Location: Bond graph model of actin-myosin sliding filaments @ 8056a8fef80b / models / XB mechanics.cellml
- Author:
- Weiwei Ai <wai484@aucklanduni.ac.nz>
- Date:
- 2024-06-23 19:11:09+12:00
- Desc:
- Add the XB diagram and models sent by Peter
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/b6f/rawfile/8056a8fef80b66124f575788438c39e20b6d7e31/models/XB mechanics.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- Energetics + HMT model of XB mechanics-->
<units name="mM">
<unit prefix="milli" units="mole"/>
</units>
<units name="um">
<unit prefix="micro" units="metre"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="um_per_s">
<unit units="um"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mM_per_s">
<unit units="mM"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_mM">
<unit exponent="-1" units="mM"/>
</units>
<units name="um_per_mM">
<unit units="um"/>
<unit exponent="-1" units="mM"/>
</units>
<units name="C_per_mM">
<unit units="coulomb"/>
<unit exponent="-1" units="mM"/>
</units>
<units name="J_per_mM">
<unit units="joule"/>
<unit exponent="-1" units="mM"/>
</units>
<units name="J_per_um">
<unit units="joule"/>
<unit exponent="-1" units="um"/>
</units>
<component name="main">
<variable initial_value="10" name="q_Ca" units="mM"/>
<variable initial_value="1" name="q_A" units="mM"/>
<variable initial_value="0" name="q_ACa" units="mM"/>
<variable initial_value="0" name="q_AA" units="mM"/>
<variable initial_value="1" name="q_AAMadpPi" units="mM"/>
<variable initial_value="0" name="q_AAMadp" units="mM"/>
<variable initial_value="0" name="q_AAM" units="mM"/>
<variable initial_value="0" name="q_Matp" units="mM"/>
<variable initial_value="0" name="q_MadpPi" units="mM"/>
<variable name="q_Actin" units="mM"/>
<variable name="q_Myosin" units="mM"/>
<variable name="q_Calcium" units="mM"/>
<variable initial_value="100" name="q_atp" units="mM"/>
<variable initial_value="0" name="q_adp" units="mM"/>
<variable initial_value="0" name="q_Pi" units="mM"/>
<variable initial_value="1" name="K_A" units="per_mM"/>
<variable initial_value="1" name="K_ACa" units="per_mM"/>
<variable initial_value="1" name="K_AA" units="per_mM"/>
<variable initial_value="10" name="K_Ca" units="per_mM"/>
<variable initial_value="1" name="K_AAMadpPi" units="per_mM"/>
<variable initial_value="1" name="K_Pi" units="per_mM"/>
<variable initial_value="1" name="K_AAMadp" units="per_mM"/>
<variable initial_value="1" name="K_adp" units="per_mM"/>
<variable initial_value="1" name="K_AAM" units="per_mM"/>
<variable initial_value="1" name="K_atp" units="per_mM"/>
<variable initial_value="1" name="K_Matp" units="per_mM"/>
<variable initial_value="1" name="K_MadpPi" units="per_mM"/>
<variable name="v_1" units="mM_per_s"/>
<variable name="v_2" units="mM_per_s"/>
<variable name="v_3" units="mM_per_s"/>
<variable name="v_4" units="mM_per_s"/>
<variable name="v_5" units="mM_per_s"/>
<variable name="v_6" units="mM_per_s"/>
<variable name="v_7" units="mM_per_s"/>
<variable name="v_8" units="mM_per_s"/>
<variable initial_value="1" name="kappa_1" units="mM_per_s"/>
<variable initial_value="1" name="kappa_2" units="mM_per_s"/>
<variable initial_value="1" name="kappa_3" units="mM_per_s"/>
<variable initial_value="10000" name="kappa_4" units="mM_per_s"/>
<variable initial_value="10000" name="kappa_5" units="mM_per_s"/>
<variable initial_value="10000" name="kappa_6" units="mM_per_s"/>
<variable initial_value="10" name="kappa_7" units="mM_per_s"/>
<variable initial_value="10000" name="kappa_8" units="mM_per_s"/>
<variable initial_value="1" name="k_Q_4" units="dimensionless"/>
<variable initial_value="1" name="k_Q_5" units="dimensionless"/>
<variable initial_value="1" name="k_Q_6" units="dimensionless"/>
<variable initial_value="1" name="k_Q_7" units="dimensionless"/>
<variable initial_value="1" name="k_Q_8" units="dimensionless"/>
<variable name="u_T" units="J_per_um"/>
<variable initial_value="1" name="u_To" units="J_per_um"/>
<variable name="v_T" units="um_per_s"/>
<variable name="u_Q" units="J_per_mM"/>
<variable initial_value="5" name="q_Q" units="mM"/>
<variable initial_value="1" name="K_Q" units="per_mM"/>
<variable name="v_Q" units="mM_per_s"/>
<variable initial_value="0.25" name="a" units="dimensionless"/>
<variable initial_value="1" name="V_max" units="um_per_s"/>
<variable initial_value="0" name="k_T_3" units="um_per_mM"/>
<variable initial_value="2.576" name="RT" units="J_per_mM"/>
<variable initial_value="0" name="t" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_T</ci>
<cn cellml:units="J_per_um">0.1</cn>
</apply>
<apply>
<eq/>
<ci>v_T</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>a</ci>
<ci>V_max</ci>
<apply>
<minus/>
<ci>u_To</ci>
<ci>u_T</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>u_T</ci>
<apply>
<times/>
<ci>a</ci>
<ci>u_To</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_Q</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Q</ci>
<ci>q_Q</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_Q</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>u_T</ci>
<ci>v_T</ci>
</apply>
<ci>u_Q</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_1</ci>
<apply>
<times/>
<ci>kappa_1</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_A</ci>
<ci>q_A</ci>
<ci>K_Ca</ci>
<ci>q_Ca</ci>
</apply>
<apply>
<times/>
<ci>K_ACa</ci>
<ci>q_ACa</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_2</ci>
<apply>
<times/>
<ci>kappa_2</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_ACa</ci>
<ci>q_ACa</ci>
</apply>
<apply>
<times/>
<ci>K_AA</ci>
<ci>q_AA</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_3</ci>
<apply>
<times/>
<ci>kappa_3</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_AA</ci>
<ci>q_AA</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_T_3</ci>
<ci>u_T</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>K_A</ci>
<ci>q_A</ci>
<ci>K_Ca</ci>
<ci>q_Ca</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_4</ci>
<apply>
<times/>
<ci>kappa_4</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_AA</ci>
<ci>q_AA</ci>
<ci>K_MadpPi</ci>
<ci>q_MadpPi</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_Q_4</ci>
<ci>u_Q</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>K_AAMadpPi</ci>
<ci>q_AAMadpPi</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_5</ci>
<apply>
<times/>
<ci>kappa_5</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_AAMadpPi</ci>
<ci>q_AAMadpPi</ci>
</apply>
<apply>
<times/>
<ci>K_AAMadp</ci>
<ci>q_AAMadp</ci>
<ci>K_Pi</ci>
<ci>q_Pi</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_Q_5</ci>
<ci>u_Q</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_6</ci>
<apply>
<times/>
<ci>kappa_6</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_AAMadp</ci>
<ci>q_AAMadp</ci>
</apply>
<apply>
<times/>
<ci>K_AAM</ci>
<ci>q_AAM</ci>
<ci>K_adp</ci>
<ci>q_adp</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_Q_6</ci>
<ci>u_Q</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_7</ci>
<apply>
<times/>
<ci>kappa_7</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_AAM</ci>
<ci>q_AAM</ci>
<ci>K_atp</ci>
<ci>q_atp</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_Q_7</ci>
<ci>u_Q</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>K_Matp</ci>
<ci>q_Matp</ci>
<ci>K_AA</ci>
<ci>q_AA</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_8</ci>
<apply>
<times/>
<ci>kappa_8</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_Matp</ci>
<ci>q_Matp</ci>
</apply>
<apply>
<times/>
<ci>K_MadpPi</ci>
<ci>q_MadpPi</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_Q_8</ci>
<ci>u_Q</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Ca</ci>
</apply>
<apply>
<minus/>
<ci>v_3</ci>
<ci>v_1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ACa</ci>
</apply>
<apply>
<minus/>
<ci>v_1</ci>
<ci>v_2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_AA</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_2</ci>
<ci>v_3</ci>
</apply>
<ci>v_4</ci>
</apply>
<ci>v_7</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_A</ci>
</apply>
<apply>
<minus/>
<ci>v_3</ci>
<ci>v_1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_AAMadpPi</ci>
</apply>
<apply>
<minus/>
<ci>v_4</ci>
<ci>v_5</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Pi</ci>
</apply>
<ci>v_5</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_AAMadp</ci>
</apply>
<apply>
<minus/>
<ci>v_5</ci>
<ci>v_6</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_adp</ci>
</apply>
<ci>v_6</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_AAM</ci>
</apply>
<apply>
<minus/>
<ci>v_6</ci>
<ci>v_7</ci>
</apply>
</apply>
<!-- ode(q_atp,t) = -v_7;-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Matp</ci>
</apply>
<apply>
<minus/>
<ci>v_7</ci>
<ci>v_8</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_MadpPi</ci>
</apply>
<apply>
<minus/>
<ci>v_8</ci>
<ci>v_4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Q</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k_Q_4</ci>
</apply>
<ci>v_4</ci>
</apply>
<apply>
<times/>
<ci>k_Q_5</ci>
<ci>v_5</ci>
</apply>
<apply>
<times/>
<ci>k_Q_6</ci>
<ci>v_6</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_Q_7</ci>
<ci>v_7</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_Q_8</ci>
<ci>v_8</ci>
</apply>
</apply>
<ci>v_Q</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Actin</ci>
<apply>
<plus/>
<ci>q_A</ci>
<ci>q_ACa</ci>
<ci>q_AA</ci>
<ci>q_AAMadpPi</ci>
<ci>q_AAMadp</ci>
<ci>q_AAM</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Myosin</ci>
<apply>
<plus/>
<ci>q_AAMadpPi</ci>
<ci>q_AAMadp</ci>
<ci>q_AAM</ci>
<ci>q_Matp</ci>
<ci>q_MadpPi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Calcium</ci>
<apply>
<plus/>
<ci>q_Ca</ci>
<ci>q_ACa</ci>
<ci>q_AA</ci>
<ci>q_AAMadpPi</ci>
<ci>q_AAMadp</ci>
<ci>q_AAM</ci>
</apply>
</apply>
</math>
</component>
</model>