Hilemann-Noble Atrial Cell Model 1987
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model is known to run in OpenCell and COR and reproduce the published results.
Model Structure
ABSTRACT: Interactions of electrogenic sodium-calcium exchange, calcium channel and sarcoplasmic reticulum in the mammalian heart have been explored by simulation of extracellular calcium transients measured with tetramethylmurexide in rabbit atrium. The approach has been to use the simplest possible formulations of these mechanisms, which together with a minimum number of additional mechanisms allow reconstruction of action potentials, intracellular calcium transients and extracellular calcium transients. A 3:1 sodium-calcium exchange stoichiometry is assumed. Calcium-channel inactivation is assumed to take place by a voltage-dependent mechanism, which is accelerated by a rise in intracellular calcium; intracellular calcium release becomes a major physiological regulator of calcium influx via calcium channels. A calcium release mechanism is assumed, which is both calcium- and voltage-sensitive, and which undergoes prolonged inactivation. 200 microM cytosolic calcium buffer is assumed. For most simulations only instantaneous potassium conductances are simulated so as to study the other mechanisms independently of time- and calcium-dependent outward current. Thus, the model reconstructs extracellular calcium transients and typical action-potential configuration changes during steady-state and non-steady-state stimulation from the mechanisms directly involved in trans-sarcolemmal calcium movements. The model predicts relatively small trans-sarcolemmal calcium movements during regular stimulation (ca. 2 mumol kg-1 fresh mass per excitation); calcium current is fully activated within 2 ms of excitation, inactivation is substantially complete within 30 ms, and sodium-calcium exchange significantly resists repolarization from approximately -30 mV. Net calcium movements many times larger are possible during non-steady-state stimulation. Long action potentials at premature excitations or after inhibition of calcium release can be supported almost exclusively by calcium current (net calcium influx 5-30 mumol kg-1 fresh mass); action potentials during potentiated post-stimulatory contractions can be supported almost exclusively by sodium-calcium exchange (net calcium efflux 4-20 mumol kg-1 fresh mass). Large calcium movements between the extracellular space and the sarcoplasmic reticulum can take place through the cytosol with virtually no contractile activation. The simulations provide integrated explanations of electrical activity, contractile function and trans-sarcolemmal calcium movements, which were outside the explanatory range of previous models.
The original paper reference is cited below:
Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of the basic cellular mechanisms, Hilemann, D.W. and Noble, D. 1987,
Proc. R. Soc. Lond.
, B230, 163-205.
PubMed ID: 2884668
cell diagram of the Hilemann-Noble model showing ionic currents across the sarcolemma
A schematic diagram describing the current flows across the cell membrane that are captured in the Hilemann-Noble model.
Intracellular Ca concentration
Time solution domain
Sarcoplasmic reticulum uptake store
Sarcoplasmic Ca transfer current
Ca transferred into releasable form
Cardiac myocyte membrane potential
Time solution domain
Ca concentration in s.r. uptake store
James Lawson
This is a CellML representation of Hilgeman et al.'s 1987 model of the basic cellular mechanisms of excitation-contraction coupling and Ca++ handling in the rabbit atrial myocyte.
Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms
230 1259
Proceedings of the Royal Society of London - Series B
keyword
calcium dynamics
electrophysiology
mouse
atrial myocyte
excitation-contraction coupling
Calcium reversal potential
Activator molecule inactive product fraction
Maximum NaK exchane pump current
Time solution domain
NaCa exchange pump current across plasma membrane
Na-Ca exchange current
Channel between two tightly packed cell.
Intercellular cleft
Potassium concentration in the extracellular cleft
Activation gating and rate coefficient for fast Ca current channel
Release channel activation rate
Release channel Ca leak rate
Rate constant of exchange between extracellular space and the muscle bath
Extracellular sodium concentration
Gating variable for h gate
Potassium concentration in the extracellular cleft
Time - Solution Domain
Activation gating and rate coefficient for fast Ca current channel
Fraction of regulatory sites occupied by Ca
Time solution domain
Potassium intracellular concentration
Secondary Ca channel inward current
Calcium component of fast Ca current
Extracellular sodium concentration
Time independent K channel current
Time independent K current
Concentration of Ca bound troponin in the cytosol
Time - Solution Domain
SR Ca release current maximal release rate
Extracellular calcium concentration
Potassium intracellular concentration
Inactivation gate and rate coefficient
Ca uptake into the sarcoplasmic reticulum
Ca uptake into SR expressed as a current
Time solution domain
Ca-calmodulin dissociation rate constant
Intracellular Ca concentration
Ca release from sarcoplasmic reticulum into cytosol of cardiac myocyte
Ca release from junctional sarcoplasmic reticulum into cytosol
Time independent K current
Time - Solution Domain
Cardiac myocyte membrane potential
SR Ca uptake forward reaction rate constant
Sodium-Potassium Pump Current
NaK exchange pump current
Release channel inactivation rate
Extracellular sodium concentration
Ca transferred into releasable form
Potassium reversal potential
Secondary Na channel inward current
Sodium component of fast Ca current
Intracellular Na concentration
Na-Ca exchange current
Potassium intracellular concentration
Cardiac myocyte membrane potential
Regulatory binding sites occupied by Ca.
Reversal potential for sodium channel
Conductance of fast sodium current channels
Sodium component of fast Ca current
Intracellular Ca concentration
Time solution domain
Active, unbound regulatory states
Time - Solution Domain
Cardiac myocyte membrane potential
Extracellular calcium concentration
Concentration of Ca bound calmodulin in the cytosol
Calcium component of fast Ca current
NaK exchange pump current
Ca concentrations in s.r. release store
NaK pump Na half activation concentration
K background current across plasma membrane of the cardiac myocyte
Background K current
Total extracellular volume
Time solution domain
Activator molecule fraction
Muscle Bath
Ca concentration in the muscle bath
Cardiac myocyte membrane potential
Cardiac myocyte membrane potential
Cardiac myocyte membrane potential
Potassium background conductance
Intracellular Na concentration
Cytosolic Ca/enzyme reaction rate
Potassium intracellular concentration
Activation gating and rate coefficient for fast Ca current channel
Intracellular Na concentration
Na background current across plasma membrane of cardiac myocyte
Sodium background current
Department of Physiology, Anatomy & Genetics, University of Oxford
James Lawson
This version was created by Penny Noble of Oxford University and is known to run in both COR and PCEnv. The integration problems experienced with Version 03 are fixed in this version. A predefined operator diff error produced by PCEnv in the component intracellular_calcium_concentration of Penny Noble's version was fixed by James Lawson on 19/04/07. Due to the small stimulus duration, for this model to produce a train of action potentials, the max step size must be set at 0.001 or below and the number of points per graph must be over 10k.
Oxford University
Department of Physiology, Anatomy & Genetics
added cmeta:id's to some variables to facilitate creation of PCEnv session file
Added stimulus protocol to allow simulation of trains of action potentials.
Made 2 new variables - dCaCalmoddt and dCaTropdt in component "intracellular_calcium_concentration," equated these variables to d(CaCalmod)/d(time) and d(CaTrop)/d(time), respectively. This was done to allow PCEnv 0.2 to run the model.
Sodium background current
Position of energy barrier controlling voltage-dependence of i_NaCa
Redundant and unused codeword
Boltzmann constant
Redundant and unused codeword
Inactivation gate and rate coefficient
Time solution domain
Chris Thompson
Stoichiometry of Na-Ca exchange
Total intracellular volume
Na-Ca exchange current
Activation gating and rate coefficient for fast Ca current channel
Time - Solution Domain
Inward K rectifier conductance
radius of preparation
Time solution domain
Fraction of channels inactivated by voltage-dependent process.
Extracellular calcium concentration
Intracellular Na concentration
Time - Solution Domain
Na-Ca exchange current
Total intracellular volume
Calcium background conductance
Inactivation gating and rate coefficient for fast Ca current channel
Secondary channel inward current
Total TTX-insensitive inward current
Faraday Constant
Intracellular Ca concentration
Secondary K channel inward current
Potassium component of fast Ca current
Time - Solution Domain
Cardiac myocyte membrane potential
NaK pump K half activation concentration
Ca concentrations in s.r. release store
Potassium concentration in the extracellular cleft
Time independent K current
Sodium reversal potential
Potassium component of fast Ca current
Time solution domain
Ratio of SR uptake component volume and total cell volume
Experimental stimulation current
Time solution domain
Background K current
Cardiac myocyte membrane potential
Cardiac myocyte membrane potential
Ca concentration in s.r. uptake store
Ca uptake into SR expressed as a current
Ca concentration in s.r. uptake store
Inactivation gating and rate coefficient for fast Ca current channel
Intracellular Ca concentration
Cardiac myocyte membrane potential
Ratio of intracellular volume and total cell volume
scaling factor for i_NaCa
Faraday Constant
Ca background current across plasma membrane of cardiac myocyte
Calcium background current
Activator precursor molecule fraction
Calcium background current
Fraction of channels inactivated by voltage-dependent process.
K half-activation concentration for inward K rectifier
Activation gate and rate coefficient
Cell volume
Denominator constant for i_NaCa
Na-Ca exchange current
Ca release from junctional sarcoplasmic reticulum into cytosol
Voltage dependence of release
Extracellular sodium concentration
Gating variable for h gate
Ratio of JSR volume and total cell volume
SR Ca/enzyme reaction rate
Ca concentrations in s.r. release store
Cardiac myocyte membrane potential
Fast sodium channel current across plasma membrane
TTX sensittive fast Na current
Time solution domain
TTX sensittive fast Na current
Extracellular calcium concentration
NaK exchange pump current
Calcium component of fast Ca current
Potassium reversal potential
Intracellular Ca concentration
Total TTX-insensitive inward current
Faraday Constant
Rate coefficient for Ca translocation
Calcium background current
Intracellular Na concentration
Sodium background conductance
Total troponin concentration in the cytosol
TTX sensittive fast Na current
Sodium background current
Activation gate and rate coefficient
Time solution domain
Ca-troponin binding rate constant
Potassium concentration in the extracellular cleft
Background K current
Activation gate and rate coefficient
Fraction of volume taken by extracellular space
Calcium background current
Cardiac myocyte membrane potential
NaK exchange pump current
Cardiac myocyte membrane potential
Total intracellular volume
Ca-troponin dissociation rate constant
Faraday Constant
Total calmodulin concentration in the cytosol
Extracellular sodium concentration
Total extracellular volume
Membrane capacitance
SR Ca uptake back ard reaction rate constant
Ca-calmodulin binding rate constant
Faraday Constant
Potassium concentration in the extracellular cleft
Intracellular Na concentration
Time - Solution Domain
Intracellular Ca concentration
Active, unbound regulatory states
length of preparation
Activation gate and rate coefficient