/Users/max_neal/Dropbox/Semantic Project/Annotated CellML models/asthagiri_lauffenburger_2001/asthagiri_lauffenburger_2001.cellml
Feedback Effects On Signal Dynamics In A Mitogen-Activated Protein Kinase (MAPK) Cascade Catherine Lloyd Bioengineering Institute, University of Auckland Model Status 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. ValidateCellML detects widespread unit inconsistency within this model. Model Structure 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. 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. The complete original paper reference is cited below: A Computational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model , Anand R. Asthagiri and Douglas A. Lauffenburger, 2001, Biotechnol. Prog , 17, 227-239. ( Full text and PDF versions are available to subscribers on the ACS Publications website. PubMed ID: 11312698 the conventional rendering of the MAPK cascade with feedback effects <imagedata fileref="asthagiri_2001.png" /> 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. 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.
<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 rdf:about="rdf:#3b81ac65-82e2-4278-9d0c-636e36c3887e"> <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>Recoded the model to remove the reaction element.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#7a503e08-326d-4cb0-b8c2-5b85ff813b79"> <dcterms:W3CDTF>2007-12-31T11:25:15+13:00</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <dc:creator> <rdf:Description rdf:about="rdf:#782c7a11-c641-48ff-be52-1ca31c01df63"> <vCard:N> <rdf:Description rdf:about="rdf:#0e69a7df-3fa5-4b86-9c3a-1f58e594c835"> <vCard:Other>May</vCard:Other> <vCard:Family>Lloyd</vCard:Family> <vCard:Given>Catherine</vCard:Given> </rdf:Description> </vCard:N> <vCard:EMAIL> <j.0:internet rdf:about="rdf:#4bdb62d2-848a-43aa-b3d7-2cd7a323b076"> <rdf:value>c.lloyd@auckland.ac.nz</rdf:value> </j.0:internet> </vCard:EMAIL> <vCard:ORG> <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 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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>
Chemical concentration
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)
Oocyte
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A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
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A physical entity that is defined using a term from an external knowledge resource.
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A physical property that is defined using a term in an external knowledge resource.
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Total number of adaptor protein A1 molecules
Total number of adaptor protein A2 molecules
Total number of activating enzymes at stage 1
Total number of activating enzymes at stage 4
Concentration of free first adaptor protein
Concentration of adaptor heterodimer
Concentration of active receptor-ligand dimer bound to adaptor 1 complex
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of the transition complex between inactive substrate E1 and its activator E0*
<eq /> a1 <minus /> 1.0 <plus /> c_star_a1 a1a2 <times /> <divide /> A2_T A1_T e0_star <times /> <divide /> E4_T A1_T e0_star_e4_star <times /> <divide /> E1_T A1_T e1_e0_star
Initial number of free receptors
Concentration of free second adaptor protein
Concentration of dimerized and activated receptor
Forward rate constant for association adaptor protein 1 (A1) with adaptor protein 2 (A2)
Backward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2)
Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Receptor-ligand dissociation rate constant
Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Time
Time domain for simulation
<eq /> <diff /> time a1a2 <minus /> <plus /> <times /> <divide /> kr_12 kr <divide /> A2_T A1_T e0_star <times /> <divide /> <times /> kc_12 A2_T kr a1 a2 <plus /> <times /> <divide /> kd_12 kr a1a2 <times /> <divide /> <times /> kf_12 R0 kr c_star a1a2
Concentration of nonfunctional second adaptor protein
<eq /> a2 <minus /> 1.0 <plus /> <times /> <divide /> A1_T A2_T a1a2 e0_star <times /> <divide /> E4_T A2_T e0_star_e4_star <times /> <divide /> E1_T A2_T e1_e0_star a2_minus
First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4*
<eq /> <diff /> time a2_minus <times /> <divide /> kcat_x kr <divide /> E4_T A2_T e0_star_e4_star
Initial ligand concentration
Concentration of free ligand-bound receptor
Concentration of ligand-bound and dimerized receptor
Rate constant for dimerization of ligand-bound receptors
Receptor-ligand association rate constant
Rate constant for dissociation of dimers
Number of free receptors in cell
Rate constant for deactivation of active receptor-ligand dimers
Rate constant for activation of dimerized receptor-ligand complexes
<eq /> <diff /> time c2 <minus /> <plus /> <times /> <divide /> R0 <divide /> kr kc <power /> c 2.0 <times /> <divide /> kc_minus kr c_star <plus /> <times /> <divide /> ku kr c <times /> <divide /> kc_plus kr c2
<eq /> <diff /> time c <minus /> <plus /> <times /> <divide /> L0 <divide /> kr kf r <times /> 2.0 <divide /> ku kr c2 <plus /> c <times /> 2.0 <divide /> R0 <divide /> kr kc <power /> c 2.0
Forward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
Backward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
Forward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
Backward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
<eq /> <diff /> time c_star_a1 <minus /> <plus /> <times /> <divide /> <times /> kf_1 R0 kr c_star a1 <times /> <divide /> kr_2 kr <divide /> A2_T A1_T e0_star <times /> <divide /> kcat_x kr <divide /> E4_T A1_T e0_star_e4_star <plus /> <times /> <divide /> kr_1 kr c_star_a1 <times /> <divide /> <times /> kf_2 A2_T kr c_star_a1 a2
<eq /> <diff /> time c_star <minus /> <plus /> <times /> <divide /> kc_plus kr c2 <times /> <divide /> kr_1 kr <divide /> A1_T R0 c_star_a1 <times /> <divide /> kr_12 kr <divide /> A2_T R0 e0_star <plus /> <times /> <divide /> kc_minus kr c_star <times /> <divide /> <times /> kf_1 A1_T kr c_star a1 <times /> <divide /> <times /> kf_12 A1_T kr c_star a1a2
Concentration of inactive signaling enzyme 1
Concentration of active signaling enzyme 4
Backward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
Forward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1*
<eq /> <diff /> time e0_star <minus /> <plus /> <times /> <divide /> <times /> kf_2 A1_T kr c_star_a1 a2 <times /> <divide /> <times /> kf_12 A1_T kr c_star a1a2 <times /> <divide /> <plus /> k1_minus kcat_1 kr <divide /> E1_T A2_T e1_e0_star <times /> <divide /> kx_minus kr <divide /> E4_T A2_T e0_star_e4_star <plus /> <times /> <divide /> kr_2 kr e0_star <times /> <divide /> kr_12 kr e0_star <times /> <divide /> <times /> k1_plus E1_T kr e0_star e1 <times /> <divide /> <times /> kx_plus E4_T kr e0_star e4_star
<eq /> <diff /> time e0_star_e4_star <minus /> <times /> <divide /> <times /> kx_plus A2_T kr e4_star e0_star <times /> <plus /> <divide /> kx_minus kr <divide /> kcat_x kr e0_star_e4_star
Total number of activating enzymes at stage 2
Total number of deactivating enzymes at stage 1
Concentration of active signaling enzyme 1
Concentration of transition complex between active substrate E1* and deactivating enzyme P1
Concentration of transition complex between inactive substrate E2 and its activator E1*
<eq /> e1 <minus /> 1.0 <plus /> e1_e0_star e1_star <times /> <divide /> E2_T E1_T e2_e1_star <times /> <divide /> P1_T E1_T e1_star_p1
<eq /> <diff /> time e1_e0_star <minus /> <times /> <divide /> <times /> k1_plus A2_T kr e1 e0_star <times /> <plus /> <divide /> k1_minus kr <divide /> kcat_1 kr e1_e0_star
Inactive signaling enzyme 2
Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*)
Concentration of deactivating enzyme P1
<eq /> <diff /> time e1_star <minus /> <plus /> <times /> <divide /> kcat_1 kr e1_e0_star <times /> <divide /> <plus /> k2_minus kcat_2 kr <divide /> E2_T E1_T e2_e1_star <times /> <divide /> kP1_minus kr <divide /> P1_T E1_T e1_star_p1 <plus /> <times /> <divide /> <times /> k2_plus E2_T kr e1_star e2 <times /> <divide /> <times /> kP1_plus P1_T kr e1_star p1
<eq /> <diff /> time e1_star_p1 <minus /> <times /> <divide /> <times /> kP1_plus E1_T kr e1_star p1 <times /> <plus /> <divide /> kP1_minus kr <divide /> kcat_P1 kr e1_star_p1
Total number of activating enzymes at stage 3
Concentration of inactive signaling enzyme 2
Concentration of nonfunctional second enzyme
Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of transition complex between active substrate E2* and deactivating enzyme P2
Concentration of transition complex between inactive substrate E3 and its activator E2*
Concentration of active signaling enzyme 3
<eq /> e2 <minus /> 1.0 <plus /> e3_e2_star e3_star <times /> <divide /> E3_T E2_T e3_e2_star <times /> <divide /> E4_T E2_T e2_star_e4_star <times /> <divide /> P2_T E2_T e2_star_p2
<eq /> <diff /> time e2_e1_star <minus /> <times /> <divide /> <times /> k2_plus E1_T kr e2 e1_star <times /> <plus /> <divide /> k2_minus kr <divide /> kcat_2 kr e2_e1_star
<eq /> <diff /> time e2_minus <times /> <divide /> kcat_z kr <divide /> E4_T E2_T e2_star_e4_star
Concentration of active signaling enzyme 2
Concentration of inactive signaling enzyme 3
Concentration of deactivating enzyme P2
<eq /> <diff /> time e2_star <minus /> <plus /> <times /> <divide /> kcat_2 kr e2_e1_star <times /> <divide /> <plus /> k3_minus kcat_3 kr <divide /> E3_T E2_T e3_e2_star <times /> <divide /> kP2_minus kr <divide /> P2_T E2_T e2_star_p2 <times /> <divide /> kz_minus kr <divide /> E4_T E2_T e2_star_e4_star <plus /> <times /> <divide /> <times /> k3_plus E3_T kr e2_star e3 <times /> <divide /> <times /> kP2_plus P2_T kr e2_star p2 <times /> <divide /> <times /> kz_plus E4_T kr e2_star e4_star
<eq /> <diff /> time e2_star_e4_star <minus /> <times /> <divide /> <times /> kz_plus E2_T kr e4_star e2_star <times /> <plus /> <divide /> kz_minus kr <divide /> kcat_z kr e2_star_e4_star
<eq /> <diff /> time e2_star_p2 <minus /> <times /> <divide /> <times /> kP2_plus E2_T kr e2_star p2 <times /> <plus /> <divide /> kP2_minus kr <divide /> kcat_P2 kr e2_star_p2
Concentration of transition complex between active substrate E3* and deactivating enzyme P3
Concentration of transition complex between inactive substrate E4 and its activator E3*
<eq /> e3 <minus /> 1.0 <plus /> e3_e2_star e3_star <times /> <divide /> E4_T E3_T e4_e3_star <times /> <divide /> P3_T E3_T e3_star_p3
<eq /> <diff /> time e3_e2_star <minus /> <times /> <divide /> <times /> k3_plus E2_T kr e3 e2_star <times /> <plus /> <divide /> k3_minus kr <divide /> kcat_3 kr e3_e2_star
Concentration of inactive signaling enzyme 4
Concentration of deactivating enzyme P3
<eq /> <diff /> time e3_star <minus /> <plus /> <times /> <divide /> kcat_3 kr e3_e2_star <times /> <divide /> <plus /> k4_minus kcat_4 kr <divide /> E4_T E3_T e4_e3_star <times /> <divide /> kP3_minus kr <divide /> P3_T E3_T e3_star_p3 <plus /> <times /> <divide /> <times /> k4_plus E4_T kr e3_star e4 <times /> <divide /> <times /> kP3_plus P3_T kr e3_star p3
<eq /> <diff /> time e3_star_p3 <minus /> <times /> <divide /> <times /> kP3_plus E3_T kr e3_star p3 <times /> <plus /> <divide /> kP3_minus kr <divide /> kcat_P3 kr e3_star_p3
Total number of activating enzymes at stage 5
Concentration of transition complex between active substrate E4* and deactivating enzyme P4
Concentration of transition complex between inactive substrate E5 and its activator E4*
<eq /> e4 <minus /> 1.0 <plus /> e4_e3_star e4_star <times /> <divide /> E5_T E4_T e5_e4_star <times /> <divide /> P4_T E4_T e4_star_p4 e0_star_e4_star e2_star_e4_star
<eq /> <diff /> time e4_e3_star <minus /> <times /> <divide /> <times /> k4_plus E3_T kr e4 e3_star <times /> <plus /> <divide /> k4_minus kr <divide /> kcat_4 kr e4_e3_star
Inactive signaling enzyme 5
Concentration of deactivating enzyme P4
<eq /> <diff /> time e4_star <minus /> <plus /> <times /> <divide /> kcat_4 kr e4_e3_star <times /> <divide /> <plus /> k5_minus kcat_5 kr <divide /> E5_T E4_T e5_e4_star <times /> <divide /> kP4_minus kr <divide /> P4_T E4_T e4_star_p4 <times /> <plus /> <divide /> kx_minus kr <divide /> kcat_x kr e0_star_e4_star <times /> <plus /> <divide /> kz_minus kr <divide /> kcat_z kr e2_star_e4_star <plus /> <times /> <divide /> <times /> k5_plus E5_T kr e4_star e5 <times /> <divide /> <times /> kP4_plus P4_T kr e4_star p4 <times /> <divide /> <times /> kx_plus A2_T kr e0_star e4_star <times /> <divide /> <times /> kz_plus E2_T kr e2_star e4_star
<eq /> <diff /> time e4_star_p4 <minus /> <times /> <divide /> <times /> kP4_plus E4_T kr e4_star p4 <times /> <plus /> <divide /> kP4_minus kr <divide /> kcat_P4 kr e4_star_p4
Concentration of inactive signaling enzyme 5
Concentration of active signaling enzyme 5
Concentration of transition complex between active substrate E5* and deactivating enzyme P5
<eq /> e5 <minus /> 1.0 <plus /> e5_e4_star e5_star <times /> <divide /> P5_T E5_T e5_star_p5
<eq /> <diff /> time e5_e4_star <minus /> <times /> <divide /> <times /> k5_plus E4_T kr e5 e4_star <times /> <plus /> <divide /> k5_minus kr <divide /> kcat_5 kr e5_e4_star
Concentration of deactivating enzyme P5
<eq /> <diff /> time e5_star <minus /> <plus /> <times /> <divide /> kcat_5 kr e5_e4_star <times /> <divide /> kP5_minus kr <divide /> P5_T E5_T e5_star_p5 <times /> <divide /> <times /> kP5_plus P5_T kr e5_star p5
<eq /> <diff /> time e5_star_p5 <minus /> <times /> <divide /> <times /> kP5_plus E5_T kr e5_star p5 <times /> <plus /> <divide /> kP5_minus kr <divide /> kcat_P5 kr e5_star_p5
Forward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2)
<eq /> r <minus /> 1.0 <plus /> c <times /> 2.0 <plus /> c2 c_star <times /> <divide /> A1_T R0 c_star_a1 <times /> <divide /> A2_T R0 e0_star <times /> <divide /> E4_T R0 e0_star_e4_star <times /> <divide /> E1_T R0 e1_e0_star