<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
<Description>
<Details>Full title: Spatio-temporal model of YAP signaling in hepatocytes after partial hepatectomy.
Date: 28.6.2018
Author: lutz.brusch@tu-dresden.de
Software: Morpheus (open-source), download from https://morpheus.gitlab.io
Reference: This model is described in the peer-reviewed publication "Bile canaliculi remodeling activates YAP via the actin cytoskeleton during liver regeneration" by Kirstin Meyer, Hernan Morales-Navarrete, Sarah Seifert, Michaela Wilsch-Braeuninger, Uta Dahmen, Elly M. Tanaka, Lutz Brusch, Yannis Kalaidzidis and Marino Zerial. Molecular Systems Biology
16:e8985, 2020.
https://doi.org/10.15252/msb.20198985
</Details>
<Title>YAP signaling</Title>
</Description>
<Space>
<Lattice class="square">
<Neighborhood>
<Order>1</Order>
</Neighborhood>
<Size symbol="size" value="30, 3, 0"/>
</Lattice>
<SpaceSymbol symbol="space"/>
</Space>
<Time>
<StartTime value="0"/>
<StopTime symbol="stop" value="5"/>
<TimeSymbol symbol="time"/>
</Time>
<CellTypes>
<CellType class="biological" name="Hepatocyte">
<Constant symbol="N" value="860" name="nucleus volume in square micron"/>
<Constant symbol="C" value="5450" name="cytoplasm volume in square micron"/>
<Property symbol="SENSOR" value="0.245*C" name="amount of SENSOR"/>
<Property symbol="inact_SENSOR" value="5.255*C" name="amount of inactive SENSOR"/>
<Property symbol="YAP" value="1*C" name="amount of YAP"/>
<Property symbol="inact_YAP" value="0*C" name="amount of inactive YAP"/>
<Property symbol="inact_YAP_SF" value="0*C" name="amount of inactive YAP bound to SF"/>
<Property symbol="N_YAP" value="1" name="concentration of nuclear YAP"/>
<System solver="adaptive45" time-scaling="1000">
<DiffEqn symbol-ref="SENSOR">
<Expression>- C * Michaelis_Menten(SENSOR / C, Km, V) + C * Michaelis_Menten(inact_SENSOR / C, Km_1, Tension)</Expression>
</DiffEqn>
<DiffEqn symbol-ref="inact_SENSOR">
<Expression>C * Michaelis_Menten(SENSOR / C, Km, V) - C * Michaelis_Menten(inact_SENSOR / C, Km_1, Tension)</Expression>
</DiffEqn>
<DiffEqn symbol-ref="YAP">
<Expression>k5 * inact_YAP - k4 * YAP * inact_SENSOR / C - k10 * YAP - k9 * YAP + k8 * N_YAP * N + C * k3_0 * s</Expression>
</DiffEqn>
<DiffEqn symbol-ref="inact_YAP">
<Expression>- k11 * inact_YAP - k5 * inact_YAP + k4 * YAP * inact_SENSOR / C - k6 * inact_YAP + k7 * inact_YAP_SF</Expression>
</DiffEqn>
<DiffEqn symbol-ref="inact_YAP_SF">
<Expression>k6 * inact_YAP - k7 * inact_YAP_SF</Expression>
</DiffEqn>
<DiffEqn symbol-ref="N_YAP">
<Expression>k9 * YAP / N - k8 * N_YAP</Expression>
</DiffEqn>
</System>
<Property symbol="Tension" value="1"/>
<Event trigger="on change" time-step="0.05" name="Tension for time t closer to 0.8d than to other measurements">
<Condition>time>0.4</Condition>
<Rule symbol-ref="Tension">
<Expression>if(cell.id==1,1.8279930944312834,
if(cell.id==2,1.7866460754759526,
if(cell.id==3,1.8374519069180288,
if(cell.id==4,1.8640351995565263,
if(cell.id==5,1.8706834857072998,
if(cell.id==6,1.8941858816263410,
if(cell.id==7,1.8511397598872272,
if(cell.id==8,1.9135216039396319,
if(cell.id==9,1.9145071129239710,
if(cell.id==10,1.8153404444156003,
1))))))))))</Expression>
</Rule>
</Event>
<Event trigger="on change" time-step="0.05" name="Tension for time t closer to 1.5d than to other measurements">
<Condition>time>1.15</Condition>
<Rule symbol-ref="Tension">
<Expression>if(cell.id==1,1.9807223334150590,
if(cell.id==2,1.9130780850583866,
if(cell.id==3,1.9643577716468286,
if(cell.id==4,2.0020827404251120,
if(cell.id==5,2.0252154507264140,
if(cell.id==6,2.0703197134079440,
if(cell.id==7,1.9915999174723278,
if(cell.id==8,2.0046213799240973,
if(cell.id==9,1.9540901073551358,
if(cell.id==10,1.8753435897018356,
1))))))))))</Expression>
</Rule>
</Event>
<Event trigger="on change" time-step="0.05" name="Tension for time t closer to 2.0d than to other measurements">
<Condition>time>1.75</Condition>
<Rule symbol-ref="Tension">
<Expression>if(cell.id==1,2.0217009184038360,
if(cell.id==2,1.9258181971655592,
if(cell.id==3,1.9518589890960070,
if(cell.id==4,1.9123363331127760,
if(cell.id==5,2.0319328550271623,
if(cell.id==6,2.0158606286091496,
if(cell.id==7,1.9434430184290816,
if(cell.id==8,1.8907841188362082,
if(cell.id==9,1.9473574849407167,
if(cell.id==10,1.8715472190966007,
1))))))))))</Expression>
</Rule>
</Event>
<Event trigger="on change" time-step="0.05" name="Tension for time t closer to 3.0d than to other measurements">
<Condition>time>2.5</Condition>
<Rule symbol-ref="Tension">
<Expression>if(cell.id==1,1.8597267890032976,
if(cell.id==2,1.7814702267887177,
if(cell.id==3,1.8292379408251978,
if(cell.id==4,1.8488155708410638,
if(cell.id==5,1.8536661678277864,
if(cell.id==6,1.8836145987139055,
if(cell.id==7,1.8442276337980785,
if(cell.id==8,1.8136740374044704,
if(cell.id==9,1.8868282103886570,
if(cell.id==10,1.8015329680486330,
1))))))))))</Expression>
</Rule>
</Event>
<Event trigger="on change" time-step="0.05" name="Tension for time t closer to 5.0d than to other measurements">
<Condition>time>4.0</Condition>
<Rule symbol-ref="Tension">
<Expression>if(cell.id==1,1.9088767623308390,
if(cell.id==2,1.8488496952244589,
if(cell.id==3,1.8616629446112190,
if(cell.id==4,1.8244687794620162,
if(cell.id==5,1.8557929833228486,
if(cell.id==6,1.8447542721681303,
if(cell.id==7,1.7726695922335742,
if(cell.id==8,1.7074409071843903,
if(cell.id==9,1.7730171801027250,
if(cell.id==10,1.7408530847107613,
1))))))))))</Expression>
</Rule>
</Event>
<Property symbol="s" value="if(cell.id==1,1.246692,
if(cell.id==2,1.383782,
if(cell.id==3,1.460713,
if(cell.id==4,1.516818,
if(cell.id==5,1.546580,
if(cell.id==6,1.650898,
if(cell.id==7,1.662168,
if(cell.id==8,1.613539,
if(cell.id==9,1.554600,
if(cell.id==10,1.324019,
1))))))))))" name="zonated (i.e. cell-dependent) YAP synthesis level"/>
<Function symbol="Michaelis_Menten" name="Henri-Michaelis-Menten kinetics (irreversible)">
<Parameter symbol="substrate"/>
<Parameter symbol="Km"/>
<Parameter symbol="V"/>
<Expression>V * substrate / (Km + substrate)</Expression>
</Function>
<Constant symbol="Km" value="0.25" name="Km"/>
<Constant symbol="V" value="2.02" name="Vmax"/>
<Constant symbol="Km_1" value="0.0008" name="Km"/>
<Constant symbol="k3_0" value="1.7" name="k3,0 YAP synthesis rate factor"/>
<Constant symbol="k4" value="0.19" name="YAP inactivation rate"/>
<Constant symbol="k5" value="1" name="YAP activation rate"/>
<Constant symbol="k6" value="0.18" name="inact_YAP binding to SF"/>
<Constant symbol="k7" value="1" name="inact_YAP unbinding from SF"/>
<Constant symbol="k8" value="1" name="nuclear export"/>
<Constant symbol="k9" value="0.17" name="nuclear import"/>
<Constant symbol="k10" value="1.8" name="YAP degradation"/>
<Constant symbol="k11" value="30" name="inact_YAP degradation rate"/>
<Property symbol="C_YAP_total" value="(YAP + inact_YAP + inact_YAP_SF) / C" name="total cytosolic YAP (t=0)"/>
<Equation symbol-ref="C_YAP_total" name="total cytosolic YAP">
<Expression>(YAP + inact_YAP + inact_YAP_SF) / C</Expression>
</Equation>
<Property symbol="YAP_total" value="(C * C_YAP_total + N * N_YAP) / (C + N)" name="total cellular YAP"/>
<Equation symbol-ref="YAP_total" name="total cellular YAP">
<Expression>(C * C_YAP_total + N * N_YAP) / (C + N)</Expression>
</Equation>
</CellType>
</CellTypes>
<CellPopulations>
<Population size="10" type="Hepatocyte">
<InitCellObjects mode="distance">
<Arrangement repetitions="10, 1, 1" displacements="3, 0, 0">
<Box size="3.0, 3.0, 1.0" origin="0.0, 0.0, 0.0"/>
</Arrangement>
</InitCellObjects>
</Population>
</CellPopulations>
<Analysis>
<Gnuplotter time-step="0.05" decorate="true">
<Terminal name="png"/>
<Plot title="nuclear YAP(x,t)">
<Cells value="N_YAP" min="0.9" max="1.7"/>
</Plot>
<Plot title="total YAP(x,t)">
<Cells value="YAP_total" min="0.9" max="1.7"/>
</Plot>
</Gnuplotter>
<Logger time-step="0.8">
<Input>
<Symbol symbol-ref="Tension"/>
<Symbol symbol-ref="N_YAP"/>
<Symbol symbol-ref="YAP_total"/>
</Input>
<Output>
<TextOutput file-numbering="time" file-separation="time"/>
</Output>
<Plots>
<Plot title="Fig.S9a: Tension(x,t)" file-numbering="time" time-step="0.8">
<Style style="lines"/>
<Terminal terminal="png"/>
<X-axis>
<Symbol symbol-ref="cell.id"/>
</X-axis>
<Y-axis minimum="0.9" maximum="2.5">
<Symbol symbol-ref="Tension"/>
</Y-axis>
</Plot>
<Plot title="Fig.S9c: nuclear YAP(x,t)" file-numbering="time" time-step="0.1">
<Style style="lines"/>
<Terminal terminal="png"/>
<X-axis>
<Symbol symbol-ref="cell.id"/>
</X-axis>
<Y-axis minimum="0.0" maximum="2.0">
<Symbol symbol-ref="N_YAP"/>
</Y-axis>
</Plot>
<Plot title="Fig.S9d: total cellular YAP(x,t)" file-numbering="time" time-step="0.1">
<Style style="lines"/>
<Terminal terminal="png"/>
<X-axis>
<Symbol symbol-ref="cell.id"/>
</X-axis>
<Y-axis minimum="0.0" maximum="2.0">
<Symbol symbol-ref="YAP_total"/>
</Y-axis>
</Plot>
</Plots>
<Restriction>
<Celltype celltype="Hepatocyte"/>
</Restriction>
</Logger>
</Analysis>
</MorpheusModel>