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 $\lambda_p = 1$,
  • ConnectivityConstraint enabled,
  • cell-medium Contact strength $ = 2$,
  • temperature $= 1$,
  • yield $= 0.1$.

Results

The cell continuously puts out protrusions in various directions.

A time sequence showing the shape of a CPM cell every $50$ time steps.
A time sequence showing the shape of a CPM cell every $50$ time steps.
Simulation video of OneCPMCell.xml

Model

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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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