- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2011-04-29 09:32:09+12:00
- Desc:
- adding an initial encoding of the Collier et al (1996) Delta-Notch model. This version is for two cells in a 1-dimensional line with zero boundary conditions. The model reproduces Figure 3 from the Collier paper, as shown in collier.png. This is a brute force approach to get an initial encoding of the model, paying no heed to best practices or model reuse. Hopefully this gives a starting point to generalise following best practices guidelines for model reuse and modularity in order to create a more useful version of the model equations.
- Permanent Source URI:
- https://models.cellml.org/w/andre/DeltaNotch/rawfile/4c4129334f8a5138d4f2b4aeb174e4183fe5edba/collier.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<model
name="DeltaNotch"
cmeta:id="DeltaNotchModel"
xmlns="http://www.cellml.org/cellml/1.1#"
xmlns:cellml="http://www.cellml.org/cellml/1.1#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:xlink="http://www.w3.org/1999/xlink">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:bqs="http://www.cellml.org/bqs/1.0#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#"
xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#"
xmlns:cg="http://www.cellml.org/metadata/graphs/1.0#">
<rdf:Description rdf:about="#DeltaNotchModel">
<cs:simulation>
<rdf:Description rdf:ID="simulation">
<cs:multistepMethod>bdf</cs:multistepMethod>
<cs:iterationMethod>newton</cs:iterationMethod>
<cs:linearSolver>dense</cs:linearSolver>
<cs:boundIntervals rdf:parseType="Collection">
<rdf:Description>
<cs:boundVariable>
<rdf:Description rdf:about="#time"/>
</cs:boundVariable>
<cs:maximumStepSize rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
0.01
</cs:maximumStepSize>
<cs:tabulationStepSize rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
0.1
</cs:tabulationStepSize>
<cs:startingValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
0
</cs:startingValue>
<cs:endingValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
25
</cs:endingValue>
</rdf:Description>
</cs:boundIntervals>
</rdf:Description>
</cs:simulation>
</rdf:Description>
<rdf:Description>
<cg:graph>
<rdf:Description rdf:ID="n1-graph">
<cg:x-label>Time</cg:x-label>
<cg:y-label>value</cg:y-label>
<cg:background-colour>#ffffff</cg:background-colour>
<cg:traces rdf:parseType="Collection">
<rdf:Description>
<cg:label>n1</cg:label>
<cg:type rdf:resource="http://www.cellml.org/metadata/graphs/1.0#line"/>
<cg:colour>#ff0000</cg:colour>
<cg:x-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#time"/>
</cg:x-variable>
<cg:y-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#n1"/>
</cg:y-variable>
</rdf:Description>
<rdf:Description>
<cg:label>n2</cg:label>
<cg:type rdf:resource="http://www.cellml.org/metadata/graphs/1.0#line"/>
<cg:colour>#0000ff</cg:colour>
<cg:x-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#time"/>
</cg:x-variable>
<cg:y-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#n2"/>
</cg:y-variable>
</rdf:Description>
<rdf:Description>
<cg:label>d1</cg:label>
<cg:type rdf:resource="http://www.cellml.org/metadata/graphs/1.0#line"/>
<cg:colour>#008000</cg:colour>
<cg:x-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#time"/>
</cg:x-variable>
<cg:y-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#d1"/>
</cg:y-variable>
</rdf:Description>
<rdf:Description>
<cg:label>d2</cg:label>
<cg:type rdf:resource="http://www.cellml.org/metadata/graphs/1.0#line"/>
<cg:colour>#000000</cg:colour>
<cg:x-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#time"/>
</cg:x-variable>
<cg:y-variable rdf:parseType="Resource">
<cs:simulation rdf:resource="#simulation"/>
<cg:variable rdf:resource="#d2"/>
</cg:y-variable>
</rdf:Description>
</cg:traces>
</rdf:Description>
</cg:graph>
</rdf:Description>
</rdf:RDF>
<component name="component">
<variable cmeta:id="n1" name="n1" units="dimensionless" initial_value="1.0"/>
<variable cmeta:id="d1" name="d1" units="dimensionless" initial_value="1.0"/>
<variable cmeta:id="n2" name="n2" units="dimensionless" initial_value="0.99"/>
<variable cmeta:id="d2" name="d2" units="dimensionless" initial_value="0.99"/>
<variable cmeta:id="a" name="a" units="dimensionless" initial_value="0.01"/>
<variable cmeta:id="b" name="b" units="dimensionless" initial_value="100"/>
<variable cmeta:id="v" name="v" units="dimensionless" initial_value="1"/>
<variable cmeta:id="k" name="k" units="dimensionless" initial_value="2"/>
<variable cmeta:id="h" name="h" units="dimensionless" initial_value="2"/>
<variable cmeta:id="time" name="time" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>n1</ci>
</apply>
<apply><minus/>
<apply><divide/>
<apply><power/>
<apply><times/><ci>d2</ci><cn cellml:units="dimensionless">0.5</cn></apply>
<ci>k</ci>
</apply>
<apply><plus/>
<ci>a</ci>
<apply><power/>
<apply><times/><ci>d2</ci><cn cellml:units="dimensionless">0.5</cn></apply>
<ci>k</ci>
</apply>
</apply>
</apply>
<ci>n1</ci>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>n2</ci>
</apply>
<apply><minus/>
<apply><divide/>
<apply><power/>
<apply><times/><ci>d1</ci><cn cellml:units="dimensionless">0.5</cn></apply>
<ci>k</ci>
</apply>
<apply><plus/>
<ci>a</ci>
<apply><power/>
<apply><times/><ci>d1</ci><cn cellml:units="dimensionless">0.5</cn></apply>
<ci>k</ci>
</apply>
</apply>
</apply>
<ci>n2</ci>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>d1</ci>
</apply>
<apply><times/>
<ci>v</ci>
<apply><minus/>
<apply><divide/>
<cn cellml:units="dimensionless">1.0</cn>
<apply><plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply><times/>
<ci>b</ci>
<apply><power/>
<ci>n1</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
</apply>
<ci>d1</ci>
</apply>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>d2</ci>
</apply>
<apply><times/>
<ci>v</ci>
<apply><minus/>
<apply><divide/>
<cn cellml:units="dimensionless">1.0</cn>
<apply><plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply><times/>
<ci>b</ci>
<apply><power/>
<ci>n2</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
</apply>
<ci>d2</ci>
</apply>
</apply>
</apply>
</math>
</component>
</model>
