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Module 4: Vascular Patterning

Author:

  • Walter de Back

Aim:

  • Learn to distinguish between alternative hypothesis/mechanisms explaning the same phenomenon
  • When two different mechanisms can reproduce the same phenomenon, how can modeling help to distinguish between these mechanisms?

Description:

  • Introduce problem and provide examples:
    • multiple mechanism, same result
  • Introduce CPM/PDE hybrid/multiscale models
    • coupling model formalisms (through production + chemotaxis)
  • Introduce vasculogenesis
    • Isolated cells into vascular network
  • Provide two models: A.xml and B.xml that show the same behavior
  • Assignment 1: What biological processes do these models reflect?
    • Autocrine model: angioblasts produce their own chemoattractant (VEGF)
    • Paracrine model: paracrine chemoattractant is bound to angioblasts-produced matrix molecules
  • Assignment 2: How can you determine which one is more plausible?
    • Theoretically?
    • Experimentally?
      • Explore how the models produce different predictions:
        • Inhibit VEGF binding (use nonbindnig isoform VEGF121)
        • Change cell densities
        • Administer fluorescent VEGF
    • Quantitative analysis?
      • Quantify parameters:
        • FRAP: diffusion
        • FRAP: rate of binding/unbindung
        • ELISA: decay
        • Microfluidic device: chemotactic strength

Paper:

  • Köhn-Luque A, de Back W, Starruß J, Mattiotti A, Deutsch A, J-M Perez-Pomares, HA Hererro. (2011) Early Embryonic Vascular Patterning by Matrix-Mediated Paracrine Signalling: A Mathematical Model Study. PLoS ONE 6(9): e24175. link

Documents:

Morpheus models:

Example: Vascular patterning

h A.xml |h

<MorpheusModel version="1">
    <Description>
        <Title>ModelA</Title>
    </Description>
    <Space>
        <Lattice class="square">
            <Size value="200 200 0"/>
            <BoundaryConditions>
                <Condition boundary="x" type="periodic"/>
                <Condition boundary="y" type="periodic"/>
            </BoundaryConditions>
            <NodeLength unit="micron" value="2"/>
            <Neighborhood>
                <Order>2</Order>
            </Neighborhood>
        </Lattice>
    </Space>
    <Time>
        <StartTime value="0"/>
        <StopTime value="4000"/>
        <SaveInterval value="0"/>
        <RandomSeed value="56"/>
    </Time>
    <CellTypes>
        <CellType class="biological" name="Angioblasts">
            <VolumeConstraint>
                <Strength value="25"/>
                <Target value="90"/>
            </VolumeConstraint>
            <Property symbol="cell" value="1.0" name="cell"/>
            <Property symbol="s" value="2000" name="chemotactic strength"/>
            <ConnectivityConstraint/>
            <Chemotaxis>
                <Layer symbol-ref="u"/>
                <Strength symbol-ref="s"/>
            </Chemotaxis>
        </CellType>
        <CellType class="medium" name="medium">
            <Property symbol="cell" value="0" name="cell"/>
        </CellType>
    </CellTypes>
    <CPM>
        <Interaction default="0">
            <Contact type1="medium" type2="Angioblasts" value="80"/>
            <Contact type1="Angioblasts" type2="Angioblasts" value="160"/>
        </Interaction>
        <MetropolisKinetics temperature="50" stepper="edgelist">
            <Neighborhood>
                <Order>2</Order>
            </Neighborhood>
        </MetropolisKinetics>
        <MCSDuration value="1.0"/>
    </CPM>
    <PDE>
        <Layer symbol="u" name="VEGF">
            <Diffusion rate="1e-6" unit="µm²/s"/>
        </Layer>
        <System solver="runge-kutta" time-step="1.0">
            <Constant symbol="gamma1" value="1e-3" />
            <Constant symbol="delta" value="1e-3" />
            <DiffEqn symbol-ref="u">
                <Expression>cell*gamma1 - (1-cell)*delta*u </Expression>
            </DiffEqn>
        </System>
    </PDE>
    <CellPopulations>
        <Population size="0" type="Angioblasts">
            <InitRectangle cells="200" type="regular">
                <Dimensions size="200 200 0" origin="0 0 0"/>
            </InitRectangle>
        </Population>
    </CellPopulations>
    <Analysis>
        <Gnuplotter clean="true" interval="50" timename="false">
            <Terminal opacity="0.65" name="png"/>
            <Cells flooding="true">
                <ColorMap>
                    <Color value="1" color="gray"/>
                    <Color value="0" color="grey"/>
                </ColorMap>
            </Cells>
            <PDE symbol-ref="u" superimpose="true" isolines="3">
                <ColorMap>
                    <Color value="1.0" color="red"/>
                    <Color value="0.5" color="yellow"/>
                    <Color value="0.0" color="white"/>
                </ColorMap>
            </PDE>
        </Gnuplotter>
    </Analysis>
</MorpheusModel>

h B.xml |h

<MorpheusModel version="1">
    <Description>
        <Title>ModelB</Title>
    </Description>
    <Space>
        <Lattice class="square">
            <Size value="200 200 0"/>
            <BoundaryConditions>
                <Condition boundary="x" type="periodic"/>
                <Condition boundary="y" type="periodic"/>
            </BoundaryConditions>
            <NodeLength unit="micron" value="2"/>
            <Neighborhood>
                <Order>2</Order>
            </Neighborhood>
        </Lattice>
    </Space>
    <Time>
        <StartTime value="0"/>
        <StopTime value="4000"/>
        <SaveInterval value="0"/>
        <RandomSeed value="56"/>
    </Time>
    <CellTypes>
        <CellType class="biological" name="Angioblasts">
            <VolumeConstraint>
                <Strength value="25"/>
                <Target value="90"/>
            </VolumeConstraint>
            <Property symbol="cell" value="1.0" name="cell"/>
            <Property symbol="s" value="2000" name="chemotactic strength"/>
            <ConnectivityConstraint/>
            <Chemotaxis>
                <Layer symbol-ref="w"/>
                <Strength symbol-ref="s"/>
            </Chemotaxis>
        </CellType>
        <CellType class="medium" name="medium">
            <Property symbol="cell" value="0" name="cell"/>
        </CellType>
    </CellTypes>
    <CPM>
        <Interaction default="0">
            <Contact type1="medium" type2="Angioblasts" value="80"/>
            <Contact type1="Angioblasts" type2="Angioblasts" value="160"/>
        </Interaction>
        <MetropolisKinetics temperature="50" stepper="edgelist">
            <Neighborhood>
                <Order>2</Order>
            </Neighborhood>
        </MetropolisKinetics>
        <MCSDuration value="1.0"/>
    </CPM>
    <PDE>
        <Layer symbol="u" name="VEGF">
            <Diffusion rate="10" unit="µm²/s"/>
        </Layer>
        <Layer symbol="v" name="ECM">
            <Diffusion rate="1e-3" unit="µm²/s"/>
        </Layer>
        <Layer symbol="w">
            <Diffusion rate="1e-3" unit="µm²/s"/>
        </Layer>
        <System solver="runge-kutta" time-step="1.0">
            <Constant symbol="gamma1" value="1e-3" />
            <Constant symbol="gamma2" value="1e-3" />
            <Constant symbol="alpha" value="1e-1" />
            <Constant symbol="delta" value="1e-2" />
            <DiffEqn symbol-ref="u">
                <Expression>gamma1 - delta*u - alpha*u*v </Expression>
            </DiffEqn>
            <DiffEqn symbol-ref="v">
                <Expression>gamma2*cell - alpha*u*v</Expression>
            </DiffEqn>
            <DiffEqn symbol-ref="w">
                <Expression>alpha*u*v</Expression>
            </DiffEqn>
        </System>
    </PDE>
    <CellPopulations>
        <Population size="0" type="Angioblasts">
            <InitRectangle cells="200" type="regular">
                <Dimensions size="200 200 0" origin="0 0 0"/>
            </InitRectangle>
        </Population>
    </CellPopulations>
    <Analysis>
        <Gnuplotter clean="true" interval="50" timename="false">
            <Terminal opacity="0.65" name="png"/>
            <Cells flooding="true">
                <ColorMap>
                    <Color value="1" color="gray"/>
                    <Color value="0" color="grey"/>
                </ColorMap>
            </Cells>
            <PDE symbol-ref="w" superimpose="true" isolines="3">
                <ColorMap>
                    <Color value="1.0" color="red"/>
                    <Color value="0.5" color="yellow"/>
                    <Color value="0.0" color="white"/>
                </ColorMap>
            </PDE>
        </Gnuplotter>
    </Analysis>
</MorpheusModel>

documentation/course/module4.1355492035.txt.gz · Last modified: 14:33 14.12.2012 by Walter
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