- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2008-01-30 03:54:44+13:00
- Desc:
- committing version01 of irvine_jafri_winslow_1999
- Permanent Source URI:
- http://models.cellml.org/workspace/irvine_jafri_winslow_1999/rawfile/6da1c18b45f4c4e936e2e5bf2d27527f6c521fba/irvine_jafri_winslow_1999.cellml
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<title>Cardiac Sodium Channel Markov Model with Temperature Dependence and Recovery from Inactivation</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
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<section id="sec_status">
<title>Model Status</title>
<para>
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal
neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819 - 829) with the following modifications: 1)
an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants
are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are
determined using a simulated annealing algorithm to minimize the error between model responses and various experimental
data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents,
steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10°C to 25°C.
The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/76/4/1868">Cardiac Sodium Channel Markov Model with Temperature Dependence and Recovery from Inactivation</ulink>, Lisa A. Irvine, M. Saleet Jafri, and Raimond L. Winslow, 1999, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 76, 1868 - 1885. (<ulink url="http://www.biophysj.org/cgi/content/full/76/4/1868"> Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/76/4/1868">PDF</ulink> versions of this article are available to subscribers on the <emphasis>Biophysical Journal</emphasis> website). <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10096885&dopt=Abstract">PubMed ID: 10096885</ulink>
</para>
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<caption>State diagram for the cardiac sodium channel Markov model. C0-C4 are closed states, O1 and O2 are open states, C0I-C4I are closed-inactivated states, and I is the inactivated state. All rate constants are voltage- and temperature-dependent except for those governing transitions between closed and closed-inactivated states, which are only temperature-dependent.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<variable units="first_order_rate_constant" public_interface="out" name="beta"/>
<variable units="first_order_rate_constant" public_interface="out" name="cf"/>
<variable units="first_order_rate_constant" public_interface="out" name="cn"/>
<variable units="first_order_rate_constant" public_interface="out" name="of"/>
<variable units="first_order_rate_constant" public_interface="out" name="on"/>
<variable units="first_order_rate_constant" public_interface="out" name="eta"/>
<variable units="first_order_rate_constant" public_interface="out" name="gamma"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta"/>
<variable units="first_order_rate_constant" public_interface="out" name="epsilon"/>
<variable units="first_order_rate_constant" public_interface="out" name="omega"/>
<variable units="first_order_rate_constant" public_interface="out" name="v"/>
<variable units="first_order_rate_constant" public_interface="out" name="gamma_gamma"/>
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<variable units="J_K" name="k" initial_value="1.3806504E-23"/>
<variable units="J_ms" name="h" initial_value="6.62607095E-31"/>
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<times/>
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<divide/>
<apply>
<times/>
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<ci> h </ci>
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<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_alpha </ci>
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<times/>
<ci> R </ci>
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<times/>
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<ci> F </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
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<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_beta </ci>
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<times/>
<ci> R </ci>
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<ci> delta_S_beta </ci>
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<times/>
<ci> z_beta </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
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<ci> h </ci>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_gamma </ci>
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<times/>
<ci> R </ci>
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<apply>
<divide/>
<ci> delta_S_gamma </ci>
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<divide/>
<apply>
<times/>
<ci> z_gamma </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<times/>
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<divide/>
<apply>
<times/>
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<ci> h </ci>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_delta </ci>
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<times/>
<ci> R </ci>
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<divide/>
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<times/>
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<times/>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="20">
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
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<ci> h </ci>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_on </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<apply>
<divide/>
<ci> delta_S_on </ci>
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<divide/>
<apply>
<times/>
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<ci> F </ci>
<ci> V </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="21">
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<eq/>
<ci> of </ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
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<ci> h </ci>
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<exp/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_of </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<apply>
<divide/>
<ci> delta_S_of </ci>
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<divide/>
<apply>
<times/>
<ci> z_of </ci>
<ci> F </ci>
<ci> V </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="22">
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<eq/>
<ci> gamma_gamma </ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
<ci> T </ci>
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<ci> h </ci>
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<exp/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_gamma_gamma </ci>
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<apply>
<times/>
<ci> R </ci>
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<apply>
<divide/>
<ci> delta_S_gamma_gamma </ci>
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<divide/>
<apply>
<times/>
<ci> z_gamma_gamma </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="23">
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<eq/>
<ci> delta_delta </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
<ci> T </ci>
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<ci> h </ci>
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<apply>
<exp/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_delta_delta </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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<apply>
<divide/>
<ci> delta_S_delta_delta </ci>
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<apply>
<divide/>
<apply>
<times/>
<ci> z_delta_delta </ci>
<ci> F </ci>
<ci> V </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="24">
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
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<ci> h </ci>
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<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_epsilon </ci>
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<apply>
<times/>
<ci> R </ci>
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<apply>
<divide/>
<ci> delta_S_epsilon </ci>
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<apply>
<divide/>
<apply>
<times/>
<ci> z_epsilon </ci>
<ci> F </ci>
<ci> V </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="25">
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<eq/>
<ci> omega </ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
<ci> T </ci>
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<ci> h </ci>
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<exp/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_omega </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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<apply>
<divide/>
<ci> delta_S_omega </ci>
<ci> R </ci>
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<apply>
<divide/>
<apply>
<times/>
<ci> z_omega </ci>
<ci> F </ci>
<ci> V </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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</apply>
</apply>
</apply>
</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="26">
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<eq/>
<ci> eta </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
<ci> T </ci>
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<ci> h </ci>
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<exp/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_eta </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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<apply>
<divide/>
<ci> delta_S_eta </ci>
<ci> R </ci>
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<apply>
<divide/>
<apply>
<times/>
<ci> z_eta </ci>
<ci> F </ci>
<ci> V </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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</apply>
</apply>
</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="27">
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<eq/>
<ci> v </ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
<ci> T </ci>
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<ci> h </ci>
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<exp/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_v </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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<apply>
<divide/>
<ci> delta_S_v </ci>
<ci> R </ci>
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<apply>
<divide/>
<apply>
<times/>
<ci> z_v </ci>
<ci> F </ci>
<ci> V </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="28">
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<ci> cn </ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k </ci>
<ci> T </ci>
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<ci> h </ci>
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<apply>
<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_cn </ci>
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<times/>
<ci> R </ci>
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<ci> z_cn </ci>
<ci> F </ci>
<ci> V </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="29">
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<times/>
<apply>
<divide/>
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<times/>
<ci> k </ci>
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<plus/>
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<ci> delta_H_cf </ci>
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<times/>
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<rdf:li>Markov</rdf:li>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<rdf:Description rdf:about="">
<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
<cmeta:comment rdf:resource="rdf:#a939fc9a-4e43-4b69-ab1a-5c6c012573df"/>
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<rdf:Description rdf:about="rdf:#1b877975-327d-4ef9-a855-e855f2c990fb">
<dc:title>Biophysical Journal</dc:title>
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<bqs:Pubmed_id>10096885</bqs:Pubmed_id>
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