Liver Zonation

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Mutual Zonated Interactions of Wnt and Hh Signaling Are Orchestrating the Metabolism of the Adult Liver in Mice and Human

Reference

This model is described in the peer-reviewed publication:

E. Kolbe, S. Aleithe, C. Rennert, L. Spormann, F. Ott, D. Meierhofer, R. Gajowski, C. Stöpel, S. Hoehme, M. Kücken, L. Brusch, M. Seifert, W. von Schoenfels, C. Schafmayer, M. Brosch, U. Hofmann, G. Damm, D. Seehofer, J. Hampe, R. Gebhardt, M. Matz-Soja: Mutual Zonated Interactions of Wnt and Hh Signaling Are Orchestrating the Metabolism of the Adult Liver in Mice and Human. Cell Rep. 29, 4553–4567, 2019.

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<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
    <Description>
        <Details>Full title: Mutual Zonated Interactions of Wnt and Hh Signaling Are Orchestrating the Metabolism of the Adult Liver in Mice and Human
Date: December 24, 2019
Author: michael.kuecken@tu-dresden.de and 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 "Mutual Zonated Interactions of Wnt and Hh Signaling Are Orchestrating the Metabolism of the Adult Liver in Mice and Human" by E. Kolbe, S. Aleithe, C. Rennert, L. Spormann, F. Ott, D. Meierhofer, R. Gajowski, C. Stöpel, S. Hoehme, M. Kücken, L. Brusch, M. Seifert, W. von Schoenfels, C. Schafmayer, M. Brosch, U. Hofmann, G. Damm, D. Seehofer, J. Hampe, R. Gebhardt, M. Matz-Soja. 
Cell Reports 29, 4553, 2019.
https://doi.org/10.1016/j.celrep.2019.11.104
</Details>
        <Title>Liver zonation</Title>
    </Description>
    <Space>
        <Lattice class="square">
            <Neighborhood>
                <Order>1</Order>
            </Neighborhood>
            <Size symbol="size" value="256,256, 0"/>
            <NodeLength value="0.1"/>
            <BoundaryConditions>
                <Condition type="periodic" boundary="x"/>
                <Condition type="periodic" boundary="-x"/>
                <Condition type="periodic" boundary="y"/>
                <Condition type="periodic" boundary="-y"/>
            </BoundaryConditions>
        </Lattice>
        <SpaceSymbol symbol="s"/>
    </Space>
    <Time>
        <StartTime value="0"/>
        <StopTime value="100"/>
        <TimeSymbol symbol="t"/>
    </Time>
    <Global>
        <System solver="runge-kutta" time-step="0.1">
            <DiffEqn symbol-ref="w">
                <Expression>0.001-k1*w + cvein</Expression>
            </DiffEqn>
            <DiffEqn symbol-ref="b">
                <Expression>b*(w-a)*(1/(1+k2*h)-b) </Expression>
            </DiffEqn>
            <DiffEqn symbol-ref="h">
                <Expression>k3*c-k4*w*h-h</Expression>
            </DiffEqn>
            <DiffEqn symbol-ref="i">
                <Expression>b*c*c-k5*i</Expression>
            </DiffEqn>
            <DiffEqn symbol-ref="g">
                <Expression>k6*i+k7*h-k8*g</Expression>
            </DiffEqn>
        </System>
        <Field symbol="w" value="0.0" name="Wnt">
            <Diffusion rate="1.0"/>
            <BoundaryValue value="0" boundary="x"/>
            <BoundaryValue value="0" boundary="-x"/>
        </Field>
        <Field symbol="b" value="0.01" name="betaCatenin">
            <Diffusion rate="0.001"/>
            <BoundaryValue value="0.1" boundary="x"/>
            <BoundaryValue value="0" boundary="x"/>
        </Field>
        <Field symbol="h" value="0.01" name="SHH">
            <Diffusion rate="0.5"/>
        </Field>
        <Field symbol="g" value="0.01" name="Gli3">
            <Diffusion rate="1.0"/>
        </Field>
        <Field symbol="i" value="0.001" name="IHH"/>
        <Field symbol="cvein" value="if((s.x-128)*(s.x-128)+(s.y-128)*(s.y-128)&lt;=25, 1, 0) + if((s.x-28)*(s.x-28)+(s.y-128)*(s.y-128)&lt;=25, 1, 0) + if((s.x-228)*(s.x-228)+(s.y-128)*(s.y-128)&lt;=25, 1, 0) + if((s.x-78)*(s.x-78)+(s.y-215)*(s.y-215)&lt;=25, 1, 0) + if((s.x-78)*(s.x-78)+(s.y-41)*(s.y-41)&lt;=25, 1, 0) + if((s.x-178)*(s.x-178)+(s.y-215)*(s.y-215)&lt;=25, 1, 0) + if((s.x-178)*(s.x-178)+(s.y-41)*(s.y-41)&lt;=25, 1, 0)" name="Wnt source at CV"/>
        <Field symbol="portal" value="if((s.x-180)*(s.x-180)+(s.y-100)*(s.y-100)&lt;=25, 1, 0) + if((s.x-20)*(s.x-20)+(s.y-100)*(s.y-100)&lt;=25, 1, 0) + if((s.x-60)*(s.x-60)+(s.y-30)*(s.y-30)&lt;=25, 1, 0)+ if((s.x-60)*(s.x-60)+(s.y-170)*(s.y-170)&lt;=25, 1, 0)+ if((s.x-140)*(s.x-140)+(s.y-30)*(s.y-30)&lt;=25, 1, 0)+ if((s.x-140)*(s.x-140)+(s.y-170)*(s.y-170)&lt;=25, 1, 0)" name="passive PV locations"/>
        <Constant symbol="a" value="0.2"/>
        <Constant symbol="c" value="1.0"/>
        <Constant symbol="k2" value="12.0"/>
        <Constant symbol="k1" value="0.1"/>
        <Constant symbol="k3" value="0.2"/>
        <Constant symbol="k4" value="12.0"/>
        <Constant symbol="k5" value="1.0"/>
        <Constant symbol="k6" value="0.5"/>
        <Constant symbol="k7" value="2.0"/>
        <Constant symbol="k8" value="1.0"/>
    </Global>
    <Analysis>
        <Gnuplotter log-commands="false" decorate="true" time-step="10">
            <Plot>
                <Field min="0" max="0.3" symbol-ref="w">
                    <ColorMap>
                        <Color color="green" value="1"/>
                        <Color color="white" value="0"/>
                    </ColorMap>
                </Field>
            </Plot>
            <Terminal name="png"/>
            <Plot>
                <Field min="0" max="0.7" symbol-ref="b">
                    <ColorMap>
                        <Color color="orange" value="0.7"/>
                        <Color color="white" value="0"/>
                    </ColorMap>
                </Field>
            </Plot>
            <Plot>
                <Field min="0" max="0.2" symbol-ref="h">
                    <ColorMap>
                        <Color color="red" value="0.2"/>
                        <Color color="white" value="0"/>
                    </ColorMap>
                </Field>
            </Plot>
            <Plot>
                <Field symbol-ref="cvein"/>
            </Plot>
            <!--    <Disabled>
        <Plot>
            <Field symbol-ref="portal"/>
        </Plot>
    </Disabled>
-->
            <Plot>
                <Field min="0" max="0.5" symbol-ref="i">
                    <ColorMap>
                        <Color color="violet" value="0.5"/>
                        <Color color="white" value="0"/>
                    </ColorMap>
                </Field>
            </Plot>
            <Plot>
                <Field min="0" max="0.4" symbol-ref="g">
                    <ColorMap>
                        <Color color="brown4" value="0.4"/>
                        <Color color="white" value="0"/>
                    </ColorMap>
                </Field>
            </Plot>
        </Gnuplotter>
        <DependencyGraph reduced="false" format="svg"/>
    </Analysis>
</MorpheusModel>

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