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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">
        <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 2, SI Figure 6, 10

A multiscale model of a control cell sheet on nano-ridge arrays with the YAP-Rac-E cadherin circuit based on experiments by

Park, J., Kim, D.H., Shah, S.R., Kim, H.N., Kim, P., Quiñones-Hinojosa, A. and Levchenko, A., 2019. Switch-like enhancement of epithelial-mesenchymal transition by YAP through feedback regulation of WT1 and Rho-family GTPases. Nature communications, 10(1), pp.1-15.

The sheet morphology over 15 hrs and 400 micro-meters distance . On nano-ridge arrays (NRAs) a few edge cells get a high Rac1 activation rate to mimic the mechanostimulation by the topography.

This simulation is the "control" YAP case.

We thank Lutz Brusch for providing a basic cell sheet simulation that we modified and adapted to this project </Details> <Title>YREsheetNRA</Title> </Description> <Space> <Lattice class="square"> <Neighborhood> <Order>2</Order> </Neighborhood> <Size value="400, 100, 0" symbol="size"/> <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 value="1500" symbol="stoptime"/> <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 flooding="true" min="0" max="3" value="R"> <ColorMap> <Color value="0" color="blue"/> <Color value="3" color="red"/> <Color value="4" color="yellow"/> </ColorMap> </Cells> </Plot> <Plot> <Cells flooding="true" min="0" max="2" 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> <Logger time-step="1.0"> <Input> <Symbol symbol-ref=""/> <Symbol symbol-ref=""/> </Input> <Output> <TextOutput/> </Output> <Plots> <Plot time-step="300"> <Style point-size="0.05" style="points"/> <Terminal terminal="png"/> <X-axis minimum="0.0" maximum="size.x"> <Symbol symbol-ref=""/> </X-axis> <Y-axis minimum="0.0" maximum="size.y"> <Symbol symbol-ref=""/> </Y-axis> <Color-bar minimum="0.0" palette="rainbow" maximum="0.3"> <Symbol symbol-ref="d.abs"/> </Color-bar> </Plot> </Plots> </Logger> <ModelGraph include-tags="#untagged" format="dot" reduced="false"/> </Analysis> <Global> <Constant value="0.1" name="Basal rate of YAP activation" symbol="ky"/> <Constant value="1.8" name="E-cadherin-dependent rate of YAP deactivation" symbol="kye"/> <Constant value="2" name="Inactivation rate of YAP" symbol="Dy"/> <Constant value="0.9" name="Initial activation rate of E-cadherin" symbol="C"/> <Constant value="0.9" name="YAP-dependent rate of E-cadherin expression" symbol="ke"/> <Constant value="1" name="Dissociation constant of YAP-WT1 transcriptional constant" symbol="K"/> <Constant value="1" name="Inactivation rate of E-cadherin" symbol="De"/> <Constant value="3" name="Hill coefficient for E-cadherin" symbol="h"/> <Constant value="1" name="YAP-dependent rate of Rac1 expression" symbol="kr"/> <Constant value="0.5" name="Michaelis-Menten-like constant for Rac1" symbol="Kr"/> <Constant value="0.5" name="Degradation rate of Rac1" symbol="Dr"/> <Constant value="6" name="Hill coefficient for Rac1" symbol="n"/> <Constant value="1" name="Rac activation fraction" symbol="alphaR"/> <Constant value="1.8" name="Rac1-dependent rate of YAP activation" symbol="kyr"/> <!– <Disabled> <Constant value="2" symbol="A2" name="basal adhesion"> <Annotation>E-cad blocking</Annotation> </Constant> </Disabled> –> <Constant value="12" name="Max E-cadherin adhesion constant" symbol="A2"> <Annotation>Control</Annotation> </Constant> <Constant value="0.85" name="E-cadherin half &quot;saturation&quot; " symbol="A3"/> <Constant value="0.4" name="basal migration" symbol="C1"/> <Constant value="4" name="Max Rac1 migration constant" symbol="C2"/> <Constant value="3" name="Rac1 half &quot;saturation&quot;" symbol="C3"/> <Constant value="100" name="max time for initial leader cells to emerge" symbol="tlim"/> <Constant value="0.2" name="fraction of neighbourhood Cr that the cell receives each time Cr spreads to it" symbol="frac"/> <!– <Disabled> <Constant value="0.5" symbol="Ytot" name="Total YAP (active (Y) + inactive)"> <Annotation>KD</Annotation> </Constant> </Disabled> –> <Constant value="1.2" name="Total YAP (active (Y) + inactive)" symbol="Ytot"> <Annotation>Control</Annotation> </Constant> <!– <Disabled> <Constant value="2" symbol="Ytot" name="Total YAP (active (Y) + inactive)"> <Annotation>OE</Annotation> </Constant> </Disabled> –> <Constant value="5" name="Total Rac1 (active (R) + inactive)" symbol="Rtot"/> <Constant value="0.02" name="parameter that determines probability of Cr spread in each time step" symbol="shareprob"/> <Variable value="0.0" name="E-cadherin" symbol="E"/> <Variable value="0.0" name="Basal Rac1 activation rate" symbol="Cr"/> <!– <Disabled> <Variable value="0.0" symbol="x_edge2"/> </Disabled> –> <!– <Disabled> <Mapper name="leftmost edge cell" time-step="1.0"> <Input value="(M>0)>10) + (M==0)size.x + (M>0)size.x(;=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 mode="aspherity" strength="1" target="1"/> <CellDivision division-plane="major"> <Condition>(rand_uni(0,1)&lt;0.006(exp(-time/300)+0.2)) * (;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>(>0.99size.x)</Condition> </CellDeath> <DirectedMotion direction="1, 0.0, 0.0" name="cell migration" strength="C1+C2R/(C3+R)"/> <Property value="0" name="YAP" symbol="Y"/> <Property value="10" name="E-cadherin" symbol="E"/> <Property value="0" name="Rac1" symbol="R"/> <Property value="0.001" symbol="Cr"/> <Property value="0.0" name="distance from right domain edge" symbol="dist"/> <Property value="0.0" name="Sum of instantaneous speeds each time step (times 100)" symbol="avspeed"/> <Property value="0.0" name="Average Speed * 100" symbol="truavspeed"/> <Property value="0.0" name="Sum of instantaneous speeds over final 200 time steps (times 100)" symbol="avspeed2"/> <Property value="0.0" name="average speed over final 200 time steps (times 100)" symbol="truavspeed2"/> <Property value="0.0" name="Contact with medium" symbol="M"/> <Property value="0.0" name="number of neighbour cells" symbol="neigh"/> <Property value="0.0" name="average neighbourhood Cr" symbol="av"/> <PropertyVector value="0.0, 0.0, 0.0" name="speed" symbol="d"/> <NeighborhoodReporter> <Input value="cell.type ==" scaling="length"/> <Output mapping="sum" symbol-ref="M"/> </NeighborhoodReporter> <NeighborhoodReporter> <Input value="cell.type ==" 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)(>20)</Expression> </Rule> <Rule name="distance from right domain edge" symbol-ref="dist"> <Expression>size.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> </System> </CellType> </CellTypes> <CellPopulations> <Population name="Initialize cell sheet at left edge of the domain" type="dividingcell" size="1"> <!– <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 mode="regular" number-of-cells="70"> <Dimensions origin="0.0, 0.0, 0.0" size="4.0, size.y, 0.0"/> </InitRectangle> </Population> </CellPopulations> <CPM> <Interaction> <Contact type2="dividingcell" value="30" type1="dividingcell"> <AddonAdhesion name="Adhesive strength" strength="5" adhesive="A2*E/(A3+E)"/> </Contact> <Contact type2="medium" value="12" type1="dividingcell"/> </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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