Multiple scale model for cell migration in monolayers: Elastic mismatch between cells enhances motility

Abstract

We propose a multiscale model for monolayer of motile cells that comprise normal and cancer cells. In the model, the two types of cells have identical properties except for their elasticity; cancer cells are softer and normal cells are stiffer. The goal is to isolate the role of elasticity mismatch on the migration potential of cancer cells in the absence of other contributions that are present in real cells. The methodology is based on a phase-field description where each cell is modeled as a highly-deformable self-propelled droplet. We simulated two types of nearly confluent monolayers. One contains a single cancer cell in a layer of normal cells and the other contains normal cells only. The simulation results demonstrate that elasticity mismatch alone is sufficient to increase the motility of the cancer cell significantly. Further, the trajectory of the cancer cell is decorated by several speed “bursts” where the cancer cell quickly relaxes from a largely deformed shape and consequently increases its translational motion. The increased motility and the amplitude and frequency of the bursts are in qualitative agreement with recent experiments.

Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media

“…Its stochastic simulation included the effect of cell migration, compression, and contact inhibition to describe the evolution of cell size distribution and the global colony growth. Furthermore, a phase field cell monolayer model with its dynamics approaching the continuous limit of the Potts model has been used to describe the increase in the motility of cells softer than their neighbors, in agreement with experimental data from human metastatic breast carcinoma cells (MDA-MB-231) co-cultured with normal epithelial cells (MCF10A) [31]. In this case, carcinoma cells are softer than normal cells [32] and the mismatch in cell elasticity causes several speed "bursts" in which the cancer cell relaxes from a largely deformed shape and consequently, its translational motion increases.…”

Computational approaches to substrate-based cell motility

“…[151][152][153] It was able to reproduce many experimentally observed effects, including inelastic scattering of colliding cells and 'activation' of nonmotile cells by moving cells owing to steric interactions 153 and the emergence of coherently moving or rotating cell clusters, 152,153 as well as the formation of tissue-like stationary clusters. 151,153 Again, computational modelling produced a number of important insights, e.g., it was shown that-at least in a non-confluent situation-cell-cell adhesion rather hinders collective migration of cells, as it induces the formation of short-living clusters of only few cells. 153 This observation sheds light, for instance, on comparative studies of adhesive (healthy) cells versus weakly adhering (cancerous) cells.…”

“…153 This observation sheds light, for instance, on comparative studies of adhesive (healthy) cells versus weakly adhering (cancerous) cells. Currently, in all multicell approaches a separate phase field was assigned to each cell, [150][151][152][153] permitting with the present power of graphic processing units to simulate about a hundred cells. This approach, however, is computationally not yet optimized, as a substantial part of the computing time is spend on updating zeros (note that most fields are typically zero outside the cells).…”

“…28,[147][148][149] Quite recently, significant progress in modelling and understanding of collective behaviour of multiple cells was achieved using phase-field methods. [150][151][152][153][154] If every cell has to be resolved in some detail, current computing power allows to study the dynamics of up to about hundred cells. A first phase-field model of multicellular systems with several (nonmotile) cells was developed in Nonomura, 150 by associating a separate phase field to each individual cell.…”

“…In an attempt to isolate the role of elasticity mismatch on cancer cell migration, a phase-field description of a confluent monolayer containing both healthy and cancerous cells was developed in Palmieri et al 151 Again each cell was described by an individual phase field, and had a self-propulsion velocity v i assigned to it. For simplicity, it was assumed that all cells have the same absolute value of velocity, v i j j, but the orientation of each cell's migration direction was changed according to a certain random process.…”