Figure 1.
Schematic illustration of a lattice-based representation of cells in the GGH model (left figure) and a lattice-free representation in the centre-based model (right figure).
Table 1.
Dimensionless intracellular parameter values for the cell detachment simulations.
Figure 2.
Plots showing a sequence of the disruption of a layer of epithelial cells due to an increase in the -catenin concentration inside the cells.
After all cells have detached from the layer of cells or from each other (EMT), -catenin concentrations eventually drop, causing cells that are close to each other to undergo re-attachment (MET) while other cells that are not close remain as mesenchymal cells. Colours of the cells correspond to concentration of
-catenin.
Figure 3.
Plots of -catenin, E-cadherin-
-catenin complex, and proteasome-
-catenin concentrations for a simulation in which cells undergo epithelial-mesenchymal transition (EMT) and subsequently recover by mesenchymal-epithelial transition (MET).
The cells reattach to adjacent cells and thereby reform an epithelial layer. The cycle of detachment and reattachment occurs about times until
MCS.
Figure 4.
Plots of -catenin, E-cadherin-
-catenin complex, and proteasome-
-catenin concentrations for a typical cell undergoing epithelial-mesenchymal transition.
Figure 5.
Plots showing the results of a simulation of tumour growth and local invasion (detachment) from a layer of cells.
The tumour grows rapidly from a single layer and eventually EMT events are observed to occur. Cell colour represents -catenin concentration.
Figure 6.
Plot of a cross sectional view showing the spatial distribution of -catenin concentration inside cells from the simulation of tumour growth from a layer of cells.
Cells in the centre of the tumour mass have a large number of binding neighbours, hence the concentration of -catenin is lower than the cells at the outer layer of tumour mass that have fewer binding neighbours and a high concentration of free
-catenin.
Figure 7.
Plots showing the effect of varying the parameter on the number of cells that detach from a primary tumour mass in a layer configuration.
The value of was varied between high, intermediate and low values and the number of cells that detach and migrate a certain distance from the tumour mass was monitored.
Figure 8.
Plots showing the results of multicellular tumour spheroid simulations.
The tumour grows from a single cell placed in the middle of a cubic lattice.
Figure 9.
Position of cell ID with respect to the centre of a cubic lattice of size
pixels during simulations of MTS using the following parameter values for
:
,
, and
.
Tumour radius is apparent from the horizontal portion of the cell position time-courses. In each case (for all three parameter values) this occurs at a pixel value of .
Figure 10.
Plots showing the number of cells removed from MTS simulations using different values of (corresponding to different levels of invasiveness).
Figure 11.
Comparison between our computational results with experimental data.
Images showing experimental data of MTS growth patterns in low collagen concentration (top left figure), a less invasive pattern, and in high collagen concentration (top right figure), a more invasive pattern. Our computational simulation results (bottom right figure with and bottom left figure with
) are comparable to the experimental data. The simulation results were taken at
MCS. Reprinted from Biophysical Journal, 89/1, L. Kaufman, C. Brangwynne, K. Kasza, E. Filippidi, V. Gordon, T. Deisboeck, and D. Weitz, Glioma expansion in collagen I matrices: analyzing collagen concentration-dependent growth and motility patterns, 635–650, Copyright (2005), with permission from Elsevier [OR APPLICABLE SOCIETY COPYRIGHT OWNER].
Figure 12.
Comparison of -catenin detachment wave simulations based on the centre model of [14] (left figure) and our CC3D-Bionetsolver simulation results (right figure).
Figure 13.
Schematic diagram showing the GGH representation of an index-copy attempt for two cells on a 2-dimensional square lattice.
The “white” pixel (source) of cell with attempts to replace the “grey” pixel (target) of cell with
. The probability of accepting the index copy is given by equation (1). Bold lines denote boundaries of the cells. Pixel colour denotes cell type. Notice that in GGH simulations we typically have multiple cells with different id
but belonging to the same type
.
Figure 14.
A schematic diagram of the E-cadherin and interactions with -catenin.