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 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.

A free boundary mechanobiological model of epithelial tissues

“…Each cell, which we consider to be a mechanical spring [8,9], is assigned potentially distinct mechanical properties, a i and k i , such that the resulting tissue is heterogeneous ( Figure 1) [7].…”

“…where m i is the mass associated with cell boundary i, F visc i is the viscous force associated with cell boundary i, and f i is the cell-to-cell interaction force acting on cell boundary i from the left [5][6][7][8].…”

“…The viscous force is generated by cell-matrix interactions, and is modelled as F visc i = −ηdx i /dt where η > 0 is the mobility coefficient [5][6][7][8]. As cells move in dissipative environments, the motion of each cell i is assumed to be overdamped, such that the left hand side of Equation (1) is zero [6,7,40].…”

“…x(ī, t) − x(ī − 1/N, t) [6,7], and define the continuous linear force law corresponding to Equation 14as a 1D stress field,…”

“…Mechanical cell properties, such as resistance to deformation and cell size, and chemical cell properties, such as intracellular signalling, impact the shape of epithelial tissues [2,4]. The role of purely mechanical cell properties on tissue dynamics has been studied using mathematical and computational models [5][6][7][8][9][10]. Other models focus on intracellular signalling to examine how chemical signalling affects tissue dynamics [11][12][13][14][15].…”