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CellPolarity_False1.xml
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<MorpheusModel version="4">
<Description>
<Title>Cell Polarity</Title>
<Details>Chemotaxis of polarized cell


----------------------------


Show feedback between cell motility, cell polarization and external gradient.





Two simple polarization models can be enabled/disabled:


- Substrate-depletion model: no repolarization


- Wave-pinning model: repolarization





PDE Equation:


- Switch on/off and change gradients </Details>
</Description>
<Global>
<Constant value="1" symbol="n"/>
<Constant value="pi" symbol="period"/>
<Constant value="pi" symbol="osc"/>
<!-- <Disabled>
<Event trigger="on change" name="Gradient field right bound condition" time-step="1.0">
<Condition>center_cell1 > 0.9*lattice.x</Condition>
<Rule symbol-ref="c">
<Expression>-1*l.x/lattice.x+1+rand_uni(0,0.1)+sin(2*pi*t/osc)</Expression>
</Rule>
</Event>
</Disabled>
-->
<Field value="((l.x < lattice.x/3) * (l.x/lattice.x)) + ((l.x >= lattice.x/3) * 1/3)" name="Gradient Field" symbol="c">
<Diffusion rate="0"/>
</Field>
<Variable value="0.0" symbol="center_cell1"/>
<Mapper>
<Input value="cell.center.x * (cell.id==1)"/>
<Output mapping="maximum" symbol-ref="center_cell1"/>
</Mapper>
<!-- <Disabled>
<Event trigger="on change" name="Gradient field left bound condition" time-step="1.0">
<Condition>center_cell1 < 0.1*lattice.x</Condition>
<Rule symbol-ref="c">
<Expression>1*l.x/lattice.x+1+rand_uni(0,0.1)+sin(2*pi*t/osc)</Expression>
</Rule>
</Event>
</Disabled>
-->
</Global>
<Space>
<Lattice class="square">
<Size value="100, 50, 0" symbol="lattice"/>
<BoundaryConditions>
<Condition boundary="x" type="noflux"/>
<Condition boundary="y" type="periodic"/>
</BoundaryConditions>
<NodeLength value="1.0"/>
<Neighborhood>
<!-- <Disabled>
<Distance>2.0</Distance>
</Disabled>
-->
<Order>2</Order>
</Neighborhood>
</Lattice>
<SpaceSymbol symbol="l"/>
<MembraneLattice>
<Resolution value="50" symbol="memsize"/>
<SpaceSymbol symbol="m"/>
</MembraneLattice>
</Space>
<Time>
<StartTime value="0"/>
<StopTime value="150"/>
<!-- <Disabled>
<SaveInterval value="0"/>
</Disabled>
-->
<RandomSeed value="0"/>
<TimeSymbol symbol="t"/>
</Time>
<CellTypes>
<CellType class="medium" name="Medium">
<Property value="0" symbol="l_c"/>
</CellType>
<CellType class="biological" name="Cell">
<VolumeConstraint strength="0.1" target="500"/>
<SurfaceConstraint strength="0.5" target="1" mode="aspherity"/>
<MembraneProperty value="0.5" name="Activator concentration" symbol="c_a">
<Diffusion rate="0"/>
</MembraneProperty>
<MembraneProperty value="0.5" name="Inhibitor 1 concentration" symbol="c_i1">
<Diffusion rate="0" well-mixed="true"/>
</MembraneProperty>
<MembraneProperty value="0.5" name="Inhibitor 2 concentration" symbol="c_i2">
<Diffusion rate="0.00001"/>
</MembraneProperty>
<Property value="0.0" name="Average c_a across cell" symbol="mean_c_a"/>
<PropertyVector value="0.0, 0.0, 0.0" symbol="move_dir"/>
<PropertyVector value="0.0, 0.0, 0.0" symbol="cell_polarity_vector"/>
<Mapper>
<Input value="c_a"/>
<Output mapping="average" symbol-ref="mean_c_a"/>
<Polarity symbol-ref="cell_polarity_vector"/>
</Mapper>
<System solver="Runge-Kutta [fixed, O(4)]" name="Meinhardt model" time-step="1.0">
<Constant value="0.02" name="Decay rate of the activator a" symbol="r_a"/>
<Constant value="0.1" name="Rate of the activator autocatalysis" symbol="b_a"/>
<Constant value="0.005" name="Saturation of the activator autocatalysis" symbol="s_a"/>
<Constant value="0.03" name="Decay rate of inhibitor 1" symbol="r_i1"/>
<Constant value="0.005" name="Production rate of the inhibitor 2" symbol="b_i2"/>
<Constant value="0.013" name="Decay rate of inhibitor 2" symbol="r_i2"/>
<Constant value="0.2" name="Michaelis-Menten Constant" symbol="s_c"/>
<Constant value="0.02" name="External asymmetry" symbol="dy"/>
<Constant value="0.01" name="Random fluctuation" symbol="dr"/>
<DiffEqn symbol-ref="c_a" name="Change of activator concentration">
<Expression>s*r_a*(c_a^2/c_i1+b_a)/(s_c+c_i2)/(1+s_a*c_a^2) </Expression>
</DiffEqn>
<DiffEqn symbol-ref="c_i1" name="Change of inhibitor 1 concentration">
<Expression>r_i1*mean_c_a*-r_i1*c_i1</Expression>
</DiffEqn>
<DiffEqn symbol-ref="c_i2" name="Change of inhibitor 2 concentration">
<Expression>b_i2*c_a-r_i2*c_i2</Expression>
</DiffEqn>
<Intermediate value="mean_c_a" symbol="mean_c_a"/>
</System>
<Mapper>
<Input value="c_a"/>
<Polarity symbol-ref="move_dir"/>
</Mapper>
<DirectedMotion direction="move_dir" strength="0.5"/>
<Mapper name="copy c(x,y,z) to s(x,y,z)">
<Input value="c"/>
<Output symbol-ref="s"/>
</Mapper>
<MembraneProperty value="0" name="signal" symbol="s">
<Diffusion rate="0"/>
</MembraneProperty>
<ConnectivityConstraint/>
<PropertyVector value="1.0, 0.0, 0.0" symbol="velocity"/>
<MotilityReporter time-step="1">
<Velocity symbol-ref="velocity"/>
</MotilityReporter>
</CellType>
</CellTypes>
<CPM>
<Interaction default="0.0">
<Contact value="-10" type1="Cell" type2="Medium"/>
<Contact value="-20" type1="Cell" type2="Cell"/>
</Interaction>
<MonteCarloSampler stepper="edgelist">
<MCSDuration value="1"/>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
<MetropolisKinetics yield="0.05" temperature="1"/>
</MonteCarloSampler>
<ShapeSurface scaling="norm">
<Neighborhood>
<Order>6</Order>
</Neighborhood>
</ShapeSurface>
</CPM>
<CellPopulations>
<Population size="1" type="Cell">
<Cell id="1" name="1">
<Nodes>25 120 0</Nodes>
</Cell>
</Population>
</CellPopulations>
<Analysis>
<!-- <Disabled>
<Gnuplotter time-step="10">
<Terminal name="png"/>
<Plot>
<Field symbol-ref="c"/>
<Disabled>
<Cells value="A"/>
</Disabled>
<Cells value="c_a"/>
</Plot>
</Gnuplotter>
</Disabled>
-->
<Logger time-step="10">
<Input>
<Symbol symbol-ref="cell.center.x"/>
<Symbol symbol-ref="cell.center.y"/>
<Symbol symbol-ref="mean_c_a"/>
<Symbol symbol-ref="velocity.x"/>
<Symbol symbol-ref="velocity.y"/>
</Input>
<Output>
<TextOutput/>
</Output>
</Logger>
<DependencyGraph include-tags="#untagged" format="svg" reduced="false"/>
</Analysis>
</MorpheusModel>