Morpheus

Author: Fabian Rost

Aim:

• learn about ODE models (dynamics in morpheus, steady states analytically)
• develop first models

Description:

• get to know what students know about ODEs and adjust the module to the pre-knowledge
• give them very simple sketches of biomolecular models, which they should translate into ODEs

• example ODEs:

\begin{align} \dot A &= c \\ \dot A &= c A \\ \dot A &= c - k * A \end{align}

• discuss those ODEs by
  • steady state analysis
  • simulate in morpheus
• then discuss the delta-notch sketch with two species
  • start with the Collier model
  • let them simplify the Collier model sketch (remove the delta or notch species)
  • let them develop an ODE for this system (they should be able to do so from the above examples)
  • they could come up with something like:

\begin{align} \dot X_1 &= c \frac{\theta^n}{\theta^n + X_2^n} - k X_1 \\ \dot X_2 &= c \frac{\theta^n}{\theta^n + X_1^n} - k X_2 \end{align}

• this system is bistable for certain parameter ranges, if the students are advanced they might find this out themselves
• bistable e.g. for $\theta=0.5$, $n=4$, $c=k=1$
• if they have this system running in morpheus go spatial and let them simulate the system on a square and hexagonal grid
• then you could also move to shaped cpm cells or even moving cells

• students won't do so much on their own in this session, it is a lot teaching on ODEs (don't be theoretical here, not enough time!) and introducing morpheus

Paper:

• Collier, J. R., McInerney, D., Schnell, S., Maini, P. K., Gavaghan, D. J., Houston, P., & Stern, C. D. (2000). A cell cycle model for somitogenesis: mathematical formulation and numerical simulation. J. Theor. Biol., 207(3), 305-316.

Morpheus models:

Link to Example page

<MorpheusModel version="1">
    <Description>
        <Title>Example-Model</Title>
    </Description>
    <Space>
        <Lattice class="linear">
            <Size value="100 0 0"/>
            <BoundaryConditions>
                <Condition boundary="x" type="periodic"/>
            </BoundaryConditions>
        </Lattice>
    </Space>
    <Time>
        <StartTime value="0"/>
        <StopTime value="100"/>
    </Time>
</MorpheusModel>