Proliferation in Three Dimensions
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Introduction
This model shows a CPM simulation of a growing cell population in 3D.
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.
In this model, two medium
cell types have been defined. One of these (called matrix) is used to represent a matrix with higher adhesivity. This is done by
- defining the matrix cell type as a
BoundaryCondition
of the $-z$ boundary in theCPM
and - providing lower contact energy for cell-matrix interaction than for cell-medium interactions.
The simulation is visualized using the TiffPlotter
that saves TIFF image stacks that can be loaded by image analysis software such as Fiji and displayed using Fiji’s 3D Viewer plugin.
Model
Examples
→ CPM
→ Proliferation_3D.xml
or
Proliferation_3D.xml
XML Preview
<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="3">
<Description>
<Title>Example-Proliferation3D</Title>
<Details></Details>
</Description>
<Global/>
<Space>
<Lattice class="cubic">
<Size symbol="size" value="100 100 100"/>
<BoundaryConditions>
<Condition boundary="x" type="periodic"/>
<Condition boundary="y" type="periodic"/>
<Condition boundary="z" type="noflux"/>
<Condition boundary="-z" type="noflux"/>
</BoundaryConditions>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
</Lattice>
<MembraneLattice>
<Resolution symbol="memsize" value="20"/>
<SpaceSymbol symbol="m"/>
</MembraneLattice>
<SpaceSymbol symbol="space"/>
</Space>
<Time>
<StartTime value="0"/>
<StopTime value="2500"/>
<TimeSymbol symbol="time"/>
<RandomSeed value="1456688742"/>
</Time>
<CellTypes>
<CellType class="medium" name="medium"/>
<CellType class="medium" name="matrix"/>
<CellType class="biological" name="cell">
<Property symbol="Vt" value="500" name="Target Volume"/>
<Property symbol="divisions" value="0"/>
<VolumeConstraint target="Vt" strength="1.0"/>
<SurfaceConstraint target="1.0" mode="aspherity" strength="1.0"/>
<CellDivision division-plane="major">
<Condition>rand_uni(0,1) < 0.0025 and cell.volume > Vt*0.9</Condition>
<Triggers>
<Rule symbol-ref="divisions">
<Expression>divisions + 0.5</Expression>
</Rule>
</Triggers>
</CellDivision>
<MembraneProperty symbol="c" value="1">
<Diffusion rate="0.0"/>
</MembraneProperty>
</CellType>
</CellTypes>
<CPM>
<Interaction default="0">
<Contact type1="cell" type2="cell" value="-6"/>
<Contact type1="cell" type2="medium" value="0"/>
<Contact type1="cell" type2="matrix" value="-2"/>
</Interaction>
<MonteCarloSampler stepper="edgelist">
<MCSDuration value="1"/>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
<MetropolisKinetics temperature="0.5"/>
</MonteCarloSampler>
<ShapeSurface scaling="norm">
<Neighborhood>
<Distance>2.5</Distance>
</Neighborhood>
</ShapeSurface>
</CPM>
<CellPopulations>
<Population size="0" type="cell">
<InitCellObjects mode="distance">
<Arrangement repetitions="1, 1, 1" displacements="1, 1, 1">
<Object>
<Sphere radius="5" center="50,50,50"/>
</Object>
</Arrangement>
</InitCellObjects>
</Population>
<BoundaryValue boundary="x" value="matrix"/>
<BoundaryValue boundary="-x" value="matrix"/>
<BoundaryValue boundary="y" value="matrix"/>
<BoundaryValue boundary="-y" value="matrix"/>
<BoundaryValue boundary="z" value="matrix"/>
<BoundaryValue boundary="-z" value="matrix"/>
</CellPopulations>
<Analysis>
<TiffPlotter timelapse="true" format="8bit" OME-header="true" compression="false" time-step="100">
<Channel symbol-ref="cell.id" exclude-medium="true"/>
<Channel symbol-ref="c" exclude-medium="true" celltype="cell" outline="true"/>
</TiffPlotter>
<Gnuplotter time-step="100" decorate="true">
<Plot>
<Cells value="cell.id" slice="50"/>
</Plot>
<Terminal name="png"/>
</Gnuplotter>
<Logger time-step="100">
<Input>
<Symbol symbol-ref="celltype.cell.size"/>
</Input>
<Output>
<TextOutput/>
</Output>
<Plots>
<Plot time-step="500">
<Style style="linespoints"/>
<Terminal terminal="png"/>
<X-axis>
<Symbol symbol-ref="time"/>
</X-axis>
<Y-axis>
<Symbol symbol-ref="celltype.cell.size"/>
</Y-axis>
</Plot>
</Plots>
</Logger>
</Analysis>
</MorpheusModel>
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