- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2009-11-11 16:10:36+13:00
- Desc:
- Updated documentation - citation and also added a link space for the diagram.
- Permanent Source URI:
- https://models.cellml.org/workspace/tabak_toporikova_freeman_bertram_2007/rawfile/07ee404582b271382d5aa0f566018dfe3c5a3bcf/tabak_toporikova_freeman_bertram_2007_b.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : tabak_model_2007.xml
CREATED : 7th August 2007
LAST MODIFIED : 7th August 2007
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Tabak, Toporikova, Freeman, and Bertram's 2007 mathematical model of a lactotroph, investigating how low doses of dopamine may stimulate prolactin secretion by increasing fast potassium currents.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="tabak_model_2007" name="tabak_model_2007_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<sect1 id="sec_status">
<title>Model Status</title>
<para>
The authors highlight that the original code they wrote for this model can be downloaded <ulink url="http://www.math.fsu.edu/~bertram/software/pituitary/JCNS_07.ode">here</ulink>. This particular CellML version of the model has the A-type potassium current switched on (gA=8). For the alternative model which has the BK-type current switched on and the A-type potassium current switched off please see version 1 of the model.
</para>
</sect1>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Prolactin (PRL) is a hormone which is synthesised and secreted by lactotrophs in the anterior lobe of the pituitary gland. It plays an important role in lactation, and influences many other physiological functions. Its release is inhibited by hypothalamic dopamine (DA), which acts through the D2 receptor to decrease PRL synthesis and secretion. The latter is decreased, at least in part, by hyperpolarisation of the lactotroph membrane, which prevents action potentials and the associated increase in intracellular calcium concentration that triggers PRL exocytosis. Membrane hyperpolarisation is caused by the activation of an inward rectifying potassium current, and an A-type potassium current is also increased by DA.
</para>
<para>
While this inhibitory effect occurs at DA concentrations between 0.1 and 10 micromolar, paradoxically, at much lower DA concentrations (less than 1 nanomolar) DA has a stimulatory effect on the release of PRL from lactotrophs. This stimulatory effect seems to be mediated, at least in part, through an increase in the intracellular calcium concentration. However, the definite biophysical mechanism underlying this phenomenon has not been identified.
</para>
<para>
In the paper described here, Tabak <emphasis>et al.</emphasis> investigate the idea that a calcium-activated fast potassium current (BK) might be responsible for the stimulatory effect of DA in lactotrophs. In addition, they explore the effects of DA on the fast, inactivating A-type potassium channel. To get a clearer understanding of the effects of DA on a lactotroph, they develop a mathematical model of the lactotroph. model simulations revealed the addition of either a BK-type current or an A-type current could transform a spontaneously spiking model to a bursting model, but the precise effect on the cytosolic calcium concentration was dependent on the type of current. Specifically, increasing the BK current increased the cytosolic calcium concentration, while increasing the A-type current could lead to either an increase or a decrease in cytosolic calcium depending on the model parameters.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents, Joel Tabak, Natalia Toporikova, Marc E. Freeman, and Richard Bertram, 2007, <emphasis>Journal of Computational Neuroscience</emphasis>, 22, 211-222. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=17058022&query_hl=1&itool=pubmed_docsum">PubMed ID: 17058022</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="tabak_2007.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the cell model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="picofarad">
<unit units="farad" prefix="pico"/>
</units>
<units name="nanosiemens">
<unit units="siemens" prefix="nano"/>
</units>
<units name="picoampere">
<unit units="ampere" prefix="pico"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar_4">
<unit units="micromolar" exponent="-4"/>
</units>
<units name="micromolar_femtocoulomb">
<unit units="micromolar"/>
<unit units="coulomb" prefix="femto" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="millisecond" exponent="-1"/>
</units>
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initial_value="-60.0"/>
<variable units="picofarad" name="C" initial_value="10.0"/>
<variable units="picoampere" public_interface="in" name="I_Ca"/>
<variable units="picoampere" public_interface="in" name="I_K"/>
<variable units="picoampere" public_interface="in" name="I_SK"/>
<variable units="picoampere" public_interface="in" name="I_DA"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
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<ci>time</ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
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<ci> I_K </ci>
<ci> I_SK </ci>
<ci> I_DA </ci>
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</apply>
</apply>
</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="I_K">
<dc:title>I_K</dc:title>
<dcterms:alternative>voltage-dependent potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_K"/>
<variable units="nanosiemens" name="gK" initial_value="4.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" name="VK"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> I_K </ci>
<apply>
<times/>
<ci> gK </ci>
<ci> n </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> VK </ci>
</apply>
</apply>
</apply>
</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="n">
<dc:title>n</dc:title>
<dcterms:alternative>voltage-dependent potassium current n gate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="n" initial_value="0.1"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="dimensionless" name="lambda" initial_value="0.7"/>
<variable units="millisecond" name="tau_n" initial_value="30.0"/>
<variable units="millivolt" name="vn" initial_value="-5.0"/>
<variable units="millivolt" name="sn" initial_value="10.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<diff/>
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<ci> n </ci>
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<apply>
<times/>
<ci> lambda </ci>
<apply>
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<ci> n_infinity </ci>
<ci> n </ci>
</apply>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
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<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> vn </ci>
<ci> V </ci>
</apply>
<ci> sn </ci>
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</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="I_Ca" name="I_Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="I_Ca">
<dc:title>I_Ca</dc:title>
<dcterms:alternative>voltage-dependent calcium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_Ca"/>
<variable units="nanosiemens" name="gCa" initial_value="2.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="VCa"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> I_Ca </ci>
<apply>
<times/>
<ci> gCa </ci>
<ci> m_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> VCa </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="m" name="m">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="m">
<dc:title>m</dc:title>
<dcterms:alternative>voltage-dependent calcium current m gate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="millivolt" name="vm" initial_value="-20.0"/>
<variable units="millivolt" name="sm" initial_value="12.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> m_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
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<divide/>
<apply>
<minus/>
<ci> vm </ci>
<ci> V </ci>
</apply>
<ci> sm </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="I_SK" name="I_SK">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="I_SK">
<dc:title>I_SK</dc:title>
<dcterms:alternative>slow, calcium-activated potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_SK"/>
<variable units="nanosiemens" name="gSK" initial_value="1.7"/>
<variable units="dimensionless" name="s_infinity"/>
<variable units="micromolar" name="ks" initial_value="0.5"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="VK"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> I_SK </ci>
<apply>
<times/>
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<ci> s_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> VK </ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> s_infinity </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Ca </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> ks </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
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</apply>
</apply>
</math>
</component>
<component cmeta:id="I_DA" name="I_DA">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="I_A">
<dc:title>I_DA</dc:title>
<dcterms:alternative>A-type dopamine-sensitive fast potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_DA"/>
<variable units="picoampere" name="I_A"/>
<variable units="nanosiemens" name="gA" initial_value="8.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" name="VK"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="a_infinity"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<ci> I_DA </ci>
<ci> I_A </ci>
</apply>
<apply>
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<ci> I_A </ci>
<apply>
<times/>
<ci> gA </ci>
<ci> a_infinity </ci>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> VK </ci>
</apply>
</apply>
</apply>
</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="a">
<dc:title>a</dc:title>
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</rdf:Description>
</rdf:RDF>
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<variable units="millivolt" name="va" initial_value="-20.0"/>
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<dc:title>h</dc:title>
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</rdf:RDF>
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<rdf:Description rdf:about="Ca">
<dc:title>Ca</dc:title>
<dcterms:alternative>calcium</dcterms:alternative>
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</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Ca" initial_value="0.1"/>
<variable units="dimensionless" name="fc" initial_value="0.01"/>
<variable units="micromolar_femtocoulomb" name="alpha" initial_value="0.0015"/>
<variable units="first_order_rate_constant" name="kc" initial_value="0.16"/>
<variable units="picoampere" public_interface="in" name="I_Ca"/>
<variable units="millisecond" public_interface="in" name="time"/>
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<apply>
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<ci> I_Ca </ci>
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<apply>
<times/>
<ci> kc </ci>
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</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="PRL">
<dc:title>PRL</dc:title>
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</rdf:Description>
</rdf:RDF>
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<variable units="micromolar_4" name="kPRL" initial_value="1.0"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
<times/>
<ci> kPRL </ci>
<apply>
<power/>
<ci> Ca </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="millivolt" public_interface="out" name="VK" initial_value="-75.0"/>
<variable units="millivolt" public_interface="out" name="VCa" initial_value="50.0"/>
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<group>
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<component_ref component="membrane">
<component_ref component="I_Ca">
<component_ref component="m"/>
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<component_ref component="I_K">
<component_ref component="n"/>
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<component_ref component="I_SK"/>
<component_ref component="I_DA">
<component_ref component="a"/>
<component_ref component="h"/>
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<relationship_ref relationship="encapsulation"/>
<component_ref component="I_Ca">
<component_ref component="m"/>
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<component_ref component="I_K">
<component_ref component="n"/>
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<component_ref component="I_DA">
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<connection>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<connection>
<map_components component_2="environment" component_1="I_DA"/>
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<connection>
<map_components component_2="environment" component_1="Ca"/>
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<connection>
<map_components component_2="I_Ca" component_1="membrane"/>
<map_variables variable_2="I_Ca" variable_1="I_Ca"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="I_K" component_1="membrane"/>
<map_variables variable_2="I_K" variable_1="I_K"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="I_SK" component_1="membrane"/>
<map_variables variable_2="I_SK" variable_1="I_SK"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="I_DA" component_1="membrane"/>
<map_variables variable_2="I_DA" variable_1="I_DA"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
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<map_variables variable_2="a_infinity" variable_1="a_infinity"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="I_DA" component_1="h"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="I_K"/>
<map_variables variable_2="VK" variable_1="VK"/>
</connection>
<connection>
<map_components component_2="I_K" component_1="n"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="I_Ca"/>
<map_variables variable_2="VCa" variable_1="VCa"/>
</connection>
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