MDCK EMT B

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Simulated sheet morphology for YAP knockdown (KD) and overexpression (OE)

Introduction

We model epithelial-mesenchymal transition (EMT) by first assembling an ODE model for intracellular Yes-associated protein (YAP) signalling and then embedding this single cell model within individual cells in a multiscale simulation.

Knockdown (KD) and overexpression (OE) experiments in Park et al. (2019) were represented by adjusting the total YAP level.

Description

We simulate YAP KD by adjusting the total YAP level, namely $Y_\text{tot}= 0.5$. YAP OE is simulated by setting $Y_\text{tot} = 2.0$.

Results

In the YAP KD simulation, the sheets expand slowly, with very low active YAP throughout. In YAP OE, multiple fingers form and grow early as cells rapidly jump to the high-YAP state. These observations are consistent with experiments in Park et al. (2019), although our fingers are wider in the YAP KD case.

Video of the model simulation NRA-Y-KD_main.xml ( | ): Simulated YAP KD sheet morphology with $Y_\text{tot} = 0.5$. Fingers take longer to form than in the control case, and active YAP is low throughout the sheet.

Video of the model simulation NRA-Y-OE.xml ( | ): Simulated YAP OE sheet morphology with $Y_\text{tot} = 2$. Note the widespread high active YAP concentrations and aggressive finger growth.

Reference

This model is the original used in the publication, up to technical updates:

N. Mukhtar, E. N. Cytrynbaum, L. Edelstein-Keshet: A multiscale computational model of YAP signaling in epithelial fingering behavior. Biophys. J. 121 (10): 1940-1948, 2022.

Model

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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.x*0.1</Annotation>
                </CellDivision>
                <CellDeath name="delete cells near right domain edge">
                    <Condition>(cell.center.x>0.99*size.x)</Condition>
                </CellDeath>
                <DirectedMotion strength="C1+C2*R/(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+kyr*R)*(Ytot-Y) - (kye*Y*E + Dy*Y)</Expression>
                    </DiffEqn>
                    <DiffEqn symbol-ref="E" name="Equation for E-cadherin">
                        <Expression>C - ke*Y^h/(K^h+Y^h) - De*E</Expression>
                    </DiffEqn>
                    <DiffEqn symbol-ref="R" name="Equation for Rac1">
                        <Expression>alphaR*(Cr + kr*Y^n/(Kr^n+Y^n))*(Rtot-R) - Dr*R</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)+frac*av*(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.abs*100</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.abs*100*(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>
    
    

    Model Graph of `NRA-Y-KD_main.xml`
    Model Graph of NRA-Y-KD_main.xml

    For more information on the models discussed here,

    • NRA-Y-KD_main.xml ( | ) (produced SI Fig. S6) and
    • NRA-Y-OE.xml ( | ) (produced SI Fig. S7),

    see the supplemental information of the referenced paper.

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