Location: Al Abed, Guo, Lovell, Dokos, 2013 (Generic Cardiac Ionic Models) @ 593f7ed7d657 / AlAbed_2013_pSAN_model / inward_generic_current

Author:
Amr Al Abed <amr_aa@gmx.com>
Date:
2016-03-18 15:30:35+11:00
Desc:
Added a documentation folder. In folder added four figures describing the model structure
Permanent Source URI:
https://models.physiomeproject.org/workspace/28b/rawfile/593f7ed7d657f8f64e91ea5fe5725ea3a5684296/AlAbed_2013_pSAN_model/inward_generic_current

<?xml version='1.0'?>
<model name="inward_generic_current" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <!--Author: Amr Al Abed
Date: 12/02/2016
Inward generic ionic current based on the (i2) formulation of Al Abed et al 2013 for a peripheral sino-atrial node cell
Define units-->
    <units name="millivolt">
        <unit prefix="milli" units="volt"/>
    </units>
    <units name="nanoA_per_cm2">
        <unit prefix="nano" units="ampere"/>
        <unit exponent="-2" prefix="centi" units="metre"/>
    </units>
    <units name="microS_per_cm2">
        <unit prefix="micro" units="siemens"/>
        <unit exponent="-2" prefix="centi" units="metre"/>
    </units>
    <units name="per_sec">
        <unit exponent="-1" units="second"/>
    </units>
    <units name="per_millivolt">
        <unit exponent="-1" units="millivolt"/>
    </units>
    <units name="millisec">
        <unit prefix="milli" units="second"/>
    </units>
    <component name="environment">
        <variable name="V" public_interface="out" units="millivolt"/>
        <variable name="t" public_interface="out" units="millisec"/>
    </component>
    <!--Define encapsulation of p2 and q2 gates-->
    <group>
        <relationship_ref relationship="encapsulation"/>
        <component_ref component="inward_generic_channel">
            <component_ref component="inward_generic_channel_p2_gate"/>
            <component_ref component="inward_generic_channel_q2_gate"/>
        </component_ref>
    </group>
    <!--Define component 'inward generic channel' -->
    <component name="inward_generic_channel">
        <!--Define units and initial conditions for variables-->
        <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
        <variable name="t" private_interface="out" public_interface="in" units="second"/>
        <variable name="p_2" private_interface="in" units="dimensionless"/>
        <variable name="q_2" private_interface="in" units="dimensionless"/>
        <variable name="i_2" public_interface="out" units="nanoA_per_cm2"/>
        <variable initial_value="2856.22" name="g_2" units="microS_per_cm2"/>
        <variable initial_value="8.12" name="E_2" units="millivolt"/>
        <variable name="i2_conductance" public_interface="out" units="microS_per_cm2"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>i2_conductance</ci>
                <apply>
                    <times/>
                    <ci>g_2</ci>
                    <ci>p_2</ci>
                    <ci>q_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>i_2</ci>
                <apply>
                    <times/>
                    <ci>i2_conductance</ci>
                    <apply>
                        <minus/>
                        <ci>V</ci>
                        <ci>E_2</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--Define component ‘inward generic channel p2 gate’-->
    <component name="inward_generic_channel_p2_gate">
        <!--Define units and initial conditions for variables-->
        <variable name="V" public_interface="in" units="millivolt"/>
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.0" name="p_2" public_interface="out" units="dimensionless"/>
        <variable name="alpha_p2" units="per_sec"/>
        <variable name="beta_p2" units="per_sec"/>
        <variable initial_value="123.81" name="k_alphaP2" units="per_sec"/>
        <variable initial_value="-4.19" name="s_alphaP2" units="per_millivolt"/>
        <variable initial_value="2643.18" name="k_betaP2" units="per_sec"/>
        <variable initial_value="0.06" name="s_betaP2" units="per_millivolt"/>
        <variable initial_value="-67.13" name="E50_p2" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>alpha_p2</ci>
                <apply>
                    <divide/>
                    <ci>k_alphaP2</ci>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>s_alphaP2</ci>
                                <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <ci>E50_p2</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>beta_p2</ci>
                <apply>
                    <divide/>
                    <ci>k_betaP2</ci>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>s_betaP2</ci>
                                <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <ci>E50_p2</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>p_2</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <ci>alpha_p2</ci>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>p_2</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>beta_p2</ci>
                        <ci>p_2</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--Define component ‘inward generic channel q1 gate’-->
    <component name="inward_generic_channel_q2_gate">
        <!--Define units and initial conditions for variables-->
        <variable name="V" public_interface="in" units="millivolt"/>
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="0.35" name="q_2" public_interface="out" units="dimensionless"/>
        <variable name="alpha_q2" units="per_sec"/>
        <variable name="beta_q2" units="per_sec"/>
        <variable initial_value="4.86" name="k_alphaQ2" units="per_sec"/>
        <variable initial_value="1.62" name="s_alphaQ2" units="per_millivolt"/>
        <variable initial_value="28.56" name="k_betaQ2" units="per_sec"/>
        <variable initial_value="-1.85" name="s_betaQ2" units="per_millivolt"/>
        <variable initial_value="-69.48" name="E50_q2" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>alpha_q2</ci>
                <apply>
                    <divide/>
                    <ci>k_alphaQ2</ci>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>s_alphaQ2</ci>
                                <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <ci>E50_q2</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>beta_q2</ci>
                <apply>
                    <divide/>
                    <ci>k_betaQ2</ci>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>s_betaQ2</ci>
                                <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <ci>E50_q2</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_2</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <ci>alpha_q2</ci>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>q_2</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>beta_q2</ci>
                        <ci>q_2</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="environment" component_2="inward_generic_channel"/>
        <map_variables variable_1="V" variable_2="V"/>
        <map_variables variable_1="t" variable_2="t"/>
    </connection>
    <connection>
        <map_components component_1="inward_generic_channel" component_2="inward_generic_channel_p2_gate"/>
        <map_variables variable_1="V" variable_2="V"/>
        <map_variables variable_1="t" variable_2="t"/>
        <map_variables variable_1="p_2" variable_2="p_2"/>
    </connection>
    <connection>
        <map_components component_1="inward_generic_channel" component_2="inward_generic_channel_q2_gate"/>
        <map_variables variable_1="V" variable_2="V"/>
        <map_variables variable_1="t" variable_2="t"/>
        <map_variables variable_1="q_2" variable_2="q_2"/>
    </connection>
</model>