<?xml version="1.0"?>
<!--
This CellML file was generated on 1/08/2011 at 12:48:20 at p.m. using:
COR (0.9.31.1409)
Copyright 2002-2011 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="larsen_olsen_kummer_2003c" name="larsen_olsen_kummer_2003c">
<units name="micromole">
<unit prefix="micro" units="mole"/>
</units>
<units name="micromolar">
<unit units="micromole"/>
<unit exponent="-1" units="litre"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="second"/>
</component>
<component name="G_a">
<variable cmeta:id="G_a_G_a" initial_value="0.01" name="G_a" public_interface="out" units="micromolar"/>
<variable name="k1" public_interface="in" units="dimensionless"/>
<variable name="k2" public_interface="in" units="dimensionless"/>
<variable name="k3" public_interface="in" units="dimensionless"/>
<variable name="PLC" public_interface="in" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="K4" public_interface="in" units="dimensionless"/>
<variable name="k5" public_interface="in" units="dimensionless"/>
<variable name="K6" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>G_a</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>k1</ci>
<apply>
<times/>
<ci>k2</ci>
<ci>G_a</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k3</ci>
<ci>G_a</ci>
<ci>PLC</ci>
</apply>
<apply>
<plus/>
<ci>G_a</ci>
<ci>K4</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k5</ci>
<ci>Ca_cyt</ci>
<ci>G_a</ci>
</apply>
<apply>
<plus/>
<ci>G_a</ci>
<ci>K6</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PLC">
<variable cmeta:id="PLC_PLC" initial_value="0.01" name="PLC" public_interface="out" units="micromolar"/>
<variable name="k7" public_interface="in" units="dimensionless"/>
<variable name="G_a" public_interface="in" units="micromolar"/>
<variable name="k8" public_interface="in" units="dimensionless"/>
<variable name="K9" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PLC</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k7</ci>
<ci>G_a</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k8</ci>
<ci>PLC</ci>
</apply>
<apply>
<plus/>
<ci>PLC</ci>
<ci>K9</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_ER">
<variable cmeta:id="Ca_ER_Ca_ER" initial_value="10" name="Ca_ER" public_interface="out" units="micromolar"/>
<variable name="k10" public_interface="in" units="dimensionless"/>
<variable name="PLC" public_interface="in" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="K11" public_interface="in" units="dimensionless"/>
<variable name="k16" public_interface="in" units="dimensionless"/>
<variable name="K17" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_ER</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Ca_ER</ci>
<ci>Ca_cyt</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k10</ci>
<ci>Ca_cyt</ci>
<apply>
<power/>
<ci>PLC</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>PLC</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<ci>K11</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k16</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<plus/>
<ci>Ca_cyt</ci>
<ci>K17</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_mit">
<variable cmeta:id="Ca_mit_Ca_mit" initial_value="0.001" name="Ca_mit" public_interface="out" units="micromolar"/>
<variable name="k18" public_interface="in" units="dimensionless"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="K19" public_interface="in" units="dimensionless"/>
<variable name="k20" public_interface="in" units="dimensionless"/>
<variable name="K21" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_mit</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k18</ci>
<apply>
<power/>
<ci>Ca_cyt</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">8</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K19</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">8</cn>
</apply>
<apply>
<power/>
<ci>Ca_cyt</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">8</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_mit</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k20</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<plus/>
<ci>Ca_cyt</ci>
<ci>K21</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_cyt">
<variable cmeta:id="Ca_cyt_Ca_cyt" initial_value="0.01" name="Ca_cyt" public_interface="out" units="micromolar"/>
<variable name="k10" public_interface="in" units="dimensionless"/>
<variable name="Ca_ER" public_interface="in" units="micromolar"/>
<variable name="Ca_mit" public_interface="in" units="micromolar"/>
<variable name="G_a" public_interface="in" units="micromolar"/>
<variable name="PLC" public_interface="in" units="micromolar"/>
<variable name="K11" public_interface="in" units="dimensionless"/>
<variable name="k12" public_interface="in" units="dimensionless"/>
<variable name="k13" public_interface="in" units="dimensionless"/>
<variable name="k14" public_interface="in" units="dimensionless"/>
<variable name="K15" public_interface="in" units="dimensionless"/>
<variable name="k16" public_interface="in" units="dimensionless"/>
<variable name="K17" public_interface="in" units="dimensionless"/>
<variable name="k18" public_interface="in" units="dimensionless"/>
<variable name="K19" public_interface="in" units="dimensionless"/>
<variable name="k20" public_interface="in" units="dimensionless"/>
<variable name="K21" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_cyt</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_ER</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k10</ci>
<ci>Ca_cyt</ci>
<apply>
<power/>
<ci>PLC</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>PLC</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<ci>K11</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>k12</ci>
<ci>PLC</ci>
</apply>
<apply>
<times/>
<ci>k13</ci>
<ci>G_a</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k14</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<plus/>
<ci>K15</ci>
<ci>Ca_cyt</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k16</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<plus/>
<ci>K17</ci>
<ci>Ca_cyt</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k18</ci>
<apply>
<power/>
<ci>Ca_cyt</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">8</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K19</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">8</cn>
</apply>
<apply>
<power/>
<ci>Ca_cyt</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">8</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_mit</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k20</ci>
<ci>Ca_cyt</ci>
</apply>
<apply>
<plus/>
<ci>Ca_cyt</ci>
<ci>K21</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Enz">
<variable cmeta:id="Enz_Enz" initial_value="0" name="Enz" public_interface="out" units="micromolar"/>
<variable initial_value="5" name="k_act" units="dimensionless"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable initial_value="0.62" name="K_M" units="dimensionless"/>
<variable initial_value="0.04" name="k_inact" units="dimensionless"/>
<variable initial_value="4" name="p" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Enz</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_act</ci>
<apply>
<power/>
<ci>Ca_cyt</ci>
<ci>p</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_M</ci>
<ci>p</ci>
</apply>
<apply>
<power/>
<ci>Ca_cyt</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>k_inact</ci>
<ci>Enz</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Pro">
<variable cmeta:id="Pro_Pro" initial_value="0" name="Pro" public_interface="out" units="micromolar"/>
<variable initial_value="3" name="k_enz" units="dimensionless"/>
<variable name="Enz" public_interface="in" units="micromolar"/>
<variable initial_value="3" name="k_rem" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Pro</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_enz</ci>
<ci>Enz</ci>
</apply>
<apply>
<times/>
<ci>k_rem</ci>
<ci>Pro</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable initial_value="0.01" name="k1" public_interface="out" units="dimensionless"/>
<variable initial_value="1.75" name="k2" public_interface="out" units="dimensionless"/>
<variable initial_value="0.64" name="k3" public_interface="out" units="dimensionless"/>
<variable initial_value="0.09" name="K4" public_interface="out" units="dimensionless"/>
<variable initial_value="4.88" name="k5" public_interface="out" units="dimensionless"/>
<variable initial_value="1.18" name="K6" public_interface="out" units="dimensionless"/>
<variable initial_value="2.08" name="k7" public_interface="out" units="dimensionless"/>
<variable initial_value="32.24" name="k8" public_interface="out" units="dimensionless"/>
<variable initial_value="29.09" name="K9" public_interface="out" units="dimensionless"/>
<variable initial_value="0.7" name="k10" public_interface="out" units="dimensionless"/>
<variable initial_value="3" name="K11" public_interface="out" units="dimensionless"/>
<variable initial_value="2.8" name="k12" public_interface="out" units="dimensionless"/>
<variable initial_value="13.4" name="k13" public_interface="out" units="dimensionless"/>
<variable initial_value="153" name="k14" public_interface="out" units="dimensionless"/>
<variable initial_value="0.16" name="K15" public_interface="out" units="dimensionless"/>
<variable initial_value="7" name="k16" public_interface="out" units="dimensionless"/>
<variable initial_value="0.05" name="K17" public_interface="out" units="dimensionless"/>
<variable initial_value="79" name="k18" public_interface="out" units="dimensionless"/>
<variable initial_value="3.5" name="K19" public_interface="out" units="dimensionless"/>
<variable initial_value="0.81" name="k20" public_interface="out" units="dimensionless"/>
<variable initial_value="4.5" name="K21" public_interface="out" units="dimensionless"/>
</component>
<connection>
<map_components component_1="environment" component_2="G_a"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="PLC"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Ca_ER"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Ca_mit"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Ca_cyt"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Enz"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Pro"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="G_a"/>
<map_variables variable_1="k1" variable_2="k1"/>
<map_variables variable_1="k2" variable_2="k2"/>
<map_variables variable_1="k3" variable_2="k3"/>
<map_variables variable_1="K4" variable_2="K4"/>
<map_variables variable_1="k5" variable_2="k5"/>
<map_variables variable_1="K6" variable_2="K6"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="PLC"/>
<map_variables variable_1="k7" variable_2="k7"/>
<map_variables variable_1="k8" variable_2="k8"/>
<map_variables variable_1="K9" variable_2="K9"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="Ca_ER"/>
<map_variables variable_1="k10" variable_2="k10"/>
<map_variables variable_1="K11" variable_2="K11"/>
<map_variables variable_1="k16" variable_2="k16"/>
<map_variables variable_1="K17" variable_2="K17"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="Ca_mit"/>
<map_variables variable_1="k18" variable_2="k18"/>
<map_variables variable_1="K19" variable_2="K19"/>
<map_variables variable_1="k20" variable_2="k20"/>
<map_variables variable_1="K21" variable_2="K21"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="Ca_cyt"/>
<map_variables variable_1="k10" variable_2="k10"/>
<map_variables variable_1="K11" variable_2="K11"/>
<map_variables variable_1="k12" variable_2="k12"/>
<map_variables variable_1="k13" variable_2="k13"/>
<map_variables variable_1="k14" variable_2="k14"/>
<map_variables variable_1="K15" variable_2="K15"/>
<map_variables variable_1="k16" variable_2="k16"/>
<map_variables variable_1="K17" variable_2="K17"/>
<map_variables variable_1="k18" variable_2="k18"/>
<map_variables variable_1="K19" variable_2="K19"/>
<map_variables variable_1="k20" variable_2="k20"/>
<map_variables variable_1="K21" variable_2="K21"/>
</connection>
<connection>
<map_components component_1="G_a" component_2="PLC"/>
<map_variables variable_1="G_a" variable_2="G_a"/>
<map_variables variable_1="PLC" variable_2="PLC"/>
</connection>
<connection>
<map_components component_1="G_a" component_2="Ca_cyt"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
<map_variables variable_1="G_a" variable_2="G_a"/>
</connection>
<connection>
<map_components component_1="PLC" component_2="Ca_ER"/>
<map_variables variable_1="PLC" variable_2="PLC"/>
</connection>
<connection>
<map_components component_1="PLC" component_2="Ca_cyt"/>
<map_variables variable_1="PLC" variable_2="PLC"/>
</connection>
<connection>
<map_components component_1="Ca_ER" component_2="Ca_cyt"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="Ca_mit" component_2="Ca_cyt"/>
<map_variables variable_1="Ca_mit" variable_2="Ca_mit"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="Enz" component_2="Ca_cyt"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="Enz" component_2="Pro"/>
<map_variables variable_1="Enz" variable_2="Enz"/>
</connection>
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On the encoding and decoding of calcium signals in hepatocytes
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