Location: Bond graph model of GPCRs @ 168f58a2f350 / GPCRs / GPCRv4.cellml
- Author:
- Weiwei Ai <wai484@aucklanduni.ac.nz>
- Date:
- 2024-07-30 09:36:53+12:00
- Desc:
- Add the doc and models from Prof. Peter Hunter
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/b89/rawfile/168f58a2f350359810f85177a43a7b86cd4c7309/GPCRs/GPCRv4.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#">
<!-- Model of GPCR-->
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="s">
<unit units="second"/>
</units>
<units name="mmol">
<unit prefix="milli" units="mole"/>
</units>
<units name="fmol">
<unit prefix="femto" units="mole"/>
</units>
<units name="per_fmol">
<unit exponent="-1" units="fmol"/>
</units>
<units name="fmol_per_s">
<unit units="fmol"/>
<unit exponent="-1" units="s"/>
</units>
<units name="J_per_mmol">
<unit units="joule"/>
<unit exponent="-1" units="mmol"/>
</units>
<component name="main">
<variable name="t" units="s"/>
<variable initial_value="2.5761" name="RT" units="J_per_mmol"/>
<!--
Input flux
-->
<variable initial_value="3" name="T1" units="s"/>
<variable initial_value="5" name="T2" units="s"/>
<!-- -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_L_input</ci>
<piecewise>
<piece>
<cn cellml:units="fmol_per_s">10</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>t</ci>
<ci>T1</ci>
</apply>
<apply>
<lt/>
<ci>t</ci>
<ci>T2</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="fmol_per_s">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!--
State variable molar quantities
-->
<variable initial_value="5.09188920026956" name="q_L" units="fmol"/>
<variable initial_value="4.18367004218109" name="q_R_G" units="fmol"/>
<variable initial_value="21.3028137054491" name="q_R_GL" units="fmol"/>
<variable initial_value="3.47404955471616" name="q_R_LBG" units="fmol"/>
<variable initial_value="25.5067002874004" name="q_R_GLP" units="fmol"/>
<variable initial_value="4.62454245115" name="q_R_L" units="fmol"/>
<variable initial_value="0.908223959103197" name="q_R" units="fmol"/>
<variable initial_value="4.97250314034647" name="q_Ga_GDP" units="fmol"/>
<variable initial_value="5.95387031010023" name="q_Ga_GTP" units="fmol"/>
<variable initial_value="0.926373450446675" name="q_G_bg" units="fmol"/>
<variable initial_value="6.13197134518977" name="q_GDP" units="fmol"/>
<variable initial_value="7.34207820952638" name="q_GTP" units="fmol"/>
<variable initial_value="4.60639295980652" name="q_Ga_GDP_bg" units="fmol"/>
<variable initial_value="1.19735119297301" name="q_P" units="fmol"/>
<variable initial_value="1" name="q_R_BG" units="fmol"/>
<variable initial_value="1" name="q_R_GP" units="fmol"/>
<!-- -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_L</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_5</ci>
<ci>v_1</ci>
</apply>
<ci>v_L_input</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_R_G</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_6</ci>
<ci>v_1</ci>
</apply>
<ci>v_10</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_R_GL</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_R_LBG</ci>
</apply>
<apply>
<minus/>
<ci>v_2</ci>
<ci>v_3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_R_GLP</ci>
</apply>
<apply>
<minus/>
<ci>v_3</ci>
<ci>v_4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_R_L</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_R</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_5</ci>
<ci>v_12</ci>
</apply>
<ci>v_6</ci>
</apply>
<ci>v_R_io</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Ga_GDP</ci>
</apply>
<apply>
<minus/>
<ci>v_8</ci>
<ci>v_7</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Ga_GTP</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_4</ci>
<ci>v_12</ci>
</apply>
<ci>v_8</ci>
</apply>
<ci>v_Ga_GTP_output</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_G_bg</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_4</ci>
<ci>v_12</ci>
</apply>
<ci>v_7</ci>
</apply>
<ci>v_G_bg_output</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_GDP</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_2</ci>
<ci>v_10</ci>
</apply>
<ci>v_9</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_GTP</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_9</ci>
<ci>v_3</ci>
</apply>
<ci>v_11</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Ga_GDP_bg</ci>
</apply>
<apply>
<minus/>
<ci>v_7</ci>
<ci>v_6</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_P</ci>
</apply>
<apply>
<minus/>
<ci>v_8</ci>
<ci>v_9</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_R_BG</ci>
</apply>
<apply>
<minus/>
<ci>v_10</ci>
<ci>v_11</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_R_GP</ci>
</apply>
<apply>
<minus/>
<ci>v_11</ci>
<ci>v_12</ci>
</apply>
</apply>
</math>
<!--
Chemical potentials for state variables
-->
<variable name="u_L" units="J_per_mmol"/>
<variable name="u_R_G" units="J_per_mmol"/>
<variable name="u_R_GL" units="J_per_mmol"/>
<variable name="u_R_LBG" units="J_per_mmol"/>
<variable name="u_R_GLP" units="J_per_mmol"/>
<variable name="u_R_L" units="J_per_mmol"/>
<variable name="u_R" units="J_per_mmol"/>
<variable name="u_Ga_GDP" units="J_per_mmol"/>
<variable name="u_Ga_GTP" units="J_per_mmol"/>
<variable name="u_G_bg" units="J_per_mmol"/>
<variable name="u_GDP" units="J_per_mmol"/>
<variable name="u_GTP" units="J_per_mmol"/>
<variable name="u_Ga_GDP_bg" units="J_per_mmol"/>
<variable name="u_P" units="J_per_mmol"/>
<variable name="u_R_BG" units="J_per_mmol"/>
<variable name="u_R_GP" units="J_per_mmol"/>
<!-- -->
<variable initial_value="1" name="k_L" units="per_fmol"/>
<variable initial_value="1" name="k_R_G" units="per_fmol"/>
<variable initial_value="1" name="k_R_GL" units="per_fmol"/>
<variable initial_value="1" name="k_R_LBG" units="per_fmol"/>
<variable initial_value="1" name="k_R_GLP" units="per_fmol"/>
<variable initial_value="1" name="k_R_L" units="per_fmol"/>
<variable initial_value="1" name="k_R" units="per_fmol"/>
<variable initial_value="1" name="k_Ga_GDP" units="per_fmol"/>
<variable initial_value="1" name="k_Ga_GTP" units="per_fmol"/>
<variable initial_value="1" name="k_G_bg" units="per_fmol"/>
<variable initial_value="1" name="k_GDP" units="per_fmol"/>
<variable initial_value="1" name="k_GTP" units="per_fmol"/>
<variable initial_value="1" name="k_Ga_GDP_bg" units="per_fmol"/>
<variable initial_value="1" name="k_P" units="per_fmol"/>
<variable initial_value="1" name="k_R_BG" units="per_fmol"/>
<variable initial_value="1" name="k_R_GP" units="per_fmol"/>
<!-- -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_L</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_L</ci>
<ci>q_L</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_G</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R_G</ci>
<ci>q_R_G</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_GL</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R_GL</ci>
<ci>q_R_GL</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_LBG</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R_LBG</ci>
<ci>q_R_LBG</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_GLP</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R_GLP</ci>
<ci>q_R_GLP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_L</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R_L</ci>
<ci>q_R_L</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R</ci>
<ci>q_R</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_Ga_GDP</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_Ga_GDP</ci>
<ci>q_Ga_GDP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_Ga_GTP</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_Ga_GTP</ci>
<ci>q_Ga_GTP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_G_bg</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_G_bg</ci>
<ci>q_G_bg</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_GDP</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_GDP</ci>
<ci>q_GDP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_GTP</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_GTP</ci>
<ci>q_GTP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_Ga_GDP_bg</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_Ga_GDP_bg</ci>
<ci>q_Ga_GDP_bg</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_P</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_P</ci>
<ci>q_P</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_BG</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R_BG</ci>
<ci>q_R_BG</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_GP</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>k_R_GP</ci>
<ci>q_R_GP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!--
Chemical potentials for reaction variables
-->
<variable name="u_1a" units="J_per_mmol"/>
<variable name="u_2b" units="J_per_mmol"/>
<variable name="u_3a" units="J_per_mmol"/>
<variable name="u_4b" units="J_per_mmol"/>
<variable name="u_5b" units="J_per_mmol"/>
<variable name="u_6a" units="J_per_mmol"/>
<variable name="u_7a" units="J_per_mmol"/>
<variable name="u_8b" units="J_per_mmol"/>
<variable name="u_9a" units="J_per_mmol"/>
<variable name="u_10b" units="J_per_mmol"/>
<variable name="u_11a" units="J_per_mmol"/>
<variable name="u_12b" units="J_per_mmol"/>
<!-- -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_1a</ci>
<apply>
<plus/>
<ci>u_R_G</ci>
<ci>u_L</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_2b</ci>
<apply>
<plus/>
<ci>u_R_LBG</ci>
<ci>u_GDP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_3a</ci>
<apply>
<plus/>
<ci>u_R_LBG</ci>
<ci>u_GTP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_4b</ci>
<apply>
<plus/>
<ci>u_R_L</ci>
<ci>u_Ga_GTP</ci>
<ci>u_G_bg</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_5b</ci>
<apply>
<plus/>
<ci>u_R</ci>
<ci>u_L</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_6a</ci>
<apply>
<plus/>
<ci>u_R</ci>
<ci>u_Ga_GDP_bg</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_7a</ci>
<apply>
<plus/>
<ci>u_Ga_GDP</ci>
<ci>u_G_bg</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_8b</ci>
<apply>
<plus/>
<ci>u_Ga_GDP</ci>
<ci>u_P</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_9a</ci>
<apply>
<plus/>
<ci>u_GDP</ci>
<ci>u_P</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_10b</ci>
<apply>
<plus/>
<ci>u_GDP</ci>
<ci>u_R_BG</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_11a</ci>
<apply>
<plus/>
<ci>u_R_BG</ci>
<ci>u_GTP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_12b</ci>
<apply>
<plus/>
<ci>u_R</ci>
<ci>u_Ga_GTP</ci>
<ci>u_G_bg</ci>
</apply>
</apply>
</math>
<!--
Flows
-->
<variable name="v_1" units="fmol_per_s"/>
<variable name="v_2" units="fmol_per_s"/>
<variable name="v_3" units="fmol_per_s"/>
<variable name="v_4" units="fmol_per_s"/>
<variable name="v_5" units="fmol_per_s"/>
<variable name="v_6" units="fmol_per_s"/>
<variable name="v_7" units="fmol_per_s"/>
<variable name="v_8" units="fmol_per_s"/>
<variable name="v_9" units="fmol_per_s"/>
<variable name="v_10" units="fmol_per_s"/>
<variable name="v_11" units="fmol_per_s"/>
<variable name="v_12" units="fmol_per_s"/>
<variable name="v_L_input" units="fmol_per_s"/>
<variable initial_value="0" name="v_R_io" units="fmol_per_s"/>
<variable initial_value="0" name="v_Ga_GTP_output" units="fmol_per_s"/>
<variable initial_value="0" name="v_G_bg_output" units="fmol_per_s"/>
<!-- -->
<variable initial_value="1" name="kappa_1" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_2" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_3" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_4" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_5" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_6" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_7" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_8" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_9" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_10" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_11" units="fmol_per_s"/>
<variable initial_value="1" name="kappa_12" units="fmol_per_s"/>
<!-- -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_1</ci>
<apply>
<times/>
<ci>kappa_1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_1a</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_GL</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_2</ci>
<apply>
<times/>
<ci>kappa_2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_GL</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_2b</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_3</ci>
<apply>
<times/>
<ci>kappa_3</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_3a</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_GLP</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_4</ci>
<apply>
<times/>
<ci>kappa_4</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_GLP</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_4b</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_5</ci>
<apply>
<times/>
<ci>kappa_5</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_L</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_5b</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_6</ci>
<apply>
<times/>
<ci>kappa_6</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_6a</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_G</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_7</ci>
<apply>
<times/>
<ci>kappa_7</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_7a</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_Ga_GDP_bg</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_8</ci>
<apply>
<times/>
<ci>kappa_8</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_Ga_GTP</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_8b</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_9</ci>
<apply>
<times/>
<ci>kappa_9</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_9a</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_GTP</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_10</ci>
<apply>
<times/>
<ci>kappa_10</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_G</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_10b</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_11</ci>
<apply>
<times/>
<ci>kappa_11</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_11a</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_GP</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_12</ci>
<apply>
<times/>
<ci>kappa_12</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_R_GP</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_12b</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>