A Mechanistic Collective Cell Model for Epithelial Colony Growth and Contact Inhibition - PubMed (original) (raw)
A Mechanistic Collective Cell Model for Epithelial Colony Growth and Contact Inhibition
Sebastian Aland et al. Biophys J. 2015.
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.
Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Figures
Figure 1
(A) A sketch of epithelial cells, for which we assume that the mechanical interactions act in the plane of the adherens junctions. (B) Two-dimensional vertex representation of epithelial cells with balancing forces on a vertex due to line tension (red) and pressure (blue). (C) Two-dimensional particle representation of epithelial cells, with balancing forces represented by springs, and a corresponding Voronoi diagram. To see this figure in color, go online.
Figure 2
Schematic description of the numerical algorithm. The artifacts of the Voronoi cells at the periphery are only graphical and do not influence the computation. To see this figure in color, go online.
Figure 3
Epithelial cell density field, ρ, at times t = 0.05 days, 1.73 days, 3.46 days, and 5.77 days (left to right), with corresponding Voronoi diagrams (lower row). The artifacts of the Voronoi cells at the periphery are only graphical and do not influence the computation. To see this figure in color, go online.
Figure 4
Analysis of cell areas and arrangements. (A) Total area of the spreading colony. The black line corresponds to exponential growth with the average epithelial cell cycle time 0.75 days. The gray line corresponds to quadratic growth, and the symbols correspond to scaled results from the experiments in Puliafito et al. (2) (see text for additional description). The blue dot-dashed, green dashed, and red lines correspond to scaled simulation results for different mobilities, η, as labeled. (B) The corresponding average cell densities remain almost constant until t¯≈2days and they grow rapidly thereafter. The plot is superimposed on the results from Fig. 1_C_ of Puliafito et al. (2) with shifted time (see text). (C) The median of the area distribution of epithelial cells in the center region (<100 _μ_m distance to the center) is nearly constant (solid black line) during exponential growth and shows a rapid decrease when contact inhibition sets in at t¯≈2days. (D) Area of a single epithelial cell as a function of time remains constant before t¯≈2days and subsequently decreases. The dashed black lines are average epithelial cell areas between mitosis events. Results correspond to η=10. (E) Radial distribution function of simulated cell distributions with η=10 at different times, as labeled. The appearance of a peak and trough in the quadratic growth regime indicates short-range ordering of cells. (F) Histogram of the distribution of the cellular coordination number (number of direct cell neighbors) at η=10. The reference distribution is from Puliafito et al. (2). To see this figure in color, go online.
Figure 5
Schematic of different cleavage-plane mechanisms. A dividing mother cell (large red circle) may align the daughters (small red circles) such that they have the most (best angle) or least space (worst angle), or are randomly aligned (random angle). The blue circles denote previously existing cells. To see this figure in color, go online.
Figure 6
Histogram of the distribution of the cellular coordination number (number of direct cell neighbors) for different cleavage-plane mechanisms using the mobility η=10. The random cleavage plane produces results closest to the reference (Fig. S1_B_ of Puliafito et al. (2)). To see this figure in color, go online.
Figure 7
Cell velocity averaged over the last 5 h of the simulation. (Left) The velocity magnitude shows that cells in general move the fastest along the colony periphery, whereas cells in the inner region move significantly more slowly. (Right) The velocity direction is color-coded by a circular color bar and indicates that cells in the periphery move away from the center, whereas inner cells have no preferred direction of movement. To see this figure in color, go online.
Figure 8
Cell compression as a function of time (left), number of cell neighbors (middle), and distance to the colony center (right). Results indicate that the average cell compression increases with time, that cells with fewer neighbors are more compressed than cells with larger numbers of neighbors, and that cell compression is relatively constant in the inner part of the colony and decays rapidly across the outer part of the colony.
Figure 9
Compression of individual cells at the final time. To see this figure in color, go online.
References
- Vincent J.-P., Fletcher A.G., Baena-Lopez L.A. Mechanisms and mechanics of cell competition in epithelia. Nat. Rev. Mol. Cell Biol. 2013;14:581–591. - PubMed
- Scianna M., Preziosi L. Multiscale developments of the cellular Potts model. Multiscal. Model. Simul. 2012;10:342–382.
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