One CPM Cell
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Time sequence showing the changing shape of a CPM cell
Introduction
Not all cell shapes are circular. In this example, a single cell undergoes a whole series of deformations resulting in the development of irregular cell shapes.
Description
For a time sequence showing the shape of a CPM cell every $50$ time-steps the following parameters were used:
- Target area (
VolumeConstraint) $a_0 = 400$,strength$\lambda_a = 1$,
- target perimeter (
SurfaceConstraint) $p_0 = 120$,strength$\lambda_p = 1$,
ConnectivityConstraintenabled,- cell-medium
Contactstrength $ = 2$, temperature$= 1$,yield$= 0.1$.
Results
The cell continuously puts out protrusions in various directions.
OneCPMCell.xmlModel
OneCPMCell.xml
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<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
<Description>
<Title>One CPM Cell</Title>
<Details>Full title: One CPM Cell
Authors: L. Edelstein-Keshet
Contributors: Y. Xiao
Date: 02.05.2022
Software: Morpheus (open-source). Download from https://morpheus.gitlab.io
Model ID: https://identifiers.org/morpheus/M2002
Reference: L. Edelstein-Keshet: Mathematical Models in Cell Biology
Comment: A time sequence showing the shape of a CPM cell every 50 time steps. The cell continuously puts out protrusions in various directions.</Details>
</Description>
<Space>
<Lattice class="square">
<Size symbol="l" value="150, 150, 0"/>
<BoundaryConditions>
<Condition type="constant" boundary="x"/>
<Condition type="constant" boundary="-x"/>
<Condition type="constant" boundary="y"/>
<Condition type="constant" boundary="-y"/>
</BoundaryConditions>
<NodeLength value="0.37"/>
<Neighborhood>
<Distance>1.5</Distance>
</Neighborhood>
</Lattice>
<SpaceSymbol symbol="space"/>
</Space>
<Time>
<StartTime value="0"/>
<StopTime symbol="end" value="750"/>
<TimeSymbol symbol="time"/>
<RandomSeed value="1227903"/>
</Time>
<CellTypes>
<CellType class="medium" name="medium"/>
<CellType class="biological" name="amoeba">
<VolumeConstraint target="400" strength="1"/>
<SurfaceConstraint target="120" strength="1" mode="surface"/>
<ConnectivityConstraint/>
</CellType>
</CellTypes>
<CPM>
<Interaction>
<Contact type1="amoeba" type2="amoeba" value="4"/>
<Contact type1="amoeba" type2="medium" value="2"/>
</Interaction>
<MonteCarloSampler stepper="edgelist">
<MCSDuration symbol="MCStime" value="0.1"/>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
<MetropolisKinetics yield="0.1" temperature="1.0"/>
</MonteCarloSampler>
<ShapeSurface scaling="norm">
<Neighborhood>
<Distance>1.5</Distance>
</Neighborhood>
</ShapeSurface>
</CPM>
<CellPopulations>
<Population type="amoeba" size="1">
<InitCircle number-of-cells="1" mode="random">
<Dimensions radius="l.x/8" center="l.x/2, l.y/2, 0"/>
</InitCircle>
</Population>
</CellPopulations>
<Analysis>
<Gnuplotter time-step="50" decorate="false">
<Terminal name="png" size="400 400 0"/>
<Plot>
<Cells opacity="0.65" min="0.0" max="10" value="cell.id">
<ColorMap>
<Color value="1" color="red"/>
<Color value="10" color="blue"/>
</ColorMap>
</Cells>
</Plot>
</Gnuplotter>
<ModelGraph format="svg" reduced="false" include-tags="#untagged"/>
</Analysis>
<Global/>
</MorpheusModel>
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