Mechanical cell competition in heterogeneous epithelial tissues

Abstract

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 discrete model and the new 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. 1In the emerging field of mechanical cell competition, winner cells compress neighbouring cells promoting tissue crowding and regions of higher density, which leads to cell death [5,21,47], while cell proliferation occurs in regions of lower density [13]. In this work, we focus on mechanical cell competition arising from the coupling of a cell-based model of epithelial tissue mechanics with celllength-dependent proliferation and death mechanisms. We consider mechanical forces to be driven by cell stiffness which is important for cancer progression [41], cancer detection [36], morphogenesis [10], and wound healing [9]. A grand challenge in cell biology is to understand how tissue-level outcomes are related to cell-based mechanisms, especially when experiments are performed by focusing on a single scale, and many cellular processes occur over multiple overlapping timescales [6,48]. Therefore, we apply mathematical modelling with in silico simulations to develop a framework to quantitatively connect cell-level mechanisms with tissue-level outcomes.Many mathematical modelling frameworks, including both discrete models and continuum models, have been used to study cell migration and cell proliferation. In discrete models individual cell properties and inter-cellular interactions can be prescribed [33,34]. However, discrete models often lack macroscopic intuition and can be computationally intensive, especially with proliferation and death included, which are commonly stochastic and require many realizations to understand the average behaviour. Continuum models commonly include proliferation and death through source/sink terms and may require constitutive equations to close the system [3,21,25,39,43]. In general, continuum models do not make the underlying cell-level processes clear [12]. However, continuum models can be less computationally expensive than discrete models and can be analysed with wellestablishe...

The role of mechanical interactions in EMT

“…To implement this model, we start with a cell-based discrete model, where we prescribe individual cell-level properties, and then derive the corresponding tissue-level continuum partial differential equation model. This approach extends previous studies [30,31,32,33,34,35,36,37,38] In this section, we present the new discrete model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by a chemically-dependent EMT process in an epithelial tissue. We then derive the corresponding continuum model.…”

“…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].…”

“…Next, given the cell positions and chemical concentrations at time t + ∆t, we determine whether a cell proliferation event or a cell detachment event occurs during the time interval [t, t+∆t). Analogous to Murphy et al [36] we proceed using rejection sampling [53] where we generate three independent random numbers from a uniform distribution,…”

“…from many discrete realisations(Figures 3, 10-13). This correspondence between the discrete and continuum model holds provided that the rate of mechanical relaxation, determined by the ratio of cell stiffness to mobility coefficient, k/η, is sufficiently fast relative to the rate of cell proliferation, see Section 3.3 of[36]; and that N (t) is sufficiently large to define a continuum, see Appendix D.3. However, when N (0) is close to ω/β the behaviour of the discrete and the continuum model may differ.…”

The role of mechanical interactions in EMT

“…To implement this model, we start with a cell-based discrete model, where we prescribe individual cell-level properties, and then derive the corresponding tissue-level continuum partial differential equation model. This approach extends previous studies [30,31,32,33,34,35,36,37,38] all of which consider mechanical cell movement, but do not consider cell detachment driven by EMT. The continuum model is useful to analyse possible behaviours of the model including tissue shrinkage, tissue homeostasis, and tissue growth depending on the initial number of cells, mechanical cell properties, the rate of proliferation, and chemical diffusivity.…”