concentration of calcium in junctional sarcoplasmic reticulum
reverse half-saturation constant for calcium ATPase
potassium permeability of L-type calcium channel
L-type calcium channel mode transition parameter
calcium current at maximum potassium permeability of L-type calcium channel
concentration of free myoplasmic calcium
fraction of open L-type calcium channels
fraction of ryanodine receptor channels in state PO2
maximum rapid potassium current conductance
magnesium-bound ATP flux from subspace to myoplasm
concentration of magnesium-bound myoplasmic ATP
transfer time constant from subspace to myoplasm
concentration of calcium-bound myoplasmic ADP
maximum time-independent potassium current conductance
transition rate out of open state for calcium mode
activation curve of reverse rapid potassium current
ryanodine receptor PC2 - PO1 rate constant
ryanodine receptor PO2 - PO1 rate constant
concentration of free myoplasmic magnesium
L-type calcium current activation variable
fraction of closed L-type calcium channels
activation time constant of rapid potassium current
volume of network sarcoplasmic reticulum
potassium half-saturation constant for sodium-potassium pump
activation potential of plateau potassium current
resting myoplasmic magnesium-bound ATP concentration in normal conditions
calcium off-rate for troponin low affinity sites
concentration of intracellular potassium
calcium on-rate for troponin low affinity sites
activation potential of rapid potassium current
potassium current through L-type calcium channel
concentration of extracellular potassium
transient outward potassium current inactivation variable
maximum background sodium current conductance
concentration of calcium-bound troponin low-affinity sites
steady-state function of time-independent potassium current activation variable
fraction of open L-type calcium channels in calcium mode
concentration of calcium-bound subspace ATP
transient outward potassium current activation variable
fraction of closed L-type calcium channels in calcium mode
total concentration of myoplasmic calmodulin
steady state function of slow potassium current activation variable
calcium half-saturation constant for calsequestrin
total concentration of troponin high-affinity sites
sodium half-saturation constant for sodium-calcium exchange
calcium-bound ADP flux from subspace to myoplasm
saturation factor of sodium-calcium exchanger current
half-saturation constant for sarcolemmal calcium pump
concentration of calcium in network sarcoplasmic reticulum
fast sodium current M-gate reversal potential
maximum sarcolemmal calcium pump current
calcium half-saturation constant for EGTA
ryanodine receptor calcium cooperativity parameter PO1 - PO2
activation curve of forward rapid potassium current
slow-activating delayed rectifier potassium current
ryanodine receptor calcium cooperativity parameter PC1 - PO1
forward cooperativity constant for SERCA pump
concentration of magnesium-bound subspace ADP
maximum ryanodine receptor channel calcium flux
slow potassium current activation variable
rapid potassium current activation variable
calcium on-rate for troponin high affinity sites
calcium flux from network sarcoplasmic reticulum to junctional sarcoplasmic reticulum
rapid-activating delayed rectifier potassium current
concentration of calcium-bound subspace ADP
activation time constant of slow potassium current
transition rate into open state for calcium mode
volume of junctional sarcoplasmic reticulum
Michailova and McCulloch's mathematical model of ATP and ADP buffering, transport of Ca and Mg, and regulation of ion pumps in ventricular myocytes.@en
<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil> </affiliation> </author> </articleinfo> Model Status This CellML model runs in both COR and OpenCell to recreate the published results. The units have been checked and they are consistent. We thank the original model author Anushka Michailova for providing us with the MATLAB code for this model. Please note when running a simultaion the step size has to be smaller than 0.005 seconds. <sect1 id="sec_structure"> Model Structure ABSTRACT: We extended the model of the ventricular myocyte by Winslow et al. (Circ. Res 1999, 84:571-586) by incorporating equations for Ca(2+) and Mg(2+) buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na(+)-K(+) pump, sarcolemmal and sarcoplasmic Ca(2+) pumps). The results indicate that, under normal conditions, Ca(2+) binding by low-affinity ATP and diffusion of CaATP may affect the amplitude and time course of intracellular Ca(2+) signals. The model also suggests that a fall in ATP/ADP ratio significantly reduces sarcoplasmic Ca(2+) content, increases diastolic Ca(2+), lowers systolic Ca(2+), increases Ca(2+) influx through L-type channels, and decreases the efficiency of the Na(+)/Ca(2+) exchanger in extruding Ca(2+) during periodic voltage-clamp stimulation. The analysis suggests that the most important reason for these changes during metabolic inhibition is the down-regulation of the sarcoplasmic Ca(2+)-ATPase pump by reduced diastolic MgATP levels. High Ca(2+) concentrations developed near the membrane might have a greater influence on Mg(2+), ATP, and ADP concentrations than that of the lower Ca(2+) concentrations in the bulk myoplasm. The model predictions are in general agreement with experimental observations measured under normal and pathological conditions. The original paper reference is cited below: Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte, Anushka Michailova and Andrew McCulloch, 2001, Biophysical Journal , 81, 614-629. PubMed ID: 11463611 <informalfigure float="0" id="fig_cell_diagram"> <mediaobject> <imageobject> <objectinfo> cell diagram </objectinfo> <imagedata fileref="michailova_mcculloch_2001.png" /> </imageobject> </mediaobject> Schematic diagram of the mechanisms involved in the model. </informalfigure> </sect1> </documentation>
time constant for transfer of magnesium-bound ADP from subspace to myoplasm
calcium-bound ATP flux from subspace to myoplasm
time constant for transfer of magnesium-bound ATP from subspace to myoplasm
calcium off-rate for troponin high affinity sites
calcium half-saturation constant for calmodulin
calcium current at half potassium permeability of L-type calcium channel
steady state function of rapid potassium current activation variable
maximum plateau potassium channel conductance
activation time constant of L-type calcium current
free calcium flux from subspace to myoplasm
maximum transient outward potassium current conductance
concentration of free subspace magnesium
calcium half-saturation constant for sodium-calcium exchange
fraction of ryanodine receptor channels in state PC1
calcium permeability of L-type calcium channel
calcium half-saturation constant for time-independent potassium current
maximum background calcium current conductance
fraction of ryanodine receptor channels in state PC2
modified sarcolemmal calcium pump current
reverse cooperativity constant for SERCA pump
maximum slow potassium current conductance
free magnesium flux from subspace to myoplasm
concentration of magnesium-bound subspace ATP
time constant for transfer of free magnesium from subspace to myoplasm
calcium flux to low-affinity troponin sites
forward half-saturation constant for calcium ATPase
calcium flux to high-affinity troponin sites
ryanodine receptor PO1 - PO2 rate constant
transfer time constant from network sarcoplasmic reticulum to junctional sarcoplasmic reticulum
steady state function of L-type calcium current activation variable
sodium current slow inactivation variable
concentration of calcium-bound myoplasmic ATP
concentration of magnesium-bound myoplasmic ADP
sodium half-saturation constant for sodium-potassium pump
ryanodine receptor PO1 - PC1 rate constant
slow delayed rectifier current reversal potential
magnesium-bound ADP flux from subspace to myoplasm
voltage dependence factor of sodium-calcium exchange
fraction of ryanodine receptor channels in state PO1
ryanodine receptor PO1 - PC2 rate constant
modified calcium uptake flux into network sarcoplasmic reticulum by SERCA pumps
time constant for transfer of calcium-bound ADP from subspace to myoplasm
concentration of calcium-bound troponin high-affinity sites
time constant for transfer of calcium-bound ATP from subspace to myoplasm
total concentration of troponin low-affinity sites
ryanodine receptor PC1 - PO1 rate constant
scale factor of sodium-calcium exchanger