# Mixed Cell Types

##### Persistent Identifier

Simulations of four types of cells with different shapes to demonstrate how the combined target volume, surface area, and medium contact interaction determine the shape of the cell

## Introduction

By setting the volume, surface, and length constraints, a CPM simulation can produce a variety of cell shapes.

## Description

In this example, there are four cell types with preferred volumes $V_i$ (area in 2D), surfaces $S_i$ (perimeter in 2D) and lengths $L_i$ set to values:

• $V_1$ $= 2100$, $L_1$ $= 120$ (red);
• $V_2$ $= 1800$, $S_2$ $= 250$ (yellow);
• $V_3$ $= 1800$, $S_3$ $= 100$ (green);
• $V_4$ $= 2250$, $S_4$ $= 400$ (blue).

The strengths of all constraints is the same $\lambda$ $= 1$.

## Results

The cells have all been assigned a low Interaction cost with the medium and a higher Interaction cost with one another. Hence, we see that all cells avoid coming into contact.

## Model

Get this model via:

•  Download: MixedCellTypes.xml
• XML Preview

<MorpheusModel version="4">
<Description>
<Title>MixedCellTypes</Title>
<Details>Full title:		Mixed Cell Types
Authors:		L. Edelstein-Keshet
Contributors:	Y. Xiao
Date:		22.06.2022
Model ID:		https://identifiers.org/morpheus/M2008
Reference:		L. Edelstein-Keshet: Mathematical Models in Cell Biology
Comment:		Simulations of four types of cells with different shapes to demonstrate how the combined target volume, surface area, and medium contact interaction work to determine the shape of the cell. Cell properties are as follows:
Type ), M=contact with medium, V=target volume, L=target length, S=target surface, C = connectivity constraint. 1) M = 3, V = 2100, L = 120, C. 2) M = 2,  V = 1800, S = 250, C. 3) M = 2, V = 1800, S = 100, C. 4) M = 5, V = 2250, S = 400, C.</Details>
</Description>
<Global>
<Variable symbol="boundary" name="Boundary length of CT1 with other cell types" value="0.0"/>
<Constant symbol="b" value="0.0"/>
<Constant symbol="b2" value="0.0"/>
</Global>
<Space>
<SpaceSymbol symbol="l"/>
<Lattice class="square">
<Size symbol="size" value="500, 500, 0"/>
<BoundaryConditions>
<Condition type="noflux" boundary="x"/>
<Condition type="noflux" boundary="y"/>
</BoundaryConditions>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
</Lattice>
</Space>
<Time>
<StartTime value="0"/>
<StopTime value="500"/>
<!--    <Disabled>
<SaveInterval value="5e3"/>
</Disabled>
-->
<!--    <Disabled>
<RandomSeed value="3362"/>
</Disabled>
-->
<TimeSymbol symbol="time"/>
</Time>
<CellTypes>
<CellType class="biological" name="ct1">
<VolumeConstraint target="2100" strength="1"/>
<LengthConstraint target="120" strength="1" mode="length"/>
<ConnectivityConstraint/>
</CellType>
<CellType class="biological" name="ct2">
<VolumeConstraint target="1800" strength="1"/>
<SurfaceConstraint target="250" strength="1" mode="surface"/>
<ConnectivityConstraint/>
</CellType>
<CellType class="biological" name="ct3">
<VolumeConstraint target="1800" strength="1"/>
<ConnectivityConstraint/>
<SurfaceConstraint target="100" strength="1" mode="surface"/>
</CellType>
<CellType class="biological" name="ct4">
<VolumeConstraint target="2250" strength="1"/>
<ConnectivityConstraint/>
<SurfaceConstraint target="400" strength="1" mode="surface"/>
</CellType>
<CellType class="medium" name="medium"/>
</CellTypes>
<CPM>
<Interaction default="0.0">
<Contact type1="ct1" type2="medium" value="3"/>
<Contact type1="ct2" type2="medium" value="2"/>
<Contact type1="ct3" type2="medium" value="2"/>
<Contact type1="ct4" type2="medium" value="5"/>
<Contact type1="ct1" type2="ct1" value="30"/>
<Contact type1="ct2" type2="ct2" value="30"/>
<Contact type1="ct1" type2="ct2" value="30"/>
<Contact type1="ct1" type2="ct3" value="30"/>
<Contact type1="ct2" type2="ct3" value="30"/>
<Contact type1="ct3" type2="ct3" value="30"/>
<Contact type1="ct1" type2="ct4" value="30"/>
<Contact type1="ct2" type2="ct4" value="30"/>
<Contact type1="ct3" type2="ct4" value="30"/>
<Contact type1="ct4" type2="ct4" value="30"/>
</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="4" mode="random">
</InitCircle>
<!--    <Disabled>
<InitRectangle number-of-cells="10" mode="random">
<Dimensions origin="size.x/2,size.y/2,0" size="size.x/2,size.y/2,0"/>
</InitRectangle>
</Disabled>
-->
</Population>
<Population type="ct2" size="0">
<InitCircle number-of-cells="3" mode="random">
</InitCircle>
</Population>
<Population type="ct3" size="0">
<!--    <Disabled>
<InitRectangle number-of-cells="10" mode="random">
<Dimensions origin="size.x/2, size.y/2, 0" size="size.x/2"/>
</InitRectangle>
</Disabled>
-->
<InitCircle number-of-cells="4" random_displacement="30.0" mode="random">
</InitCircle>
</Population>
<Population type="ct4" size="1">
<InitCircle number-of-cells="5" mode="random">
</InitCircle>
</Population>
</CellPopulations>
<Analysis>
<Gnuplotter time-step="20" decorate="false">
<Terminal name="png"/>
<Plot>
<Cells flooding="true" value="cell.type"/>
</Plot>
</Gnuplotter>
<ModelGraph format="svg" reduced="false" include-tags="#untagged"/>
</Analysis>
</MorpheusModel>