- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-07-21 14:01:07+12:00
- Desc:
- Added image in ai and svg format
- Permanent Source URI:
- http://models.cellml.org/workspace/hatakeyama_kimura_naka_kawasaki_yumoto_ichikawa_kim_saito_saeki_shirouzu_yokoyama_konagaya_2003/rawfile/4719e515dbf17714e65ac8d2085a1a44e8f84862/hatakeyama_kimura_naka_kawasaki_yumoto_ichikawa_kim_saito_saeki_shirouzu_yokoyama_konagaya_2003.cellml
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This CellML file was generated on 20/06/2007 at 12:39:18 at a.m. using:
COR (0.9.31.649)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
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<title>A computational model on the modulation of mitogen-activated protein kinase (MAPK) and Akt pathways in heregulin-induced ErbB signalling</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
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<title>Model Status</title>
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This version of the model has been checked in COR and PCEnv and it runs to replicate the published results. The units have been checked and they are consistent.
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ErbB receptor tyrosine kinases play an essential role in the proliferation and differentiation of cells. The ErbB receptor family includes ErbB1 - also known as the epidermal growth factor receptor (EGFR) - and the signalling pathways which involve this receptor have been extensively analysed, both experimentally and also via mathematical modelling. ErbB receptors share a common ability to bind a diverse range of ligands, in turn producing a wide range of biological responses. In the study described here, Mariko Hatakeyama <emphasis>et al.</emphasis> examined heregulin (HRG)-induced signal transduction of the ErbB4 receptor, and they produced a mathematical model to capture the features of the signal transduction cascade (described in more detail in the figure below). This model is described here in CellML.
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<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biochemj.org/bj/373/bj3730451.htm">A computational model on the modulation of mitogen-activated protein kinase (MAPK) and Akt pathways in heregulin-induced ErbB signalling</ulink>, Mariko Hatakeyama, Shuhei Kimura, Takashi Naka, Takuji Kawasaki, Noriko Yumoto, Mio Ichikawa, Jae-Hoon Kim, Kazuki Saito, Mihoro Saeki, Mikako Shirouzu, Shigeyuki Yokoyama, and Akihiko Konagaya, 2003, <ulink url="http://www.biochemj.org/bj/">
<emphasis>The Biochemical Journal</emphasis>
</ulink>, 373, 451-463. (<ulink url="http://www.biochemj.org/bj/373/0451/bj3730451.htm">Full text</ulink> and <ulink url="http://www.biochemj.org/bj/373/0451/3730451.pdf">PDF</ulink> versions of the article are available to journal subscribers on <emphasis>The Biochemical Journal</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12691603&dopt=Abstract">PubMed ID: 12691603</ulink>
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<caption>A schematic diagram of the complete signalling network.</caption>
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<ci>RasGTP</ci>
</apply>
<apply>
<plus/>
<ci>k12</ci>
<ci>RasGTP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>RasGTP</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf11</ci>
<ci>ShGS</ci>
<ci>RasGDP</ci>
</apply>
<apply>
<plus/>
<ci>k11</ci>
<ci>RasGDP</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>V12</ci>
<ci>RasGTP</ci>
</apply>
<apply>
<plus/>
<ci>k12</ci>
<ci>RasGTP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="RAF">
<variable units="s" public_interface="in" name="time"/>
<variable units="nm" public_interface="in" name="RasGTP"/>
<variable units="nm" public_interface="in" name="Akt_PIPP"/>
<variable units="nm" public_interface="out" name="RAF_star" initial_value="100"/>
<variable units="first_order_rate_constant" name="kf13" initial_value="1.53"/>
<variable units="nm" name="k13" initial_value="11.7"/>
<variable units="first_order_rate_constant" name="kf14" initial_value="0.00673"/>
<variable units="nm" name="k14" initial_value="8.07"/>
<variable units="nm" name="E" initial_value="7"/>
<variable units="nm" name="RAF" initial_value="0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>RAF</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf14</ci>
<apply>
<plus/>
<ci>Akt_PIPP</ci>
<ci>E</ci>
</apply>
<ci>RAF_star</ci>
</apply>
<apply>
<plus/>
<ci>k14</ci>
<ci>RAF_star</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf13</ci>
<ci>RasGTP</ci>
<ci>RAF</ci>
</apply>
<apply>
<plus/>
<ci>k13</ci>
<ci>RAF</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>RAF_star</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf14</ci>
<apply>
<plus/>
<ci>Akt_PIPP</ci>
<ci>E</ci>
</apply>
<ci>RAF_star</ci>
</apply>
<apply>
<plus/>
<ci>k14</ci>
<ci>RAF_star</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf13</ci>
<ci>RasGTP</ci>
<ci>RAF</ci>
</apply>
<apply>
<plus/>
<ci>k13</ci>
<ci>RAF</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Akt">
<variable units="s" public_interface="in" name="time"/>
<variable units="nm" public_interface="in" name="PI3Kstar"/>
<variable units="nm" public_interface="out" name="Akt_PIPP" initial_value="0.0"/>
<variable units="nm" public_interface="in" name="MEKP"/>
<variable units="nm" public_interface="in" name="MEKPP"/>
<variable units="first_order_rate_constant" name="kf27" initial_value="16.9"/>
<variable units="nm" name="k27" initial_value="39.1"/>
<variable units="flux" name="V28" initial_value="17000"/>
<variable units="nm" name="k28" initial_value="9.02"/>
<variable units="second_order_rate_constant" name="kf29" initial_value="507"/>
<variable units="first_order_rate_constant" name="kb29" initial_value="234"/>
<variable units="flux" name="V30" initial_value="20000"/>
<variable units="nm" name="k30" initial_value="80000"/>
<variable units="first_order_rate_constant" name="kf31" initial_value="0.107"/>
<variable units="nm" name="k31" initial_value="4.35"/>
<variable units="flux" name="V32" initial_value="20000"/>
<variable units="nm" name="k32" initial_value="80000"/>
<variable units="first_order_rate_constant" name="kf33" initial_value="0.211"/>
<variable units="nm" name="k33" initial_value="12"/>
<variable units="nm" name="k16" initial_value="2200"/>
<variable units="nm" name="k18" initial_value="60"/>
<variable units="nm" name="P" initial_value="800"/>
<variable units="nm" name="PIP3" initial_value="0"/>
<variable units="nm" name="Akt" initial_value="10"/>
<variable units="nm" name="Akt_PIP3" initial_value="0"/>
<variable units="nm" public_interface="out" name="Akt_PIP" initial_value="0"/>
<variable units="nm" name="PP2A" initial_value="11.4"/>
<variable units="dimensionless" name="one" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>V28</ci>
<ci>PIP3</ci>
</apply>
<apply>
<plus/>
<ci>k28</ci>
<ci>PIP3</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf27</ci>
<ci>PI3Kstar</ci>
<ci>P</ci>
</apply>
<apply>
<plus/>
<ci>k27</ci>
<ci>P</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PIP3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>V28</ci>
<ci>PIP3</ci>
</apply>
<apply>
<plus/>
<ci>k28</ci>
<ci>PIP3</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf27</ci>
<ci>PI3Kstar</ci>
<ci>P</ci>
</apply>
<apply>
<plus/>
<ci>k27</ci>
<ci>P</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kf29</ci>
<ci>PIP3</ci>
<ci>Akt</ci>
</apply>
<apply>
<times/>
<ci>kb29</ci>
<ci>Akt_PIP3</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Akt</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kf29</ci>
<ci>PIP3</ci>
<ci>Akt</ci>
</apply>
<apply>
<times/>
<ci>kb29</ci>
<ci>Akt_PIP3</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Akt_PIP3</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kf29</ci>
<ci>PIP3</ci>
<ci>Akt</ci>
</apply>
<apply>
<times/>
<ci>kb29</ci>
<ci>Akt_PIP3</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>V30</ci>
<ci>Akt_PIP3</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k30</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k32</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIP3</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf31</ci>
<ci>PP2A</ci>
<ci>Akt_PIP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k31</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k16</ci>
</apply>
<apply>
<divide/>
<ci>MEKPP</ci>
<ci>k18</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIPP</ci>
<ci>k33</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Akt_PIP</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>V30</ci>
<ci>Akt_PIP3</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k30</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k32</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIP3</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf31</ci>
<ci>PP2A</ci>
<ci>Akt_PIP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k31</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k16</ci>
</apply>
<apply>
<divide/>
<ci>MEKPP</ci>
<ci>k18</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIPP</ci>
<ci>k33</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIP</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>V32</ci>
<ci>Akt_PIP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k32</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>Akt_PIP3</ci>
<ci>k30</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIP</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf33</ci>
<ci>PP2A</ci>
<ci>Akt_PIPP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k33</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k16</ci>
</apply>
<apply>
<divide/>
<ci>MEKPP</ci>
<ci>k18</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k31</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIPP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Akt_PIPP</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>V32</ci>
<ci>Akt_PIP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k32</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>Akt_PIP3</ci>
<ci>k30</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIP</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf33</ci>
<ci>PP2A</ci>
<ci>Akt_PIPP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k33</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k16</ci>
</apply>
<apply>
<divide/>
<ci>MEKPP</ci>
<ci>k18</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k31</ci>
</apply>
</apply>
</apply>
<ci>Akt_PIPP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MEK">
<variable units="s" public_interface="in" name="time"/>
<variable units="nm" public_interface="in" name="RAF_star"/>
<variable units="nm" public_interface="out" name="MEKPP" initial_value="0"/>
<variable units="nm" name="PP2A" initial_value="11.4"/>
<variable units="nm" public_interface="out" name="MEKP" initial_value="0"/>
<variable units="nm" name="MEK" initial_value="120"/>
<variable units="nm" public_interface="in" name="Akt_PIP"/>
<variable units="nm" public_interface="in" name="Akt_PIPP"/>
<variable units="first_order_rate_constant" name="kf15" initial_value="3.5"/>
<variable units="nm" name="k15" initial_value="317"/>
<variable units="first_order_rate_constant" name="kf16" initial_value="0.058"/>
<variable units="nm" name="k16" initial_value="2200"/>
<variable units="first_order_rate_constant" name="kf17" initial_value="2.9"/>
<variable units="nm" name="k17" initial_value="317"/>
<variable units="first_order_rate_constant" name="kf18" initial_value="0.058"/>
<variable units="nm" name="k18" initial_value="60"/>
<variable units="nm" name="k31" initial_value="4.35"/>
<variable units="nm" name="k33" initial_value="12"/>
<variable units="dimensionless" name="one" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>MEK</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf15</ci>
<ci>RAF_star</ci>
<ci>MEK</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k15</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k17</ci>
</apply>
</apply>
</apply>
<ci>MEK</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf16</ci>
<ci>PP2A</ci>
<ci>MEKP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k16</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKPP</ci>
<ci>k18</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k31</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIPP</ci>
<ci>k33</ci>
</apply>
</apply>
</apply>
<ci>MEKP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>MEKP</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf15</ci>
<ci>RAF_star</ci>
<ci>MEK</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k15</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k17</ci>
</apply>
</apply>
</apply>
<ci>MEK</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf16</ci>
<ci>PP2A</ci>
<ci>MEKP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k16</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKPP</ci>
<ci>k18</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k31</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIPP</ci>
<ci>k33</ci>
</apply>
</apply>
</apply>
<ci>MEKP</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf17</ci>
<ci>RAF_star</ci>
<ci>MEKP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k17</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEK</ci>
<ci>k15</ci>
</apply>
</apply>
</apply>
<ci>MEKP</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf18</ci>
<ci>PP2A</ci>
<ci>MEKPP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k18</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k16</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k31</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIPP</ci>
<ci>k33</ci>
</apply>
</apply>
</apply>
<ci>MEKPP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>MEKPP</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf17</ci>
<ci>RAF_star</ci>
<ci>MEKP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k17</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEK</ci>
<ci>k15</ci>
</apply>
</apply>
</apply>
<ci>MEKP</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf18</ci>
<ci>PP2A</ci>
<ci>MEKPP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k18</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>MEKP</ci>
<ci>k16</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIP</ci>
<ci>k31</ci>
</apply>
<apply>
<divide/>
<ci>Akt_PIPP</ci>
<ci>k33</ci>
</apply>
</apply>
</apply>
<ci>MEKPP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ERK">
<variable units="s" public_interface="in" name="time"/>
<variable units="nm" public_interface="in" name="MEKPP"/>
<variable units="nm" name="MKP3" initial_value="2.4"/>
<variable units="nm" name="ERK" initial_value="1000"/>
<variable units="nm" name="ERKP" initial_value="0"/>
<variable units="nm" name="ERKPP" initial_value="0"/>
<variable units="first_order_rate_constant" name="kf19" initial_value="9.5"/>
<variable units="nm" name="k19" initial_value="146000"/>
<variable units="first_order_rate_constant" name="kf20" initial_value="0.3"/>
<variable units="nm" name="k20" initial_value="160"/>
<variable units="first_order_rate_constant" name="kf21" initial_value="16"/>
<variable units="nm" name="k21" initial_value="146000"/>
<variable units="first_order_rate_constant" name="kf22" initial_value="0.27"/>
<variable units="nm" name="k22" initial_value="60"/>
<variable units="dimensionless" name="one" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ERK</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf19</ci>
<ci>MEKPP</ci>
<ci>ERK</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k19</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>ERKP</ci>
<ci>k21</ci>
</apply>
</apply>
</apply>
<ci>ERK</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kf20</ci>
<ci>MKP3</ci>
<ci>ERKP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k20</ci>
<apply>
<plus/>
<ci>one</ci>
<apply>
<divide/>
<ci>ERKPP</ci>
<ci>k22</ci>
</apply>
</apply>
</apply>
<ci>ERKP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ERKPP</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>kf21</ci>
<ci>MEKPP</ci>
<ci>ERKP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k21</ci>
<apply>
<plus/>
<ci>one</ci>
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