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<articleinfo>
<title>A multiscale model to investigate circadian rhythmicity of pacemaker neurons in the suprachiasmatic nucleus</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>
This model runs in both OpenCell and COR to replicate the published results (figure 2). This CellML model translation is based on the curated SBML model in the BioModels database (BIOMD0000000246.xml) which in turn was based on the original author's Matlab code. Note that in order to replicate figure 2 the model has to be run for at least 200 hours to allow the oscillations to stabilise (and for 500 hours to clearly see the stablisation).
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The suprachiasmatic nucleus (SCN) of the hypothalamus is a multicellular system that drives daily rhythms in mammalian behavior and physiology. Although the gene regulatory network that produces daily oscillations within individual neurons is well characterized, less is known about the electrophysiology of the SCN cells and how firing rate correlates with circadian gene expression. We developed a firing rate code model to incorporate known electrophysiological properties of SCN pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances. Calcium dynamics were included in the model as the putative link between electrical firing and gene expression. Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships. VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression. Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents (nimodipine, IP3- and ryanodine-blockers) reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription. The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity. The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
A multiscale model to investigate circadian rhythmicity of pacemaker neurons in the suprachiasmatic nucleus, Vasalou C, Henson MA, 2010, <emphasis>PLoS Computational Biology</emphasis>, 6, e1000706. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/20300645">PubMed ID: 20300645</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram1">
<mediaobject>
<imageobject>
<imagedata fileref="vasalou_henson_2010.png"/>
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<caption>Schematic representation of the SCN neuron model</caption>
</informalfigure>
<informalfigure float="0" id="fig_cell_diagram1">
<mediaobject>
<imageobject>
<imagedata fileref="leloup_2003.png"/>
</imageobject>
</mediaobject>
<caption>Leloup and Goldbeter 2003 model for circadian oscillations in mammals involving interlocked negative and positive regulations of <emphasis>Per</emphasis>, <emphasis>Cry</emphasis>, <emphasis>Bmal1</emphasis>, and <emphasis>Rev-Erb</emphasis> genes by their protein products.</caption>
</informalfigure>
</sect1>
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<ci> E_Na </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> E_Na_0 </ci>
<apply>
<plus/>
<ci> T </ci>
<ci> T_abs </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> T_room </ci>
<ci> T_abs </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> E_L </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> E_L_0 </ci>
<apply>
<plus/>
<ci> T </ci>
<ci> T_abs </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> T_room </ci>
<ci> T_abs </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> k_q </ci>
<apply>
<plus/>
<ci> T </ci>
<ci> T_abs </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ca_ex </ci>
<ci> Ca_in </ci>
</apply>
</apply>
<cn cellml:units="milliV"> 1000.0 </cn>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> E_inhib </ci>
<apply>
<times/>
<apply>
<minus/>
<ci> k_q </ci>
</apply>
<apply>
<plus/>
<ci> T </ci>
<ci> T_abs </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cl_ex </ci>
<ci> Cl_in </ci>
</apply>
</apply>
<cn cellml:units="milliV"> 1000.0 </cn>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<minus/>
<ci> V_rest </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_abs_calculation">
<eq/>
<ci> i_Na_abs </ci>
<apply>
<root/>
<apply>
<power/>
<ci> i_Na </ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_K_calculation">
<eq/>
<ci> g_K </ci>
<apply>
<plus/>
<ci> g_K0 </ci>
<apply>
<times/>
<ci> v_gk </ci>
<apply>
<divide/>
<ci> MP </ci>
<apply>
<plus/>
<ci> K_gk </ci>
<ci> MP </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K </ci>
<apply>
<minus/>
<ci> V_rest </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_Ca_calculation">
<eq/>
<ci> g_Ca </ci>
<apply>
<times/>
<ci> v_Ca </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> MP </ci>
<ci> nca </ci>
</apply>
<apply>
<plus/>
<ci> K_Ca </ci>
<apply>
<power/>
<ci> MP </ci>
<ci> nca </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_calculation">
<eq/>
<ci> i_Ca </ci>
<apply>
<times/>
<ci> g_Ca </ci>
<apply>
<minus/>
<ci> V_rest </ci>
<ci> E_Ca </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_KCa_calculation">
<eq/>
<ci> g_KCa </ci>
<apply>
<times/>
<ci> v_KCa </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> CC </ci>
<ci> nkca </ci>
</apply>
<apply>
<plus/>
<ci> K_KCa </ci>
<apply>
<power/>
<ci> CC </ci>
<ci> nkca </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_KCa_calculation">
<eq/>
<ci> i_KCa </ci>
<apply>
<times/>
<ci> g_KCa </ci>
<apply>
<minus/>
<ci> V_rest </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_L_calculation">
<eq/>
<ci> g_L </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1 </cn>
<ci> Res </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_L_calculation">
<eq/>
<ci> i_L </ci>
<apply>
<times/>
<ci> g_L </ci>
<apply>
<minus/>
<ci> V_rest </ci>
<ci> E_L </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_ex_calculation">
<eq/>
<ci> g_ex </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> v_ex1 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> i_Na_abs </ci>
<ci> nex1 </ci>
</apply>
<apply>
<plus/>
<ci> K_ex1 </ci>
<apply>
<power/>
<ci> i_Na_abs </ci>
<ci> nex1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> v_ex2 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_in </ci>
<ci> nex2 </ci>
</apply>
<apply>
<plus/>
<ci> K_ex2 </ci>
<apply>
<power/>
<ci> Ca_in </ci>
<ci> nex2 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_ex_calculation">
<eq/>
<ci> i_ex </ci>
<apply>
<times/>
<ci> g_ex </ci>
<apply>
<minus/>
<ci> V_rest </ci>
<ci> E_ex </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_inhib_calculation">
<eq/>
<ci> i_inhib </ci>
<apply>
<times/>
<ci> g_inhib </ci>
<apply>
<minus/>
<ci> V_rest </ci>
<ci> E_inhib </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="GABA_calculation">
<eq/>
<ci> GABA </ci>
<apply>
<plus/>
<ci> GABA0 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> v_GABA </ci>
<ci> VIP </ci>
</apply>
<apply>
<plus/>
<ci> K_GABA </ci>
<ci> VIP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="beta_calculation">
<eq/>
<ci> beta </ci>
<apply>
<divide/>
<ci> VIP </ci>
<apply>
<plus/>
<ci> VIP </ci>
<ci> K_D </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="v_sPC_calculation">
<eq/>
<ci> v_sPC </ci>
<apply>
<plus/>
<ci> v_sP0 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> C_T </ci>
<ci> CB </ci>
</apply>
<apply>
<plus/>
<ci> K_C </ci>
<ci> CB </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cl_in_calculation">
<eq/>
<ci> Cl_in </ci>
<apply>
<plus/>
<ci> Cl0 </ci>
<apply>
<times/>
<ci> v_Cl1 </ci>
<apply>
<divide/>
<ci> MP </ci>
<apply>
<plus/>
<ci> K_Cl1 </ci>
<ci> MP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> v_Cl2 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> GABA </ci>
<ci> nCl </ci>
</apply>
<apply>
<plus/>
<ci> K_Cl2 </ci>
<apply>
<power/>
<ci> GABA </ci>
<ci> nCl </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_K_calculation">
<eq/>
<ci> V_K </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci> V_MK </ci>
<ci> Ca_in </ci>
</apply>
<apply>
<plus/>
<ci> k_MK </ci>
<ci> Ca_in </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V_b </ci>
<ci> beta </ci>
</apply>
<apply>
<plus/>
<ci> k_b </ci>
<ci> beta </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_in" cmeta:id="Ca_in">
<rdf:RDF>
<rdf:Description rdf:about="#Ca_in">
<dc:title>Ca_in</dc:title>
<dcterms:alternative>cytosolic calcium concentration</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="microM" public_interface="out" name="Ca_in" initial_value="0.1"/>
<variable units="dimensionless" name="beta_IP3" initial_value="0.5"/>
<variable units="nanoM" name="Ca_store" initial_value="0.1"/>
<variable units="microM_per_hour" name="v0"/>
<variable units="microM_per_hour" name="v1"/>
<variable units="microM_per_hour" name="v2"/>
<variable units="microM_per_hour" name="v3"/>
<variable units="per_microM_per_hour" name="v_kk" initial_value="3.3"/>
<variable units="microM_per_hour" name="v_v0" initial_value="0.09"/>
<variable units="per_hour" name="kf" initial_value="0.001"/>
<variable units="per_microM_per_hour" name="k"/>
<variable units="dimensionless" name="nkk" initial_value="0.1"/>
<variable units="dimensionless" name="nv0" initial_value="4.5"/>
<variable units="dimensionless" name="m" initial_value="6.0"/>
<variable units="dimensionless" name="n" initial_value="2.2"/>
<variable units="dimensionless" name="p" initial_value="4.2"/>
<variable units="dimensionless" name="v" initial_value="2.0"/>
<variable units="nanoM_0_1" name="K_kk" initial_value="0.02"/>
<variable units="nanoM_4_5" name="K_v0" initial_value="4.5"/>
<variable units="microM" name="K_2" initial_value="5.0"/>
<variable units="microM" name="K_R" initial_value="3.0"/>
<variable units="microM" name="K_A" initial_value="0.67"/>
<variable units="microM_per_hour" name="v_M1" initial_value="0.0003"/>
<variable units="microM_per_hour" name="v_M2" initial_value="149.5"/>
<variable units="microM_per_hour" name="v_M3" initial_value="400.0"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="nanoM" public_interface="in" name="MP"/>
<variable units="nanoM" public_interface="in" name="CC"/>
<variable units="nanoM" public_interface="in" name="BC"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_in </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> v0 </ci>
<ci> v1 </ci>
<ci> v3 </ci>
<apply>
<times/>
<ci> kf </ci>
<ci> Ca_store </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> v2 </ci>
<apply>
<times/>
<ci> k </ci>
<apply>
<power/>
<ci> Ca_in </ci>
<ci> v </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_store_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_store </ci>
</apply>
<apply>
<minus/>
<ci> v2 </ci>
<apply>
<plus/>
<ci> v3 </ci>
<apply>
<times/>
<ci> kf </ci>
<ci> Ca_store </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k_calculation">
<eq/>
<ci> k </ci>
<apply>
<times/>
<ci> v_kk </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> CC </ci>
<ci> nkk </ci>
</apply>
<apply>
<plus/>
<ci> K_kk </ci>
<apply>
<power/>
<ci> CC </ci>
<ci> nkk </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="v0_calculation">
<eq/>
<ci> v0 </ci>
<apply>
<times/>
<ci> v_v0 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> BC </ci>
<ci> nv0 </ci>
</apply>
<apply>
<plus/>
<ci> K_v0 </ci>
<apply>
<power/>
<ci> BC </ci>
<ci> nv0 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="v1_calculation">
<eq/>
<ci> v1 </ci>
<apply>
<times/>
<ci> v_M1 </ci>
<ci> beta_IP3 </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="v2_calculation">
<eq/>
<ci> v2 </ci>
<apply>
<times/>
<ci> v_M2 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_in </ci>
<ci> n </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K_2 </ci>
<ci> n </ci>
</apply>
<apply>
<power/>
<ci> Ca_in </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="v3_calculation">
<eq/>
<ci> v3 </ci>
<apply>
<times/>
<ci> v_M3 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_store </ci>
<ci> m </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K_R </ci>
<ci> m </ci>
</apply>
<apply>
<power/>
<ci> Ca_store </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_in </ci>
<ci> p </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K_A </ci>
<ci> p </ci>
</apply>
<apply>
<power/>
<ci> Ca_in </ci>
<ci> p </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="VIP" cmeta:id="VIP">
<rdf:RDF>
<rdf:Description rdf:about="#VIP">
<dc:title>VIP</dc:title>
<dcterms:alternative>vasoactive intestinal polypeptide</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="VIP" initial_value="0.0"/>
<variable units="flux" name="v_VIP" initial_value="0.5"/>
<variable units="hertz_1_9" name="K_VIP" initial_value="15.0"/>
<variable units="nanoM_0_8_per_hour" name="kd_VIP" initial_value="0.5"/>
<variable units="dimensionless" name="nd_VIP" initial_value="0.2"/>
<variable units="dimensionless" name="n_VIP" initial_value="1.9"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="hertz" public_interface="in" name="fr"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="VIP_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> VIP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> v_VIP </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> fr </ci>
<ci> n_VIP </ci>
</apply>
<apply>
<plus/>
<ci> K_VIP </ci>
<apply>
<power/>
<ci> fr </ci>
<ci> n_VIP </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kd_VIP </ci>
<apply>
<power/>
<ci> VIP </ci>
<ci> nd_VIP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MP" cmeta:id="MP">
<rdf:RDF>
<rdf:Description rdf:about="#MP">
<dc:title>MP</dc:title>
<dcterms:alternative>Per mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="MP" cmeta:id="MP_MP" initial_value="2.8"/>
<variable units="flux" name="vmP" initial_value="1.1"/>
<variable units="first_order_rate_constant" name="kdmp" initial_value="0.01"/>
<variable units="nanoM" name="KAP" initial_value="0.6"/>
<variable units="nanoM" name="KmP" initial_value="0.31"/>
<variable units="dimensionless" public_interface="in" name="n"/>
<variable units="nanoM" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="flux" public_interface="in" name="v_sPC"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> MP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> v_sPC </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KAP </ci>
<ci> n </ci>
</apply>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> vmP </ci>
<apply>
<divide/>
<ci> MP </ci>
<apply>
<plus/>
<ci> KmP </ci>
<ci> MP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdmp </ci>
<ci> MP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MC" cmeta:id="MC">
<rdf:RDF>
<rdf:Description rdf:about="#MC">
<dc:title>MC</dc:title>
<dcterms:alternative>Cry mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="MC" cmeta:id="MC_MC" initial_value="2.0"/>
<variable units="flux" name="vsC" initial_value="1.1"/>
<variable units="flux" name="vmC" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="kdmc" initial_value="0.01"/>
<variable units="nanoM" name="KAC" initial_value="0.6"/>
<variable units="nanoM" name="KmC" initial_value="0.4"/>
<variable units="dimensionless" public_interface="in" name="n"/>
<variable units="nanoM" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> MC </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> vsC </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KAC </ci>
<ci> n </ci>
</apply>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> vmC </ci>
<apply>
<divide/>
<ci> MC </ci>
<apply>
<plus/>
<ci> KmC </ci>
<ci> MC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdmc </ci>
<ci> MC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MB" cmeta:id="MB">
<rdf:RDF>
<rdf:Description rdf:about="#MB">
<dc:title>MB</dc:title>
<dcterms:alternative>Bmal1 mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="MB" cmeta:id="MB_MB" initial_value="7.94"/>
<variable units="flux" name="vsB" initial_value="1.0"/>
<variable units="flux" name="vmB" initial_value="0.8"/>
<variable units="first_order_rate_constant" name="kdmb" initial_value="0.01"/>
<variable units="nanoM" name="KIB" initial_value="2.2"/>
<variable units="nanoM" name="KmB" initial_value="0.4"/>
<variable units="nanoM" public_interface="in" name="BN"/>
<variable units="dimensionless" public_interface="in" name="m"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> MB </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> vsB </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> KIB </ci>
<ci> m </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KIB </ci>
<ci> m </ci>
</apply>
<apply>
<power/>
<ci> BN </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> vmB </ci>
<apply>
<divide/>
<ci> MB </ci>
<apply>
<plus/>
<ci> KmB </ci>
<ci> MB </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdmb </ci>
<ci> MB </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PC" cmeta:id="PC">
<rdf:RDF>
<rdf:Description rdf:about="#PC">
<dc:title>PC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated PER protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="PC" cmeta:id="PC_PC" initial_value="0.4"/>
<variable units="first_order_rate_constant" public_interface="in" name="ksP"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="second_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k4"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1P"/>
<variable units="flux" public_interface="in" name="V2P"/>
<variable units="nanoM" public_interface="in" name="PCP"/>
<variable units="nanoM" public_interface="in" name="PCC"/>
<variable units="nanoM" public_interface="in" name="CC"/>
<variable units="nanoM" public_interface="in" name="MP"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> ksP </ci>
<ci> MP </ci>
</apply>
<apply>
<times/>
<ci> V2P </ci>
<apply>
<divide/>
<ci> PCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k4 </ci>
<ci> PCC </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V1P </ci>
<apply>
<divide/>
<ci> PC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> PC </ci>
<ci> CC </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CC" cmeta:id="CC">
<rdf:RDF>
<rdf:Description rdf:about="#CC">
<dc:title>CC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated CRY protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="CC" cmeta:id="CC_CC" initial_value="12.0"/>
<variable units="first_order_rate_constant" public_interface="in" name="ksC"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="second_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k4"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdnc"/>
<variable units="flux" public_interface="in" name="V1C"/>
<variable units="flux" public_interface="in" name="V2C"/>
<variable units="nanoM" public_interface="in" name="CCP"/>
<variable units="nanoM" public_interface="in" name="PC"/>
<variable units="nanoM" public_interface="in" name="PCC"/>
<variable units="nanoM" public_interface="in" name="MC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> CC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> ksC </ci>
<ci> MC </ci>
</apply>
<apply>
<times/>
<ci> V2C </ci>
<apply>
<divide/>
<ci> CCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> CCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k4 </ci>
<ci> PCC </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V1C </ci>
<apply>
<divide/>
<ci> CC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> CC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> PC </ci>
<ci> CC </ci>
</apply>
<apply>
<times/>
<ci> kdnc </ci>
<ci> CC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCP" cmeta:id="PCP">
<rdf:RDF>
<rdf:Description rdf:about="#PCP">
<dc:title>PCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated PER protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="PCP" cmeta:id="PCP_PCP" initial_value="0.13"/>
<variable units="flux" public_interface="in" name="vdPC"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="nanoM" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1P"/>
<variable units="flux" public_interface="in" name="V2P"/>
<variable units="nanoM" public_interface="in" name="PC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1P </ci>
<apply>
<divide/>
<ci> PC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2P </ci>
<apply>
<divide/>
<ci> PCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdPC </ci>
<apply>
<divide/>
<ci> PCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CCP" cmeta:id="CCP">
<rdf:RDF>
<rdf:Description rdf:about="#CCP">
<dc:title>CCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated CRY protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="CCP" cmeta:id="CCP_CCP" initial_value="9.0"/>
<variable units="flux" public_interface="in" name="vdCC"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="nanoM" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1C"/>
<variable units="flux" public_interface="in" name="V2C"/>
<variable units="nanoM" public_interface="in" name="CC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> CCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1C </ci>
<apply>
<divide/>
<ci> CC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> CC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2C </ci>
<apply>
<divide/>
<ci> CCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> CCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdCC </ci>
<apply>
<divide/>
<ci> CCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> CCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> CCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCC" cmeta:id="PCC">
<rdf:RDF>
<rdf:Description rdf:about="#PCC">
<dc:title>PCC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="PCC" cmeta:id="PCC_PCC" initial_value="1.26"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="k1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k2"/>
<variable units="second_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k4"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1PC"/>
<variable units="flux" public_interface="in" name="V2PC"/>
<variable units="nanoM" public_interface="in" name="PCCP"/>
<variable units="nanoM" public_interface="in" name="PCN"/>
<variable units="nanoM" public_interface="in" name="PC"/>
<variable units="nanoM" public_interface="in" name="CC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V2PC </ci>
<apply>
<divide/>
<ci> PCCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> PC </ci>
<ci> CC </ci>
</apply>
<apply>
<times/>
<ci> k2 </ci>
<ci> PCN </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V1PC </ci>
<apply>
<divide/>
<ci> PCC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k4 </ci>
<ci> PCC </ci>
</apply>
<apply>
<times/>
<ci> k1 </ci>
<ci> PCC </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCN" cmeta:id="PCN">
<rdf:RDF>
<rdf:Description rdf:about="#PCN">
<dc:title>PCN</dc:title>
<dcterms:alternative>nuclear non-phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="PCN" cmeta:id="PCN_PCN" initial_value="0.16"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="k1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k2"/>
<variable units="second_order_rate_constant" public_interface="in" name="k7"/>
<variable units="first_order_rate_constant" public_interface="in" name="k8"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3PC"/>
<variable units="flux" public_interface="in" name="V4PC"/>
<variable units="nanoM" public_interface="in" name="PCNP"/>
<variable units="nanoM" public_interface="in" name="PCC"/>
<variable units="nanoM" public_interface="in" name="BN"/>
<variable units="nanoM" public_interface="in" name="IN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCN </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V4PC </ci>
<apply>
<divide/>
<ci> PCNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k1 </ci>
<ci> PCC </ci>
</apply>
<apply>
<times/>
<ci> k8 </ci>
<ci> IN </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V3PC </ci>
<apply>
<divide/>
<ci> PCN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCN </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k2 </ci>
<ci> PCN </ci>
</apply>
<apply>
<times/>
<ci> k7 </ci>
<ci> BN </ci>
<ci> PCN </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCCP" cmeta:id="PCCP">
<rdf:RDF>
<rdf:Description rdf:about="#PCCP">
<dc:title>PCCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="PCCP" cmeta:id="PCCP_PCCP" initial_value="0.2"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="nanoM" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1PC"/>
<variable units="flux" public_interface="in" name="V2PC"/>
<variable units="flux" public_interface="in" name="vdPCC"/>
<variable units="nanoM" public_interface="in" name="PCC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1PC </ci>
<apply>
<divide/>
<ci> PCC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2PC </ci>
<apply>
<divide/>
<ci> PCCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdPCC </ci>
<apply>
<divide/>
<ci> PCCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCNP" cmeta:id="PCNP">
<rdf:RDF>
<rdf:Description rdf:about="#PCNP">
<dc:title>PCNP</dc:title>
<dcterms:alternative>nuclear phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="PCNP" cmeta:id="PCNP_PCNP" initial_value="0.091"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="nanoM" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3PC"/>
<variable units="flux" public_interface="in" name="V4PC"/>
<variable units="flux" public_interface="in" name="vdPCN"/>
<variable units="nanoM" public_interface="in" name="PCN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCNP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V3PC </ci>
<apply>
<divide/>
<ci> PCN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCN </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V4PC </ci>
<apply>
<divide/>
<ci> PCNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdPCN </ci>
<apply>
<divide/>
<ci> PCNP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BC" cmeta:id="BC">
<rdf:RDF>
<rdf:Description rdf:about="#BC">
<dc:title>BC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="BC" cmeta:id="BC_BC" initial_value="2.41"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="ksB"/>
<variable units="first_order_rate_constant" public_interface="in" name="k5"/>
<variable units="first_order_rate_constant" public_interface="in" name="k6"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1B"/>
<variable units="flux" public_interface="in" name="V2B"/>
<variable units="nanoM" public_interface="in" name="MB"/>
<variable units="nanoM" public_interface="in" name="BCP"/>
<variable units="nanoM" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V2B </ci>
<apply>
<divide/>
<ci> BCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k6 </ci>
<ci> BN </ci>
</apply>
<apply>
<times/>
<ci> ksB </ci>
<ci> MB </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V1B </ci>
<apply>
<divide/>
<ci> BC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k5 </ci>
<ci> BC </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BCP" cmeta:id="BCP">
<rdf:RDF>
<rdf:Description rdf:about="#BCP">
<dc:title>BCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="BCP" cmeta:id="BCP_BCP" initial_value="0.48"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="nanoM" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1B"/>
<variable units="flux" public_interface="in" name="V2B"/>
<variable units="flux" public_interface="in" name="vdBC"/>
<variable units="nanoM" public_interface="in" name="BC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1B </ci>
<apply>
<divide/>
<ci> BC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2B </ci>
<apply>
<divide/>
<ci> BCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdBC </ci>
<apply>
<divide/>
<ci> BCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BN" cmeta:id="BN">
<rdf:RDF>
<rdf:Description rdf:about="#PCN">
<dc:title>BN</dc:title>
<dcterms:alternative>nuclear non-phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="BN" cmeta:id="BN_BN" initial_value="1.94"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="k5"/>
<variable units="first_order_rate_constant" public_interface="in" name="k6"/>
<variable units="second_order_rate_constant" public_interface="in" name="k7"/>
<variable units="first_order_rate_constant" public_interface="in" name="k8"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3B"/>
<variable units="flux" public_interface="in" name="V4B"/>
<variable units="nanoM" public_interface="in" name="BNP"/>
<variable units="nanoM" public_interface="in" name="BC"/>
<variable units="nanoM" public_interface="in" name="PCN"/>
<variable units="nanoM" public_interface="in" name="IN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BN </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V4B </ci>
<apply>
<divide/>
<ci> BNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k5 </ci>
<ci> BC </ci>
</apply>
<apply>
<times/>
<ci> k8 </ci>
<ci> IN </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V3B </ci>
<apply>
<divide/>
<ci> BN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BN </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k6 </ci>
<ci> BN </ci>
</apply>
<apply>
<times/>
<ci> k7 </ci>
<ci> BN </ci>
<ci> PCN </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BNP" cmeta:id="BNP">
<rdf:RDF>
<rdf:Description rdf:about="#BNP">
<dc:title>BNP</dc:title>
<dcterms:alternative>nuclear phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="BNP" cmeta:id="BNP_BNP" initial_value="0.32"/>
<variable units="nanoM" public_interface="in" name="Kp"/>
<variable units="nanoM" public_interface="in" name="Kdp"/>
<variable units="nanoM" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3B"/>
<variable units="flux" public_interface="in" name="V4B"/>
<variable units="flux" public_interface="in" name="vdBN"/>
<variable units="nanoM" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BNP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V3B </ci>
<apply>
<divide/>
<ci> BN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BN </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V4B </ci>
<apply>
<divide/>
<ci> BNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdBN </ci>
<apply>
<divide/>
<ci> BNP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="IN" cmeta:id="IN">
<rdf:RDF>
<rdf:Description rdf:about="#IN">
<dc:title>IN</dc:title>
<dcterms:alternative>nuclear inactive complex between PER-CRY and CLOCK-BMAL1</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="IN" cmeta:id="IN_IN" initial_value="0.05"/>
<variable units="nanoM" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="second_order_rate_constant" public_interface="in" name="k7"/>
<variable units="first_order_rate_constant" public_interface="in" name="k8"/>
<variable units="flux" public_interface="in" name="vdIN"/>
<variable units="nanoM" public_interface="in" name="PCN"/>
<variable units="nanoM" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> IN </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k7 </ci>
<ci> BN </ci>
<ci> PCN </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k8 </ci>
<ci> IN </ci>
</apply>
<apply>
<times/>
<ci> vdIN </ci>
<apply>
<divide/>
<ci> IN </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> IN </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> IN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CB" cmeta:id="CB">
<rdf:RDF>
<rdf:Description rdf:about="#CB">
<dc:title>CB</dc:title>
<dcterms:alternative>nuclear inactive complex between PER-CRY and CLOCK-BMAL1</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanoM" public_interface="out" name="CB" cmeta:id="CB_CB" initial_value="0.12"/>
<variable units="nanoM" name="K1CB" initial_value="0.01"/>
<variable units="nanoM" name="K2CB" initial_value="0.01"/>
<variable units="hour" name="WT" initial_value="1.0"/>
<variable units="nanoM" name="vP" initial_value="1.0"/>
<variable units="nanoM" public_interface="in" name="V_K"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> CB </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci> V_K </ci>
<apply>
<minus/>
<cn cellml:units="nanoM"> 1.0 </cn>
<ci> CB </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> K1CB </ci>
<cn cellml:units="nanoM"> 1.0 </cn>
</apply>
<ci> CB </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> vP </ci>
<ci> CB </ci>
</apply>
<apply>
<plus/>
<ci> K2CB </ci>
<ci> CB </ci>
</apply>
</apply>
</apply>
<ci> WT </ci>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="first_order_rate_constant" public_interface="out" name="k1" initial_value="0.45"/>
<variable units="first_order_rate_constant" public_interface="out" name="k2" initial_value="0.2"/>
<variable units="second_order_rate_constant" public_interface="out" name="k3" initial_value="0.4"/>
<variable units="first_order_rate_constant" public_interface="out" name="k4" initial_value="0.2"/>
<variable units="first_order_rate_constant" public_interface="out" name="k5" initial_value="0.4"/>
<variable units="first_order_rate_constant" public_interface="out" name="k6" initial_value="0.2"/>
<variable units="second_order_rate_constant" public_interface="out" name="k7" initial_value="0.5"/>
<variable units="first_order_rate_constant" public_interface="out" name="k8" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="out" name="kdnc" initial_value="0.12"/>
<variable units="first_order_rate_constant" public_interface="out" name="kdn" initial_value="0.01"/>
<variable units="first_order_rate_constant" public_interface="out" name="ksB" initial_value="0.12"/>
<variable units="first_order_rate_constant" public_interface="out" name="ksC" initial_value="1.6"/>
<variable units="first_order_rate_constant" public_interface="out" name="ksP" initial_value="0.6"/>
<variable units="dimensionless" public_interface="out" name="m" initial_value="2.0"/>
<variable units="dimensionless" public_interface="out" name="n" initial_value="4.0"/>
<variable units="nanoM" public_interface="out" name="Kd" initial_value="0.3"/>
<variable units="nanoM" public_interface="out" name="Kdp" initial_value="0.1"/>
<variable units="nanoM" public_interface="out" name="Kp" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="V1C" initial_value="0.6"/>
<variable units="flux" public_interface="out" name="V1P" initial_value="0.4"/>
<variable units="flux" public_interface="out" name="V1B" initial_value="0.5"/>
<variable units="flux" public_interface="out" name="V2B" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="V3B" initial_value="0.5"/>
<variable units="flux" public_interface="out" name="V4B" initial_value="0.2"/>
<variable units="flux" public_interface="out" name="V1PC" initial_value="0.4"/>
<variable units="flux" public_interface="out" name="V2C" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="V2P" initial_value="0.3"/>
<variable units="flux" public_interface="out" name="V2PC" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="V3PC" initial_value="0.4"/>
<variable units="flux" public_interface="out" name="V4PC" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="vdBC" initial_value="0.5"/>
<variable units="flux" public_interface="out" name="vdBN" initial_value="0.6"/>
<variable units="flux" public_interface="out" name="vdCC" initial_value="0.7"/>
<variable units="flux" public_interface="out" name="vdIN" initial_value="0.8"/>
<variable units="flux" public_interface="out" name="vdPC" initial_value="0.7"/>
<variable units="flux" public_interface="out" name="vdPCC" initial_value="0.7"/>
<variable units="flux" public_interface="out" name="vdPCN" initial_value="0.7"/>
</component>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_in"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="VIP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MB"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="CB"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="CC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="CCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCN"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCNP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BN"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BNP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="IN"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Ca_in"/>
<map_variables variable_2="Ca_in" variable_1="Ca_in"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="BC"/>
<map_variables variable_2="BC" variable_1="BC"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="MP"/>
<map_variables variable_2="MP" variable_1="MP"/>
<map_variables variable_2="v_sPC" variable_1="v_sPC"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="VIP"/>
<map_variables variable_2="VIP" variable_1="VIP"/>
<map_variables variable_2="fr" variable_1="fr"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="CC"/>
<map_variables variable_2="CC" variable_1="CC"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="CB"/>
<map_variables variable_2="CB" variable_1="CB"/>
<map_variables variable_2="V_K" variable_1="V_K"/>
</connection>
<connection>
<map_components component_2="Ca_in" component_1="MP"/>
<map_variables variable_2="MP" variable_1="MP"/>
</connection>
<connection>
<map_components component_2="Ca_in" component_1="CC"/>
<map_variables variable_2="CC" variable_1="CC"/>
</connection>
<connection>
<map_components component_2="Ca_in" component_1="BC"/>
<map_variables variable_2="BC" variable_1="BC"/>
</connection>
<connection>
<map_components component_2="BN" component_1="MP"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="MP"/>
<map_variables variable_2="n" variable_1="n"/>
</connection>
<connection>
<map_components component_2="BN" component_1="MC"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="MC"/>
<map_variables variable_2="n" variable_1="n"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="MB"/>
<map_variables variable_2="m" variable_1="m"/>
</connection>
<connection>
<map_components component_2="MP" component_1="PC"/>
<map_variables variable_2="MP" variable_1="MP"/>
</connection>
<connection>
<map_components component_2="PCP" component_1="PC"/>
<map_variables variable_2="PC" variable_1="PC"/>
<map_variables variable_2="PCP" variable_1="PCP"/>
</connection>
<connection>
<map_components component_2="PCC" component_1="PC"/>
<map_variables variable_2="PC" variable_1="PC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
</connection>
<connection>
<map_components component_2="CC" component_1="PC"/>
<map_variables variable_2="PC" variable_1="PC"/>
<map_variables variable_2="CC" variable_1="CC"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PC"/>
<map_variables variable_2="ksP" variable_1="ksP"/>
<map_variables variable_2="V1P" variable_1="V1P"/>
<map_variables variable_2="V2P" variable_1="V2P"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k3" variable_1="k3"/>
<map_variables variable_2="k4" variable_1="k4"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="MC" component_1="CC"/>
<map_variables variable_2="MC" variable_1="MC"/>
</connection>
<connection>
<map_components component_2="CCP" component_1="CC"/>
<map_variables variable_2="CC" variable_1="CC"/>
<map_variables variable_2="CCP" variable_1="CCP"/>
</connection>
<connection>
<map_components component_2="PCC" component_1="CC"/>
<map_variables variable_2="CC" variable_1="CC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="CC"/>
<map_variables variable_2="ksC" variable_1="ksC"/>
<map_variables variable_2="V1C" variable_1="V1C"/>
<map_variables variable_2="V2C" variable_1="V2C"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k3" variable_1="k3"/>
<map_variables variable_2="k4" variable_1="k4"/>
<map_variables variable_2="kdnc" variable_1="kdnc"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PCP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V1P" variable_1="V1P"/>
<map_variables variable_2="V2P" variable_1="V2P"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdPC" variable_1="vdPC"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="CCP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V1C" variable_1="V1C"/>
<map_variables variable_2="V2C" variable_1="V2C"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdCC" variable_1="vdCC"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="PCCP" component_1="PCC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
<map_variables variable_2="PCCP" variable_1="PCCP"/>
</connection>
<connection>
<map_components component_2="PCN" component_1="PCC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PCC"/>
<map_variables variable_2="k1" variable_1="k1"/>
<map_variables variable_2="k2" variable_1="k2"/>
<map_variables variable_2="V1PC" variable_1="V1PC"/>
<map_variables variable_2="V2PC" variable_1="V2PC"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k3" variable_1="k3"/>
<map_variables variable_2="k4" variable_1="k4"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="BN" component_1="PCN"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="IN" component_1="PCN"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
<map_variables variable_2="IN" variable_1="IN"/>
</connection>
<connection>
<map_components component_2="PCN" component_1="PCNP"/>
<map_variables variable_2="PCNP" variable_1="PCNP"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
</connection>
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A multiscale model to investigate circadian rhythmicity of pacemaker neurons in the suprachiasmatic nucleus
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