each cell is assumed to act like a mechanical spring [22, 30, 31, 32, 35, 36]. The tissue has a fixed boundary at x = 0 and a free boundary at x = L ( t ) > 0.…”

Section: Model Descriptionmentioning

confidence: 99%

“…However, many previous studies specify a classical one-phase Stefan condition [23] at the free boundary, where the rate of expansion of the free boundary is assumed proportional to the spatial gradient of the density without strong biological justification, or the evolution of the tissue length is specified according to experimental observations [24, 25, 26, 27, 28, 29]. Here, the evolution of the tissue boundary arises naturally from the cell-scale processes of cell proliferation, mechanical cellular relaxation [30, 31, 32], and cell detachment.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The role of mechanical interactions in EMT

Murphy

Buenzli

Tambyah

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-β, produced by surrounding tissue can be up-taken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The role of mechanical interactions in EMT

Murphy

Buenzli

Tambyah

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We consider a one-dimensional chain of cells to represent the cross-section of an epithelial tissue (Figure 1). Each cell is assumed to act like a mechanical spring [30,31,32,35,36].…”

Section: Discrete Modelmentioning

confidence: 99%

“…However, many previous studies specify a classical one-phase Stefan condition [23] at the free boundary, where the rate of expansion of the free boundary is assumed proportional to the spatial gradient of the density without strong biological justification, or the evolution of the tissue length is specified according to experimental observations [24,25,26,27,28,29]. Here, the evolution of the tissue boundary arises naturally from the cell-scale processes of cell proliferation, mechanical cellular relaxation [30,31,32], and cell detachment.…”

Section: Introductionmentioning

confidence: 99%

The role of mechanical interactions in EMT

et al. 2021

Self Cite

View full text Add to dashboard Cite

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-β, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

show abstract

Mechanical Cell Competition in Heterogeneous Epithelial Tissues

et al. 2020

Self Cite

View full text Add to dashboard Cite

Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the new discrete model and continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than by having some intrinsic proliferative advantage. We advise when the continuum model is beneficial and demonstrate why naively adding source/sink terms to a continuum model without considering the underlying discrete model may lead to incorrect results.

show abstract

Travelling waves in a free boundary mechanobiological model of an epithelial tissue

Cited by 10 publications

References 18 publications

The role of mechanical interactions in EMT

The role of mechanical interactions in EMT

The role of mechanical interactions in EMT

Mechanical Cell Competition in Heterogeneous Epithelial Tissues

Contact Info

Product

Resources

About