MDCK EMT B

<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
    <Description>
        <Details>Naba Mukhtar, Eric N Cytrynbaum, and Leah Edelstein-Keshet (2022) A Multiscale computational model of YAP signaling in epithelial fingering behaviour
Produced SI Figure 6.
We thank Lutz Brusch for providing a basic cell sheet simulation that we modified and adapted to this project </Details>
<Title>NRA-Y-KD</Title>
</Description>
<Space>
<Lattice class="square">
<Neighborhood>
<Order>2</Order>
</Neighborhood>
<Size symbol="size" value="400, 100, 0"/>
<BoundaryConditions>
<Condition type="constant" boundary="x"/>
<Condition type="noflux" boundary="-x"/>
<Condition type="periodic" boundary="y"/>
<Condition type="periodic" boundary="-y"/>
</BoundaryConditions>
</Lattice>
<SpaceSymbol symbol="space"/>
</Space>
<Time>
<StartTime value="0"/>
<StopTime symbol="stoptime" value="1500"/>
<TimeSymbol symbol="time"/>
<RandomSeed value="1"/>
</Time>
<Analysis>
<Gnuplotter decorate="true" time-step="50">
<Terminal name="png"/>
<Plot>
<Cells flooding="true" value="Y">
<Disabled>
<ColorMap>
<Color value="0" color="lemonchiffon"/>
<Color value="0.05" color="light-blue"/>
<Color value="0.1" color="light-red"/>
</ColorMap>
</Disabled>
</Cells>
</Plot>
<Plot title="Rac1">
<Cells min="0" max="3" flooding="true" value="R">
<ColorMap>
<Color value="0" color="blue"/>
<Color value="3" color="red"/>
<Color value="4" color="yellow"/>
</ColorMap>
</Cells>
</Plot>
<Plot>
<Cells min="0" max="2" flooding="true" value="E">
<Disabled>
<ColorMap>
<Color value="0" color="plum"/>
<Color value="4" color="blue"/>
<Color value="7" color="cyan"/>
</ColorMap>
</Disabled>
</Cells>
</Plot>
<Plot>
<Cells flooding="true" value="d.abs">
<!–    <Disabled>
<ColorMap>
<Color value="0" color="skyblue"/>
<Color value="0.1" color="violet"/>
<Color value="0.2" color="salmon"/>
</ColorMap>
</Disabled>
–>
</Cells>
</Plot>
<!–    <Disabled>
<Plot>
<Cells value="Cr" flooding="true">
<Disabled>
<ColorMap>
<Color value="0" color="red"/>
<Color value="0" color="red"/>
</ColorMap>
</Disabled>
</Cells>
</Plot>
</Disabled>
–>
</Gnuplotter>
<ModelGraph format="dot" include-tags="#untagged" reduced="false"/>
</Analysis>
<Global>
<Constant symbol="ky" value="0.1" name="Basal rate of YAP activation"/>
<Constant symbol="kye" value="1.8" name="E-cadherin-dependent rate of YAP deactivation"/>
<Constant symbol="Dy" value="2" name="Inactivation rate of YAP"/>
<Constant symbol="C" value="0.9" name="Initial activation rate of E-cadherin"/>
<Constant symbol="ke" value="0.9" name="YAP-dependent rate of E-cadherin expression"/>
<Constant symbol="K" value="1" name="Dissociation constant of YAP-WT1 transcriptional constant"/>
<Constant symbol="De" value="1" name="Inactivation rate of E-cadherin"/>
<Constant symbol="h" value="3" name="Hill coefficient for E-cadherin"/>
<Constant symbol="kr" value="1" name="YAP-dependent rate of Rac1 expression"/>
<Constant symbol="Kr" value="0.5" name="Michaelis-Menten-like constant for Rac1"/>
<Constant symbol="Dr" value="0.5" name="Degradation rate of Rac1"/>
<Constant symbol="n" value="6" name="Hill coefficient for Rac1"/>
<Constant symbol="alphaR" value="1" name="Rac activation fraction"/>
<Constant symbol="kyr" value="1.8" name="Rac1-dependent rate of YAP activation"/>
<!–    <Disabled>
<Constant value="2" symbol="A2" name="basal adhesion">
<Annotation>E-cad blocking</Annotation>
</Constant>
</Disabled>
–>
<Constant symbol="A2" value="12" name="Max E-cadherin adhesion constant">
<Annotation>Control</Annotation>
</Constant>
<Constant symbol="A3" value="0.85" name="E-cadherin half &quot;saturation&quot; "/>
<Constant symbol="C1" value="0.4" name="basal migration"/>
<Constant symbol="C2" value="4" name="Max Rac1 migration constant"/>
<Constant symbol="C3" value="3" name="Rac1 half &quot;saturation&quot;"/>
<Constant symbol="tlim" value="100" name="max time for initial leader cells to emerge"/>
<Constant symbol="frac" value="0.2" name="fraction of neighbourhood Cr that the cell receives each time Cr spreads to it"/>
<Constant symbol="Ytot" value="0.5" name="Total YAP (active (Y) + inactive)">
<Annotation>KD</Annotation>
</Constant>
<!–    <Disabled>
<Constant symbol="Ytot" value="1.2" name="Total YAP (active (Y) + inactive)">
<Annotation>Control</Annotation>
</Constant>
</Disabled>
–>
<!–    <Disabled>
<Constant symbol="Ytot" value="2" name="Total YAP (active (Y) + inactive)">
<Annotation>OE</Annotation>
</Constant>
</Disabled>
–>
<Constant symbol="Rtot" value="5" name="Total Rac1 (active (R) + inactive)"/>
<Constant symbol="shareprob" value="0.02" name="parameter that determines probability of Cr spread in each time step"/>
<Variable symbol="E" value="0.0" name="E-cadherin"/>
<Variable symbol="Cr" value="0.0" name="Basal Rac1 activation rate"/>
<!–    <Disabled>
<Variable value="0.0" symbol="x_edge2"/>
</Disabled>
–>
<!–    <Disabled>
<Mapper name="leftmost edge cell" time-step="1.0">
<Input value="(M>0)cell.center.x(cell.center.x>10) + (M==0)size.x + (M>0)size.x(cell.center.x&lt;=10)"/>
<Output mapping="minimum" symbol-ref="x_edge2"/>
</Mapper>
</Disabled>
–>
</Global>
<CellTypes>
<CellType class="medium" name="medium"/>
<CellType class="biological" name="dividingcell">
<VolumeConstraint strength="1" target="50"/>
<ConnectivityConstraint/>
<SurfaceConstraint strength="1" mode="aspherity" target="1"/>
<CellDivision division-plane="major">
<Condition>(rand_uni(0,1)&lt;0.006(exp(-time/300)+0.2)) * (cell.center.x&lt;40)</Condition>
<Triggers/>
<Annotation>Only cells in the first 40 pixels can divide, regardless of domain size. Before, this was size.x0.1</Annotation>
</CellDivision>
<CellDeath name="delete cells near right domain edge">
<Condition>(cell.center.x>0.99size.x)</Condition>
</CellDeath>
<DirectedMotion strength="C1+C2R/(C3+R)" name="cell migration" direction="1, 0.0, 0.0"/>
<Property symbol="Y" value="0" name="YAP"/>
<Property symbol="E" value="10" name="E-cadherin"/>
<Property symbol="R" value="0" name="Rac1"/>
<Property symbol="Cr" value="0.001"/>
<Property symbol="dist" value="0.0" name="distance from right domain edge"/>
<Property symbol="avspeed" value="0.0" name="Sum of instantaneous speeds each time step (times 100)"/>
<Property symbol="truavspeed" value="0.0" name="Average Speed * 100"/>
<Property symbol="avspeed2" value="0.0" name="Sum of instantaneous speeds over final 200 time steps (times 100)"/>
<Property symbol="truavspeed2" value="0.0" name="average speed over final 200 time steps (times 100)"/>
<Property symbol="M" value="0.0" name="Contact with medium"/>
<Property symbol="neigh" value="0.0" name="number of neighbour cells"/>
<Property symbol="av" value="0.0" name="average neighbourhood Cr"/>
<PropertyVector symbol="d" value="0.0, 0.0, 0.0" name="speed"/>
<NeighborhoodReporter>
<Input scaling="length" value="cell.type == celltype.medium.id"/>
<Output symbol-ref="M" mapping="sum"/>
</NeighborhoodReporter>
<NeighborhoodReporter>
<Input scaling="cell" value="cell.type == celltype.dividingcell.id"/>
<Output symbol-ref="neigh" mapping="sum"/>
</NeighborhoodReporter>
<NeighborhoodReporter>
<Input scaling="cell" value="Cr"/>
<Output symbol-ref="av" mapping="average"/>
</NeighborhoodReporter>
<MotilityReporter time-step="50">
<Velocity symbol-ref="d"/>
</MotilityReporter>
<System solver="Dormand-Prince [adaptive, O(5)]">
<DiffEqn symbol-ref="Y" name="Equation for YAP">
<Expression>(ky+kyrR)(Ytot-Y) - (kyeYE + DyY)</Expression>
</DiffEqn>
<DiffEqn symbol-ref="E" name="Equation for E-cadherin">
<Expression>C - keY^h/(K^h+Y^h) - DeE</Expression>
</DiffEqn>
<DiffEqn symbol-ref="R" name="Equation for Rac1">
<Expression>alphaR*(Cr + krY^n/(Kr^n+Y^n))(Rtot-R) - DrR</Expression>
</DiffEqn>
<Rule symbol-ref="Cr" name="Equation for Cr spread; at each time step before tlim, cells in contact with the medium have a small chance of being endowed with high Cr; at each time step, each cell has a small chance of having its Cr be augmented by the average neighbourhood Cr (up to a max value); cells at the left edge of the domain retain low Cr">
<Expression>Cr+(0.1(M>8)(rand_uni(0,1)&lt;0.008)(time&lt;tlim)+fracav(rand_uni(0,1)&lt;shareprob))(Cr&lt;0.1)(cell.center.x>20)</Expression>
</Rule>
<Rule symbol-ref="dist" name="distance from right domain edge">
<Expression>size.x - cell.center.x</Expression>
</Rule>
<Rule symbol-ref="avspeed" name="Sum of instantaneous speeds each time step (times 100)">
<Expression>avspeed+d.abs100</Expression>
</Rule>
<Rule symbol-ref="truavspeed" name="average speed over the simulation (times 100)">
<Expression>avspeed/time</Expression>
</Rule>
<Rule symbol-ref="avspeed2" name="Sum of instantaneous speeds over final 100 time steps (times 100)">
<Expression>avspeed2 + d.abs100*(time > stoptime-201)</Expression>
</Rule>
<Rule symbol-ref="truavspeed2" name="average speed over 100 time steps (times 100)">
<Expression>avspeed2/200</Expression>
</Rule>
</System>
</CellType>
</CellTypes>
<CellPopulations>
<Population size="1" type="dividingcell" name="Initialize cell sheet at left edge of the domain">
<!–    <Disabled>
<InitRectangle mode="regular" number-of-cells="70">
<Dimensions origin="size.x/100, 0, 0" size="size.x/100, size.y, size.z"/>
</InitRectangle>
</Disabled>
–>
<InitRectangle number-of-cells="70" mode="regular">
<Dimensions size="4.0, size.y, 0.0" origin="0.0, 0.0, 0.0"/>
</InitRectangle>
</Population>
</CellPopulations>
<CPM>
<Interaction>
<Contact type2="dividingcell" type1="dividingcell" value="30">
<AddonAdhesion strength="5" adhesive="A2*E/(A3+E)" name="Adhesive strength"/>
</Contact>
<Contact type2="medium" type1="dividingcell" value="12"/>
</Interaction>
<ShapeSurface scaling="norm">
<Neighborhood>
<Order>2</Order>
</Neighborhood>
</ShapeSurface>
<MonteCarloSampler stepper="edgelist">
<MCSDuration value="1"/>
<MetropolisKinetics temperature="1"/>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
</MonteCarloSampler>
</CPM>
</MorpheusModel>