- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-02-05 13:09:07+13:00
- Desc:
- Added annotations to chay_lee_fan_1995.cellml model
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/chay_lee_fan_1995/rawfile/72b2d781533dd3c024def49f84340285604bf468/chay_lee_fan_1995.cellml
<?xml version='1.0'?>
<!-- FILE : chay_model_1995.xml
CREATED : 18th May 2007
LAST MODIFIED : 18th May 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 Chay et al's
1995 mathematical model of intracellular calcium spikes in non-excitable cells.
CHANGES:
-->
<model name="chay_model_1995_version02" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="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:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Intracellular Ca2+ Spikes in Non-excitable Cell Models</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model produces an oscillating output but this result has not been checked against the publication.</para>
<para>
ValidateCellML verifies this model as valid CellML, but detects some unit inconsistencies.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Intracellular Ca<superscript>2+</superscript> ions are essential for the initiation of cellular events such as the fertilisation of eggs, muscle contraction and hormone and peptide secretion. In excitable cells such as neurons, an increase in intracellular Ca<superscript>2+</superscript> is brought about by the Ca<superscript>2+</superscript> channels in the plasma membrane when these channels open during depolarisation, permitting extracellular Ca<superscript>2+</superscript> to enter the cell. By contrast, in non-excitable cells Ca<superscript>2+</superscript> is supplied mainly by internal stores. These stores release Ca<superscript>2+</superscript> when neurotransmitters and hormones engage in the phospholinositide signalling pathway.
</para>
<para>
Oscillatory signals in [Ca<superscript>2+</superscript>]<subscript>i</subscript> in non-excitable cells are frequency encoded. These patterns are similar to action potential responses observed in excitable cells upon stimulation. A model exclusively studied in this paper is based on the receptor-operated model of Cuthberson and Chay (1991) (see <xref linkend="fig_schematic_diagram"/> below). The essence of this model is that the resting period between the Ca<superscript>2+</superscript> spikes are timed by the build up of GTP-binding proteins combined with positive feedback effects and co-operation, leading to the sudden activation of phospholipase C (PLC). Activated PLC converts phosphatidylinositol 4,5-bisphosphate (PIP<subscript>2</subscript>) into two second messengers, diacylglycerol (DAG) and inositol 1,4,5-triphosphate (IP<subscript>3</subscript>), which releases Ca<superscript>2+</superscript> from intracellular stores (see <xref linkend="fig_signaling_pathway"/> below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Appearance of phase-locked wenckebach-like rhythms, devil's staircase and universality in intracellular calcium spikes in non-excitable cell models, Teresa Ree Chay, Young Seek Lee and Yin Shui Fan, 1995,
<emphasis>Journal Of Theoretical Biology</emphasis>
, 174, 21-44. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7643604&dopt=Abstract">PubMed ID: 7643604</ulink>
</para>
<para>
The raw CellML description of the intracellular Ca<superscript>2+</superscript> spikes in non-excitable cells model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_schematic_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>A schematic diagram of the G-protein pathway</title>
</objectinfo>
<imagedata fileref="chay_1995a.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the Bourne-Stryer mechanism, PLC acts as a protein activating G-alpha-GTP. PLC is an effector which is activated when bound to G-alpha-GTP. The exchange of GTP for bound GDP is catalysed by the hormone-receptor complex R*, with the help of the G-beta-gamma subunit. Hydrolysis of the bound GTP brings the G-protein back to the inactive state. GTP hydrolysis by the G-alpha_GTP complexed with PLC is much faster than that of G-alpha-GTP alone. The model is based on these four reaction steps.</caption>
</informalfigure>
<informalfigure float="0" id="fig_signaling_pathway">
<mediaobject>
<imageobject>
<objectinfo>
<title>A diagram of the G-protein signaling pathway</title>
</objectinfo>
<imagedata fileref="chay_1995b.png"/>
</imageobject>
</mediaobject>
<caption>The Ca<superscript>2+</superscript>-phosphatidylinositol signalling pathway plays a major role in transmembrane signalling in a large number of different cell types. In this pathway hormonal stimuli lead to the activation of G-proteins as an effector system. This initiates PLC activation and the subsequent formation of DAG and IP<subscript>3</subscript> which triggers the generation of repetitive [Ca<superscript>2+</superscript>]<subscript>i</subscript> spikes varying in frequency, amplitude and duration depending on the strength and the type of the extracellular agonist.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="nanomolar">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="fifth_order_rate_constant">
<unit exponent="-4" units="nanomolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="second"/>
</units>
<units name="second_order_rate_constant">
<unit exponent="-1" units="nanomolar"/>
<unit exponent="-1" units="second"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<!--
The following components describe all the reactants and products involved in
reactions.
-->
<component cmeta:id="id_000000001" name="G_alpha_GTP">
<variable cmeta:id="id_000000002" name="G_alpha_GTP" public_interface="out" units="nanomolar"/>
<variable name="kp" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="25.0" name="KD" public_interface="out" units="nanomolar"/>
<variable initial_value="0.005" name="kg" units="first_order_rate_constant"/>
<variable initial_value="2.0E-7" name="kp_" units="fifth_order_rate_constant"/>
<variable initial_value="0.0" name="hg" units="first_order_rate_constant"/>
<variable cmeta:id="id_000000003" name="PLC" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000012" name="DAG" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000016" name="G_alpha_GDP" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>G_alpha_GTP</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kg</ci>
<ci>G_alpha_GDP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci>kp</ci>
<apply>
<power/>
<ci>G_alpha_GTP</ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci>PLC</ci>
</apply>
<apply>
<times/>
<ci>hg</ci>
<ci>G_alpha_GTP</ci>
</apply>
</apply>
</apply>
</apply>
<apply id="kp_calculation">
<eq/>
<ci> kp </ci>
<apply>
<times/>
<ci> kp_ </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> DAG </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KD </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> DAG </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000013" name="DAG">
<variable cmeta:id="id_000000014" name="DAG" public_interface="out" units="nanomolar"/>
<variable name="kd" units="first_order_rate_constant"/>
<variable initial_value="700.0" name="kd_" units="first_order_rate_constant"/>
<variable initial_value="100.0" name="hd" units="first_order_rate_constant"/>
<variable initial_value="250.0" name="ld" units="second_order_rate_constant"/>
<variable name="KD" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000015" name="PLC_active" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="DAG_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>DAG</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kd</ci>
<ci>PLC_active</ci>
</apply>
<apply>
<times/>
<ci>hd</ci>
<ci>DAG</ci>
</apply>
</apply>
<ci> ld </ci>
</apply>
</apply>
<apply id="kd_calculation">
<eq/>
<ci> kd </ci>
<apply>
<times/>
<ci> kd_ </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> DAG </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KD </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> DAG </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000022" name="Ca_i">
<variable cmeta:id="id_000000023" name="Ca_i" units="nanomolar"/>
<variable initial_value="90000.0" name="rho_kc" units="second_order_rate_constant"/>
<variable initial_value="1.0" name="rho_hc" units="first_order_rate_constant"/>
<variable initial_value="200.0" name="rho_lc" units="second_order_rate_constant"/>
<variable cmeta:id="id_000000024" name="IP3" units="nanomolar"/>
<variable initial_value="300.0" name="Ks" units="nanomolar"/>
<variable name="DAG" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> rho_kc </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> IP3 </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Ks </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> IP3 </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>rho_hc</ci>
<ci>Ca_i</ci>
</apply>
</apply>
<ci> rho_lc </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> IP3 </ci>
<ci> DAG </ci>
</apply>
</math>
</component>
<component cmeta:id="id_000000004" name="PLC_active">
<variable cmeta:id="id_000000006" name="PLC_active" public_interface="out" units="nanomolar"/>
<variable name="hp" units="first_order_rate_constant"/>
<variable initial_value="0.5" name="hp_" units="first_order_rate_constant"/>
<variable name="kp" public_interface="in" units="first_order_rate_constant"/>
<variable name="KD" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000020" name="G_alpha_GTP" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000007" name="PLC" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000019" name="DAG" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PLC_active</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kp</ci>
<apply>
<power/>
<ci>G_alpha_GTP</ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci>PLC</ci>
</apply>
<apply>
<times/>
<ci>hp</ci>
<ci>PLC_active</ci>
</apply>
</apply>
</apply>
<apply id="hp_calculation">
<eq/>
<ci> hp </ci>
<apply>
<times/>
<ci> hp_ </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> DAG </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KD </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> DAG </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000005" name="PLC">
<variable cmeta:id="id_000000008" name="PLC" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_000000009" initial_value="10.0" name="PLC_total" units="nanomolar"/>
<variable cmeta:id="id_000000010" name="PLC_active" public_interface="in" units="nanomolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>PLC</ci>
<apply>
<minus/>
<ci>PLC_total</ci>
<ci>PLC_active</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000021" name="G_alpha_GDP">
<variable cmeta:id="id_000000017" name="G_alpha_GDP" public_interface="out" units="nanomolar"/>
<variable initial_value="200.0" name="G_total" units="nanomolar"/>
<variable cmeta:id="id_000000018" name="G_alpha_GTP" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000011" name="PLC_active" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>G_alpha_GDP</ci>
</apply>
<apply>
<minus/>
<ci>G_total</ci>
<apply>
<plus/>
<ci>G_alpha_GTP</ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci>PLC_active</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="G_alpha_GTP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="G_alpha_GDP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="PLC_active" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="DAG" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_i" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="G_alpha_GTP" component_2="G_alpha_GDP"/>
<map_variables variable_1="G_alpha_GTP" variable_2="G_alpha_GTP"/>
<map_variables variable_1="G_alpha_GDP" variable_2="G_alpha_GDP"/>
</connection>
<connection>
<map_components component_1="G_alpha_GTP" component_2="PLC"/>
<map_variables variable_1="PLC" variable_2="PLC"/>
</connection>
<connection>
<map_components component_1="G_alpha_GTP" component_2="DAG"/>
<map_variables variable_1="DAG" variable_2="DAG"/>
<map_variables variable_1="KD" variable_2="KD"/>
</connection>
<connection>
<map_components component_1="Ca_i" component_2="DAG"/>
<map_variables variable_1="DAG" variable_2="DAG"/>
</connection>
<connection>
<map_components component_1="PLC_active" component_2="DAG"/>
<map_variables variable_1="PLC_active" variable_2="PLC_active"/>
<map_variables variable_1="DAG" variable_2="DAG"/>
</connection>
<connection>
<map_components component_1="PLC_active" component_2="G_alpha_GTP"/>
<map_variables variable_1="kp" variable_2="kp"/>
<map_variables variable_1="KD" variable_2="KD"/>
<map_variables variable_1="G_alpha_GTP" variable_2="G_alpha_GTP"/>
</connection>
<connection>
<map_components component_1="PLC_active" component_2="PLC"/>
<map_variables variable_1="PLC" variable_2="PLC"/>
<map_variables variable_1="PLC_active" variable_2="PLC_active"/>
</connection>
<connection>
<map_components component_1="PLC_active" component_2="G_alpha_GDP"/>
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