Jafri-Rice-Winslow Ventricular Model 1998
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model is known to run in both PCEnv and COR, and has been curated by Penny Noble of Oxford University. This variant also contains an embedded CellML description of Niederer, Hunter and Smith's quantitative model of cardiac myocyte regulation. The reference for this paper is given below.
Model Structure
ABSTRACT: We construct a detailed mathematical model for Ca2+ regulation in the ventricular myocyte that includes novel descriptions of subcellular mechanisms based on recent experimental findings: 1) the Keizer-Levine model for the ryanodine receptor (RyR), which displays adaptation at elevated Ca2+; 2) a model for the L-type Ca2+ channel that inactivates by mode switching; and 3) a restricted subspace into which the RyRs and L-type Ca2+ channels empty and interact via Ca2+. We add membrane currents from the Luo-Rudy Phase II ventricular cell model to our description of Ca2+ handling to formulate a new model for ventricular action potentials and Ca2+ regulation. The model can simulate Ca2+ transients during an action potential similar to those seen experimentally. The subspace [Ca2+] rises more rapidly and reaches a higher level (10-30 microM) than the bulk myoplasmic Ca2+ (peak [Ca2+]i approximately 1 microM). Termination of sarcoplasmic reticulum (SR) Ca2+ release is predominately due to emptying of the SR, but is influenced by RyR adaptation. Because force generation is roughly proportional to peak myoplasmic Ca2+, we use [Ca2+]i in the model to explore the effects of pacing rate on force generation. The model reproduces transitions seen in force generation due to changes in pacing that cannot be simulated by previous models. Simulation of such complex phenomena requires an interplay of both RyR adaptation and the degree of SR Ca2+ loading. This model, therefore, shows improved behavior over existing models that lack detailed descriptions of subcellular Ca2+ regulatory mechanisms.
The original paper reference is cited below:
Cardiac Calcium Dynamics: The Roles of Ryanodine Receptor Adaptation and Sarcoplasmic Reticulum Load, M. Saleet Jafri, J. Jeremy Rice and Raimond L. Winslow, 1998,
Biophysical Journal, 74, 1149-1168. PubMed ID: 9512016
The reference for the embedded Niederer Hunter Smith model of cardiac myocyte relaxation is: "A Quantitative Analysis of Cardiac Myocyte Relaxation: A Simulation Study" Niederer, S.A., Hunter, P.J., Smith, N.P, Biophysical Journal, Volume 90, March 2006, pp. 1697-1722.
cell diagram of the Jafri-Rice-Winslow 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 Jafri-Rice-Winslow model.
M
Jafri
Saleet
Rate constants for state changes in mode normal.
The voltage- and time-dependent activation gate for the
time-dependent potassium current - the X gate.
The potassium permeability of the channel, which depends on the
calcium current component.
Calculate the uptake flux into the NSR from the myoplasm.
The voltage-dependent inactivation gate for the L-type calcium
channel - the y gate.
The time-independent inactivation gate for the time-dependent
potassium channel.
Removed document type definition as this is declared as optional
according to the W3C recommendation.
Calculate the translocation flux between the uptake (NSR) and
release (JSR) stores.
Calculation of the background sodium current.
Ventricular Myocyte
The Jafri-Rice-Winslow Model for Calcium Regulation in the Ventricular
Myocyte, 1997
Mammalia
keyword
Ventricular Myocyte
calcium dynamics
electrophysiology
ryanodine receptor
The plateau potassium current component contains the equations which
describe the contribution of a time independent [K]o-insensitive
channel at plateau potentials.
Calculate the current.
2007-05-24T11:52:30+12:00
The fast sodium current component contains the differential
equations governing the influx of sodium ions through the cell
surface membrane into the cell.
Catherine
Lloyd
May
The kinetics of the h gate.
The kinetics of calcium binding to the myoplasm buffer troponin -
both high and low affinity binding sites.
Added some initial values from Penny Noble's documentation.
The closing rate of the j gate.
The rate of change of intracellular sodium ion concentration.
This model has been curated by Penny Noble of Oxford University and is known to run in PCEnv and COR. A PCEnv session is also associated with this file.
9512016
The reversal potential for the background sodium channel.
The time constants for the K1 gate are small enough that the gating
variable can be approximated with it's steady-state value.
The following equation calculates the reversal potential of the
time-independent potassium current.
The total nonspecific calcium activated current.
The "open" RyR's are those P_O1 and P_O2 states.
Catherine
Lloyd
May
The opening rate of the h gate.
3000
100000
0.1
The opening rate of the K1 gate.
2002-02-28
M
Jafri
Saleet
2002-01-04
The University of Auckland
The Bioengineering Research Group
The time-independent potassium current.
The time-dependent potassium current has an X^2 dependence on it's
activation gate, and an Xi inactivation gate. This channel is also
assumed permeable to sodium ions.
The voltage-dependent slow inactivation gate for the fast sodium
current - the j gate.
In the JRW model, subcellular calcium regulatory mechanisms are
described in detail. There are six calcium fluxes to consider;
J_rel, J_leak, J_up, J_tr, J_xfer and J_trpn. In addition, three
membrane current fluxes are also necessary for the formulation of
calcium regulation; i_p_Ca, i_Ca_L_Ca and i_NaCa.
The kinetics of the state transitions in mode Ca.
Calcium binding to the Ca channel induces a conformational change
from normal mode to mode Ca. This effectively inhibits the
conduction of calcium ions because in mode Ca, the calcium channel
makes the transition to the open, conducting state (O) extremely
slowly.
The sodium component of the channel's current.
Catherine
Lloyd
May
The closing rate of the h gate.
The kinetics of the calcium ion concentration changes in the various
compartments of the model.
The closing rate of the m gate.
Biophysical Journal
Calculation of the maximal channel conductance, dependent on
extracellular potassium concentration.
The rate of change of intracellular potassium ion concentration.
The sodium background current is a time-independent diffusion of
Na ions down their electrochemical gradient, through the cell
surface membrane into the cytosol.
2003-06-04
The rate of change of extracellular potassium ion concentration.
James Lawson
Calculation of the time-dependent potassium current.
This model has been curated and the output checked against the original paper.
The maximal potassium component current.
Catherine
Lloyd
May
Catherine
Lloyd
May
Calculation of the plateau potassium current.
2001-12-07
James
Lawson
Richard
The calcium pump current.
Several variables have been given cmeta:id's to allow creation of a PCEnv session file.
2002-02-25
The maximal sodium component current.
Catherine Lloyd
Calculation of the Na/Ca exchanger current.
This is the CellML description of Jafri, Rice and Winslow's mathematical model for calcium regulation in the ventricular myocyte. It is based on an accurate model of the membrane currents and adds a more sophisticated model of calcium handling. The JRW model is based on the LR-II model for ventricular action potentials, with several modifications.
Cardiac Ca2+ Dynamics: The Roles of Ryanodine Receptor Adaptation and Sarcoplasmic Reticulum Load (Extended Model)
The University of Auckland, Bioengineering Research Group
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
The main component of the model which defines the action potential.
The channel's reversal potential.
Calculation of the fast sodium current using the three
Hodkin-Huxley type voltage-dependent gating variables m, h, and j.
The sarcolemmal calcium pump is an additional mechanism for removing
Ca ions from the myoplasm to help maintain a low intracellular
calcium concentration when at rest.
The kinetics of the y gate.
Raimond
Winslow
L
Calculation of the potassium current component of the total channel
current.
Raimond
Winslow
L
The steady-state approximation for the K1 gating kinetics.
Corrected equations: alpha_j_calculation and beta_j_calculation in
fast_sodium_current_j_gate, alpha_X_calculation and beta_X_calculation in time_dependent_potassium_current_X_gate, and f_NaK_calculation and
i_NaK_calculation in Ca_release_current_from_JSR.
The closing rate of the X gate.
Penny
Noble
J
The nonspecific calcium activated current describes a channel which
is activated by calcium ions, but is permeable to only sodium and
potassium ions.
Cardiac Ca2+ Dynamics: The Roles of Ryanodine Receptor Adaptation and Sarcoplasmic Reticulum Load
74
1149
1168
Rate constant for switching between mode normal and mode Ca.
Changed tau_y_calculation after checking mathml using the validator.
Calculation of the background calcium current.
The kinetics of the X gate.
The opening rate of the m gate.
The potassium component of the channel's current.
Catherine
Lloyd
May
Corrected several equations.
2003-07-30
John
Rice
Jeremy
John
Rice
Jeremy
Xi is the inward rectification parameter and is given by the
following equation.
The calcium background current describes a time-independent
diffusion of Ca ions down their electrochemical gradient through the
cell surface membrane into the cytosol. However, calcium is not
allowed to accumulate to high intracellular concentrations. This
influx is balanced by the Ca ion extrusion through the Na-Ca
exchanger and the sarcolemmal Ca pump.
2002-05-06
The potential offset for the channel.
The maximal calcium current through the channel.
Keep track of the concentration of calcium ions bound to high and
low affinity troponin binding sites.
The descriptions of the rate of change of [Na]i and [K]i are the
same as the LR-II model.
Calculation of the maximal channel conductance, dependent on
extracellular potassium concentration.
Catherine
Lloyd
May
The sodium potassium pump is an active protein in the cell membrane
which couples the free energy released by the hydrolysis of ATP to
the movement of Na and K ions against their electrochemical
gradients through the cell membrane.
The sodium reversal potential.
The kinetics of the transmembrane potential, defined as the sum of
all the sarcolemmal currents and an applied stimulus current.
Catherine
Lloyd
May
The reversal potential of the channel.
Calculation of the calcium current component of the total channel
current, given as the maximal current multiplied by the
voltage-dependent inactivation gate and the open probability of the
channel based on the mode-switching model.
Rate constants for state changes in mode Ca (corresponding to
alpha-prime and beta-prime in the JRW paper).
Calculate the leakage flux from the NSR into the myoplasm.
The voltage-dependent activation gate for the fast sodium current -
the m gate.
Catherine
Lloyd
May
Calcium is buffered by calmodulin (CMDN) in the subspace and
myoplasm, and by calsequestrin (CSQN) in the JSR. These are fast
buffers and their effect is modelled using the rapid buffering
approximation.
2001-09-24T00:00:00+00:00
The calcium release flux from the JSR into the restricted subspace
is governed by the fraction of RyR channels in an open state.
Altered some of the connections.
1998-03-01
The opening rate of the j gate.
Calculate some volume fractions as proportions of the total
myoplasmic volume.
The Na/Ca exchanger component describes how a protein molecule in
the cell surface membrane transports Na ions into the cytosol and
exports Ca ions into the extracellular volume, in a ratio of 3:1
respectively.
2007-06-22T12:55:26+12:00
The voltage-dependent inactivation gate for the fast sodium current
- the h gate.
The closing rate of the K1 gate.
The opening rate of the X gate.
The reversal potential for the background calcium current.
The reversal potential of the channel.
Calculation of the Na/K pump current.
2001-10-19
Calculate the calcium flux from the diffusion of calcium out of the
restricted subspace into the myoplasm.
The kinetic equations governing the transitions between the four
states used to model the RyR's.
The kinetics of the state transitions in mode normal.
In the normal mode, the calcium channel is able to make the
transition to the open, conducting state (O) from the closed state
(C) at a normal rate.
c.lloyd@auckland.ac.nz
The kinetics of the j gate.
The JWR model creates a new mathematical model to describe the
L-type calcium channel that is based on the experimentally observed
mode-switching behaviour of the channel. Inactivation occurs as
calcium ion binding induces the channel to switch (from mode normal)
to a mode in which transitions to open states are extremely slow
(mode Ca). The channel has one voltage inactivation gate, y. As well
as Ca, the channel is assumed permeable to K ions also.
The activation variable.
Corrected equations.
Corrected several equations, variable units and their initial values.
The kinetics of the m gate.