Simplified Cell Sorting

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A simplified version of the Morpheus cell sorting example

Introduction

A simplified version of the Morpheus built-in example of cell sorting showing the effect of cell-cell and cell-medium contact energies on the tissue configuration.

Description

The different cell configurations were simulated with the parameters in the table attached, with b) being the preset behavior in CellSortingLEK.xml ( | ).

Type $J_{11}$ $J_{22}$ $J_{12}$ $J_{1 \mathrm m}$ $J_{2 \mathrm m}$ $T$ $\lambda$
a) Checkerboard $10$ $8$ $6$ $12$ $12$ $10$ $1$
b) Separation $6$ $6$ $16$ $12$ $6$ $2$ $1$
c) Engulfment $14$ $2$ $11$ $16$ $16$ $2$ $1$
d) Reversal $14$ $2$ $11$ $30$ $16$ $2$ $1$
e) Dispersal 1 $14$ $2$ $9$ $16$ $16$ $5$ $1$
f) Dispersal 2 $14$ $4$ $11$ $2$ $16$ $5$ $1$
Parameters as in Glazier et al., 1993 used for the simulations

Results

Regimes that can be found in a mixture of two cell types: a) checkerboard, b) separation (default in [`CellSortingLEK.xml`](#model)), c) engulfment, d) reversal, e) dispersal 1, f) dispersal 2.
Regimes that can be found in a mixture of two cell types: a) checkerboard, b) separation (default in CellSortingLEK.xml), c) engulfment, d) reversal, e) dispersal 1, f) dispersal 2.
Simulation video of CellSortingLEK.xml with default behavior b)

Reference

J. A. Glazier, F. Graner: Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47 (3): 2128, 1993.

Model

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  • Morpheus-Link or
  •  Download: CellSortingLEK.xml
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    <MorpheusModel version="4">
        <Description>
            <Title>CellSorting2D</Title>
            <Details>Full title:		Simplified Cell Sorting
    Authors:		L. Edelstein-Keshet
    Contributors:	Y. Xiao
    Date:		04.06.2022
    Software:		Morpheus (open-source). Download from https://morpheus.gitlab.io
    Model ID:		https://identifiers.org/morpheus/M2007
    Reference:		L. Edelstein-Keshet: Mathematical Models in Cell Biology
    Comment:		A simplified version of the example model CellSorting_2D.xml provided in Morpheus (Morpheus Model ID: M0021, https://identifiers.org/morpheus/M0021), showing only the way that the cells sort. Reference: Graner and Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett. 69, 2013–2016 (1992).</Details>
        </Description>
        <Global/>
        <Space>
            <SpaceSymbol symbol="l"/>
            <Lattice class="square">
                <Size symbol="size" value="200, 200, 0"/>
                <BoundaryConditions>
                    <Condition type="periodic" boundary="x"/>
                    <Condition type="periodic" boundary="y"/>
                </BoundaryConditions>
                <Neighborhood>
                    <Order>2</Order>
                </Neighborhood>
            </Lattice>
        </Space>
        <Time>
            <StartTime value="0"/>
            <StopTime value="5000"/>
            <RandomSeed value="0"/>
            <TimeSymbol symbol="time"/>
        </Time>
        <CellTypes>
            <CellType class="biological" name="ct1">
                <VolumeConstraint target="200" strength="1"/>
            </CellType>
            <CellType class="biological" name="ct2">
                <VolumeConstraint target="200" strength="1"/>
            </CellType>
            <CellType class="medium" name="medium"/>
        </CellTypes>
        <CPM>
            <Interaction default="0.0">
                <Contact type1="ct1" type2="medium" value="12"/>
                <Contact type1="ct2" type2="medium" value="6"/>
                <Contact type1="ct1" type2="ct1" value="6"/>
                <Contact type1="ct2" type2="ct2" value="6"/>
                <Contact type1="ct1" type2="ct2" value="16"/>
            </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="50" mode="random">
                    <Dimensions radius="size.x/3" center="size.x/2, size.y/2, 0"/>
                </InitCircle>
            </Population>
            <Population type="ct2" size="0">
                <InitCircle number-of-cells="50" mode="random">
                    <Dimensions radius="size.x/3" center="size.x/2, size.y/2, 0"/>
                </InitCircle>
            </Population>
        </CellPopulations>
        <Analysis>
            <Gnuplotter time-step="100" 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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