Di Francesco-Noble Purkinje Fibre Model 1985
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model has been curated and unit-checked by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.
Model Structure
During the years that followed the formulation of the McAllister-Noble-Tsien Purkinje fibre model in 1975 and the Beeler-Reuter mammalian ventricular model in 1977, many experiments were performed which provided a greater insight into the working of the ion channels in cardiac tissue. D. Di Francesco and D. Noble (1985) constructed a new model of cardiac electrical activity which sought to incorporate much of this new data (see the figure below).
The complete original paper reference is cited below:
A Model of the Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes - Simulations of Ionic Currents and Concentration Changes, Di Francesco, D. and Noble, D.
Phil. Trans. R. Soc. Lond.
, B307, 353-398. (The
full text
of the article is available to members on the JSTOR website.)
PubMed ID: 2578676
cell diagram of the DFN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum
A schematic diagram describing the current flows across the cell membrane that are captured in the DFN model.
the cellml rendering of the DFN model
The network defined in the CellML description of the Di Francesco-Noble model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the
notation guide
. For simplicity, not all the variables are shown.
The membrane physically contains the currents, exchangers and pumps, as indicated by the blue arrows in
. The currents act independently and are not connected to each other. Several of the channels encapsulate
and
contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model.
The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models.
Time solution domain
Fast sodium channel current across plasma membrane
TTX sensittive fast Na current
Time constant for s.r. uptake of calcium
Cardiac myocyte membrane potential
Time solution domain
K conductance of if channels
Channel between two tightly packed cell.
Intercellular cleft
Hyperpolarizing activated K channel current
K component of hyperpolarising activated current
Delayed K rate coefficient
Calcium equilibrium potential
Gating variable for fast Ca current channel f gate
Potassium concentration in the extracellular cleft
Time solution domain
Rate coefficient of p
Time solution domain
Potassium concentration in the extracellular cleft
Total extracellular volume
Rate coefficient of p
Time solution domain
K component of hyperpolarising activated current
Calcium equilibrium potential
Ca background current across plasma membrane of cardiac myocyte
Calcium background current
NaK exchange pump current
NaK exchange pump current
Na background current across plasma membrane of cardiac myocyte
Sodium background current
Secondary K channel inward current
Potassium component of fast Ca current
Intracellular Ca dependent inactivation of fast calcium current
Extracellular calcium concentration
Secondary Na channel inward current
Sodium component of fast Ca current
Potassium equilibrium potential
Potassium concentration in the extracellular cleft
Total intracellular volume
Gating variable for h gate
Cardiac myocyte membrane potential
Sodium equilibrium potential
Time solution domain
Secondary Ca channel inward current
Calcium component of fast current
Inactivation gating and rate coefficient for fast Ca current channel
Potassium component of fast Ca current
Hyperpolarising activated channel current
Hyperpolarizing-activated NaK current
Extracellular calcium concentration
Time independent K channel current
Time independent K current
Cardiac myocyte membrane potential
Inactivation gate and rate coefficient
Delayed K current gating variable
Time- and voltage-dependence of the exchange between storage
and release sites.
Time solution domain
Cardiac myocyte membrane potential
Potassium intracellular concentration
Intracellular Ca concentration
Time solution domain
K transient outward channel current
Transient outward current
Extracellular sodium concentration
Volume of sarcoplasmic reticulum (s.r.) uptake store
Extracellular sodium concentration
Time constant for Ca release
Transient outward current
Intracellular Na concentration
NaCa exchange pump current across plasma membrane
Na-Ca exchange current
Cardiac myocyte membrane potential
Reversal potential for sodium channel
Conductance of fast sodium current channels
Rate coefficient for hyperpolarizing-activated NaK current
Sodium component of fast Ca current
Extracellular sodium concentration
Potassium concentration in the extracellular cleft
Length of preparation
Sodium background current
Time solution domain
Calcium component of fast current
Chris Thompson
A MODEL OF CARDIAC ELECTRICAL A C T I V I T Y INCORPORATING IONIC PUMPS AND CONCENTRATION CHANGES
Intracellular Ca dependent inactivation of fast calcium current
Net membrane potassium flux
Ionic half-activation concentration for hyperpolarising current
Cardiac myocyte membrane potential
Stoichiometry of Na-Ca exchange
Calcium background current
NaK pump Na half activation concentration
Time solution domain
Sodium equilibrium potential
Time solution domain
Transient outward current
Cardiac myocyte membrane potential
Cardiac myocyte membrane potential
Cardiac myocyte membrane potential
Time constant for repriming release store
Hyperpolarizing-activated NaK current
Activation gating and rate coefficient for fast Ca current channel
Intracellular Ca dependent inactivation of fast calcium current
Time solution domain
Cardiac myocyte membrane potential
Delayed K rate coefficient
added metadata
Oxford University
Department of Physiology, Anatomy & Genetics, University of Oxford
James Lawson
This model has been curated by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.
Oxford University
Department of Physiology, Anatomy & Genetics
added cmeta:id's to some variables to allow referencing by PCEnv session file
Units checked, curated.
Position of energy barrier controlling voltage-dependence of i_NaCa
K half activation concentration for transient outward current
Sodium background current
Potassium concentration in the extracellular cleft
Boltzmann constant
Inactivation gate and rate coefficient
Time solution domain
Time solution domain
Time solution domain
Maximum outward potassium current
Stoichiometry of Na-Ca exchange
Na-Ca exchange current
Cardiac myocyte membrane potential
Gating variable for Hyperpolarizing-activated NaK current
Inward K rectifier conductance
Total intracellular volume
Delayed rectifier K channel current
Delayed K current
Time solution domain
Time solution domain
Experimental stimulation current
Na-Ca exchange current
Intracellular Ca dependent inactivation of fast calcium current
Cardiac myocyte membrane potential
Gating variable for Hyperpolarizing-activated NaK current
Cardiac myocyte membrane potential
Gating variable for transient outward current
Half activation concentration for extracellular K activation of hyperpolarizing-activated NaK current
Intracellular Ca concentration
Faraday Constant
Potassium intracellular concentration
NaK exchange pump current
Cardiac myocyte membrane potential
Gating variable for fast Ca current channel d gate
Maximum Ca concentration in s.r. uptake store
Time solution domain
Rate coefficient for transient outward current
Extracellular sodium concentration
scaling factor for i_NaCa
NaK pump K half activation concentration
Time independent K current
Membrane capacitance
Potassium concentration in the extracellular cleft
Calcium background current
Sodium equilibrium potential
Number of Ca ions required to bind to activate release
NaK exchange pump current
Cardiac myocyte membrane potential
Potassium intracellular concentration
Gating variable for transient outward current
Time solution domain
Time solution domain
Delayed K current
Rate constant for K exchange between bulk and cleft space
Maximum NaK exchane pump current
Inactivation gating and rate coefficient for fast Ca current channel
Time solution domain
Total intracellular volume
Bulk extracellular potassium
Cardiac myocyte membrane potential
Sarcoplasmic reticulum uptake store
Ca uptake into the sarcoplasmic reticulum
Ca uptake into s.r. expressed as a current
Na conductance of if channels
Intracellular Na concentration
Ca concentration in s.r. uptake store
Rate coefficient for hyperpolarizing-activated NaK current
Calcium background conductance
Cardiac myocyte membrane potential
Intracellular Na concentration
Intracellular Ca concentration
Potassium concentration in the extracellular cleft
Conductance for transient outward K rectification
Faraday Constant
Net membrane potassium flux
NaK exchange pump current
Stoichiometry of Na-Ca exchange
Sarcoplasmic Ca transfer current
Ca transferred into releasable form
Intracellular Ca concentration
Intracellular Na concentration
Cardiac myocyte membrane potential
Total intracellular volume
Potassium concentration in the extracellular cleft
Extracellular sodium concentration
Activation gate and rate coefficient
Denominator constant for i_NaCa
Na-Ca exchange current
K half-activation concentration for inward K rectifier
Extracellular calcium concentration
Ca release from sarcoplasmic reticulum into cytosol of cardiac myocyte
Ca release from junctional sarcoplasmic reticulum into cytosol
Rate coefficient for transient outward current
Fraction occupied by extracellular space
Gating variable for h gate
Intracellular Na concentration
Secondary channel inward current
Total TTX-insensitive inward current
Intracellular Ca concentration
Ca concentrations in s.r. release store
TTX sensittive fast Na current
Time solution domain
Inactivation gating and rate coefficient for fast Ca current channel d gate
TTX sensittive fast Na current
Radius of preparation
Hyperpolarizing activated Na channel current
Na component of hyperpolarising activated current
Faraday Constant
Potassium equilibrium potential
Intracellular Ca concentration
Total TTX-insensitive inward current
Potassium intracellular concentration
Na component of hyperpolarising activated current
Fully activated value of delayed K current
Potassium intracellular concentration
Ca half activation concentration for transient outward current
Potassium intracellular concentration
Activation gate and rate coefficient
Volume of store of releasable calcium
Gating variable for fast Ca current channel d gate
Sodium background conductance
Time independent K current
A Model of Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes
Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
keyword
Purkinje Fibre
cardiac
electrophysiology
James Lawson
This is a CellML description of the model described in the paper "A Model of the Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes - Simulations of Ionic Currents and Concentration Changes," by Di Francesco, D. and Noble, D.
Time solution domain
Delayed K current gating variable
Intracellular Na concentration
Activation gate and rate coefficient
Cardiac myocyte membrane potential
Faraday Constant
Extracellular calcium concentration
Delayed K current
Gating variable for fast Ca current channel f gate
Faraday Constant
Cardiac myocyte membrane potential
Time solution domain
Activation gate and rate coefficient
Half activation concentration for Ca binding to release site