This is the CellML description of Boyett et al's mathematical model of pacemaker activity in the sinoatrial node. Their model is a development of Zhang et al's earlier 2000 model of action potentials in SA node cells by considering intracellular Ca2+ handling. The SA node is functionally, anatomically and electrophysiologically heterogeneous. Boyett et al have considered this heterogeneity and they define two distinct models for the peripheral SA node and the central SA node. These models have the same equations but they vary in their parameters. Below is a CellML description of the model of action potentials in the periphery of the sinoatrial(SA) node. For a model of the central SA node action potential, use the equations below but substitute some parameters with the appropriate ones listed in the original paper.
electrophysiology
pacemaker
calcium dynamics
cardiac
atrial myocyte
sinoatrial node
2005-04-20
Other SA node models have included computation of concentrations of
intracellular Na+ and Ca2+. In this model, Zhang et al have assumed
that all ion concentrations remain constant.
c.lloyd@auckland.ac.nz
Catherine
Lloyd
May
Lloyd
May
Catherine
A.
Garny
Sinoatrial Node Cell
Boyett et al's 2001 mathematical model of control of pacemaker
activity of the sinoatrial node
J
Peter
Villiger
Corrected several equations.
2009-05-28T15:58:34+12:00
The University of Auckland, Auckland Bioengineering Institute
2002-02-25
Catherine
May
Lloyd
Boyett
M
R
James
Richard
Lawson
2002-07-19
Added more metadata.
fixed e-notation errors
updated curation status
removed reference link in documentation
Holden
A
V
i_f is a mixed current composed of both Na+ and K+ ions. In the
equation to describe i_f, Zhang et al included i_f_Na and i_f_K as
separate components and they also included a single activation
variable y.
Catherine Lloyd
2002-01-28T00:00:00+00:00
1045
Control of the pacemaker activity of the sinoatrial node by intracellular Ca2+. Experiments and modelling
1337
359
Updated syntax to conform with cellml1.1 specs
The University of Auckland
Auckland Bioengineering Institute
Philosophical Transactions of The Royal Society, Mathematical, Physical and Engineering Sciences
2001-01-01
Zhang
H.
Experimental evidence suggests that intracellular calcium controls a
number of ionic currents. Boyett et al incorporated intracellular
calcium handling into the model of Zhang et al (2000).
The sodium current was originally thought to be absent in SA node
cells and consequently, most of the earlier models of the SA node
action potential do not include i_Na. However, more recent
experimental results show that i_Na is present and that it is
physiologically important. The sodium channel has one activation
gate m and one inactivation gate which has two components, a fast and
a slow inactivation variable; h1 and h2.
The L-type calcium channel has two gates, an activation gate d_L and
an inactivation gate f_L.
The T-type calcium channel has two gates, an activation gate d_T and
an inactivation gate f_T.
In their model, Boyett et al added the sustained inward current
described by Guo et al (1995) and Shinagawa et al (2000) in rabbit
and rat SA node cells. The equations defined below are taken from
Shinagawa et al (2000).
i_to and i_sus are respectively the transient and sustained
components of the 4-Aminopyridine-sensitive current. The current has
an activation variable r and and inactivation variable q.
The potassium cuurent in rabbit SA node cells can be divided into two
kinetically different components, a fast cuurent i_K_r and a slow
current i_K_s. Activation and inactivation of i_K_r has
double-exponential time courses. To model this, Zhang et al have
used two activation variables; a fast one (P_a_f) and a slow one
(P_a_s). There is a single inactivation variable P_i.
The slow sigmoidal activation of i_K_s is modelled by squaring the
gating variable xs. The i_K_s channel is also slightly permeable to
Na+ ions.
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