MDCK EMT B

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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

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>

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