Mixed Cell Types
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Simulations of four types of cells with different shapes to demonstrate how the combined target volume, surface area, and medium contact interaction determine the shape of the cell
Introduction
By setting the volume, surface, and length constraints, a CPM simulation can produce a variety of cell shapes.
Description
In this example, there are four cell types with preferred volumes $V_i$ (area in 2D), surfaces $S_i$ (perimeter in 2D) and lengths $L_i$ set to values:
- $V_1$ $= 2100$, $L_1$ $= 120$ (red);
- $V_2$ $= 1800$, $S_2$ $= 250$ (yellow);
- $V_3$ $= 1800$, $S_3$ $= 100$ (green);
- $V_4$ $= 2250$, $S_4$ $= 400$ (blue).
The strengths of all constraints is the same $\lambda$ $= 1$.
Results
The cells have all been assigned a low Interaction cost with the medium and a higher Interaction cost with one another. Hence, we see that all cells avoid coming into contact.
MixedCellTypes.xml
Model
MixedCellTypes.xml
XML Preview
<MorpheusModel version="4">
<Description>
<Title>MixedCellTypes</Title>
<Details>Full title: Mixed Cell Types
Authors: L. Edelstein-Keshet
Contributors: Y. Xiao
Date: 22.06.2022
Software: Morpheus (open-source). Download from https://morpheus.gitlab.io
Model ID: https://identifiers.org/morpheus/M2008
Reference: L. Edelstein-Keshet: Mathematical Models in Cell Biology
Comment: Simulations of four types of cells with different shapes to demonstrate how the combined target volume, surface area, and medium contact interaction work to determine the shape of the cell. Cell properties are as follows:
Type ), M=contact with medium, V=target volume, L=target length, S=target surface, C = connectivity constraint. 1) M = 3, V = 2100, L = 120, C. 2) M = 2, V = 1800, S = 250, C. 3) M = 2, V = 1800, S = 100, C. 4) M = 5, V = 2250, S = 400, C.</Details>
</Description>
<Global>
<Variable symbol="boundary" name="Boundary length of CT1 with other cell types" value="0.0"/>
<Constant symbol="b" value="0.0"/>
<Constant symbol="b2" value="0.0"/>
</Global>
<Space>
<SpaceSymbol symbol="l"/>
<Lattice class="square">
<Size symbol="size" value="500, 500, 0"/>
<BoundaryConditions>
<Condition type="noflux" boundary="x"/>
<Condition type="noflux" boundary="y"/>
</BoundaryConditions>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
</Lattice>
</Space>
<Time>
<StartTime value="0"/>
<StopTime value="500"/>
<!-- <Disabled>
<SaveInterval value="5e3"/>
</Disabled>
-->
<!-- <Disabled>
<RandomSeed value="3362"/>
</Disabled>
-->
<TimeSymbol symbol="time"/>
</Time>
<CellTypes>
<CellType class="biological" name="ct1">
<VolumeConstraint target="2100" strength="1"/>
<LengthConstraint target="120" strength="1" mode="length"/>
<ConnectivityConstraint/>
</CellType>
<CellType class="biological" name="ct2">
<VolumeConstraint target="1800" strength="1"/>
<SurfaceConstraint target="250" strength="1" mode="surface"/>
<ConnectivityConstraint/>
</CellType>
<CellType class="biological" name="ct3">
<VolumeConstraint target="1800" strength="1"/>
<ConnectivityConstraint/>
<SurfaceConstraint target="100" strength="1" mode="surface"/>
</CellType>
<CellType class="biological" name="ct4">
<VolumeConstraint target="2250" strength="1"/>
<ConnectivityConstraint/>
<SurfaceConstraint target="400" strength="1" mode="surface"/>
</CellType>
<CellType class="medium" name="medium"/>
</CellTypes>
<CPM>
<Interaction default="0.0">
<Contact type1="ct1" type2="medium" value="3"/>
<Contact type1="ct2" type2="medium" value="2"/>
<Contact type1="ct3" type2="medium" value="2"/>
<Contact type1="ct4" type2="medium" value="5"/>
<Contact type1="ct1" type2="ct1" value="30"/>
<Contact type1="ct2" type2="ct2" value="30"/>
<Contact type1="ct1" type2="ct2" value="30"/>
<Contact type1="ct1" type2="ct3" value="30"/>
<Contact type1="ct2" type2="ct3" value="30"/>
<Contact type1="ct3" type2="ct3" value="30"/>
<Contact type1="ct1" type2="ct4" value="30"/>
<Contact type1="ct2" type2="ct4" value="30"/>
<Contact type1="ct3" type2="ct4" value="30"/>
<Contact type1="ct4" type2="ct4" value="30"/>
</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="4" mode="random">
<Dimensions radius="size.x/3" center="size.x/2, size.y/2, 0"/>
</InitCircle>
<!-- <Disabled>
<InitRectangle number-of-cells="10" mode="random">
<Dimensions origin="size.x/2,size.y/2,0" size="size.x/2,size.y/2,0"/>
</InitRectangle>
</Disabled>
-->
</Population>
<Population type="ct2" size="0">
<InitCircle number-of-cells="3" mode="random">
<Dimensions radius="size.x/3" center="size.x/2, size.y/2, 0"/>
</InitCircle>
</Population>
<Population type="ct3" size="0">
<!-- <Disabled>
<InitRectangle number-of-cells="10" mode="random">
<Dimensions origin="size.x/2, size.y/2, 0" size="size.x/2"/>
</InitRectangle>
</Disabled>
-->
<InitCircle number-of-cells="4" random_displacement="30.0" mode="random">
<Dimensions radius="size.x/3" center="size.x/2, size.y/2,0"/>
</InitCircle>
</Population>
<Population type="ct4" size="1">
<InitCircle number-of-cells="5" mode="random">
<Dimensions radius="size.x/3" center="size.x/2,size.y/2,0"/>
</InitCircle>
</Population>
</CellPopulations>
<Analysis>
<Gnuplotter time-step="20" 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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