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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>
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<title>Model Status</title>
<para>
This CellML model is known to run in both PCEnv and COR to recreate the published results. The units have been checked and they are consistent. In this particular version of the model the membrane potential is held at -120mV. Thanks to Joseph Greenstein, Stefan Mann, Alan Garny and Martin Fink for their help in curating this model. There is also a PCEnv session associated with this model.
</para>
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<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 10C to 25C.
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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<title>state diagram</title>
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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>
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</sect1>
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<variable units="first_order_rate_constant" public_interface="out" name="gamma_gamma"/>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_alpha </ci>
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<plus/>
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<divide/>
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<ci> delta_H_beta </ci>
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<ci> delta_S_beta </ci>
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<ci> gamma </ci>
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<times/>
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<divide/>
<apply>
<times/>
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<exp/>
<apply>
<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_gamma </ci>
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<apply>
<times/>
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<apply>
<divide/>
<ci> delta_S_gamma </ci>
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<apply>
<divide/>
<apply>
<times/>
<ci> z_gamma </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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<ci> delta </ci>
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<times/>
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<divide/>
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<times/>
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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/>
<ci> delta_S_delta </ci>
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<divide/>
<apply>
<times/>
<ci> z_delta </ci>
<ci> F </ci>
<ci> V </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<times/>
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<times/>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_on </ci>
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<apply>
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<ci> R </ci>
<ci> T </ci>
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<apply>
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<ci> delta_S_on </ci>
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<times/>
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<ci> F </ci>
<ci> V </ci>
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<ci> R </ci>
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<ci> of </ci>
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<times/>
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<divide/>
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<times/>
<ci> k </ci>
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<apply>
<exp/>
<apply>
<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_of </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<apply>
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<ci> delta_S_of </ci>
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<times/>
<ci> z_of </ci>
<ci> F </ci>
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<ci> R </ci>
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<ci> gamma_gamma </ci>
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<times/>
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<divide/>
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<times/>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_gamma_gamma </ci>
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<apply>
<times/>
<ci> R </ci>
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<apply>
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<ci> delta_S_gamma_gamma </ci>
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<apply>
<times/>
<ci> z_gamma_gamma </ci>
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<times/>
<ci> R </ci>
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<ci> delta_delta </ci>
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<times/>
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<divide/>
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<times/>
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<apply>
<exp/>
<apply>
<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_delta_delta </ci>
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<apply>
<times/>
<ci> R </ci>
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<apply>
<divide/>
<ci> delta_S_delta_delta </ci>
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<divide/>
<apply>
<times/>
<ci> z_delta_delta </ci>
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<ci> V </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
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<ci> epsilon </ci>
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<times/>
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<divide/>
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<ci> k </ci>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_epsilon </ci>
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<apply>
<times/>
<ci> R </ci>
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<ci> delta_S_epsilon </ci>
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<times/>
<ci> z_epsilon </ci>
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<ci> V </ci>
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<times/>
<ci> R </ci>
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<ci> omega </ci>
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<times/>
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<divide/>
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<exp/>
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<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_omega </ci>
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<apply>
<times/>
<ci> R </ci>
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<apply>
<divide/>
<ci> delta_S_omega </ci>
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<divide/>
<apply>
<times/>
<ci> z_omega </ci>
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<ci> V </ci>
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<times/>
<ci> R </ci>
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</apply>
</apply>
</apply>
</apply>
</apply>
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<eq/>
<ci> eta </ci>
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<times/>
<apply>
<divide/>
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<times/>
<ci> k </ci>
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<ci> h </ci>
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<exp/>
<apply>
<plus/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_eta </ci>
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<apply>
<times/>
<ci> R </ci>
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<divide/>
<ci> delta_S_eta </ci>
<ci> R </ci>
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<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>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="27">
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<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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<apply>
<exp/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_H_v </ci>
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<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
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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>
</apply>
</apply>
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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/>
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<divide/>
<apply>
<minus/>
<ci> delta_H_cn </ci>
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<times/>
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<divide/>
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<times/>
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<plus/>
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<apply>
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<ci> delta_H_cf </ci>
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<apply>
<divide/>
<ci> delta_S_cf </ci>
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<apply>
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<ci> z_cf </ci>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
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</apply>
</apply>
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</math>
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<connection>
<map_components component_2="environment" component_1="sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<connection>
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<connection>
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<dcterms:W3CDTF>2008-02-13T09:58:46+13:00</dcterms:W3CDTF>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<rdf:value>This is a CellML description of Lisa Irvine et al.'s 1999 Markov model of the cardiac sodium channel.</rdf:value>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dc:title>Lisa Irvine et al.'s 1999 Markov model of the cardiac sodium channel.</dc:title>
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<dc:title>Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation</dc:title>
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<vCard:Given>Saleet</vCard:Given>
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<dc:title>Biophysical Journal</dc:title>
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