Model3CatchSlipBondRacRhoECMPDEsIn1D

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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 III

R= Rac, P = Rho, E = ECM

Based on: Model 2, with ECM represented as catch-slip bonds Same Rac-Rho Equations. ECM Equation given by

dE/dt=epsilon*(K*(Et-E) - E*min(k0*exp(force/(p*(E+En)))+k0c*exp(-force/(p*(E+En)))

where the force depends on Rac and Rho</Details> <Title>Model3CatchSlipBondRacRhoECMPDEsIn1D</Title> </Description> <Space> <Lattice class="linear"> <Neighborhood> <Order>1</Order> </Neighborhood> <Size symbol="size" value="60, 0, 0"/> <NodeLength symbol="dx" value="0.05"/> <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="3" 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="epsilon" value="0.001" name="1/( ECM timescale)"/> <Constant symbol="K" value="10" name="ECM basal rate of increase"/> <Constant symbol="E0" value="300" name="ECM level for half-max Rho activation"/> <Constant symbol="n" value="3" name="Hill coefficient"/> <Constant symbol="k0" value="exp(-7.78)" name="ECM decay rate due to slip bond"/> <Constant symbol="En" value="100" name="small ECM contact"/> <Constant symbol="p" value="0.08" name="Force per bond reference value"/> <Constant symbol="betaR" value="1000" name="Maximal Rac-dependent force magnitude"/> <Constant symbol="betaP" value="1600" name="Maximal Rho-dependent force magnitude"/> <Constant symbol="Et0" value="1000" name="Maximal adhesion size at zero force"/> <Constant symbol="k0c" value="exp(4.02)" name="catch bond part of ECM decay rate"/> <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="50&#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="ECM" value="0.0"/> <Field symbol="forcefield" value="0.0"/> <Field symbol="plotR" value="0.0" name="Rac for plotting"/> <Function symbol="x"> <Expression>dxspace.x</Expression> </Function> <System solver="adaptive45" time-step="0.1"> <DiffEqn symbol-ref="R"> <Expression>(bR/(1+P^n))RI-1deltaR</Expression> </DiffEqn> <DiffEqn symbol-ref="P"> <Expression>(kE+GammaEf_E1())PI/(1+R^n)-1P</Expression> </DiffEqn> <DiffEqn symbol-ref="E"> <Expression>epsilon(K*(Et-E) - E*min(k0*exp(force/(p*(E+En)))+k0c*exp(-force/(p*(E+En))),1000000))</Expression> </DiffEqn> <Function symbol="f_E1"> <Expression>E^3/(E0^3+E^3)</Expression> </Function> <DiffEqn symbol-ref="RI"> <Expression>(-bR/(1+P^n))*RI+1*delta*R</Expression> </DiffEqn> <DiffEqn symbol-ref="PI"> <Expression>-(kE+GammaE*f_E1())*PI/(1+R^n)+1*P</Expression> </DiffEqn> <Function symbol="force"> <Expression>max(0,-betaR*R/(1+R)+betaP*P/(1+P))</Expression> </Function> <Rule symbol-ref="ECM"> <Expression>E/100</Expression> </Rule> <Rule symbol-ref="forcefield"> <Expression>force/200</Expression> </Rule> <Function symbol="Et"> <Expression>Et0</Expression> </Function> <Rule symbol-ref="plotR"> <Expression>min(R,2)</Expression> </Rule> </System> </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="2.0" 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="forcefield"/> <Symbol symbol-ref="R"/> </Y-axis> <Range> <Time mode="current" history="1.0"/> </Range> </Plot> </Plots> </Logger> </Analysis> </MorpheusModel>

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