documentation:course:module1
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| documentation:course:module1 [12:53 11.01.2013] – [Description] Fabian Rost | documentation:course:module1 [16:20 13.11.2017] (current) – [Delta-Notch] Fabian Rost | ||
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| ===== Description ===== | ===== Description ===== | ||
| + | ==== Basic ODEs ==== | ||
| * get to know what students know about ODEs and adjust the module to the pre-knowledge | * get to know what students know about ODEs and adjust the module to the pre-knowledge | ||
| Line 71: | Line 72: | ||
| \dot A &= k_2 A \\ | \dot A &= k_2 A \\ | ||
| \dot A &= - k_3 A \\ | \dot A &= - k_3 A \\ | ||
| - | \dot A &= k_4 - k_3 A | + | \dot A &= k_4 - k_5 A |
| \end{align} | \end{align} | ||
| * discuss those ODEs by | * discuss those ODEs by | ||
| - | * steady state analysis | + | * calculate |
| * simulate in morpheus | * simulate in morpheus | ||
| + | * typical models for biochemistry/ | ||
| + | |||
| + | < | ||
| + | digraph { | ||
| + | size=" | ||
| + | |||
| + | node [shape = circle]; | ||
| + | a[label="", | ||
| + | ab[label="", | ||
| + | c[label="", | ||
| + | |||
| + | a -> ab[arrowhead=None]; | ||
| + | ab -> A; | ||
| + | A -> c | ||
| + | B -> ab[arrowhead=tee]; | ||
| + | |||
| + | {rank=same; a; ab; A; c}; | ||
| + | } | ||
| + | |||
| + | </ | ||
| + | |||
| + | \begin{align} | ||
| + | \dot A &= \frac{\theta^n}{\theta^n + B^n} - k A | ||
| + | \end{align} | ||
| + | ==== Delta-Notch ==== | ||
| + | |||
| * then discuss the delta-notch sketch with two species | * then discuss the delta-notch sketch with two species | ||
| * start with the Collier model | * start with the Collier model | ||
| Line 83: | Line 110: | ||
| * they could come up with something like: | * they could come up with something like: | ||
| \begin{align} | \begin{align} | ||
| - | \dot X_1 & | + | \dot A_1 &= \frac{\theta^n}{\theta^n + A_2^n} - A_1 \\ |
| - | \dot X_2 & | + | \dot A_2 &= \frac{\theta^n}{\theta^n + A_1^n} - A_2 |
| \end{align} | \end{align} | ||
| * this system is bistable for certain parameter ranges, if the students are advanced they might find this out themselves | * this system is bistable for certain parameter ranges, if the students are advanced they might find this out themselves | ||
| - | * bistable e.g. for $\theta=0.5$, | + | * bistable e.g. for $\theta=0.5$, |
| * if they have this system running in morpheus go spatial and let them simulate the system on a square and hexagonal grid | * 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 | * then you could also move to shaped cpm cells or even moving cells | ||
| Line 94: | Line 121: | ||
| * 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 | * 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: | Paper: | ||
| - | * Collier, | + | * Joanne R. Collier, |
| + | |||
| + | |||
| + | |||
| + | |||
| Line 100: | Line 132: | ||
| - | <code xml |h ExponentialGrowth.xml | + | <file xml ExponentialGrowth.xml> |
| <?xml version=' | <?xml version=' | ||
| - | < | + | < |
| < | < | ||
| - | < | + | |
| + | | ||
| </ | </ | ||
| < | < | ||
| <Lattice class=" | <Lattice class=" | ||
| - | <Size value=" | + | |
| + | < | ||
| + | </ | ||
| + | | ||
| </ | </ | ||
| + | < | ||
| </ | </ | ||
| < | < | ||
| < | < | ||
| - | < | + | < |
| + | < | ||
| + | </ | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | <System solver=" | ||
| + | <DiffEqn symbol-ref=" | ||
| + | < | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | < | ||
| + | <Logger time-step=" | ||
| + | < | ||
| + | <Symbol symbol-ref=" | ||
| + | </ | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | <Plot time-step=" | ||
| + | <Style style=" | ||
| + | < | ||
| + | < | ||
| + | <Symbol symbol-ref=" | ||
| + | </ | ||
| + | < | ||
| + | <Symbol symbol-ref=" | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | |||
| + | </ | ||
| + | |||
| + | <file xml | LateralInhibition_2cell.xml> | ||
| + | |||
| + | <?xml version=' | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | <Lattice class=" | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | <Size symbol=" | ||
| + | </ | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | <System solver=" | ||
| + | <DiffEqn symbol-ref=" | ||
| + | < | ||
| + | - k * A</ | ||
| + | </ | ||
| + | <DiffEqn symbol-ref=" | ||
| + | < | ||
| + | - k * A_neighbour</ | ||
| + | </ | ||
| + | </ | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | <Logger time-step=" | ||
| + | < | ||
| + | <Symbol symbol-ref=" | ||
| + | </ | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | <Plot time-step=" | ||
| + | <Style style=" | ||
| + | < | ||
| + | < | ||
| + | <Symbol symbol-ref=" | ||
| + | </ | ||
| + | < | ||
| + | <Symbol symbol-ref=" | ||
| + | <Symbol symbol-ref=" | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | </ | ||
| + | |||
| + | |||
| + | </ | ||
| + | |||
| + | <file xml | LateralInhibition_space.xml> | ||
| + | |||
| + | <?xml version=' | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | <Lattice class=" | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | <Size symbol=" | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | </ | ||
| + | < | ||
| + | </ | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| </ | </ | ||
| < | < | ||
| - | < | + | < |
| - | <System time-step=" | + | < |
| - | <DiffEqn symbol-ref=" | + | < |
| - | < | + | < |
| + | < | ||
| + | < | ||
| + | <Input scaling=" | ||
| + | <Output symbol-ref=" | ||
| + | </ | ||
| + | < | ||
| + | <DiffEqn symbol-ref=" | ||
| + | < | ||
| + | - X</ | ||
| </ | </ | ||
| </ | </ | ||
| - | < | ||
| - | < | ||
| </ | </ | ||
| </ | </ | ||
| < | < | ||
| - | < | + | < |
| + | < | ||
| + | < | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| + | --> | ||
| + | < | ||
| + | </ | ||
| + | </Population> | ||
| </ | </ | ||
| < | < | ||
| - | <Logger interval="1"> | + | <Gnuplotter time-step="50"> |
| - | <Format string=" | + | <Plot> |
| - | <Input> | + | <Cells value=" |
| - | <Cell mapping="all" celltype=" | + | |
| - | </ | + | |
| - | <Plot interval=" | + | |
| - | <X-axis column=" | + | |
| - | <Y-axis columns=" | + | |
| </ | </ | ||
| - | | + | |
| + | </ | ||
| </ | </ | ||
| + | < | ||
| + | < | ||
| + | </ | ||
| </ | </ | ||
| - | + | </file> | |
| - | </code> | + | |
documentation/course/module1.1357905221.txt.gz · Last modified: 12:53 11.01.2013 by Fabian Rost