- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-07-07 01:49:12+12:00
- Desc:
- Extensively curated the model (equations, units and initial conditions) such that it now runs to reproduce the published results. Also fixed metadata. Created the second model from the paper from new and curated it.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/butera_rinzel_smith_1999/rawfile/84580fcd68ad99c92876a448d03b75ed1be90543/butera_rinzel_smith_1999.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : butera_model_1999.xml
CREATED : 9th May 2002
LAST MODIFIED : 20th April 2005
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Butera et al's first 1999 mathematical model of respiratory rhythm generation in the pre-Botzinger complex in bursting pacemaker neurons.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
20/04/2005 - PJV - Made MathML id's unique
-->
<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#" name="butera_1999" cmeta:id="butera_1999">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Models Of Respiratory Rhythm Generation In The Pre-Botzinger Complex. I. Bursting Pacemaker Neurons</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in OpenCell and COR to reproduce the published results (Figure 4 A3 where E_L = -57.5 mv). Please note that the model has to be run for a duration of 10000 ms with a step size of 0.01 ms and a high point density of 100000 points/graph. This model represents model 1 from the published paper (which does not include a slow potassium current).
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: A network of oscillatory bursting neurons with excitatory coupling is hypothesized to define the primary kernel for respiratory rhythm generation in the pre-Botzinger complex (pre-BotC) in mammals. Two minimal models of these neurons are proposed. In model 1, bursting arises via fast activation and slow inactivation of a persistent Na+ current INaP-h. In model 2, bursting arises via a fast-activating persistent Na+ current INaP and slow activation of a K+ current IKS. In both models, action potentials are generated via fast Na+ and K+ currents. The two models have few differences in parameters to facilitate a rigorous comparison of the two different burst-generating mechanisms. Both models are consistent with many of the dynamic features of electrophysiological recordings from pre-BotC oscillatory bursting neurons in vitro, including voltage-dependent activity modes (silence, bursting, and beating), a voltage-dependent burst frequency that can vary from 0.05 to >1 Hz, and a decaying spike frequency during bursting. These results are robust and persist across a wide range of parameter values for both models. However, the dynamics of model 1 are more consistent with experimental data in that the burst duration decreases as the baseline membrane potential is depolarized and the model has a relatively flat membrane potential trajectory during the interburst interval. We propose several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Models of Respiratory Rhythm Generation in the Pre-Botzinger Complex. I. Bursting Pacemaker Neurons, Robert J. Butera, Jr., John Rinzel and Jeffrey C. Smith, 1999, <emphasis>Journal of Neurophysiology</emphasis>, 81, 382-397. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/10400966">PubMed ID: 10400966</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram1">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the first model</title>
</objectinfo>
<imagedata fileref="butera_1999a.png"/>
</imageobject>
</mediaobject>
<caption>The first mathematical model is based on a single-compartment Hodgkin-Huxley type formalism. It is composed of five ionic currents across the plasma membrane: a fast sodium current, I<subscript>Na</subscript>; a delayed rectifier potassium current, I<subscript>K</subscript>; a persistent sodium current, I<subscript>NaP</subscript>; a passive leakage current, I<subscript>L</subscript>; and a tonic current, I<subscript>tonic_e</subscript> (although this last current is considered to be inactive in these models).</caption>
</informalfigure>
<informalfigure float="0" id="fig_cell_diagram2">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the first model</title>
</objectinfo>
<imagedata fileref="butera_1999b.png"/>
</imageobject>
</mediaobject>
<caption>The second model appears identical to the first except with the addition of a slow K<superscript>+</superscript> current, I<subscript>KS</subscript>. (The removal of the inactivation term "h" from I<subscript>NaP</subscript> is not visible in the model diagram.)</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="picoA">
<unit units="ampere" prefix="nano"/>
</units>
<units name="nanoS">
<unit units="siemens" prefix="nano"/>
</units>
<units name="picoF">
<unit units="farad" prefix="pico"/>
</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="-50.0"/>
<variable units="picoF" name="C" initial_value="21.0"/>
<variable units="picoA" name="i_app" initial_value="0.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="picoA" public_interface="in" name="i_NaP"/>
<variable units="picoA" public_interface="in" name="i_Na"/>
<variable units="picoA" public_interface="in" name="i_K"/>
<variable units="picoA" public_interface="in" name="i_L"/>
<variable units="picoA" public_interface="in" name="i_tonic_e"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_NaP </ci>
<ci> i_Na </ci>
<ci> i_K </ci>
<ci> i_L </ci>
<ci> i_tonic_e </ci>
</apply>
</apply>
<ci> i_app </ci>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="picoA" public_interface="out" name="i_Na"/>
<variable units="millivolt" public_interface="out" name="E_Na" initial_value="50.0"/>
<variable units="nanoS" name="g_Na" initial_value="28.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m_infinity"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m_infinity </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> n </ci>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="millivolt" name="theta_m" initial_value="-34.0"/>
<variable units="millivolt" name="sigma_m" initial_value="-5.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="fast_sodium_current_m_gate_m_infinity_calculation">
<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/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_m </ci>
</apply>
<ci> sigma_m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n" initial_value="0.01"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millisecond" name="tau_n"/>
<variable units="millisecond" name="tau_n_max" initial_value="10.0"/>
<variable units="millivolt" name="theta_n" initial_value="-29.0"/>
<variable units="millivolt" name="sigma_n" initial_value="-4.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="fast_sodium_current_n_gate_n_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> n_infinity </ci>
<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="fast_sodium_current_n_gate_n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_n </ci>
</apply>
<ci> sigma_n </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="fast_sodium_current_n_gate_tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<ci> tau_n_max </ci>
<apply>
<cosh/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_n </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> sigma_n </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_current">
<variable units="picoA" public_interface="out" name="i_K"/>
<variable units="nanoS" name="g_K" initial_value="11.2"/>
<variable units="millivolt" name="E_K" initial_value="-85.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<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 id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K </ci>
<apply>
<power/>
<ci> n </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n" initial_value="0.01"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millisecond" name="tau_n"/>
<variable units="millisecond" name="tau_n_max" initial_value="10.0"/>
<variable units="millivolt" name="theta_n" initial_value="-29.0"/>
<variable units="millivolt" name="sigma_n" initial_value="-4.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="potassium_current_n_gate_n_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> n_infinity </ci>
<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="potassium_current_n_gate_n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_n </ci>
</apply>
<ci> sigma_n </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_current_n_gate_tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<ci> tau_n_max </ci>
<apply>
<cosh/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_n </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> sigma_n </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="persistent_sodium_current">
<variable units="picoA" public_interface="out" name="i_NaP"/>
<variable units="nanoS" name="g_NaP" initial_value="2.8"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="dimensionless" private_interface="in" name="m_infinity"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaP_calculation">
<eq/>
<ci> i_NaP </ci>
<apply>
<times/>
<ci> g_NaP </ci>
<ci> m_infinity </ci>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="persistent_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="millivolt" name="theta_m" initial_value="-40.0"/>
<variable units="millivolt" name="sigma_m" initial_value="-6.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="persistent_sodium_current_m_gate_m_infinity_calculation">
<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/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_m </ci>
</apply>
<ci> sigma_m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="persistent_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.46"/>
<variable units="dimensionless" name="h_infinity"/>
<variable units="millisecond" name="tau_h"/>
<variable units="millisecond" name="tau_h_max" initial_value="10000.0"/>
<variable units="millivolt" name="theta_h" initial_value="-48.0"/>
<variable units="millivolt" name="sigma_h" initial_value="6.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="h_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h_infinity </ci>
<ci> h </ci>
</apply>
<ci> tau_h </ci>
</apply>
</apply>
<apply id="h_infinity_calculation">
<eq/>
<ci> h_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_h </ci>
</apply>
<ci> sigma_h </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_h_calculation">
<eq/>
<ci> tau_h </ci>
<apply>
<divide/>
<ci> tau_h_max </ci>
<apply>
<cosh/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> theta_h </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> sigma_h </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="leakage_current">
<variable units="picoA" public_interface="out" name="i_L"/>
<variable units="nanoS" name="g_L" initial_value="2.8"/>
<variable units="millivolt" name="E_L" initial_value="-57.5"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_L_calculation">
<eq/>
<ci> i_L </ci>
<apply>
<times/>
<ci> g_L </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_L </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="tonic_current">
<variable units="picoA" public_interface="out" name="i_tonic_e"/>
<variable units="nanoS" name="g_tonic_e" initial_value="0.0"/>
<variable units="millivolt" name="E_syn_e" initial_value="0.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_tonic_e_calculation">
<eq/>
<ci> i_tonic_e </ci>
<apply>
<times/>
<ci> g_tonic_e </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_syn_e </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_n_gate"/>
</component_ref>
<component_ref component="potassium_current">
<component_ref component="potassium_current_n_gate"/>
</component_ref>
<component_ref component="persistent_sodium_current">
<component_ref component="persistent_sodium_current_m_gate"/>
<component_ref component="persistent_sodium_current_h_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="persistent_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="fast_sodium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="persistent_sodium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaP" variable_1="i_NaP"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="leakage_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_L" variable_1="i_L"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="tonic_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_tonic_e" variable_1="i_tonic_e"/>
</connection>
<connection>
<map_components component_2="persistent_sodium_current" component_1="fast_sodium_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="m_infinity" variable_1="m_infinity"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_n_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="potassium_current_n_gate" component_1="potassium_current"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="persistent_sodium_current_m_gate" component_1="persistent_sodium_current"/>
<map_variables variable_2="m_infinity" variable_1="m_infinity"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="persistent_sodium_current_h_gate" component_1="persistent_sodium_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" 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#">
<rdf:Description rdf:about="">
<dc:title>Models of Respiratory Rhythm Generation in the Pre-Botzinger Complex. I. Bursting Pacemaker Neurons: model 1 (which does not include a slow potassium current)</dc:title>
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
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Models of Respiratory Rhythm Generation in the Pre-Botzinger Complex. I. Bursting Pacemaker Neurons
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