Tissue Size Control

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Bile Pressure Drives YAP Signaling During Liver Regeneration

Introduction

During development and regeneration, tissues must grow to the proper size. But tissue growth is just the result of independent cell cycle control systems in the individual cells. How does each cell sense the state of the tissue as a whole?

This fundamental problem has been studied for tissue growth during liver regeneration in mice after partial hepatectomy (removal of a large part of the organ).

This model considers the metabolic (bile) overload and following mechano-sensory mechanism that activated nuclear YAP to drive cell proliferation in response to the organ state. The study is published in the open access journal Molecular Systems Biology. See also the appendix for details on the model.

YAP signaling pathway as considered in the model. See [linked publication](#reference) for details.
YAP signaling pathway as considered in the model. See linked publication for details.

Description

The simulation is visualised in this movie:

Reference

This model is described in the peer-reviewed publication:

K. Meyer, H. Morales‐Navarrete, S. Seifert, M. Wilsch‐Braeuninger, U. Dahmen, E. M. Tanaka, L. Brusch, Y. Kalaidzidis, M. Zerial: Bile canaliculi remodeling activates YAP via the actin cytoskeleton during liver regeneration. Mol. Syst. Biol. 16 (2), e8985, 2020.

Model

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<?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,&#xa;if(cell.id==2,1.383782,&#xa;if(cell.id==3,1.460713,&#xa;if(cell.id==4,1.516818,&#xa;if(cell.id==5,1.546580,&#xa;if(cell.id==6,1.650898,&#xa;if(cell.id==7,1.662168,&#xa;if(cell.id==8,1.613539,&#xa;if(cell.id==9,1.554600,&#xa;if(cell.id==10,1.324019,&#xa;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>

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