Location: Borghans 1997 @ 382a1ae3ccd0 / borghans_dupont_goldbeter_1997a.cellml

Author:
Tommy Yu <tommy.yu@auckland.ac.nz>
Date:
2010-08-25 18:15:11+12:00
Desc:
xml:base fix
Permanent Source URI:
http://models.cellml.org/workspace/borghans_1997/rawfile/382a1ae3ccd06d67e2687b1f47f745f1915ca58b/borghans_dupont_goldbeter_1997a.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#" cmeta:id="borghans_model_1997a" name="borghans_model_1997a">

	<documentation xmlns="http://cellml.org/tmp-documentation">
		<article>
			<articleinfo>
				<title>Complex intracellular calcium oscillations.  A theoretical exploration of possible mechanisms</title>
				<author>
					<firstname>Mark</firstname>
					<surname>Hanna</surname>
					<affiliation>
						<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
					</affiliation>
				</author>
			</articleinfo>
			<section id="sec_status">
				<title>Model Status</title>
				<para>This CellML model runs in both OpenCell and COR to reproduce the published output (figure 4, but using parameters for figure 5 i.e. beta = 1.0 instead of 0.5). The units have been checked and they are consistent.</para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>ABSTRACT: Intracellular Ca2+ oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist.  In most cell types the mechanism of regular spiking is well understood and models based on Ca2+-induced Ca2+ release (CICR) can account for many experimental observations.  However, cells do not always exhibit simple Ca2+ oscillations.  In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca2+ spikes separated by silent phases.  Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca2+ oscillations.  The models are all based on one- or two-pool models based on CICR.  We extend these models by (i) considering the inhibition of the Ca2+-release channel on a unique intracellular store at high cytosolic Ca2+ concentrations, (ii) taking into account the Ca2+-activated degradation of inositol 1,4,5-trisphosphate (IP3), or (iii) considering explicitly the evolution of the Ca2+ concentration in two different pools, one sensitive and the other one insensitive to IP3.  Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting.  Moreover, the model that takes the kinetics of IP3 into account shows chaotic behaviour.</para>
				<para>Complex intracellular calcium oscillations.  A theoretical exploration of possible mechanisms, Jose A.M. Borghans, Genevieve Dupont, Albert Goldbeter, 1997, <emphasis>Biophysical Chemistry</emphasis>, 66, 25-41. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=17029867&amp;dopt=Abstract">PubMed ID: 17029867</ulink></para>
				<informalfigure float="0" id="fig_cell_diagram">
					<mediaobject>
						<imageobject>
							<objectinfo>
								<title>cell diagram</title>
							</objectinfo>
							<imagedata fileref="borghans_1997a.png"/>
						</imageobject>
					</mediaobject>
					<caption>Schematic representation of the one-pool model for Ca2+ oscillations based on CICR.</caption>
				</informalfigure>
			</sect1>
		</article>
	</documentation>

	<!-- Units -->
	<units name="min">
		<!-- time: minute -->
		<unit multiplier="60" units="second"/>
	</units>

	<units name="per_min">
		<!-- per time: per minute -->
		<unit exponent="-1" units="min"/>
	</units>

	<units name="uM">
		<!-- concentration: micromolar -->
		<unit prefix="micro" units="mole"/>
		<unit exponent="-1" units="litre"/>
	</units>

	<units name="per_uM4">
		<!-- "Fudge factor": micromolar^-4 -->
		<unit exponent="-4" units="uM"/>
	</units>

	<units name="uM_per_min">
		<!-- flux: micromolar per minute -->
		<unit units="uM"/>
		<unit units="per_min"/>
	</units>

	<!-- Components -->
	<component name="environment">
		<variable cmeta:id="environment_time" name="time" public_interface="out" units="min"/>
	</component>

	<component cmeta:id="Ca_component" name="Ca">

		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:about="#Ca_component">This component stores information about Calcium ion (Ca2+) concentrations in various cellular compartments</rdf:Description>
			<rdf:Description rdf:about="#Z">Ca2+ concentration in the cytosol</rdf:Description>
			<rdf:Description rdf:about="#Y">Ca2+ concentration in the intracellular Ca2+ pool</rdf:Description>
		</rdf:RDF>
		<variable name="time" private_interface="out" public_interface="in" units="min"/>

		<!-- Species -->
		<variable cmeta:id="Z" initial_value="0.3" name="Z" private_interface="out" units="uM"/>
		<variable cmeta:id="Y" initial_value="2.7" name="Y" private_interface="out" units="uM"/>

		<!-- Flux -->
		<variable name="V_in" private_interface="in" units="uM_per_min"/>
		<variable name="V_2" private_interface="in" units="uM_per_min"/>
		<variable name="V_3" private_interface="in" units="uM_per_min"/>

		<!-- Rate constants -->
		<variable initial_value="1" name="K_f" units="per_min"/>
		<variable initial_value="10" name="K" units="per_min"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML" id="Ca_maths">
			<apply id="dZ/dt_eq"><eq/>
				<apply><diff/>
					<bvar><ci>time</ci></bvar>
					<ci>Z</ci>
				</apply>
				<apply><plus/>
					<apply><minus/>
						<ci>V_in</ci>
						<ci>V_2</ci>
					</apply>
					<ci>V_3</ci>
					<apply><minus/>
						<apply><times/>
							<ci>K_f</ci>
							<ci>Y</ci>
						</apply>
						<apply><times/>
							<ci>K</ci>
							<ci>Z</ci>
						</apply>
					</apply>
				</apply>
			</apply>

			<apply id="dY/dt_eq"><eq/>
				<apply><diff/>
					<bvar><ci>time</ci></bvar>
					<ci>Y</ci>
				</apply>
				<apply><minus/>
					<apply><minus/>
						<ci>V_2</ci>
						<ci>V_3</ci>
					</apply>
					<apply><times/>
						<ci>K_f</ci>
						<ci>Y</ci>
					</apply>
				</apply>
			</apply>
		</math>
	</component>

	<component cmeta:id="Ca_flux_component" name="Ca_flux">

		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#Ca_flux_component">Container for Ca2+ flux-related components</rdf:Description>
			<rdf:Description rdf:about="#beta">Stimulation level</rdf:Description>
		</rdf:RDF>
		<variable name="time" private_interface="out" public_interface="in" units="min"/>

		<variable cmeta:id="beta" initial_value="1" name="beta" private_interface="out" units="dimensionless"/>

		<variable name="Z" private_interface="out" public_interface="in" units="uM"/>
		<variable name="Y" private_interface="out" public_interface="in" units="uM"/>

		<variable name="V_in" private_interface="in" public_interface="out" units="uM_per_min"/>
		<variable name="V_2" private_interface="in" public_interface="out" units="uM_per_min"/>
		<variable name="V_3" private_interface="in" public_interface="out" units="uM_per_min"/>
	</component>

	<component cmeta:id="V_in_component" name="V_in">

		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#V_in_component">Component for the calculation of V_in</rdf:Description>
			<rdf:Description rdf:about="#V_in">Flux of Ca2+ from the extracellular medium into the cytosol</rdf:Description>
			<rdf:Description rdf:about="#v_0">Passive Ca2+ &quot;leak&quot; from the extracellular medium into the cytosol</rdf:Description>
			<rdf:Description rdf:about="#v_1">Activated Ca2+ transport from the extracellular medium into the cytosol</rdf:Description>
		</rdf:RDF>

		<variable cmeta:id="V_in" name="V_in" public_interface="out" units="uM_per_min"/>

		<variable cmeta:id="v_0" initial_value="1" name="v_0" units="uM_per_min"/>
		<variable cmeta:id="v_1" initial_value="1" name="v_1" units="uM_per_min"/>
		<variable name="beta" public_interface="in" units="dimensionless"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML" id="V_in_maths">
			<apply id="V_in_eq"><eq/>
				<ci>V_in</ci>
				<apply><plus/>
					<ci>v_0</ci>
					<apply><times/>
						<ci>v_1</ci>
						<ci>beta</ci>
					</apply>
				</apply>
			</apply>
		</math>
	</component>

	<component cmeta:id="V_2_component" name="V_2">

		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#V_2_component">Component for the calculation of V_2</rdf:Description>
			<rdf:Description rdf:about="#V_2">Ca2+ pumping rate into the Ca2+ pool</rdf:Description>
			<rdf:Description rdf:about="#V_M2">Maximum Ca2+ pumping rate into the Ca2+ pool</rdf:Description>
			<rdf:Description rdf:about="#K_2">Threshold concentration for Ca2+ pumping into the Ca2+ pool</rdf:Description>
		</rdf:RDF>

		<variable name="Z" public_interface="in" units="uM"/>

		<variable cmeta:id="V_2" name="V_2" public_interface="out" units="uM_per_min"/>

		<variable cmeta:id="V_M2" initial_value="6.5" name="V_M2" units="uM_per_min"/>
		<variable cmeta:id="K_2" initial_value="0.1" name="K_2" units="uM"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML" id="V_2_maths">
			<apply id="V_2_eq"><eq/>
				<ci>V_2</ci>
				<apply><times/>
					<ci>V_M2</ci>
					<apply><divide/>
						<apply><power/>
							<ci>Z</ci>
							<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
						</apply>
						<apply><plus/>
							<apply><power/>
								<ci>K_2</ci>
								<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
							</apply>
							<apply><power/>
								<ci>Z</ci>
								<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
							</apply>
						</apply>
					</apply>
				</apply>
			</apply>
		</math>
	</component>

	<component cmeta:id="V_3_component" name="V_3">

		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#V_3_component">Component for the calculation of V_3</rdf:Description>
			<rdf:Description rdf:about="#V_3">Ca2+ release rate from the Ca2+ pool</rdf:Description>
			<rdf:Description rdf:about="#K_y">Threshold concentration for Ca2+ release</rdf:Description>
			<rdf:Description rdf:about="#V_M3">Maximum Ca2+ release rate from the Ca2+ pool</rdf:Description>
		</rdf:RDF>
		<variable name="time" private_interface="out" public_interface="in" units="min"/>

		<variable name="Z" private_interface="out" public_interface="in" units="uM"/>
		<variable name="Y" public_interface="in" units="uM"/>

		<variable cmeta:id="V_3" name="V_3" public_interface="out" units="uM_per_min"/>

		<variable cmeta:id="K_y" initial_value="0.2" name="K_y" units="uM"/>
		<variable cmeta:id="V_M3" initial_value="50" name="V_M3" units="uM_per_min"/>
		<variable name="beta" public_interface="in" units="dimensionless"/>
		<variable name="R_plus" private_interface="in" units="dimensionless"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML" id="V_3_maths">
			<apply id="V_3_eq"><eq/>
				<ci>V_3</ci>
				<apply><times/>
					<ci>beta</ci>
					<ci>R_plus</ci>
					<ci>V_M3</ci>
					<apply><divide/>
						<apply><power/>
							<ci>Y</ci>
							<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
						</apply>
						<apply><plus/>
							<apply><power/>
								<ci>K_y</ci>
								<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
							</apply>
							<apply><power/>
								<ci>Y</ci>
								<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
							</apply>
						</apply>
					</apply>
				</apply>
			</apply>
		</math>
	</component>

	<component cmeta:id="Ca_channels_component" name="Ca_channels">

		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#Ca_channels_component">Component for the calculation of R_plus</rdf:Description>
			<rdf:Description rdf:about="#rho">Fraction of activatable channels</rdf:Description>
			<rdf:Description rdf:about="#k_d">Rate at which channels inactivate following binding of Ca2+ to inhibitory site</rdf:Description>
			<rdf:Description rdf:about="#k_r">Rate at which channels activate following unbinding of Ca2+ to inhibitory site</rdf:Description>
			<rdf:Description rdf:about="#R_plus">Proportion of channels with Ca2+ bound to the activatory site but not to the inhibitory site</rdf:Description>
		</rdf:RDF>
		<variable name="time" public_interface="in" units="min"/>

		<variable name="Z" private_interface="out" public_interface="in" units="uM"/>

		<variable cmeta:id="rho" initial_value="0.2" name="rho" units="dimensionless"/>
		<variable name="gamma" private_interface="in" units="dimensionless"/>

		<variable cmeta:id="k_d" initial_value="5000.0" name="k_d" units="per_min"/>
		<variable cmeta:id="k_r" initial_value="5.0" name="k_r" units="per_min"/>

		<variable cmeta:id="R_plus" name="R_plus" public_interface="out" units="dimensionless"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML" id="Ca_channels_maths">
			<apply id="R_plus_eq"><eq/>
				<ci>R_plus</ci>
				<apply><times/>
					<ci>gamma</ci>
					<apply><divide/>
						<ci>rho</ci>
						<apply><plus/>
							<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
							<ci>gamma</ci>
						</apply>
					</apply>
				</apply>
			</apply>

			<apply id="drho/dt_eq"><eq/>
				<apply><diff/>
					<bvar><ci>time</ci></bvar>
					<ci>rho</ci>
				</apply>
				<apply><plus/>
					<apply><minus/>
						<apply><times/>
							<ci>k_d</ci>
							<apply><power/>
								<ci>Z</ci>
								<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
							</apply>
							<ci>rho</ci>
							<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_uM4">1</cn>
						</apply>
					</apply>
					<apply><times/>
						<ci>k_r</ci>
						<apply><minus/>
							<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
							<ci>rho</ci>
						</apply>
					</apply>
				</apply>
			</apply>
		</math>
	</component>

	<component cmeta:id="gamma_component" name="gamma">

		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#gamma_component">Component for the calculation of gamma</rdf:Description>
			<rdf:Description rdf:about="#gamma">A scaling factor: the number of channels with Ca2+ bound to the activatory site divided by the number of channels without Ca2+ bound to the activatory site.</rdf:Description>
			<rdf:Description rdf:about="#a">Kinetic constant for activatory Ca2+ binding</rdf:Description>
			<rdf:Description rdf:about="#d">Kinetic constant for deactivatory Ca2+ unbinding</rdf:Description>
		</rdf:RDF>
		<variable name="Z" public_interface="in" units="uM"/>

		<variable cmeta:id="gamma" name="gamma" public_interface="out" units="dimensionless"/>

		<variable cmeta:id="a" initial_value="10000.0" name="a" units="per_min"/>
		<variable cmeta:id="d" initial_value="100.0" name="d" units="per_min"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML" id="gamma_maths">
			<apply id="gamma_eq"><eq/>
				<ci>gamma</ci>
				<apply><times/>
					<apply><divide/>
						<ci>a</ci>
						<ci>d</ci>
					</apply>
					<apply><power/>
						<ci>Z</ci>
						<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
					</apply>
					<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_uM4">1</cn>
				</apply>
			</apply>
		</math>
	</component>

	<!-- groups -->
	<group>
		<relationship_ref relationship="encapsulation"/>
		<component_ref component="Ca">
			<component_ref component="Ca_flux">
				<component_ref component="V_in"/>
				<component_ref component="V_2"/>
				<component_ref component="V_3">
					<component_ref component="Ca_channels">
						<component_ref component="gamma"/>
					</component_ref>
				</component_ref>
			</component_ref>
		</component_ref>
	</group>

	<!-- connections -->
	<connection>
		<map_components component_1="environment" component_2="Ca"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection>

	<connection>
		<map_components component_1="Ca" component_2="Ca_flux"/>
		<map_variables variable_1="time" variable_2="time"/>
		<map_variables variable_1="V_in" variable_2="V_in"/>
		<map_variables variable_1="V_2" variable_2="V_2"/>
		<map_variables variable_1="V_3" variable_2="V_3"/>
		<map_variables variable_1="Z" variable_2="Z"/>
		<map_variables variable_1="Y" variable_2="Y"/>
	</connection>

	<connection>
		<map_components component_1="Ca_flux" component_2="V_in"/>
		<map_variables variable_1="beta" variable_2="beta"/>
		<map_variables variable_1="V_in" variable_2="V_in"/>
	</connection>

	<connection>
		<map_components component_1="Ca_flux" component_2="V_2"/>
		<map_variables variable_1="V_2" variable_2="V_2"/>
		<map_variables variable_1="Z" variable_2="Z"/>
	</connection>

	<connection>
		<map_components component_1="Ca_flux" component_2="V_3"/>
		<map_variables variable_1="time" variable_2="time"/>
		<map_variables variable_1="beta" variable_2="beta"/>
		<map_variables variable_1="V_3" variable_2="V_3"/>
		<map_variables variable_1="Z" variable_2="Z"/>
		<map_variables variable_1="Y" variable_2="Y"/>
	</connection>

	<connection>
		<map_components component_1="V_3" component_2="Ca_channels"/>
		<map_variables variable_1="time" variable_2="time"/>
		<map_variables variable_1="Z" variable_2="Z"/>
		<map_variables variable_1="R_plus" variable_2="R_plus"/>
	</connection>

	<connection>
		<map_components component_1="Ca_channels" component_2="gamma"/>
		<map_variables variable_1="Z" variable_2="Z"/>
		<map_variables variable_1="gamma" variable_2="gamma"/>
	</connection>

	<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
    <foo xmlns="http://www.example.org/foo/bar/baz"/>

		<rdf:Description rdf:about="">

			<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Complex intracellular calcium oscillations.  A theoretical exploration of possible mechanisms (Model A)</dc:title>
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				<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
					<vCard:Family>Hanna</vCard:Family>
					<vCard:Given>Mark</vCard:Given>
					<vCard:Other>James</vCard:Other>
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					<rdf:value>mark@hanna.net.nz</rdf:value>
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				<dcterms:W3CDTF>2009-11-30</dcterms:W3CDTF>
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			<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Complex intracellular calcium oscillations.  A theoretical exploration of possible mechanisms</dc:title>

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					<rdf:value>
						<rdf:Bag>
							<rdf:li>Calcium Signalling</rdf:li>
							<rdf:li>Calcium Oscillations</rdf:li>
							<rdf:li>Bursting</rdf:li>
							<rdf:li>Chaos</rdf:li>
							<rdf:li>Calcium Dynamics</rdf:li>
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					</rdf:value>
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			<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource">
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									<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
										<vCard:Family>Borghans</vCard:Family>
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										<vCard:Other>O.M.</vCard:Other>
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										<vCard:Family>Dupont</vCard:Family>
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										<vCard:Family>Goldbeter</vCard:Family>
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					</dc:creator>
					<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Complex intracellular calcium oscillations.  A theoretical exploration of possible mechanisms</dc:title>
					<dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource">
						<dcterms:W3CDTF>1997-01-16</dcterms:W3CDTF>
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						<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Biophysical Chemistry</dc:title>
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					<bqs:first_page>25</bqs:first_page>
					<bqs:last_page>41</bqs:last_page>
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