A Mechanistic Collective Cell Model for Epithelial Colony Growth and Contact Inhibition

Abstract

We present a mechanistic hybrid continuum-discrete model to simulate the dynamics of epithelial cell colonies. Collective cell dynamics are modeled using continuum equations that capture plastic, viscoelastic, and elastic deformations in the clusters while providing single-cell resolution. The continuum equations can be viewed as a coarse-grained version of previously developed discrete models that treat epithelial clusters as a two-dimensional network of vertices or stochastic interacting particles and follow the framework of dynamic density functional theory appropriately modified to account for cell size and shape variability. The discrete component of the model implements cell division and thus influences cell size and shape that couple to the continuum component. The model is validated against recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. In good agreement with experiments, we find that mechanical interactions and constraints on the local expansion of cell size cause inhibition of cell motion and reductive cell division. This leads to successively smaller cells and a transition from exponential to quadratic growth of the colony that is associated with a constant-thickness rim of growing cells at the cluster edge, as well as the emergence of short-range ordering and solid-like behavior. A detailed analysis of the model reveals a scale invariance of the growth and provides insight into the generation of stresses and their influence on the dynamics of the colonies. Compared to previous models, our approach has several advantages: it is independent of dimension, it can be parameterized using classical elastic properties (Poisson's ratio and Young's modulus), and it can easily be extended to incorporate multiple cell types and general substrate geometries.

A microscopic field theoretical approach for active systems

“…in [41] and [34,[42][43][44], respectively. Other variants of the phase field crystal model have also been used to simulate the dynamics of epithelial cell colonies [45]. Together with efficient numerical algorithms, see e.g.…”

Active Vertex Model for Cell-Resolution Description of Epithelial Tissue Mechanics

“…Particle-based models have also been very successful at capturing many aspects of cell migration in tissues [42][43][44][45][46]. However, when it comes to modelling confluent epithelial layers with the resolution of individual cells, one of the most widely and successfully used models is the Vertex Model (VM).…”

Computational approaches to substrate-based cell motility

“…Consequently, the phasefield approach is best suited for nonconfluent situations when the motion of individual cells needs to be accurately resolved. For confluent layers, the approach may be too detailed as effects average out, and more coarse-grained methods, such as CPMs, 94,95 phase-field crystal models 165 or phenomenological and continuum approaches, 66,173 may be computationally more efficient. In turn, the mesoscale phase-field approach could establish important connections between single-cell behaviour and coarse-grained or continuum approaches of cell monolayers, aggregates and tissues.…”

“…In this respect, a phase-field method capable of describing multiple moving cells within a single or few phase fields is highly desirable. In Aland et al 165 and Alaimo et al, 166 a so-called 'phase-field crystal' model 167,168 was applied to describe cell migration in epithelial colony growth. In this approach, a single mass-conserving phase-field equation is used to describe multiple cells.…”