# Field-Cell Interaction

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Cells' consumption of cytokine concentration

## Introduction

This example serves to demonstrate the implementation of cells consuming a substrate field, e.g. cytokine. Please also see the built-in docu at MorpheuML/Global/Field and Global/System/DiffEqn. This example was motivated by Victoria Ponce in the Morpheus user forum.

## Description

The logic is like this: In the PDE that describes the reaction and diffusion of the substrate, you include a negative term (i.e. for decrease) that is nonzero where there is a cell and zero where there is no cell. Steps to reproduce:

1. Define a Field in Global, e.g. called cytokine with an inital concentration $1.0$ and Diffusion.
2. Define a System with a differential equation with a negative term, e.g. -r*cell*cytokine where r is the consumption rate of cells. (Here it is constant, but could also be a cell property to specify that each cell has its own consumption rate.)
3. Define a Constant called cell which is $0$ everywhere, except for where there is a cell. To do this, specify cell in Global and set it to $0$. But in CellType , the value of the constant is overwritten with a value of $1$.

In this way, the term -r*cell*cytokine is negative ‘within’ cells and zero outside. Therefore, the cytokine concentration is only decreased at locations with cells.

Movie visualising the consumption of cytokine only where the cell is: The panel shows the area covered by the cell (left) and the cytokine concentration over time (right).

## Model

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<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
<Description>
<Details>This example serves to demonstrate the implementation of cells consuming a substrate field e.g. cytokine.
The logic is like this: In the PDE that describes the reaction and diffusion of the substrate, you include a negative term (i.e. for decrease) that is nonzero where there is a cell and zero where there is no cell.
Steps to reproduce:

Define a Field in Global/ e.g. called "cytokine" with an inital concentration 1.0 and diffusion
Define a System with a differential equation with a negative term, e.g. "-rcellcytokine" where "r" is the consumption rate of cells. (Here it is constant, but could also be a cell property to specify that each cell has its own consumption rate)
Define a Constant called "cell" which is "0" everywhere, except for where there is a cell.
To do this specify "cell" in Global and set it to "0".
But in CellType , the value of the constant is overwritten with a value of "1".

In this way, the term "-rcellcytokine" is negative ‘within’ cells and zero outside. Therefore, the cytokine concentration is only decreased at locations with cells.
Date: March 4, 2022
Author: walter@deback.net
Contributor: ferras_mahmoud.el-hendi@tu-dresden.de
Software: Morpheus (open-source), download from https://morpheus.gitlab.io
</Details>
<Title>Cells' Cytokine Consumption</Title>
</Description>
<Space>
<Lattice class="square">
<Neighborhood>
<Order>2</Order>
</Neighborhood>
<Size symbol="size" value="200, 200, 0"/>
</Lattice>
<SpaceSymbol symbol="space"/>
</Space>
<Time>
<StartTime value="0"/>
<StopTime value="100"/>
<TimeSymbol symbol="time"/>
</Time>
<CellTypes>
<CellType class="biological" name="cells">
<Constant symbol="cell" value="1"/>
</CellType>
</CellTypes>
<CellPopulations>
<Population type="cells" size="1">
<InitCellObjects mode="distance">
<Arrangement displacements="0,0,0" repetitions="1,1,0">
<Sphere radius="25.0" center="size/2"/>
</Arrangement>
</InitCellObjects>
</Population>
</CellPopulations>
<Global>
<Constant symbol="cell" value="0.0" name="Presence of cell"/>
<Field symbol="cytokine" value="1.0" name="Cytokine concentration">
<Diffusion rate="1"/>
</Field>
<System solver="Dormand-Prince [adaptive, O(5)]">
<Constant symbol="r" value="0.05" name="consumption rate"/>
<DiffEqn symbol-ref="cytokine">
<Expression>-rcellcytokine</Expression>
</DiffEqn>
</System>
</Global>
<Analysis>
<Gnuplotter time-step="1">
<Plot>
<Cells min="0" value="cell" max="1"/>
</Plot>
<Plot>
<Field symbol-ref="cytokine" min="0" max="1">
<ColorMap>
<Color color="red" value="1"/>
<Color color="white" value="0"/>
</ColorMap>
</Field>
</Plot>
<Terminal name="png"/>
</Gnuplotter>
<ModelGraph format="dot" include-tags="#untagged" reduced="false"/>
</Analysis>
</MorpheusModel>


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