Simplified Cell Sorting

Y. Xiao (Contributor)

L. Edelstein-Keshet: Mathematical Models in Cell Biology

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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	$J_{11}$	$J_{22}$	$J_{12}$	$J_{1 m}$	$J_{2 m}$	$T$	$λ$
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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Download: CellSortingLEK.xml

XML Preview

<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>

Downloads

Files associated with this model:

Adhesion Adhesion Energy Cell Sorting Cell-cell Contact Cell-medium Contact Cellular Potts Model Checkerboard Contact Contact Energy Contributed Examples CPM DAH Differential Adhesion Differential Adhesion Hypothesis Dispersal Engulfment Glazier-Graner Model Glazier-Graner-Hogeweg Model Interaction Medium MetropolisKinetics Reversal Separation Steinberg Target Area Target Volume Temperature Tissue Configuration VolumeConstraint

Last updated on Fri, 21 Mar 2025