- Author:
- neilstephen2001 <npar276@aucklanduni.ac.nz>
- Date:
- 2021-01-26 14:35:03+13:00
- Desc:
- modifying rdf files
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/7f1/rawfile/4d6408caaf3e7b1b86d33d53d26105360ef95347/bertram_sherman_2004/model/bertram_sherman_2004.rdf
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:semsim="http://www.bhi.washington.edu/SemSim#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bqmodel="http://biomodels.net/model-qualifiers/"
xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current_n_gate.n">
<dcterms:description>delayed rectifier activation variable</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current.n">
<dcterms:description>delayed rectifier activation variable</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
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<bqbiol:isPartOf>
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</rdf:Description>
</bqbiol:isPartOf>
<bqbiol:is rdf:resource="http://identifiers.org/go/GO:0005829"/>
</rdf:Description>
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</rdf:Description>
</bqbiol:isPropertyOf>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of IP3</dcterms:description>
</rdf:Description>
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<bqbiol:isPropertyOf>
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<bqbiol:isPartOf>
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<bqbiol:is rdf:resource="http://identifiers.org/fma/FMA:260691"/>
</rdf:Description>
</bqbiol:isPartOf>
<bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:29108"/>
</rdf:Description>
</bqbiol:isPropertyOf>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current.V_Ca">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>calcium reversal potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#membrane.i_K_Ca">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>calcium-dependent potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.V_K">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>potassium reversal potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current_omega_gate.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#membrane.Cm">
<dcterms:description>membrane capacitance</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#net_calcium_efflux_out_of_the_ER.JIP3">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>calcium flux out of the endoplasmic reticulum through IP3 receptors</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#cytosolic_free_calcium_concentration.fcyt">
<dcterms:description>fraction of free to total cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#membrane.i_K">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>delayed rectifier potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.a_infinity">
<dcterms:description>equilibrium function of ADP to ATP nucleotide ratio</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current.V">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current.V">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>membrane potential</dcterms:description>
</rdf:Description>
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<bqbiol:isPropertyOf>
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<bqbiol:isPartOf>
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<bqbiol:is rdf:resource="http://identifiers.org/fma/FMA:63842"/>
</rdf:Description>
</bqbiol:isPartOf>
<bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:29108"/>
</rdf:Description>
</bqbiol:isPropertyOf>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of calcium in endoplasmic reticulum</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_influx_into_the_ER.kSERCA">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296"/>
<dcterms:description>rate constant of SERCA pumps</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.sa">
<bqbiol:isPropertyOf>
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<bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:36976"/>
</rdf:Description>
</bqbiol:isPropertyOf>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>saturation nucleotide ratio of ATP-sensitive potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_flux_through_the_membrane.Jmem">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>net calcium flux through plasma membrane</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current_m_gate.vm">
<dcterms:description>activation potential of calcium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current_n_gate.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_influx_into_the_ER.J_SERCA">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>calcium flux into endoplasmic reticulum via SERCA pumps</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current.V_K">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>potassium reversal potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_leak_out_of_the_ER.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current.i_K">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>delayed rectifier potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#membrane.i_Ca">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>calcium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#membrane.i_K_ATP">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>ATP-sensitive potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current_m_gate.m_infinity">
<dcterms:description>steady state function of calcium channel activation variable</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_efflux_through_the_IP3R.JIP3">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>calcium flux out of the endoplasmic reticulum through IP3 receptors</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#ER_calcium_concentration.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current.omega">
<dcterms:description>fraction of calcium-activated potassium channels activated by cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_efflux_through_the_IP3R.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_leak_out_of_the_ER.pleak">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296"/>
<dcterms:description>leak rate constant</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_influx_into_the_ER.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#cytosolic_free_calcium_concentration.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current_n_gate.sn">
<dcterms:description>saturation voltage of delayed rectifier potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#cytosolic_free_calcium_concentration.Jmem">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>net calcium flux through plasma membrane</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#net_calcium_efflux_out_of_the_ER.Jer">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>net calcium flux through the endoplasmic reticulum membrane</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#net_calcium_efflux_out_of_the_ER.Jleak">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>calcium leak flux out of endoplasmic reticulum</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.V">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current.g_K">
<dcterms:description>maximum conductance of delayed rectifier potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_flux_through_the_membrane.alpha">
<dcterms:description>current to flux converter</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_efflux_through_the_IP3R.O_infinity">
<dcterms:description>fraction of open IP3 channels</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.g_K_ATP">
<dcterms:description>conductance of ATP-sensitive potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.i_K_ATP">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>ATP-sensitive potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_efflux_through_the_IP3R.d_inact">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>Michaelis-Menten constant of IP3 receptor inactivation by cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current_omega_gate.kD">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>dissociation constant for calcium binding to potassium channel</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#membrane.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current.V">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#ER_calcium_concentration.fer">
<dcterms:description>fraction of free to total calcium in the endoplasmic reticulum</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current.g_K_Ca">
<dcterms:description>maximum conductance of calcium-activated potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_efflux_through_the_IP3R.d_IP3">
<bqbiol:isPropertyOf>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#entity_6">
<bqbiol:isPartOf rdf:resource="./bertram_sherman_2004.cellml#entity_1"/>
<bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:16595"/>
</rdf:Description>
</bqbiol:isPropertyOf>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>Michaelis-Menten constant of IP3 receptor activation by IP3</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#membrane.V">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_flux_through_the_membrane.kPMCA">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296"/>
<dcterms:description>rate constant of plasma membrane calcium ATPase</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#cytosolic_free_calcium_concentration.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#ER_calcium_concentration.Vcyt_Ver">
<dcterms:description>ratio of cytosolic to endoplasmic reticulum volume</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current_n_gate.vn">
<dcterms:description>activation potential of delayed rectifier potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current.i_Ca">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>calcium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#ER_calcium_concentration.Jer">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>net calcium flux through the endoplasmic reticulum membrane</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_flux_through_the_membrane.i_Ca">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>calcium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.tau_a">
<dcterms:description>time constant of nucleotide oscillations</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#bertram_sherman_2004_version01"
semsim:modelName="bertram_sherman_2004_version01"
bqmodel:isDescribedBy="15294427">
<semsim:hasCellMLdocumentation><documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Calcium-based Phantom Bursting Model for Pancreatic Islets</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This model is has consistent units and has been verified as valid CellML by ValidateCellML. It is currently unsuitably constrained and can not be solved.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>Pancreatic beta-cells are located in clusters within the pancreas called the islets of Langerhans. Beta-cells secrete the hormone insulin in response to elevated blood glucose levels, and in doing so, they play an essential role in glucose homeostasis. When beta-cells fail to function properly, this can lead to pathologies such as type II diabetes.</para>
<para>
Insulin secretion is oscillatory, and it is in-phase with oscillations in the free cytosolic calcium concentration ([Ca
<superscript>2+</superscript>
]
<subscript>i</subscript>
), and theses Ca
<superscript>2+</superscript>
oscillations reflect a bursting pattern in the beta-cell electrical activity. Electrical bursting consists of periodic active phases of cell firing (excitation) followed by silent phases of hyperpolarisation (rest). These oscillations can be divided into three categories:
</para>
<itemizedlist>
<listitem>
<para>
<emphasis>Fast bursting</emphasis>
, which has a period between 2 and 5 seconds and which often occurs in single cells and in islets where acetylcholine is present;
</para>
</listitem>
<listitem>
<para>
<emphasis>Medium bursting</emphasis>
, which has a period of 10 to 60 seconds and which occurs in islets where there is a stimulatory glucose concentration; and
</para>
</listitem>
<listitem>
<para>
<emphasis>Slow bursting</emphasis>
, which has a period of 2 to 4 minutes and which occurs in single cells and in islets.
</para>
</listitem>
</itemizedlist>
<para>
The first mathematical models of beta-cells were developed to describe medium bursting, and the first models to address the variability in beta-cell oscillations were developed by Chay in 1995 and 1997 (see
<ulink url="${HTML_EXMPL_CHAY_MODEL97}">Extracellular and Intracellular Calcium Effects on Pancreatic Beta Cells, Chay, 1997</ulink>
for more details). In these models the main mechanism for oscillations was variation in the Ca
<superscript>2+</superscript>
concentration in the ER, which directly or indirectly modulates one or more Ca
<superscript>2+</superscript>
-dependent channels. In the Bertram and Sherman model described here the authors analyse in detail how the ER exerts its affects using a phantom bursting model (see
<xref linkend="fig_cell_diagram" />
below).
</para>
<para>
The phantom bursting model is a general paradigm for temporal plasticity in bursting in beta-cells in which bursting is driven by the interaction of two slow variables with disparate time constants (see
<ulink url="${HTML_EXMPL_BERTRAM_MODEL}">The Phantom Burster Model for Pancreatic Beta-Cells, 2000</ulink>
for more details). There are three potential slow variables which could drive the phantom bursting
<emphasis>in vivo</emphasis>
:
</para>
<itemizedlist>
<listitem>
<para>
cytosolic Ca
<superscript>2+</superscript>
concentration;
</para>
</listitem>
<listitem>
<para>
ER Ca
<superscript>2+</superscript>
concentration;
</para>
</listitem>
<listitem>
<para>and the ADP to ATP ratio.</para>
</listitem>
</itemizedlist>
<para>
The model has been described here in CellML (the raw CellML description of the Bertram and Sherman 2004 model can be downloaded in various formats as described in
<xref linkend="sec_download_this_model" />
).
</para>
<para>The complete original paper reference is cited below:</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WC7-4BS4GC2-1&amp;_user=140507&amp;_coverDate=09%2F30%2F2004&amp;_alid=197872630&amp;_rdoc=1&amp;_fmt=summary&amp;_orig=search&amp;_qd=1&amp;_cdi=6731&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=e1fdd19a27b1c7938c1d568e59a560e0">A Calcium-based Phantom Bursting Model for Pancreatic Islets</ulink>
, Richard Bertram and Arthur Sherman, 2004,
<ulink url="http://www.molbiolcell.org/">
<emphasis>Bulletin of Mathematical Biology</emphasis>
</ulink>
, 66, 1313-1344. (
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WC7-4BS4GC2-1&amp;_coverDate=09%2F30%2F2004&amp;_alid=197872630&amp;_rdoc=1&amp;_fmt=&amp;_orig=search&amp;_qd=1&amp;_cdi=6731&amp;_sort=d&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=b34962c344ab1a8911383073cd53016f">Full text (HTML)</ulink>
and
<ulink url="http://www.sciencedirect.com/science?_ob=MImg&amp;_imagekey=B6WC7-4BS4GC2-1-3Y&amp;_cdi=6731&amp;_orig=search&amp;_coverDate=09%2F30%2F2004&amp;_qd=1&amp;_sk=999339994&amp;view=c&amp;wchp=dGLbVzz-zSkWz&amp;_acct=C000011498&amp;_version=1&amp;_userid=140507&amp;md5=4f701b4338556df3136f0c4815596563&amp;ie=f.pdf">PDF</ulink>
versions of the article are available to subscribers on the
<emphasis>Bulletin of Mathematical Biology</emphasis>
website.)
<ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=15294427&amp;dopt=Abstract">PubMed ID: 15294427</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="bertram_2004.png" />
</imageobject>
</mediaobject>
<caption>A schematic diagram of the ionic currents and fluxes across the ER and the cell surface membranes, which are described by the mathematical model.</caption>
</informalfigure>
</sect1>
</article>
</documentation></semsim:hasCellMLdocumentation>
<semsim:unknown>Pancreatic Islets</semsim:unknown>
<semsim:unknown>Bertram and Sherman's calcium-based phantom bursting model for pancreatic islets.</semsim:unknown>
<semsim:modelName>bertram_sherman_2004</semsim:modelName>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current.m_infinity">
<dcterms:description>steady state function of calcium channel activation variable</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_leak_out_of_the_ER.c_er">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_4"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of calcium in endoplasmic reticulum</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current_omega_gate.omega">
<dcterms:description>fraction of calcium-activated potassium channels activated by cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#cytosolic_free_calcium_concentration.Jer">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>net calcium flux through the endoplasmic reticulum membrane</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.a">
<dcterms:description>nucleotide ratio of ADP to ATP</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current_m_gate.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#net_calcium_efflux_out_of_the_ER.J_SERCA">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>calcium flux into endoplasmic reticulum via SERCA pumps</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_leak_out_of_the_ER.Jleak">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00593"/>
<dcterms:description>calcium leak flux out of endoplasmic reticulum</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#environment.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023"/>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current_n_gate.V">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_efflux_through_the_IP3R.d_act">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>Michaelis-Menten constant of IP3 receptor activation by cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current.g_Ca">
<dcterms:description>maximum conductance of calcium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current_n_gate.n_infinity">
<dcterms:description>steady state function of delayed rectifier activation variable</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.a">
<dcterms:description>nucleotide ratio of ADP to ATP</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current.i_K_Ca">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00318"/>
<dcterms:description>calcium-dependent potassium current</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#delayed_rectifier_potassium_current_n_gate.tau_n">
<dcterms:description>activation time constant for delayed rectifier channel</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current_m_gate.V">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_efflux_through_the_IP3R.c_er">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_4"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of calcium in endoplasmic reticulum</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_flux_through_the_membrane.c">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>concentration of free cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.r">
<bqbiol:isPropertyOf rdf:resource="./bertram_sherman_2004.cellml#entity_0"/>
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00340"/>
<dcterms:description>total concentration of cytosolic calcium</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_dependent_potassium_current.V_K">
<bqbiol:isVersionOf rdf:resource="https://identifiers.org/opb/OPB_00506"/>
<dcterms:description>potassium reversal potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="./bertram_sherman_2004.cellml#calcium_current_m_gate.sm">
<dcterms:description>saturation voltage of calcium current</dcterms:description>
</rdf:Description>
</rdf:RDF>
