Proliferation in Two Dimensions
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Introduction
This model shows a simulation of a growing cell population, using the cellular Potts model.
Description
The model specifies CellType which has a VolumeConstraint and a Proliferation plugin.
In the Proliferation plugin, the Conditions for a cell to divide are given. Here, each cell that has more than 90% of the target volume has a small probability to divide. Once a division has taken place, the Equation defined in the Triggers elements are triggered.
Model
Examples → CPM → Proliferation_2D.xml or
Proliferation_2D.xml
XML Preview
<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="3">
<Description>
<Title>Example-Proliferation2D</Title>
<Details></Details>
</Description>
<Global>
<Variable symbol="c" value="0.0"/>
</Global>
<Space>
<Lattice class="hexagonal">
<Size symbol="size" value="500 500 0"/>
<BoundaryConditions>
<Condition boundary="x" type="periodic"/>
<Condition boundary="y" type="periodic"/>
</BoundaryConditions>
<Neighborhood>
<Order>1</Order>
</Neighborhood>
</Lattice>
<SpaceSymbol symbol="space"/>
</Space>
<Time>
<StartTime value="0"/>
<StopTime symbol="stoptime" value="4e4"/>
<TimeSymbol symbol="time"/>
</Time>
<CellTypes>
<CellType class="biological" name="cells">
<Property symbol="p" value="5e-5" name="proliferation rate"/>
<Property symbol="d" value="0" name="divisions"/>
<Property symbol="c" value="0" name="color"/>
<VolumeConstraint target="500" strength="1"/>
<SurfaceConstraint target="0.9" mode="aspherity" strength="1"/>
<System solver="euler" time-step="1.0">
<Rule symbol-ref="c">
<Expression>if( c > 0, c-1, 0)</Expression>
</Rule>
</System>
<CellDivision division-plane="random">
<Condition>rand_uni(0,1) < p</Condition>
<Triggers>
<Rule symbol-ref="d">
<Expression>d+1</Expression>
</Rule>
<Rule symbol-ref="c" name="color after division">
<Expression>1000</Expression>
</Rule>
</Triggers>
</CellDivision>
</CellType>
</CellTypes>
<CPM>
<Interaction default="0">
<Contact type1="cells" type2="cells" value="-4"/>
</Interaction>
<MonteCarloSampler stepper="edgelist">
<MCSDuration value="1.0"/>
<Neighborhood>
<Order>1</Order>
</Neighborhood>
<MetropolisKinetics temperature="3" yield="0.1"/>
</MonteCarloSampler>
<ShapeSurface scaling="norm">
<Neighborhood>
<Order>3</Order>
</Neighborhood>
</ShapeSurface>
</CPM>
<CellPopulations>
<Population size="1" type="cells">
<InitCircle mode="regular" number-of-cells="20">
<Dimensions radius="35" center="250, 250, 0"/>
</InitCircle>
</Population>
</CellPopulations>
<Analysis>
<Gnuplotter time-step="1000" decorate="false">
<Terminal name="png"/>
<Plot>
<Cells value="c" min="0.0" max="1">
<ColorMap>
<Color value="1" color="red"/>
<Color value="0.0" color="green"/>
</ColorMap>
</Cells>
<CellLabels fontsize="8" value="d"/>
</Plot>
</Gnuplotter>
<Logger time-step="100">
<Input>
<Symbol symbol-ref="celltype.cells.size"/>
</Input>
<Output>
<TextOutput/>
</Output>
<Plots>
<Plot log-commands="true" time-step="10000">
<Style point-size="0.5" grid="true" style="linespoints"/>
<Terminal terminal="png"/>
<X-axis minimum="0" maximum="stoptime">
<Symbol symbol-ref="time"/>
</X-axis>
<Y-axis minimum="0" maximum="100">
<Symbol symbol-ref="celltype.cells.size"/>
</Y-axis>
</Plot>
</Plots>
</Logger>
</Analysis>
</MorpheusModel>
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