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).

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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:

  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. "-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)
  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 "-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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