/Users/max_neal/Dropbox/Semantic Project/Annotated CellML models/asthagiri_lauffenburger_2001/asthagiri_lauffenburger_2001.cellml 0.2 <documentation xmlns="http://cellml.org/tmp-documentation"> <article> <articleinfo> <title>Feedback Effects On Signal Dynamics In A Mitogen-Activated Protein Kinase (MAPK) Cascade</title> <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Bioengineering Institute, University of Auckland</shortaffil> </affiliation> </author> </articleinfo> <section id="sec_status"> <title>Model Status</title> <para>This model has been recoded in CellML without the use of the reaction element. The parameters and differential equations described in the original publication were used. This CellML model is known to read in both COR and PCEnv although currently it is unable to recreate the published results from the original model.</para> <para>ValidateCellML detects widespread unit inconsistency within this model.</para> </section> <sect1 id="sec_structure"> <title>Model Structure</title> <para>In 2001, Anand Asthagiri and Douglas Lauffenburger published a mathematical model which examined the mechanisms that govern MAPK pathway dynamics (see the figure below). Their model builds upon the MAPK cascade model of Chi-Ying Huang and James Ferrell (1996). This earlier model focused on the steady-state effects of signaling, whereas more recently, it has been discovered that a signal's information content partly resides in its dynamics.</para> <para>In their model, Anand Asthagiri and Douglas Lauffenburger concentrate on the role of negative feedback mechanisms in the generation of signal adaptation - a term referring to the reset of a signal to prestimulation levels. They assess how different modes of feedback affect the properties of MAPK signalling dynamics.</para> <para>The complete original paper reference is cited below:</para> <para> <ulink url="http://pubs.acs.org/cgi-bin/abstract.cgi/bipret/2001/17/i02/abs/bp010009k.html">A Computational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model</ulink> , Anand R. Asthagiri and Douglas A. Lauffenburger, 2001, <ulink url="http://pubs.acs.org/journals/bipret/index.html"> <emphasis>Biotechnol. Prog</emphasis> </ulink> , 17, 227-239. ( <ulink url="http://pubs.acs.org/cgi-bin/article.cgi/bipret/2001/17/i02/html/bp010009k.html">Full text</ulink> and PDF versions are available to subscribers on the ACS Publications website. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11312698&amp;dopt=Abstract">PubMed ID: 11312698</ulink> </para> <informalfigure float="0" id="fig_pathway_diagram"> <mediaobject> <imageobject> <objectinfo> <title>the conventional rendering of the MAPK cascade with feedback effects</title> </objectinfo> <imagedata fileref="asthagiri_2001.png" /> </imageobject> </mediaobject> <caption>A rendering of the MAPK cascade with feedback effects. Species are represented by rounded rectangles, and reactions by arrows. The action of a catalyst on a reaction is represented by dashed lines.</caption> </informalfigure> <para>In CellML, models are thought of as connected networks of discrete components. These components may correspond to physiologically separated regions or chemically distinct objects, or may be useful modelling abstractions. This model has 71 components representing chemically distinct objects (41 chemical species and 30 reactions) and one component defined for modelling convenience which stores the universal variable time. Because this model has so many components, its CellML rendering would be complex. For an example of a CellML rendering of a reaction pathway see The Bhalla Iyengar EGF Pathway Model, 1999.</para> </sect1> </article> </documentation> <rdf:RDF xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:j.0="http://imc.org/vCard/3.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/"> <rdf:Description rdf:about="http://www.cellml.org/p5"> <dc:title>p5</dc:title> <dcterms:alternative>deactivating enzyme 5</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e5"> <dc:title>e5</dc:title> <dcterms:alternative>inactive signalling enzyme 5</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e1_e0_star"> <dc:title>e1_e0_star</dc:title> <dcterms:alternative>transition complex between an inactive substate and its activator (1)</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0"> <cmeta:modification> <rdf:Description rdf:about="rdf:#409f387f-9cd8-494c-88c3-0de609f3bf1f"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#e8e4d40e-7077-452b-9861-a17c1d895a6b"> <vCard:N> <rdf:Description rdf:about="rdf:#dfb7b2f6-a488-4b16-a1f7-c7720d678405"> <vCard:Other>Richard</vCard:Other> <vCard:Family>Lawson</vCard:Family> <vCard:Given>James</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Updated curation status</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#d398f452-6bcf-4dc5-923c-f57ede0a101d"> <dcterms:W3CDTF>2009-04-30T16:16:27+12:00</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#4c70a99e-bdc6-401d-ae4e-aca9b19bd1e6"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#569114dc-d6f2-4dd7-8e62-27e466c5085d"> <vCard:N> <rdf:Description rdf:about="rdf:#ddfadf74-23f9-431a-b0ec-05574021c9f3"> <vCard:Other>May</vCard:Other> <vCard:Family>Lloyd</vCard:Family> <vCard:Given>Catherine</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Altered connections after chacking the model with the validator.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#1f7657b2-5b51-446b-b717-51d244578419"> <dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:comment> <rdf:Description rdf:about="rdf:#79e36828-c7a4-42e7-8578-b4bf6ec7f463"> <rdf:value>This model has been recoded in CellML without the use of the reaction element. The parameters and differential equations described in the original publication were used. This CellML model is known to read in both COR and PCEnv although currently it is unable to recreate the published results from the original model.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#3ab0996c-5e45-4a86-9d51-70b588781e02"> <vCard:FN>Catherine Lloyd</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <cmeta:modification> <rdf:Description rdf:about="rdf:#7adc44a2-7647-49dc-a911-8dc51298114e"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#c3fb9a68-a752-4381-bf47-85a4c4c76556"> <vCard:N> <rdf:Description rdf:about="rdf:#12c302ca-93d4-4750-829c-270cebc71f30"> <vCard:Other>May</vCard:Other> <vCard:Family>Lloyd</vCard:Family> <vCard:Given>Catherine</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Added more metadata.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#cf517459-10b4-46bd-b2c0-684177f00d7b"> <dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#3309c051-39e0-4e52-b794-37b3b004785e"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#8d98a1d3-8e8a-4cc6-83c9-5420ec4e5249"> <vCard:N> <rdf:Description rdf:about="rdf:#278fffe8-6d65-44af-8cc0-d1531a03f9df"> <vCard:Other>J</vCard:Other> <vCard:Family>Villiger</vCard:Family> <vCard:Given>Peter</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Changed unit dimensions E1_ to make them consistent.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#848ff2c4-2759-4879-a9f5-76551b7979c9"> <dcterms:W3CDTF>2005-04-26</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#61772937-6fa0-487e-b63a-b84fc405fc90"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#3beddaa9-b945-4b6f-9ad3-76dd66e7e6a2"> <vCard:N> <rdf:Description 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<rdf:Description rdf:about="rdf:#a291236e-3a6d-4303-a815-5a8b6f6ceb66"> <vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit> <vCard:Orgname>The University of Auckland</vCard:Orgname> </rdf:Description> </vCard:ORG> </rdf:Description> </dc:creator> <cmeta:modification> <rdf:Description rdf:about="rdf:#6d05c7d8-009e-4bca-9e3d-dfa4bcd3f293"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#4e052047-d825-4434-8d2c-54208d7bf566"> <vCard:N> <rdf:Description rdf:about="rdf:#cd12c312-b0c5-481b-8aa9-c8503cd17711"> <vCard:Other>A.</vCard:Other> <vCard:Family>Cuellar</vCard:Family> <vCard:Given>Autumn</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Updated metadata to conform to the 16/1/02 CellML Metadata 1.0 Specification.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#f70cbe00-00e7-4145-9f1c-c0ebfc3e48bd"> <dcterms:W3CDTF>2002-01-22</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#186b7d65-1176-4297-a817-9feb5ecfae3e"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#587d23ee-3a7b-4f94-b889-b33187a55bae"> <vCard:N> <rdf:Description rdf:about="rdf:#296115a5-a320-4113-9390-7194c208710f"> <vCard:Other>A</vCard:Other> <vCard:Family>Cuellar</vCard:Family> <vCard:Given>Autumn</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Added publication date information.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#6eb02915-423c-473a-90f0-25ffdf39aacc"> <dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <dc:publisher>The University of Auckland, Bioengineering Research Group</dc:publisher> <cmeta:modification> <rdf:Description rdf:about="rdf:#254c5b36-a8b1-48fa-b7b0-5d3402de7912"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#a0b0c2bf-a81e-41f5-99d8-3aa262feca36"> <vCard:N> <rdf:Description rdf:about="rdf:#fd7db35c-8c68-4afb-ad5f-2a329af6eeb3"> <vCard:Other>May</vCard:Other> <vCard:Family>Lloyd</vCard:Family> <vCard:Given>Catherine</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Completely re-wrote the model to remove the reaction element.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#221d2a11-1e70-42a7-b79d-74df4dabd9bf"> <dcterms:W3CDTF>2007-12-27</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <dcterms:created> <rdf:Description rdf:about="rdf:#ee3ebc1a-f98e-4459-a052-0aa6d4294edc"> <dcterms:W3CDTF>2001-10-25T00:00:00+00:00</dcterms:W3CDTF> </rdf:Description> </dcterms:created> <cmeta:modification> <rdf:Description rdf:about="rdf:#2080cf23-3665-443b-8f94-ab6aef7163b6"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#64403c15-677d-49df-8507-1cde5cdc073d"> <vCard:N> <rdf:Description 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rdf:about="rdf:#3aa396b9-d0ed-4a66-9d6d-dd4f549232a7"> <rdf:li>signal transduction</rdf:li> <rdf:li>MAPK</rdf:li> <rdf:li>kinase</rdf:li> <rdf:li>pathway</rdf:li> <rdf:li>cascade</rdf:li> </rdf:Bag> </rdf:value> <bqs:subject_type>keyword</bqs:subject_type> </rdf:Description> </dc:subject> </rdf:Description> </bqs:reference> <bqs:reference> <rdf:Description rdf:about="rdf:#0bf41ebd-c600-4a14-95f0-b0e573599401"> <bqs:JournalArticle> <rdf:Description rdf:about="rdf:#3a159fb0-5742-483f-80db-b7c2af344945"> <bqs:last_page>239</bqs:last_page> <dcterms:issued> <rdf:Description rdf:about="rdf:#132ab91f-5112-4243-b15e-cd7f656c6653"> <dcterms:W3CDTF>2001-03</dcterms:W3CDTF> </rdf:Description> </dcterms:issued> <bqs:Journal> <rdf:Description rdf:about="rdf:#f4e72e5b-6b30-45e9-83b5-7b06baea4211"> <dc:title>Biotechnology Progress</dc:title> </rdf:Description> </bqs:Journal> <bqs:first_page>227</bqs:first_page> <bqs:volume>17</bqs:volume> <dc:title>A Compuational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model</dc:title> <dc:creator> <rdf:Seq rdf:about="rdf:#6a8d522c-bfa4-4010-a658-bac295b2a18c"> <rdf:li> <bqs:Person rdf:about="rdf:#f4532efe-c855-426b-9d47-9ddc76369546"> <vCard:N> <rdf:Description rdf:about="rdf:#dc9a3938-af2f-426b-8da9-173b83157f78"> <vCard:Other>R</vCard:Other> <vCard:Family>Asthagiri</vCard:Family> <vCard:Given>Anand</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#81cf568e-561f-4f52-9ac6-64716fc97589"> <vCard:N> <rdf:Description rdf:about="rdf:#52baaf6c-7dc0-48c1-8a56-015b05fbf1f7"> <vCard:Other>A</vCard:Other> <vCard:Family>Lauffenburger</vCard:Family> <vCard:Given>Douglas</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> </rdf:Seq> </dc:creator> </rdf:Description> </bqs:JournalArticle> <bqs:Pubmed_id>11312698</bqs:Pubmed_id> </rdf:Description> </bqs:reference> <cmeta:comment> <rdf:Description rdf:about="rdf:#cc206bb4-0147-4b90-a315-9f92a7834c23"> <rdf:value>This is the CellML description of Asthagiri and Lauffenburger's mathematical model of the mitogen-activated protein kinase (MAPK) cascade (2001). They examine MAPK pathway dynamics, especially the role of negative feedback mechanisms in generating signal adaptation.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#0e234b83-1df4-4639-bcbc-c5e8bcf26eac"> <vCard:FN>Catherine Lloyd</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:title>The mitogen-activated protein kinase (MAPK) cascade, 2001</dc:title> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/c_star"> <dc:title>c_star</dc:title> <dcterms:alternative>dimerised and activated receptor</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/r"> <dc:title>r</dc:title> <dcterms:alternative>free receptor</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e3_star"> <dc:title>e3_star</dc:title> <dcterms:alternative>activated signalling enzyme 3</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/a1"> <dc:title>a1</dc:title> <dcterms:alternative>free first adaptor</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e2_star_p2"> <dc:title>e2_star_p2</dc:title> <dcterms:alternative>transition complex between an active substate and its deactivating enzyme (2)</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/p2"> <dc:title>p2</dc:title> <dcterms:alternative>deactivating enzyme 2</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e4_star_p4"> <dc:title>e5_star_p5</dc:title> <dc:title>e4_star_p4</dc:title> <dcterms:alternative>transition complex between an active substate and its deactivating enzyme (5)</dcterms:alternative> <dcterms:alternative>transition complex between an active substate and its deactivating enzyme (4)</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/a2_minus"> <dc:title>a2_minus</dc:title> <dcterms:alternative>nonfunctional second adaptor</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e2_star"> <dc:title>e2_star</dc:title> <dcterms:alternative>activated signalling enzyme 2</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e0_star"> <dc:title>e0_star</dc:title> <dcterms:alternative>receptor-ligand dimer:adaptors 1 and 2 complex</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e3"> <dc:title>e3</dc:title> <dcterms:alternative>inactive signalling enzyme 3</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e4_star"> <dc:title>e4_star</dc:title> <dcterms:alternative>activated signalling enzyme 4</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e2_minus"> <dc:title>e2_minus</dc:title> <dcterms:alternative>nonfunctional second enzyme</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e3_star_p3"> <dc:title>e3_star_p3</dc:title> <dcterms:alternative>transition complex between an active substate and its deactivating enzyme (3)</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/p3"> <dc:title>p3</dc:title> <dcterms:alternative>deactivating enzyme 3</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/c"> <dc:title>c</dc:title> <dcterms:alternative>ligand-bound receptor</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e3_e2_star"> <dc:title>e3_e2_star</dc:title> <dcterms:alternative>transition complex between an inactive substate and its activator (3)</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e2_star_e4_star"> <dc:title>e2_star_e4_star</dc:title> <dcterms:alternative>transition complex in feedback mediated by enzyme E4*</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e2"> <dc:title>e2</dc:title> <dcterms:alternative>inactive signalling enzyme 2</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/c_star_a1"> <dc:title>c_star_a1</dc:title> <dcterms:alternative>active receptor-ligand dimer:adaptor 1 complex</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e1_star"> <dc:title>e1_star</dc:title> <dcterms:alternative>activated signalling enzyme 1</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e4"> <dc:title>e4</dc:title> <dcterms:alternative>inactive signalling enzyme 4</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e0_star_e4_star"> <dc:title>e0_star_e4_star</dc:title> <dcterms:alternative>transition complex in feedback mediated by enzyme E4*</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/p4"> <dc:title>p4</dc:title> <dcterms:alternative>deactivating enzyme 4</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e1"> <dc:title>e1</dc:title> <dcterms:alternative>inactive signalling enzyme 1</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e2_e1_star"> <dc:title>e2_e1_star</dc:title> <dcterms:alternative>transition complex between an inactive substate and its activator (2)</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e5_e4_star"> <dc:title>e5_e4_star</dc:title> <dcterms:alternative>transition complex between an inactive substate and its activator (5)</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/e5_star"> <dc:title>e5_star</dc:title> <dcterms:alternative>activated signalling enzyme 5</dcterms:alternative> </rdf:Description> </rdf:RDF> asthagiri_model_2001 asthagiri_model_2001 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Mitogen-activated protein kinase 1 (MAP kinase 1) (MAPK 1) (EC 2.7.11.24) (ERT1) (Extracellular signal-regulated kinase 2) (ERK-2) (MAP kinase isoform p42) (p42-MAPK) (Mitogen-activated protein kinase 2) (MAP kinase 2) (MAPK 2) (P28482) http://identifiers.org/uniprot/P28482 Oocyte http://purl.org/sig/ont/fma/fma18644 A physical entity that is defined by linking multiple physical entity terms with structural relations. A mathematical and/or logical expression that determines the value of a data structure. An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities. A physical dependency defined in a specific SemSim model. A physical entity defined in a specific SemSim model. A physical process defined in a specific SemSim model. A physical property defined in a specific SemSim model. A computational element that stores numerical and/or logical information related to the model. A data structure whose value is limited to decimals. A data structure whose value is limited to the whole numbers. A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime. A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process. A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants. A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element. A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process. A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values. A data structure whose value is limited to the real numbers. A physical dependency that is defined using a term in an external knowledge resource. A physical entity that is defined using a term from an external knowledge resource. A physical process that is defined using a term in an external knowledge resource. A physical property that is defined using a term in an external knowledge resource. A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0. A computational or physical element of a SemSim model. A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel. A physical quantity chosen as a standard in terms of which other physical quantities may be expressed. Oocyte http://purl.org/sig/ont/fma/fma18644 Mitogen-activated protein kinase 1 (MAP kinase 1) (MAPK 1) (EC 2.7.11.24) (ERT1) (Extracellular signal-regulated kinase 2) (ERK-2) (MAP kinase isoform p42) (p42-MAPK) (Mitogen-activated protein kinase 2) (MAP kinase 2) (MAPK 2) (P28482) http://identifiers.org/uniprot/P28482 cell true first_order_rate_constant -1.0 litre true minute molar -1.0 mole true number true number_per_cell -1.0 second true second_order_rate_constant -1.0 -1.0 a1 false false in true Total number of adaptor protein A1 molecules false false in true Total number of adaptor protein A2 molecules false false in true Total number of activating enzymes at stage 1 false false in true Total number of activating enzymes at stage 4 false false out true Concentration of free first adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of adaptor heterodimer Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active receptor-ligand dimer bound to adaptor 1 complex Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of the transition complex between inactive substrate E1 and its activator E0* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="6b"> <apply> <eq /> <ci>a1</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <ci>c_star_a1</ci> <ci>a1a2</ci> <apply> <times /> <apply> <divide /> <ci>A2_T</ci> <ci>A1_T</ci> </apply> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>E4_T</ci> <ci>A1_T</ci> </apply> <ci>e0_star_e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>E1_T</ci> <ci>A1_T</ci> </apply> <ci>e1_e0_star</ci> </apply> </apply> </apply> </apply> </math> a1a2 false false in true Total number of adaptor protein A1 molecules false false in true Total number of adaptor protein A2 molecules false false in true Initial number of free receptors false false in true Concentration of free first adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of adaptor heterodimer Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of free second adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of dimerized and activated receptor Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Forward rate constant for association adaptor protein 1 (A1) with adaptor protein 2 (A2) false false in true Backward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2) false false in true Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) false false in true Receptor-ligand dissociation rate constant false false in true Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="6"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>a1a2</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kr_12</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>A2_T</ci> <ci>A1_T</ci> </apply> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kc_12</ci> <ci>A2_T</ci> </apply> <ci>kr</ci> </apply> <ci>a1</ci> <ci>a2</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kd_12</ci> <ci>kr</ci> </apply> <ci>a1a2</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kf_12</ci> <ci>R0</ci> </apply> <ci>kr</ci> </apply> <ci>c_star</ci> <ci>a1a2</ci> </apply> </apply> </apply> </apply> </math> a2 false false in true Total number of adaptor protein A1 molecules false false in true Total number of adaptor protein A2 molecules false false in true Total number of activating enzymes at stage 1 false false in true Total number of activating enzymes at stage 4 false false in true Concentration of adaptor heterodimer Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false out true Concentration of free second adaptor protein false false in true Concentration of nonfunctional second adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of the transition complex between inactive substrate E1 and its activator E0* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="6c"> <apply> <eq /> <ci>a2</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>A1_T</ci> <ci>A2_T</ci> </apply> <ci>a1a2</ci> </apply> <ci>e0_star</ci> <apply> <times /> <apply> <divide /> <ci>E4_T</ci> <ci>A2_T</ci> </apply> <ci>e0_star_e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>E1_T</ci> <ci>A2_T</ci> </apply> <ci>e1_e0_star</ci> </apply> <ci>a2_minus</ci> </apply> </apply> </apply> </math> a2_minus false false in true Total number of adaptor protein A2 molecules false false in true Total number of activating enzymes at stage 4 0.0 false false out true Concentration of nonfunctional second adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4* false false in true Receptor-ligand dissociation rate constant Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="7"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>a2_minus</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kcat_x</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>E4_T</ci> <ci>A2_T</ci> </apply> <ci>e0_star_e4_star</ci> </apply> </apply> </math> c false false in true Initial ligand concentration false false in true Initial number of free receptors 0.0 false false out true Concentration of free ligand-bound receptor false false in true Concentration of ligand-bound and dimerized receptor Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Rate constant for dimerization of ligand-bound receptors false false in true Receptor-ligand association rate constant false false in true Receptor-ligand dissociation rate constant false false in true Rate constant for dissociation of dimers false false in true Number of free receptors in cell Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation c2 false false in true Initial number of free receptors false false in true Concentration of free ligand-bound receptor 0.0 false false out true Concentration of ligand-bound and dimerized receptor Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of dimerized and activated receptor Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Rate constant for dimerization of ligand-bound receptors false false in true Rate constant for deactivation of active receptor-ligand dimers false false in true Rate constant for activation of dimerized receptor-ligand complexes false false in true Receptor-ligand association rate constant false false in true Receptor-ligand dissociation rate constant false false in true Rate constant for dissociation of dimers Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="2"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>c2</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>R0</ci> <apply> <divide /> <ci>kr</ci> <ci>kc</ci> </apply> </apply> <apply> <power /> <ci>c</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> </apply> </apply> <apply> <times /> <apply> <divide /> <ci>kc_minus</ci> <ci>kr</ci> </apply> <ci>c_star</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>ku</ci> <ci>kr</ci> </apply> <ci>c</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kc_plus</ci> <ci>kr</ci> </apply> <ci>c2</ci> </apply> </apply> </apply> </apply> </math> <math xmlns="http://www.w3.org/1998/Math/MathML" id="1"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>c</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>L0</ci> <apply> <divide /> <ci>kr</ci> <ci>kf</ci> </apply> </apply> <ci>r</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> <apply> <divide /> <ci>ku</ci> <ci>kr</ci> </apply> <ci>c2</ci> </apply> </apply> <apply> <plus /> <ci>c</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> <apply> <divide /> <ci>R0</ci> <apply> <divide /> <ci>kr</ci> <ci>kc</ci> </apply> </apply> <apply> <power /> <ci>c</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> </apply> </apply> </apply> </apply> </apply> </math> c_star false false in true Total number of adaptor protein A1 molecules false false in true Total number of adaptor protein A2 molecules false false in true Initial number of free receptors false false in true Concentration of free first adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of adaptor heterodimer Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of ligand-bound and dimerized receptor Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of dimerized and activated receptor false false in true Concentration of active receptor-ligand dimer bound to adaptor 1 complex Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Rate constant for deactivation of active receptor-ligand dimers false false in true Rate constant for activation of dimerized receptor-ligand complexes false false in true Forward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1) false false in true Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) false false in true Receptor-ligand dissociation rate constant false false in true Backward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1) false false in true Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation c_star_a1 false false in true Total number of adaptor protein A1 molecules false false in true Total number of adaptor protein A2 molecules false false in true Total number of activating enzymes at stage 4 false false in true Initial number of free receptors false false in true Concentration of free first adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of free second adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of dimerized and activated receptor 0.0 false false out true Concentration of active receptor-ligand dimer bound to adaptor 1 complex Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Rate constant for deactivation of active receptor-ligand dimers false false in true Rate constant for activation of dimerized receptor-ligand complexes false false in true First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4* false false in true Forward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1) false false in true Forward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2) false false in true Receptor-ligand dissociation rate constant false false in true Backward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1) false false in true Backward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2) Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="4"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>c_star_a1</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kf_1</ci> <ci>R0</ci> </apply> <ci>kr</ci> </apply> <ci>c_star</ci> <ci>a1</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kr_2</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>A2_T</ci> <ci>A1_T</ci> </apply> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kcat_x</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>E4_T</ci> <ci>A1_T</ci> </apply> <ci>e0_star_e4_star</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kr_1</ci> <ci>kr</ci> </apply> <ci>c_star_a1</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kf_2</ci> <ci>A2_T</ci> </apply> <ci>kr</ci> </apply> <ci>c_star_a1</ci> <ci>a2</ci> </apply> </apply> </apply> </apply> </math> <math xmlns="http://www.w3.org/1998/Math/MathML" id="3"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>c_star</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kc_plus</ci> <ci>kr</ci> </apply> <ci>c2</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kr_1</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>A1_T</ci> <ci>R0</ci> </apply> <ci>c_star_a1</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kr_12</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>A2_T</ci> <ci>R0</ci> </apply> <ci>e0_star</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kc_minus</ci> <ci>kr</ci> </apply> <ci>c_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kf_1</ci> <ci>A1_T</ci> </apply> <ci>kr</ci> </apply> <ci>c_star</ci> <ci>a1</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kf_12</ci> <ci>A1_T</ci> </apply> <ci>kr</ci> </apply> <ci>c_star</ci> <ci>a1a2</ci> </apply> </apply> </apply> </apply> </math> e0_star false false in true Total number of adaptor protein A1 molecules false false in true Total number of adaptor protein A2 molecules false false in true Total number of activating enzymes at stage 1 false false in true Total number of activating enzymes at stage 4 false false in true Concentration of adaptor heterodimer Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of free second adaptor protein Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of dimerized and activated receptor false false in true Concentration of active receptor-ligand dimer bound to adaptor 1 complex Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of inactive signaling enzyme 1 false false in true Concentration of the transition complex between inactive substrate E1 and its activator E0* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Backward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*) false false in true Forward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*) false false in true First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1* false false in true Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) false false in true Forward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2) false false in true Receptor-ligand dissociation rate constant false false in true Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) false false in true Backward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2) false false in true false false in true Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="5"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e0_star</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kf_2</ci> <ci>A1_T</ci> </apply> <ci>kr</ci> </apply> <ci>c_star_a1</ci> <ci>a2</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kf_12</ci> <ci>A1_T</ci> </apply> <ci>kr</ci> </apply> <ci>c_star</ci> <ci>a1a2</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <plus /> <ci>k1_minus</ci> <ci>kcat_1</ci> </apply> <ci>kr</ci> </apply> <apply> <divide /> <ci>E1_T</ci> <ci>A2_T</ci> </apply> <ci>e1_e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kx_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>E4_T</ci> <ci>A2_T</ci> </apply> <ci>e0_star_e4_star</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kr_2</ci> <ci>kr</ci> </apply> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kr_12</ci> <ci>kr</ci> </apply> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k1_plus</ci> <ci>E1_T</ci> </apply> <ci>kr</ci> </apply> <ci>e0_star</ci> <ci>e1</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kx_plus</ci> <ci>E4_T</ci> </apply> <ci>kr</ci> </apply> <ci>e0_star</ci> <ci>e4_star</ci> </apply> </apply> </apply> </apply> </math> e0_star_e4_star false false in true Total number of adaptor protein A2 molecules false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 0.0 false false out true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4* false false in true Receptor-ligand dissociation rate constant false false in true false false in true Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="19"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e0_star_e4_star</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kx_plus</ci> <ci>A2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e4_star</ci> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kx_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_x</ci> <ci>kr</ci> </apply> </apply> <ci>e0_star_e4_star</ci> </apply> </apply> </apply> </math> e1 false false in true Total number of activating enzymes at stage 1 false false in true Total number of activating enzymes at stage 2 false false in true Total number of deactivating enzymes at stage 1 false false out true Concentration of inactive signaling enzyme 1 false false in true Concentration of the transition complex between inactive substrate E1 and its activator E0* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 1 false false in true Concentration of transition complex between active substrate E1* and deactivating enzyme P1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of transition complex between inactive substrate E2 and its activator E1* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="31"> <apply> <eq /> <ci>e1</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <ci>e1_e0_star</ci> <ci>e1_star</ci> <apply> <times /> <apply> <divide /> <ci>E2_T</ci> <ci>E1_T</ci> </apply> <ci>e2_e1_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>P1_T</ci> <ci>E1_T</ci> </apply> <ci>e1_star_p1</ci> </apply> </apply> </apply> </apply> </math> e1_e0_star false false in true Total number of adaptor protein A2 molecules false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of inactive signaling enzyme 1 0.0 false false out true Concentration of the transition complex between inactive substrate E1 and its activator E0* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Backward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*) false false in true Forward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*) false false in true First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1* false false in true Receptor-ligand dissociation rate constant Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="13"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e1_e0_star</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k1_plus</ci> <ci>A2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e1</ci> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>k1_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_1</ci> <ci>kr</ci> </apply> </apply> <ci>e1_e0_star</ci> </apply> </apply> </apply> </math> e1_star false false in true Total number of activating enzymes at stage 1 false false in true Total number of activating enzymes at stage 2 false false in true Total number of deactivating enzymes at stage 1 false false in true Concentration of the transition complex between inactive substrate E1 and its activator E0* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of active signaling enzyme 1 false false in true Concentration of transition complex between active substrate E1* and deactivating enzyme P1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Inactive signaling enzyme 2 false false in true Concentration of transition complex between inactive substrate E2 and its activator E1* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*) false false in true false false in true false false in true First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1* false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="21"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e1_star</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kcat_1</ci> <ci>kr</ci> </apply> <ci>e1_e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <plus /> <ci>k2_minus</ci> <ci>kcat_2</ci> </apply> <ci>kr</ci> </apply> <apply> <divide /> <ci>E2_T</ci> <ci>E1_T</ci> </apply> <ci>e2_e1_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kP1_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>P1_T</ci> <ci>E1_T</ci> </apply> <ci>e1_star_p1</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k2_plus</ci> <ci>E2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e1_star</ci> <ci>e2</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP1_plus</ci> <ci>P1_T</ci> </apply> <ci>kr</ci> </apply> <ci>e1_star</ci> <ci>p1</ci> </apply> </apply> </apply> </apply> </math> e1_star_p1 false false in true Total number of activating enzymes at stage 1 false false in true Concentration of active signaling enzyme 1 0.0 false false out true Concentration of transition complex between active substrate E1* and deactivating enzyme P1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="8"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e1_star_p1</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP1_plus</ci> <ci>E1_T</ci> </apply> <ci>kr</ci> </apply> <ci>e1_star</ci> <ci>p1</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kP1_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_P1</ci> <ci>kr</ci> </apply> </apply> <ci>e1_star_p1</ci> </apply> </apply> </apply> </math> e2 false false in true Total number of activating enzymes at stage 2 false false in true Total number of activating enzymes at stage 3 false false in true Total number of activating enzymes at stage 4 false false in true Total number of activating enzymes at stage 2 false false out true Concentration of inactive signaling enzyme 2 false false in true Concentration of transition complex between inactive substrate E2 and its activator E1* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of nonfunctional second enzyme Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of transition complex between active substrate E2* and deactivating enzyme P2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of transition complex between inactive substrate E3 and its activator E2* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="34"> <apply> <eq /> <ci>e2</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <ci>e3_e2_star</ci> <ci>e3_star</ci> <apply> <times /> <apply> <divide /> <ci>E3_T</ci> <ci>E2_T</ci> </apply> <ci>e3_e2_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>E4_T</ci> <ci>E2_T</ci> </apply> <ci>e2_star_e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>P2_T</ci> <ci>E2_T</ci> </apply> <ci>e2_star_p2</ci> </apply> </apply> </apply> </apply> </math> e2_e1_star false false in true Total number of activating enzymes at stage 1 false false in true Concentration of active signaling enzyme 1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Inactive signaling enzyme 2 0.0 false false out true Concentration of transition complex between inactive substrate E2 and its activator E1* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*) false false in true false false in true Receptor-ligand dissociation rate constant Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="14"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e2_e1_star</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k2_plus</ci> <ci>E1_T</ci> </apply> <ci>kr</ci> </apply> <ci>e2</ci> <ci>e1_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>k2_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_2</ci> <ci>kr</ci> </apply> </apply> <ci>e2_e1_star</ci> </apply> </apply> </apply> </math> e2_minus false false in true Total number of activating enzymes at stage 2 false false in true Total number of activating enzymes at stage 4 0.0 false false out true Concentration of nonfunctional second enzyme Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true Receptor-ligand dissociation rate constant Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="20"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e2_minus</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kcat_z</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>E4_T</ci> <ci>E2_T</ci> </apply> <ci>e2_star_e4_star</ci> </apply> </apply> </math> e2_star false false in true Total number of activating enzymes at stage 2 false false in true Total number of activating enzymes at stage 3 false false in true Total number of activating enzymes at stage 4 false false in true Total number of activating enzymes at stage 2 false false in true Concentration of transition complex between inactive substrate E2 and its activator E1* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of active signaling enzyme 2 false false in true Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of transition complex between active substrate E2* and deactivating enzyme P2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of inactive signaling enzyme 3 false false in true Concentration of transition complex between inactive substrate E3 and its activator E2* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true false false in true false false in true Concentration of deactivating enzyme P2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="24"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e2_star</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kcat_2</ci> <ci>kr</ci> </apply> <ci>e2_e1_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <plus /> <ci>k3_minus</ci> <ci>kcat_3</ci> </apply> <ci>kr</ci> </apply> <apply> <divide /> <ci>E3_T</ci> <ci>E2_T</ci> </apply> <ci>e3_e2_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kP2_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>P2_T</ci> <ci>E2_T</ci> </apply> <ci>e2_star_p2</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kz_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>E4_T</ci> <ci>E2_T</ci> </apply> <ci>e2_star_e4_star</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k3_plus</ci> <ci>E3_T</ci> </apply> <ci>kr</ci> </apply> <ci>e2_star</ci> <ci>e3</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP2_plus</ci> <ci>P2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e2_star</ci> <ci>p2</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kz_plus</ci> <ci>E4_T</ci> </apply> <ci>kr</ci> </apply> <ci>e2_star</ci> <ci>e4_star</ci> </apply> </apply> </apply> </apply> </math> e2_star_e4_star false false in true Total number of activating enzymes at stage 2 false false in true Concentration of active signaling enzyme 2 0.0 false false out true Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*) false false in true false false in true Receptor-ligand dissociation rate constant false false in true false false in true Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="18"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e2_star_e4_star</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kz_plus</ci> <ci>E2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e4_star</ci> <ci>e2_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kz_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_z</ci> <ci>kr</ci> </apply> </apply> <ci>e2_star_e4_star</ci> </apply> </apply> </apply> </math> e2_star_p2 false false in true Total number of activating enzymes at stage 2 false false in true Concentration of active signaling enzyme 2 0.0 false false out true Concentration of transition complex between active substrate E2* and deactivating enzyme P2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="9"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e2_star_p2</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP2_plus</ci> <ci>E2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e2_star</ci> <ci>p2</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kP2_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_P2</ci> <ci>kr</ci> </apply> </apply> <ci>e2_star_p2</ci> </apply> </apply> </apply> </math> e3 false false in true Total number of activating enzymes at stage 3 false false in true Total number of activating enzymes at stage 4 false false in true Total number of activating enzymes at stage 3 false false out true Concentration of inactive signaling enzyme 3 false false in true Concentration of transition complex between inactive substrate E3 and its activator E2* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 3 false false in true Concentration of transition complex between active substrate E3* and deactivating enzyme P3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of transition complex between inactive substrate E4 and its activator E3* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="32"> <apply> <eq /> <ci>e3</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <ci>e3_e2_star</ci> <ci>e3_star</ci> <apply> <times /> <apply> <divide /> <ci>E4_T</ci> <ci>E3_T</ci> </apply> <ci>e4_e3_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>P3_T</ci> <ci>E3_T</ci> </apply> <ci>e3_star_p3</ci> </apply> </apply> </apply> </apply> </math> e3_e2_star false false in true Total number of activating enzymes at stage 2 false false in true Concentration of active signaling enzyme 2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of inactive signaling enzyme 3 0.0 false false out true Concentration of transition complex between inactive substrate E3 and its activator E2* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="15"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e3_e2_star</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k3_plus</ci> <ci>E2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e3</ci> <ci>e2_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>k3_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_3</ci> <ci>kr</ci> </apply> </apply> <ci>e3_e2_star</ci> </apply> </apply> </apply> </math> e3_star false false in true Total number of activating enzymes at stage 3 false false in true Total number of activating enzymes at stage 4 false false in true Total number of activating enzymes at stage 3 false false in true Concentration of transition complex between inactive substrate E3 and its activator E2* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of active signaling enzyme 3 false false in true Concentration of transition complex between active substrate E3* and deactivating enzyme P3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of inactive signaling enzyme 4 false false in true Concentration of transition complex between inactive substrate E4 and its activator E3* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="22"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e3_star</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kcat_3</ci> <ci>kr</ci> </apply> <ci>e3_e2_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <plus /> <ci>k4_minus</ci> <ci>kcat_4</ci> </apply> <ci>kr</ci> </apply> <apply> <divide /> <ci>E4_T</ci> <ci>E3_T</ci> </apply> <ci>e4_e3_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kP3_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>P3_T</ci> <ci>E3_T</ci> </apply> <ci>e3_star_p3</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k4_plus</ci> <ci>E4_T</ci> </apply> <ci>kr</ci> </apply> <ci>e3_star</ci> <ci>e4</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP3_plus</ci> <ci>P3_T</ci> </apply> <ci>kr</ci> </apply> <ci>e3_star</ci> <ci>p3</ci> </apply> </apply> </apply> </apply> </math> e3_star_p3 false false in true Total number of activating enzymes at stage 3 false false in true Concentration of active signaling enzyme 3 0.0 false false out true Concentration of transition complex between active substrate E3* and deactivating enzyme P3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="10"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e3_star_p3</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP3_plus</ci> <ci>E3_T</ci> </apply> <ci>kr</ci> </apply> <ci>e3_star</ci> <ci>p3</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kP3_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_P3</ci> <ci>kr</ci> </apply> </apply> <ci>e3_star_p3</ci> </apply> </apply> </apply> </math> e4 false false in true Total number of activating enzymes at stage 4 false false in true Total number of activating enzymes at stage 5 false false in true Total number of activating enzymes at stage 4 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false out true Concentration of inactive signaling enzyme 4 false false in true Concentration of transition complex between inactive substrate E4 and its activator E3* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 4 false false in true Concentration of transition complex between active substrate E4* and deactivating enzyme P4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of transition complex between inactive substrate E5 and its activator E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="35"> <apply> <eq /> <ci>e4</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <ci>e4_e3_star</ci> <ci>e4_star</ci> <apply> <times /> <apply> <divide /> <ci>E5_T</ci> <ci>E4_T</ci> </apply> <ci>e5_e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>P4_T</ci> <ci>E4_T</ci> </apply> <ci>e4_star_p4</ci> </apply> <ci>e0_star_e4_star</ci> <ci>e2_star_e4_star</ci> </apply> </apply> </apply> </math> e4_e3_star false false in true Total number of activating enzymes at stage 3 false false in true Concentration of active signaling enzyme 3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of inactive signaling enzyme 4 0.0 false false out true Concentration of transition complex between inactive substrate E4 and its activator E3* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="16"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e4_e3_star</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k4_plus</ci> <ci>E3_T</ci> </apply> <ci>kr</ci> </apply> <ci>e4</ci> <ci>e3_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>k4_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_4</ci> <ci>kr</ci> </apply> </apply> <ci>e4_e3_star</ci> </apply> </apply> </apply> </math> e4_star false false in true Total number of adaptor protein A2 molecules false false in true Total number of activating enzymes at stage 2 false false in true Total number of activating enzymes at stage 4 false false in true Total number of activating enzymes at stage 5 false false in true Total number of activating enzymes at stage 4 false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 2 false false in true Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of transition complex between inactive substrate E4 and its activator E3* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of active signaling enzyme 4 false false in true Concentration of transition complex between active substrate E4* and deactivating enzyme P4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Inactive signaling enzyme 5 false false in true Concentration of transition complex between inactive substrate E5 and its activator E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true false false in true false false in true false false in true First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4* false false in true false false in true Receptor-ligand dissociation rate constant false false in true false false in true false false in true false false in true false false in true Concentration of deactivating enzyme P4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="25"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e4_star</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kcat_4</ci> <ci>kr</ci> </apply> <ci>e4_e3_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <plus /> <ci>k5_minus</ci> <ci>kcat_5</ci> </apply> <ci>kr</ci> </apply> <apply> <divide /> <ci>E5_T</ci> <ci>E4_T</ci> </apply> <ci>e5_e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kP4_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>P4_T</ci> <ci>E4_T</ci> </apply> <ci>e4_star_p4</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kx_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_x</ci> <ci>kr</ci> </apply> </apply> <ci>e0_star_e4_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kz_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_z</ci> <ci>kr</ci> </apply> </apply> <ci>e2_star_e4_star</ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k5_plus</ci> <ci>E5_T</ci> </apply> <ci>kr</ci> </apply> <ci>e4_star</ci> <ci>e5</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP4_plus</ci> <ci>P4_T</ci> </apply> <ci>kr</ci> </apply> <ci>e4_star</ci> <ci>p4</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kx_plus</ci> <ci>A2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e0_star</ci> <ci>e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kz_plus</ci> <ci>E2_T</ci> </apply> <ci>kr</ci> </apply> <ci>e2_star</ci> <ci>e4_star</ci> </apply> </apply> </apply> </apply> </math> e4_star_p4 false false in true Total number of activating enzymes at stage 4 false false in true Concentration of active signaling enzyme 4 0.0 false false out true Concentration of transition complex between active substrate E4* and deactivating enzyme P4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="11"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e4_star_p4</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP4_plus</ci> <ci>E4_T</ci> </apply> <ci>kr</ci> </apply> <ci>e4_star</ci> <ci>p4</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kP4_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_P4</ci> <ci>kr</ci> </apply> </apply> <ci>e4_star_p4</ci> </apply> </apply> </apply> </math> e5 false false in true Total number of activating enzymes at stage 5 false false in true Total number of activating enzymes at stage 5 false false out true Concentration of inactive signaling enzyme 5 false false in true Concentration of transition complex between inactive substrate E5 and its activator E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of active signaling enzyme 5 false false in true Concentration of transition complex between active substrate E5* and deactivating enzyme P5 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="33"> <apply> <eq /> <ci>e5</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <ci>e5_e4_star</ci> <ci>e5_star</ci> <apply> <times /> <apply> <divide /> <ci>P5_T</ci> <ci>E5_T</ci> </apply> <ci>e5_star_p5</ci> </apply> </apply> </apply> </apply> </math> e5_e4_star false false in true Total number of activating enzymes at stage 4 false false in true Concentration of active signaling enzyme 4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Inactive signaling enzyme 5 0.0 false false out true Concentration of transition complex between inactive substrate E5 and its activator E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="17"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e5_e4_star</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>k5_plus</ci> <ci>E4_T</ci> </apply> <ci>kr</ci> </apply> <ci>e5</ci> <ci>e4_star</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>k5_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_5</ci> <ci>kr</ci> </apply> </apply> <ci>e5_e4_star</ci> </apply> </apply> </apply> </math> e5_star false false in true Total number of activating enzymes at stage 5 false false in true Total number of activating enzymes at stage 5 false false in true Concentration of transition complex between inactive substrate E5 and its activator E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 0.0 false false out true Concentration of active signaling enzyme 5 false false in true Concentration of transition complex between active substrate E5* and deactivating enzyme P5 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P5 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="23"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e5_star</ci> </apply> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <ci>kcat_5</ci> <ci>kr</ci> </apply> <ci>e5_e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>kP5_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>P5_T</ci> <ci>E5_T</ci> </apply> <ci>e5_star_p5</ci> </apply> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP5_plus</ci> <ci>P5_T</ci> </apply> <ci>kr</ci> </apply> <ci>e5_star</ci> <ci>p5</ci> </apply> </apply> </apply> </math> e5_star_p5 false false in true Total number of activating enzymes at stage 5 false false in true Concentration of active signaling enzyme 5 0.0 false false out true Concentration of transition complex between active substrate E5* and deactivating enzyme P5 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true false false in true false false in true false false in true Receptor-ligand dissociation rate constant false false in true Concentration of deactivating enzyme P5 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Time domain for simulation <math xmlns="http://www.w3.org/1998/Math/MathML" id="12"> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>e5_star_p5</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>kP5_plus</ci> <ci>E5_T</ci> </apply> <ci>kr</ci> </apply> <ci>e5_star</ci> <ci>p5</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <divide /> <ci>kP5_minus</ci> <ci>kr</ci> </apply> <apply> <divide /> <ci>kcat_P5</ci> <ci>kr</ci> </apply> </apply> <ci>e5_star_p5</ci> </apply> </apply> </apply> </math> environment Time false false http://bhi.washington.edu/OPB#OPB_01023 out true Time domain for simulation model_parameters 1E4 false false out true Total number of adaptor protein A1 molecules 1E4 false false out true Total number of adaptor protein A2 molecules 1E4 false false out true Total number of activating enzymes at stage 1 1E4 false false out true Total number of activating enzymes at stage 2 1E4 false false out true Total number of activating enzymes at stage 3 1E4 false false out true Total number of activating enzymes at stage 4 1E4 false false out true Total number of activating enzymes at stage 5 false false out true Initial ligand concentration 5E3 false false out true Total number of deactivating enzymes at stage 1 5E3 false false out true Total number of activating enzymes at stage 2 5E3 false false out true Total number of activating enzymes at stage 3 5E3 false false out true Total number of activating enzymes at stage 4 5E3 false false out true Total number of activating enzymes at stage 5 1E5 false false out true Initial number of free receptors 30 false false out true Backward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*) 6E8 false false out true Forward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*) 30 false false out true 6E8 false false out true Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*) 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true 6E7 false false out true Rate constant for dimerization of ligand-bound receptors 3E8 false false out true Forward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2) 5.0 false false out true Rate constant for deactivation of active receptor-ligand dimers 50.0 false false out true Rate constant for activation of dimerized receptor-ligand complexes 6 false false out true First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1* 6 false false out true 6 false false out true 6 false false out true 6 false false out true 6 false false out true 6 false false out true 6 false false out true 6 false false out true 6 false false out true 6 false false out true First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4* 6 false false out true false false out true Backward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2) 1E7 false false out true Receptor-ligand association rate constant 3E8 false false out true Forward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1) 3E8 false false out true Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) 3E8 false false out true Forward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2) 0.3 false false out true Receptor-ligand dissociation rate constant false false out true Backward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1) false false out true Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*) false false out true Backward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2) 60.0 false false out true Rate constant for dissociation of dimers 30 false false out true 6E8 false false out true 30 false false out true 6E8 false false out true <math xmlns="http://www.w3.org/1998/Math/MathML" id="36"> <apply> <eq /> <ci>L0</ci> <apply> <divide /> <ci>kr</ci> <ci>kf</ci> </apply> </apply> <apply> <eq /> <ci>kr_1</ci> <apply> <times /> <ci>kf_1</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1E-7</cn> </apply> </apply> <apply> <eq /> <ci>kr_2</ci> <apply> <times /> <ci>kf_2</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1E-7</cn> </apply> </apply> <apply> <eq /> <ci>kr_12</ci> <apply> <times /> <ci>kf_12</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1E-7</cn> </apply> </apply> <apply> <eq /> <ci>kd_12</ci> <apply> <times /> <ci>kc_12</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1E-7</cn> </apply> </apply> </math> p1 false false in true Concentration of transition complex between active substrate E1* and deactivating enzyme P1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 5E3 false false out true Concentration of deactivating enzyme P1 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="26"> <apply> <eq /> <ci>p1</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <ci>e1_star_p1</ci> </apply> </apply> </math> p2 false false in true Concentration of transition complex between active substrate E2* and deactivating enzyme P2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 5E3 false false out true Concentration of deactivating enzyme P2 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="27"> <apply> <eq /> <ci>p2</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <ci>e2_star_p2</ci> </apply> </apply> </math> p3 false false in true Concentration of transition complex between active substrate E3* and deactivating enzyme P3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 5E3 false false out true Concentration of deactivating enzyme P3 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="28"> <apply> <eq /> <ci>p3</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <ci>e3_star_p3</ci> </apply> </apply> </math> p4 false false in true Concentration of transition complex between active substrate E4* and deactivating enzyme P4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 5E3 false false out true Concentration of deactivating enzyme P4 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="29"> <apply> <eq /> <ci>p4</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <ci>e4_star_p4</ci> </apply> </apply> </math> p5 false false in true Concentration of transition complex between active substrate E5* and deactivating enzyme P5 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 5E3 false false out true Concentration of deactivating enzyme P5 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 <math xmlns="http://www.w3.org/1998/Math/MathML" id="30"> <apply> <eq /> <ci>p5</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <ci>e5_star_p5</ci> </apply> </apply> </math> r false false in true Total number of adaptor protein A1 molecules false false in true Total number of adaptor protein A2 molecules false false in true Total number of activating enzymes at stage 1 false false in true Total number of activating enzymes at stage 4 false false in true Initial number of free receptors false false in true Concentration of free ligand-bound receptor false false in true Concentration of ligand-bound and dimerized receptor Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of dimerized and activated receptor false false in true Concentration of active receptor-ligand dimer bound to adaptor 1 complex Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of receptor-ligand dimer bound to adaptors 1 and 2 false false in true Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of the transition complex between inactive substrate E1 and its activator E0* Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false out true Number of free receptors in cell <math xmlns="http://www.w3.org/1998/Math/MathML" id="6a"> <apply> <eq /> <ci>r</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1.0</cn> <apply> <plus /> <ci>c</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> <apply> <plus /> <ci>c2</ci> <ci>c_star</ci> <apply> <times /> <apply> <divide /> <ci>A1_T</ci> <ci>R0</ci> </apply> <ci>c_star_a1</ci> </apply> <apply> <times /> <apply> <divide /> <ci>A2_T</ci> <ci>R0</ci> </apply> <ci>e0_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>E4_T</ci> <ci>R0</ci> </apply> <ci>e0_star_e4_star</ci> </apply> <apply> <times /> <apply> <divide /> <ci>E1_T</ci> <ci>R0</ci> </apply> <ci>e1_e0_star</ci> </apply> </apply> </apply> </apply> </apply> </apply> </math>