MDCK EMT C

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This model is used in the publication by Mukhtar et al. under review.

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<?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

This xml file was used to produce Figure 5, by varying A2 = 6,12,24 and C2 = 1,4,8.

Similar to the file YREsheetNRA.xml, but with cell division restricted to cells beyond some size.

We thank Lutz Brusch for providing a basic cell sheet simulation that we modified and adapted to this project </Details> <Title>YREsheetNRAShapeFactorq</Title> </Description> <Space> <Lattice class="square"> <Neighborhood> <Order>2</Order> </Neighborhood> <Size symbol="size" value="400, 100, 0"/> <BoundaryConditions> <Condition boundary="x" type="constant"/> <Condition boundary="-x" type="noflux"/> <Condition boundary="y" type="periodic"/> <Condition boundary="-y" type="periodic"/> </BoundaryConditions> </Lattice> <SpaceSymbol symbol="space"/> </Space> <Time> <StartTime value="0"/> <StopTime symbol="stoptime" value="1500"/> <TimeSymbol symbol="time"/> <RandomSeed value="1"/> </Time> <Analysis> <Gnuplotter time-step="50" decorate="true"> <Terminal name="png"/> <!– <Disabled> <Plot> <Cells max="5" value="q" min="3" flooding="true"> <Disabled> <ColorMap> <Color color="lemonchiffon" value="0"/> <Color color="light-blue" value="0.05"/> <Color color="light-red" value="0.1"/> </ColorMap> </Disabled> </Cells> </Plot> </Disabled> –> <!– <Disabled> <Plot title="Rac1"> <Cells max="3" value="R" min="0" flooding="true"> <ColorMap> <Color color="blue" value="0"/> <Color color="red" value="3"/> <Color color="yellow" value="4"/> </ColorMap> </Cells> </Plot> </Disabled> –> <Plot> <Cells max="2" value="E" min="0" flooding="true"> <Disabled> <ColorMap> <Color color="plum" value="0"/> <Color color="blue" value="4"/> <Color color="cyan" value="7"/> </ColorMap> </Disabled> </Cells> </Plot> <!– <Disabled> <Plot> <Cells value="d.abs" flooding="true"> <Disabled> <ColorMap> <Color color="skyblue" value="0"/> <Color color="violet" value="0.1"/> <Color color="salmon" value="0.2"/> </ColorMap> </Disabled> </Cells> </Plot> </Disabled> –> <!– <Disabled> <Plot> <Cells value="Cr" flooding="true"> <Disabled> <ColorMap> <Color color="red" value="0"/> <Color color="red" value="0"/> </ColorMap> </Disabled> </Cells> </Plot> </Disabled> –> </Gnuplotter> <!– <Disabled> <Logger time-step="1.0"> <Input> <Symbol symbol-ref="cell.center.x"/> <Symbol symbol-ref="cell.center.y"/> <Symbol symbol-ref="q"/> </Input> <Output> <TextOutput/> </Output> <Plots> <Plot time-step="-1"> <Style style="points" point-size="0.05"/> <Terminal terminal="png"/> <X-axis maximum="size.x" minimum="0.0"> <Symbol symbol-ref="cell.center.x"/> </X-axis> <Y-axis maximum="stoptime" minimum="0"> <Symbol symbol-ref="time"/> </Y-axis> <Color-bar maximum="5" palette="default" minimum="3"> <Symbol symbol-ref="q"/> </Color-bar> </Plot> </Plots> </Logger> </Disabled> –> <ModelGraph include-tags="#untagged" reduced="false" format="dot"/> </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 symbol="A2" value="2" 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"/> <!– <Disabled> <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> <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 symbol="x_edge2" value="0.0"/> </Disabled> –> <!– <Disabled> <Mapper time-step="1.0" name="leftmost edge cell"> <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 name="medium" class="medium"/> <CellType name="dividingcell" class="biological"> <VolumeConstraint strength="1" target="50"/> <ConnectivityConstraint/> <SurfaceConstraint strength="1" target="1" mode="aspherity"/> <CellDivision division-plane="major"> <Condition>(rand_uni(0,1)&lt;0.006(exp(-time/300)+0.2)) * (cell.center.x&lt;40) * (cell.volume>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)" direction="1, 0.0, 0.0" name="cell migration"/> <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 value="cell.type == celltype.medium.id" scaling="length"/> <Output mapping="sum" symbol-ref="M"/> </NeighborhoodReporter> <NeighborhoodReporter> <Input value="cell.type == celltype.dividingcell.id" scaling="cell"/> <Output mapping="sum" symbol-ref="neigh"/> </NeighborhoodReporter> <NeighborhoodReporter> <Input value="Cr" scaling="cell"/> <Output mapping="average" symbol-ref="av"/> </NeighborhoodReporter> <MotilityReporter time-step="50"> <Velocity symbol-ref="d"/> </MotilityReporter> <System solver="Dormand-Prince [adaptive, O(5)]"> <DiffEqn name="Equation for YAP" symbol-ref="Y"> <Expression>(ky+kyrR)(Ytot-Y) - (kyeYE + DyY)</Expression> </DiffEqn> <DiffEqn name="Equation for E-cadherin" symbol-ref="E"> <Expression>C - keY^h/(K^h+Y^h) - DeE</Expression> </DiffEqn> <DiffEqn name="Equation for Rac1" symbol-ref="R"> <Expression>alphaR*(Cr + krY^n/(Kr^n+Y^n))(Rtot-R) - DrR</Expression> </DiffEqn> <Rule 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" symbol-ref="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 name="distance from right domain edge" symbol-ref="dist"> <Expression>size.x - cell.center.x</Expression> </Rule> <Rule name="Sum of instantaneous speeds each time step (times 100)" symbol-ref="avspeed"> <Expression>avspeed+d.abs100</Expression> </Rule> <Rule name="average speed over the simulation (times 100)" symbol-ref="truavspeed"> <Expression>avspeed/time</Expression> </Rule> <Rule name="Sum of instantaneous speeds over final 100 time steps (times 100)" symbol-ref="avspeed2"> <Expression>avspeed2 + d.abs100*(time > stoptime-201)</Expression> </Rule> <Rule name="average speed over 100 time steps (times 100)" symbol-ref="truavspeed2"> <Expression>avspeed2/200</Expression> </Rule> <Rule symbol-ref="q"> <Expression>cell.surface/sqrt(cell.volume)</Expression> </Rule> <!– <Disabled> <Rule symbol-ref="q"> <Expression>cell.volume</Expression> </Rule> </Disabled> –> </System> <Property symbol="q" value="0.0" name="shape index"/> </CellType> </CellTypes> <CellPopulations> <Population name="Initialize cell sheet at left edge of the domain" type="dividingcell" size="1"> <!– <Disabled> <InitRectangle number-of-cells="70" mode="regular"> <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 origin="0.0, 0.0, 0.0" size="4.0, size.y, 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>

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