RyR Adaptation and Ca2+ Oscillations
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Structure
The ryanodine receptor (RyR) from cardiac cells and skeletal muscle undergoes a Ca2+-dependent process called adaptation. Adaptation occurs during the slow, spontaneous decrease in the open probability of a channel after it has been rapidly activated by a pulse of cytosolic calcium ([Ca2+]i). RyR activation occurs within milliseconds, whereas inactivation occurs on a timescale of a few seconds. The RyR is said to have "adapted" during inactivation because a subsequent increase in [Ca2+]i produces a nearly identical rise in the open probability.
In their 1996 paper, Joel Keizer and Leslie Levine develop a simplified model that mimics the "adaptation" of the RyR, and they investigate its significance for Ca2+-induced Ca2+ release and Ca2+ oscillations in cardiac cells. The mechanism used to mimic adaptation of the RyR is shown schematically in below. States C1 and C2 are closed states and O1 and O2 are open states. Transitions from C1 to O1 and from O1 to O2 are assumed to be Ca2+-dependent. These steps correspond to the phenomenon of Ca2+-induced Ca2+ release (CICR). To analyse the mechanism in , Keizer and Levine translated the schematic diagram into kinetic equations. In addition, they test these equations in a closed-cell kinetic model, and they find that RyR adaptation can cause Ca2+ oscillations. However, in an open-cell, CICR, not RyR adaptation, produces Ca2+ oscillations.
The complete original paper reference is cited below:
Ryanodine Receptor Adaptation and Ca2+-Induced Ca2+ Release-Dependent Ca2+ Oscillations, Joel Keizer and Leslie Levine, 1996,
Biophysical Journal
, 71, 3477-3487. PubMed ID: 8968617
The raw CellML description of the kinetic model of cardiac RyR adaptation can be downloaded in various formats as described in .
Schematic diagram of the RyR model
Schematic diagram of transitions among the four states of the RyR used to describe adaptation. States C1 and C2 are closed states and O1 and O2 represent open states, assumed to have the same single-channel conductance. The k are rate constants: only steps a and b are Ca2+ dependent.
$\frac{d \mathrm{P\_C1}}{d \mathrm{time}}=-(\mathrm{ka}\mathrm{Cai}^{n}\mathrm{P\_C1})+\mathrm{ka\_}\mathrm{P\_O1}$
$\frac{d \mathrm{P\_O1}}{d \mathrm{time}}=\mathrm{ka}\mathrm{Cai}^{n}\mathrm{P\_C1}+-(\mathrm{ka\_}\mathrm{P\_O1}+\mathrm{kb}\mathrm{Cai}^{m}\mathrm{P\_O1})+\mathrm{kb\_}\mathrm{P\_O2}+-(\mathrm{kc}\mathrm{P\_O1})+\mathrm{kc\_}\mathrm{P\_C2}$
$\frac{d \mathrm{P\_O2}}{d \mathrm{time}}=-(\mathrm{kb}\mathrm{Cai}^{m}\mathrm{P\_O1})+\mathrm{kb\_}\mathrm{P\_O2}$
$\frac{d \mathrm{P\_C2}}{d \mathrm{time}}=\mathrm{kc}\mathrm{P\_O1}-\mathrm{kc\_}\mathrm{P\_C2}$
$\mathrm{P\_O\_slow}=\frac{w(1.0+\left(\frac{\mathrm{Cai}}{\mathrm{Kb}}\right)^{3.0})}{1.0+\left(\frac{\mathrm{Ka}}{\mathrm{Cai}}\right)^{4.0}+\left(\frac{\mathrm{Cai}}{\mathrm{Kb}}\right)^{3.0}}\mathrm{w\_init}=1.0-\mathrm{P\_C2}\mathrm{w\_infinity\_Cai}=\frac{1.0+\left(\frac{\mathrm{Ka}}{\mathrm{Cai}}\right)^{4.0}+\left(\frac{\mathrm{Cai}}{\mathrm{Kb}}\right)^{3.0}}{1.0+\frac{1.0}{\mathrm{Kc}}+\left(\frac{\mathrm{Ka}}{\mathrm{Cai}}\right)^{4.0}+\left(\frac{\mathrm{Cai}}{\mathrm{Kb}}\right)^{3.0}}\mathrm{tau\_Cai}=\frac{\mathrm{w\_infinity\_Cai}}{\mathrm{kc\_}}\mathrm{Ka}=\frac{\mathrm{ka\_}}{\mathrm{ka}}\mathrm{Kb}=\frac{\mathrm{kb\_}}{\mathrm{kb}}\mathrm{Kc}=\frac{\mathrm{kc\_}}{\mathrm{kc}}\frac{d w}{d \mathrm{time}}=\frac{-(w-\mathrm{w\_infinity\_Cai}\mathrm{Cai})}{\mathrm{tau\_Cai}\mathrm{Cai}}$
$\frac{d \mathrm{Cai}}{d \mathrm{time}}=\mathrm{fi}((\mathrm{v1}\mathrm{P\_O\_slow}+\mathrm{v2})(\mathrm{Cas}-\mathrm{Cai})-\mathrm{v3}\frac{\mathrm{Cai}^{2.0}}{\mathrm{Cai}^{2.0}+\mathrm{K3}^{2.0}})\mathrm{Cas}=\frac{\mathrm{Co}-\mathrm{Cai}}{\mathrm{c1}}$
calcium dynamics
ryanodine receptor
oscillator
Cardiac Myocyte
electrophysiology
cardiac
ryanodine receptors
cicr
Open state on a slow time scale
P_O_slow
The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology.
The model runs in the PCEnv simulator but gives NaNs.
The University of Auckland, Bioengineering Institute
Leslie
Levine
1996-12-01
c.lloyd@auckland.ac.nz
8968617
Biophysical Journal
Keizer and Levine's 1996 model of a gating scheme for ryanodine
receptors.
Cardiac Myocyte
Ryanodine Receptor Adaptation and Ca2+-Induced Ca2+
Release-Dependent Ca2+ Oscillations
71
3477
3487
Open state 2
P_O2
Open state 1
P_O1
Joel
Keizer
Intracellular calcium concentration in a closed cell
Cai
Catherine
Lloyd
May
This is the CellML description of Keizer and Levine's 1996 model of a
gating scheme for ryanodine receptors in cardiac muscle.
Closed state 2
P_C2
2007-06-05T09:35:57+12:00
Catherine Lloyd
Closed state 1
P_C1
Catherine
Lloyd
May
2007-05-18
The University of Auckland
The Bioengineering Institute
keyword