Model1RacRhoECMPDEsIn1D

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

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<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
    <Description>
        <Details>Spatially distributed Model I (Related to the Model 3 in Holmes et al (2017)

R= Rac, P = Rho, E = ECM

Rac-Rho equations d R/dt= {b_R }/{1+\rho_a^3}R_I - \delta R +D_R Laplacian( R), d \rho/dt ={b_\rho }{1+R_a^3}\rho_I - \delta \rho +D_\rho Laplacian( Rho)

ECM equation

dE/dt= epsilon*((K+GammaR*f_R1())-E*(kP+GammaP*f_P1())) where the f’s are Hill functions of Rac or Rho.</Details> <Title>Model1RacRhoECMPDEsIn1D</Title> </Description> <Space> <Lattice class="linear"> <Neighborhood> <Order>1</Order> </Neighborhood> <Size symbol="size" value="30, 0, 0"/> <NodeLength symbol="dx" value="0.1"/> <BoundaryConditions> <Condition boundary="x" type="noflux"/> </BoundaryConditions> </Lattice> <SpaceSymbol symbol="space"/> </Space> <Time> <StartTime value="0"/> <StopTime value="1000"/> <TimeSymbol symbol="time"/> </Time> <Global> <Constant symbol="bR" value="5" name="Rac activation rate"/> <Constant symbol="delta" value="1.0" name="Rac decay rate"/> <Constant symbol="kE" value="2" name="Rho basal activation rate"/> <Constant symbol="GammaE" value="4" name="Rho activation due to ECM feedback"/> <Constant symbol="GammaP" value="10" name="Rho feedback to ECM reduction"/> <Constant symbol="GammaR" value="5.0" name="Rac-dependent ECM rate of increase"/> <Constant symbol="R0" value="1.0" name="Rac level for half-max ECM activation"/> <Constant symbol="P0" value="2.4" name="Rho level for half-max ECM inhibition"/> <Constant symbol="epsilon" value="0.001" name="1/( ECM timescale)"/> <Constant symbol="K" value="0.1" name="ECM basal rate of increase"/> <Constant symbol="kP" value="0.45" name="Rho-induced ECM downregulation"/> <Constant symbol="E0" value="1.5" name="ECM level for half-max Rho activation"/> <Constant symbol="n" value="3" name="Hill coefficient"/> <Function symbol="x"> <Expression>dx*space.x</Expression> </Function> <Field symbol="P" value="0.0" name="Rho"> <Diffusion rate="0.1"/> </Field> <Field symbol="R" value="if(x&lt;=0.3, 4, 0)" name="Rac"> <Diffusion rate="0.1"/> </Field> <Field symbol="E" value="0&#xa;" name="ECM contact"> <Diffusion rate="0"/> </Field> <Field symbol="RI" value="1.5" name="Inactive Rac"> <Diffusion rate="1"/> </Field> <Field symbol="PI" value="1.5" name="Inactive Rho"> <Diffusion rate="1"/> </Field> <Field symbol="plotR" value="0.0" name="Rac for plotting"/> <System solver="adaptive45" time-step="0.1"> <DiffEqn symbol-ref="R" name="PDE for active Rac"> <Expression>(bR/(1+P^n))*RI-1*delta*R</Expression> </DiffEqn> <DiffEqn symbol-ref="P" name="PDE for active Rho"> <Expression>(kE+GammaE*f_E1())*PI/(1+R^n)-1*P</Expression> </DiffEqn> <Function symbol="f_E1" name="function for ECM-dependent rate of Rho activation "> <Expression>E^3/(E0^3+E^3)</Expression> </Function> <DiffEqn symbol-ref="E" name="PDE for ECM variable"> <Expression>epsilon*((K+GammaR*f_R1())-E*(kP+GammaP*f_P1()))</Expression> </DiffEqn> <Function symbol="f_R1" name="Formula for Rac-dependent ECM activation"> <Expression>R^n/(R0^n+R^n)</Expression> </Function> <Function symbol="f_P1" name="formula for Rho-dependent ECM supression"> <Expression>P^n/(P0^n+P^n)</Expression> </Function> <DiffEqn symbol-ref="RI" name="PDE for inactive Rac"> <Expression>(-bR/(1+P^n))*RI+1*delta*R</Expression> </DiffEqn> <DiffEqn symbol-ref="PI" name="PDE for inactive Rho"> <Expression>-(kE+GammaE*f_E1())*PI/(1+R^n)+1*P</Expression> </DiffEqn> <Rule symbol-ref="ECM" name="ECM"> <Expression>E</Expression> </Rule> <Rule symbol-ref="plotR"> <Expression>min(R,2)</Expression> </Rule> </System> <Field symbol="ECM" value="0"/> </Global> <Analysis> <Logger time-step="1" name="chemical profiles"> <Input> <Symbol symbol-ref="R"/> <Symbol symbol-ref="P"/> <Symbol symbol-ref="E"/> <Symbol symbol-ref="PI"/> <Symbol symbol-ref="RI"/> </Input> <Output> <TextOutput/> </Output> <Plots> <Plot time-step="-1"> <Style point-size="4.0" style="points" decorate="false"/> <Terminal terminal="png"/> <X-axis> <Symbol symbol-ref="x"/> </X-axis> <Y-axis> <Symbol symbol-ref="time"/> </Y-axis> <Color-bar minimum="0.0" maximum="2"> <Symbol symbol-ref="plotR"/> </Color-bar> </Plot> <Plot time-step="10"> <Style style="lines" line-width="2.0"/> <Terminal terminal="png"/> <X-axis> <Symbol symbol-ref="x"/> </X-axis> <Y-axis minimum="0.0" maximum="7"> <Symbol symbol-ref="P"/> <Symbol symbol-ref="ECM"/> <Symbol symbol-ref="R"/> </Y-axis> <Range> <Time mode="current" history="1.0"/> </Range> </Plot> </Plots> </Logger> </Analysis> </MorpheusModel>

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