Simplified Cell Sorting
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A simplified version of the Morpheus cell sorting example
Introduction
A simplified version of the Morpheus built-in example of cell sorting showing the effect of cell-cell and cell-medium contact energies on the tissue configuration.
Description
The different cell configurations were simulated with the parameters in the table attached, with b) being the preset behavior in CellSortingLEK.xml ( | ).
| Type | $J_{11}$ | $J_{22}$ | $J_{12}$ | $J_{1 \mathrm m}$ | $J_{2 \mathrm m}$ | $T$ | $\lambda$ |
|---|---|---|---|---|---|---|---|
| a) Checkerboard | $10$ | $8$ | $6$ | $12$ | $12$ | $10$ | $1$ |
| b) Separation | $6$ | $6$ | $16$ | $12$ | $6$ | $2$ | $1$ |
| c) Engulfment | $14$ | $2$ | $11$ | $16$ | $16$ | $2$ | $1$ |
| d) Reversal | $14$ | $2$ | $11$ | $30$ | $16$ | $2$ | $1$ |
| e) Dispersal 1 | $14$ | $2$ | $9$ | $16$ | $16$ | $5$ | $1$ |
| f) Dispersal 2 | $14$ | $4$ | $11$ | $2$ | $16$ | $5$ | $1$ |
Results
), c) engulfment, d) reversal, e) dispersal 1, f) dispersal 2.](https://d33wubrfki0l68.cloudfront.net/0a0bc1b4bd70c3c7956c36a27fc7d3bcf3f29468/d7150/media/model/m2007/cellsortinglek_hu8b196c058c12b79b6719d32258df5aaa_221816_662a1ca35f86057280d878f9a1a70db1.png)
CellSortingLEK.xml), c) engulfment, d) reversal, e) dispersal 1, f) dispersal 2.
CellSortingLEK.xml with default behavior b)
Reference
J. A. Glazier, F. Graner: Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47 (3): 2128, 1993.
Model
CellSortingLEK.xml
XML Preview
<MorpheusModel version="4">
<Description>
<Title>CellSorting2D</Title>
<Details>Full title: Simplified Cell Sorting
Authors: L. Edelstein-Keshet
Contributors: Y. Xiao
Date: 04.06.2022
Software: Morpheus (open-source). Download from https://morpheus.gitlab.io
Model ID: https://identifiers.org/morpheus/M2007
Reference: L. Edelstein-Keshet: Mathematical Models in Cell Biology
Comment: A simplified version of the example model CellSorting_2D.xml provided in Morpheus (Morpheus Model ID: M0021, https://identifiers.org/morpheus/M0021), showing only the way that the cells sort. Reference: Graner and Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett. 69, 2013–2016 (1992).</Details>
</Description>
<Global/>
<Space>
<SpaceSymbol symbol="l"/>
<Lattice class="square">
<Size symbol="size" value="200, 200, 0"/>
<BoundaryConditions>
<Condition type="periodic" boundary="x"/>
<Condition type="periodic" boundary="y"/>
</BoundaryConditions>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
</Lattice>
</Space>
<Time>
<StartTime value="0"/>
<StopTime value="5000"/>
<RandomSeed value="0"/>
<TimeSymbol symbol="time"/>
</Time>
<CellTypes>
<CellType class="biological" name="ct1">
<VolumeConstraint target="200" strength="1"/>
</CellType>
<CellType class="biological" name="ct2">
<VolumeConstraint target="200" strength="1"/>
</CellType>
<CellType class="medium" name="medium"/>
</CellTypes>
<CPM>
<Interaction default="0.0">
<Contact type1="ct1" type2="medium" value="12"/>
<Contact type1="ct2" type2="medium" value="6"/>
<Contact type1="ct1" type2="ct1" value="6"/>
<Contact type1="ct2" type2="ct2" value="6"/>
<Contact type1="ct1" type2="ct2" value="16"/>
</Interaction>
<MonteCarloSampler stepper="edgelist">
<MCSDuration value="1"/>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
<MetropolisKinetics temperature="2"/>
</MonteCarloSampler>
<ShapeSurface scaling="norm">
<Neighborhood>
<Order>6</Order>
</Neighborhood>
</ShapeSurface>
</CPM>
<CellPopulations>
<Population type="ct1" size="0">
<InitCircle number-of-cells="50" mode="random">
<Dimensions radius="size.x/3" center="size.x/2, size.y/2, 0"/>
</InitCircle>
</Population>
<Population type="ct2" size="0">
<InitCircle number-of-cells="50" mode="random">
<Dimensions radius="size.x/3" center="size.x/2, size.y/2, 0"/>
</InitCircle>
</Population>
</CellPopulations>
<Analysis>
<Gnuplotter time-step="100" decorate="false">
<Terminal name="png"/>
<Plot>
<Cells flooding="true" value="cell.type"/>
</Plot>
</Gnuplotter>
<ModelGraph format="svg" reduced="false" include-tags="#untagged"/>
</Analysis>
</MorpheusModel>
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