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?
    • Explore differences in parameter sensitivity:
      • Sensitivity analysis: ParamSweep (see "parameter sweep" in FAQ)
  • 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:

• Assignment (handout, pdf)
• Diff (handout, pdf)

Morpheus models:

• Example: Vascular patterning

• h A.xml (autocrine chemotaxis)|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 (paracrine chemotaxis)|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>