Abstract
By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.
Highlights
We have modeled how epithelial cell aggregates advance through empty spaces and collisions between aggregates using an active vertex model with dynamics for cell centers that includes collective tissue forces [39], and velocity alignment and inertia [16]
Our underdamped active vertex model (AVM) predicts that cells at the interface and the fingers have larger area than those well inside the tissue, which has been corroborated by recent experiments [44]
We observe in numerical simulations of tissue spreading that the velocity of the fastest cells in a finger may oscillate with a short period in a range between 30 minutes to about one hour
Summary
Confluent motion of epithelial cell monolayers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] is crucial in many biological processes, such as morphogenesis [3, 26], biological pattern formation [9, 23], biological aggregation and swarming [17, 21], tissue repair [6, 18, 19], development [4], and tumor invasion and metastasis [1,2,3, 28] It serves as a relatively simple paradigm for collective motion of cells that retain their cell-cell junctions as they move on a two dimensional (2D) substrate. Different aspects of these phenomena have been studied by models ranging from macroscopic continuum mechanics to detailed subcellular agent models [25, 29, 37, 39, 40]
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