- Author:
- Dougal Cowan <devnull@localhost>
- Date:
- 2013-02-05 12:27:11+13:00
- Desc:
- Replaced the annotated model file with a new version containing identifiers.org URIs instead of MIRIAM URNs.
This version was created by Alan Garny after discussion with Camille Laibe.
These annotated models were used in development of OpenCOR's annotation features.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/goldbeter_1991/rawfile/d4499286b0a177a10456a48c41e3fe34e63e827d/goldbeter_annotated_1991.cellml
<?xml version='1.0' encoding='utf-8'?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" cmeta:id="goldbeter_1991" name="goldbeter_1991">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Minimal Cascade Model for the Mitotic Oscillator Involving Cyclin and cdc2 Kinase</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
The CellML model runs in OpenCell to reproduce figure 3 of the published paper. The model also runs in COR but doe to the long duration of the simulation (100 minutes) COR is not reall suitable for such a simulation. The units have been checked and they are consistent. Please note that this particular version of the CellML model has been annotated using MIRIAM URIs. These annotations were based on the <ulink url="http://www.ebi.ac.uk/biomodels-main/BIOMD0000000003">SBML version</ulink> of this model in the BioModels Database.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Felix, M. A., Labbe, J. C., Doree, M., Hunt, T. and Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase, Albert Goldbeter, 1991, <emphasis>Proceedings of the National Academy of Sciences</emphasis>, 88, 9107-9111. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/1833774">PubMed ID: 1833774</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="goldbeter_1991_diagram.png"/>
</imageobject>
</mediaobject>
<caption>Minimal cascade model for the mitotic oscillations between cyclin and cdc2 kinase (M) during the cell cycle. X represents the fraction of active (phosphorylated) cyclin protease. * represents the fraction of inactive enzymes.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="minute">
<unit units="second" multiplier="60"/>
</units>
<units name="first_order_rate_constant">
<unit units="minute" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<component name="environment">
<variable units="minute" public_interface="out" cmeta:id="environment_time" name="time"/>
</component>
<component cmeta:id="C" name="C">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="#C">
<dc:title>C</dc:title>
<dcterms:alternative>cyclin concentration</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" cmeta:id="C_C" name="C" initial_value="0.01">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#C_C">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/uniprot/Q4KLA0"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/interpro/IPR006670"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000252"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="in" name="X"/>
<variable units="first_order_rate_constant" public_interface="in" name="kd"/>
<variable units="micromolar" public_interface="in" name="Kd"/>
<variable units="flux" public_interface="in" name="vi"/>
<variable units="flux" public_interface="in" name="vd"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>vd</ci>
<ci>X</ci>
<ci>C</ci>
</apply>
<apply>
<plus/>
<ci>Kd</ci>
<ci>C</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kd</ci>
<ci>C</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="M" name="M">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="#M">
<dc:title>M</dc:title>
<dcterms:alternative>fraction of active cdc2 kinase</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" cmeta:id="M_M" name="M" initial_value="0.01">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#M_M">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/uniprot/P24033"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/uniprot/P35567"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000252"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="in" name="M_star" cmeta:id="M_M_"/>
<variable units="first_order_rate_constant" public_interface="in" name="V1"/>
<variable units="first_order_rate_constant" public_interface="in" name="V2"/>
<variable units="dimensionless" public_interface="in" name="K1"/>
<variable units="dimensionless" public_interface="in" name="K2"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>V1</ci>
<ci>M_star</ci>
</apply>
<apply>
<plus/>
<ci>K1</ci>
<ci>M_star</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>V2</ci>
<ci>M</ci>
</apply>
<apply>
<plus/>
<ci>K2</ci>
<ci>M</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="M_star" name="M_star">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="#M_star">
<dc:title>M_star</dc:title>
<dcterms:alternative>fraction of inactive cdc2 kinase</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="M_star" cmeta:id="M_M_" >
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#M_M_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/uniprot/P24033"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/uniprot/P35567"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000252"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="in" cmeta:id="M_M" name="M"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>M_star</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>M</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="X" name="X">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="#X">
<dc:title>X</dc:title>
<dcterms:alternative>fraction of active cyclin protease</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" cmeta:id="X_X" name="X" initial_value="0.01">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#X_X">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.go/GO:0005680"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000297"/>
<bqbiol:hasVersion rdf:resource="http://identifiers.org/reactome/REACT_7165.1"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="in" name="X_star" cmeta:id="X_X_"/>
<variable units="first_order_rate_constant" public_interface="in" name="V3"/>
<variable units="first_order_rate_constant" public_interface="in" name="V4"/>
<variable units="dimensionless" public_interface="in" name="K3"/>
<variable units="dimensionless" public_interface="in" name="K4"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>V3</ci>
<ci>X_star</ci>
</apply>
<apply>
<plus/>
<ci>K3</ci>
<ci>X_star</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>V4</ci>
<ci>X</ci>
</apply>
<apply>
<plus/>
<ci>K4</ci>
<ci>X</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="X_star" name="X_star">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="#X_star">
<dc:title>X_star</dc:title>
<dcterms:alternative>fraction of inactive cyclin protease</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="X_star" cmeta:id="X_X_">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#X_X_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.go/GO:0005680"/>
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000297"/>
<bqbiol:hasVersion rdf:resource="http://identifiers.org/reactome/REACT_7165.1"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="in" cmeta:id="X_X" name="X"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>X_star</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>X</ci>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="flux" public_interface="out" name="vi" cmeta:id="vi_" initial_value="0.025">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#vi_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000048"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="flux" public_interface="out" name="vd" cmeta:id="vd_" initial_value="0.25">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#vd_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000186"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="first_order_rate_constant" public_interface="out" name="kd" cmeta:id="kd_" initial_value="0.01">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#kd_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000022"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="micromolar" public_interface="out" name="Kd" cmeta:id="Kd_" initial_value="0.02">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#Kd_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000027"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="micromolar" public_interface="out" name="Kc" cmeta:id="kc_" initial_value="0.5">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#kc_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000027"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="out" name="K1" cmeta:id="K1_" initial_value="0.005">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#K1_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000027"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="out" name="K2" cmeta:id="K2_" initial_value="0.005">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#K2_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000027"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="out" name="K3" cmeta:id="K3_" initial_value="0.005">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#K3_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000027"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="dimensionless" public_interface="out" name="K4" cmeta:id="K4_" initial_value="0.005">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#K4_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000027"/>
</rdf:Description>
</rdf:RDF>
</variable>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#V1_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000186"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="first_order_rate_constant" public_interface="out" name="V2" cmeta:id="V2_" initial_value="1.5">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#V2_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000186"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="first_order_rate_constant" public_interface="out" name="V3" cmeta:id="V3_">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
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<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000186"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="first_order_rate_constant" public_interface="out" name="V4" cmeta:id="V4_" initial_value="0.5">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#V4_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000186"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="first_order_rate_constant" public_interface="out" name="VM1" cmeta:id="VM1_" initial_value="3">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#VM1_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000025"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="first_order_rate_constant" public_interface="out" name="VM3" cmeta:id="VM3_" initial_value="1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="#VM1_">
<bqbiol:isVersionOf rdf:resource="http://identifiers.org/obo.sbo/SBO:0000186"/>
</rdf:Description>
</rdf:RDF>
</variable>
<variable units="micromolar" public_interface="in" name="C"/>
<variable units="dimensionless" public_interface="in" name="M"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>VM1</ci>
<ci>C</ci>
</apply>
<apply>
<plus/>
<ci>Kc</ci>
<ci>C</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V3</ci>
<apply>
<times/>
<ci>M</ci>
<ci>VM3</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="C" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="M" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="X" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="M" component_1="M_star"/>
<map_variables variable_2="M" variable_1="M"/>
<map_variables variable_2="M_star" variable_1="M_star"/>
</connection>
<connection>
<map_components component_2="X" component_1="X_star"/>
<map_variables variable_2="X" variable_1="X"/>
<map_variables variable_2="X_star" variable_1="X_star"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="C"/>
<map_variables variable_2="kd" variable_1="kd"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="vi" variable_1="vi"/>
<map_variables variable_2="vd" variable_1="vd"/>
<map_variables variable_2="C" variable_1="C"/>
</connection>
<connection>
<map_components component_2="X" component_1="C"/>
<map_variables variable_2="X" variable_1="X"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="M"/>
<map_variables variable_2="V1" variable_1="V1"/>
<map_variables variable_2="V2" variable_1="V2"/>
<map_variables variable_2="K1" variable_1="K1"/>
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A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase
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