Location: A Simple Voltage-Modulated Markov Chain Model for the Piezo1 Ion Channel to Investigate Electromechanical Pacing @ 8465ce0a385c / models / channels / ks_channel.cellml

Author:

termi-official <termi-official@users.noreply.github.com>

Date:

2025-05-15 16:01:20+02:00

Desc:

Add documentation for submission

Permanent Source URI:

https://staging.physiomeproject.org/workspace/d20/rawfile/8465ce0a385cdc40e2f79b001798d600e9f9e4d2/models/channels/ks_channel.cellml

<?xml version='1.0' encoding='UTF-8'?>
<!-- TODO read mahajan paper and find out which one this is.-->
<model name="ks_channel" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
    <import xlink:href="../../units.cellml">
        <units name="ms" units_ref="ms"/>
        <units name="per_ms" units_ref="per_ms"/>
        <units name="mV" units_ref="mV"/>
        <units name="per_mV" units_ref="per_mV"/>
        <units name="uS_per_nF" units_ref="uS_per_nF"/>
        <units name="nA_per_nF" units_ref="nA_per_nF"/>
    </import>
    <component name="IKs">
        <variable name="V" public_interface="in" units="mV"/>
        <variable name="Ca_i" public_interface="in" units="uM"/>
        <variable name="time" public_interface="in" units="ms"/>
        <variable initial_value="0.1386" name="gks" units="uS_per_nF"/>
        <variable initial_value="0.048267587131" name="xs1" units="dimensionless"/>
        <variable initial_value="0.105468807033" name="xs2" units="dimensionless"/>
        <variable name="eks" public_interface="in" units="mV"/>
        <variable name="xs1ss" units="dimensionless"/>
        <variable name="xs2ss" units="dimensionless"/>
        <variable name="tauxs1" units="ms"/>
        <variable name="tauxs2" units="ms"/>
        <variable name="gksx" units="dimensionless"/>
        <variable name="xiks" public_interface="out" units="nA_per_nF"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>xs1ss</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">1</cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <minus/>
                                        <ci>V</ci>
                                        <cn cellml:units="mV">1.5</cn>
                                    </apply>
                                </apply>
                                <cn cellml:units="mV">16.7</cn>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>xs2ss</ci>
                <ci>xs1ss</ci>
            </apply>
            <apply>
                <eq/>
                <ci>tauxs1</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <divide/>
                            <cn cellml:units="ms">1</cn>
                            <apply>
                                <plus/>
                                <apply>
                                    <divide/>
                                    <cn cellml:units="dimensionless">0.0000719</cn>
                                    <cn cellml:units="dimensionless">0.148</cn>
                                </apply>
                                <apply>
                                    <divide/>
                                    <cn cellml:units="dimensionless">0.000131</cn>
                                    <cn cellml:units="dimensionless">0.0687</cn>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <lt/>
                            <apply>
                                <abs/>
                                <apply>
                                    <plus/>
                                    <ci>V</ci>
                                    <cn cellml:units="mV">30</cn>
                                </apply>
                            </apply>
                            <apply>
                                <divide/>
                                <cn cellml:units="mV">0.001</cn>
                                <cn cellml:units="dimensionless">0.0687</cn>
                            </apply>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <divide/>
                            <cn cellml:units="ms">1</cn>
                            <apply>
                                <plus/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <cn cellml:units="per_mV">0.0000719</cn>
                                        <apply>
                                            <plus/>
                                            <ci>V</ci>
                                            <cn cellml:units="mV">30</cn>
                                        </apply>
                                    </apply>
                                    <apply>
                                        <minus/>
                                        <cn cellml:units="dimensionless">1</cn>
                                        <apply>
                                            <exp/>
                                            <apply>
                                                <times/>
                                                <apply>
                                                    <minus/>
                                                    <cn cellml:units="per_mV">0.148</cn>
                                                </apply>
                                                <apply>
                                                    <plus/>
                                                    <ci>V</ci>
                                                    <cn cellml:units="mV">30</cn>
                                                </apply>
                                            </apply>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <cn cellml:units="per_mV">0.000131</cn>
                                        <apply>
                                            <plus/>
                                            <ci>V</ci>
                                            <cn cellml:units="mV">30</cn>
                                        </apply>
                                    </apply>
                                    <apply>
                                        <minus/>
                                        <apply>
                                            <exp/>
                                            <apply>
                                                <times/>
                                                <cn cellml:units="per_mV">0.0687</cn>
                                                <apply>
                                                    <plus/>
                                                    <ci>V</ci>
                                                    <cn cellml:units="mV">30</cn>
                                                </apply>
                                            </apply>
                                        </apply>
                                        <cn cellml:units="dimensionless">1</cn>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>tauxs2</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">4</cn>
                    <ci>tauxs1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>gksx</ci>
                <apply>
                    <plus/>
                    <cn cellml:units="dimensionless">1</cn>
                    <apply>
                        <divide/>
                        <cn cellml:units="dimensionless">0.8</cn>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <power/>
                                <apply>
                                    <divide/>
                                    <cn cellml:units="uM">0.5</cn>
                                    <ci>Ca_i</ci>
                                </apply>
                                <cn cellml:units="dimensionless">3</cn>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>xiks</ci>
                <apply>
                    <times/>
                    <ci>gks</ci>
                    <ci>gksx</ci>
                    <ci>xs1</ci>
                    <ci>xs2</ci>
                    <apply>
                        <minus/>
                        <ci>V</ci>
                        <ci>eks</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>xs1</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>xs1ss</ci>
                        <ci>xs1</ci>
                    </apply>
                    <ci>tauxs1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>xs2</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>xs2ss</ci>
                        <ci>xs2</ci>
                    </apply>
                    <ci>tauxs2</ci>
                </apply>
            </apply>
        </math>
    </component>
</model>