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Electrical interactions between a rabbit atrial cell
and a nodal cell model
RONALD W. JOYNER,1 RAJIV KUMAR,1 DAVID A. GOLOD,1 RONALD WILDERS,2,3
HABO J. JONGSMA,2 E. ETIENNE VERHEIJCK,2,3 LENNART BOUMAN,3
WILLIAM N. GOOLSBY,1 AND ANTONI C. G. VAN GINNEKEN2
1Todd Franklin Cardiac Research Laboratory, The Children’s Heart Center, Department
of Pediatrics, Emory University, Atlanta, Georgia 30322; 2Department of Medical Physiology
and Sports Medicine, Utrecht University, 3584 CG Utrecht; and 3Department of Physiology,
Academic Medical Center, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
action potential; cell coupling; arrhythmia; mathematical
model; sinoatrial node; atrioventricular node
several different cell types that
are regionally specialized. Two major classifications are
1) nodal cells, which are present predominantly within
the sinoatrial (SA) node and the atrioventricular (AV)
node and which have properties of spontaneous activity
and a low maximum rate of rise of the action potential
upstroke (dV/dt), and 2) cells with stable, strongly
negative resting potentials and a rapid maximum dV/dt
of the upstroke, which seem to make up the majority of
the atrial walls and septum. The second group of cells
may themselves be regionally inhomogeneous in terms
of their electrical coupling and their action potential
and membrane conductance properties (27, 28, 39).
Surrounding both the SA and the AV node are cells that
have been described as transitional in action potential
properties (1, 3, 5, 13–15, 21, 32). Other cells within
THE ATRIUM CONTAINS
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some regions of the atrium have been described as
‘‘latent pacemakers’’ (26, 41). A general problem in the
interpretation of the electrical interactions among cells
of different intrinsic membrane properties is that the
current flows are complex and multidimensional. Previous studies on the interactions between the fastupstroke atrial cells and the nodal cells have consisted
of simulations in which mathematical models have
been used to represent the different cell types. In our
earlier work (18, 19) we used either a pair of simulated
cells or a two-dimensional sheet of cells to study the
electrotonic interactions and to clarify the effects of
intercellular coupling conductance (Gc ). This work has
been extended in recent studies (6) to incorporate more
complete models of the intrinsic membrane properties
of the cells. Related studies have been performed in
which we used our ‘‘coupling clamp’’ technique (37) to
couple together either two isolated ventricular cells (17,
30) or an isolated ventricular cell to a mathematical
model of a ventricular cell (16, 37). Using this coupling
technique, Spitzer et al. (29) recently evaluated the
effects of coupling conductance on pairs of isolated cells
in which one cell was an AV node cell (or cluster of cells)
and the other cell was either a real atrial or ventricular
cell or a cell model with a resistance-capacitance circuit
to represent the input impedance of an isolated cell.
Watanabe et al. (35) also used this coupling technique
to couple an SA node cell to an atrial cell model
consisting of a resistor and a capacitor. We have
recently extended this technique to couple together a
mathematical model of an SA node cell (SAN model
cell) (36) to an isolated ventricular cell to examine the
interactions between an ectopic focus and a ventricular
cell (22, 34).
Within the atrium there are several regions in which
cells of the slow-response, automatic type electrotonically interact with cells of the fast-response, quiescent
type. Two obvious regions are the transitional boundaries of the SA node and the AV node (31). However,
other regions of the atrium can also demonstrate
automaticity, either as a consequence of normal membrane properties or because of pathological alterations
leading to the formation of an atrial ectopic focus (8).
During normal atrial activation, the SA node activates
a propagating wave throughout the atrium such that
the atrial cells surrounding the AV node, although
intrinsically quiescent, are driven at a rate higher than
the automaticity of the slow-response, automatic rate
0363-6135/98 $5.00 Copyright r 1998 the American Physiological Society
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Joyner, Ronald W., Rajiv Kumar, David A. Golod,
Ronald Wilders, Habo J. Jongsma, E. Etienne Verheijck, Lennart Bouman, William N. Goolsby, and Antoni C. G. van Ginneken. Electrical interactions between a
rabbit atrial cell and a nodal cell model. Am. J. Physiol. 274
(Heart Circ. Physiol. 43): H2152–H2162, 1998.—Atrial activation involves interactions between cells with automaticity
and slow-response action potentials with cells that are intrinsically quiescent with fast-response action potentials. Understanding normal and abnormal atrial activity requires an
understanding of this process. We studied interactions of a
cell with spontaneous activity, represented by a ‘‘real-time’’
simulation of a model of the rabbit sinoatrial (SA) node cell,
simultaneously being electrically coupled via our ‘‘coupling
clamp’’ circuit to a real, isolated atrial myocyte with variations in coupling conductance (Gc ) or stimulus frequency. The
atrial cells were able to be driven at a regular rate by a single
SA node model (SAN model) cell. Critical Gc for entrainment
of the SAN model cell to a nonstimulated atrial cell was
0.55 6 0.05 nS (n 5 7), and the critical Gc that allowed
entrainment when the atrial cell was directly paced at a basic
cycle length of 300 ms was 0.32 6 0.01 nS (n 5 7). For each
atrial cell we found periodic phenomena of synchronization
other than 1:1 entrainment when Gc was between 0.1 and 0.3
nS, below the value required for frequency entrainment,
when the atrial cell was directly driven at a basic cycle length
of either 300 or 600 ms. In conclusion, the high input
resistance of the atrial cells allows successful entrainment of
nodal and atrial cells at low values of Gc, but further
uncoupling produces arrhythmic interactions.
ATRIAL CELL CONNECTED TO NODAL MODEL
METHODS
Cell isolation. Single atrial myocytes were prepared from
adult New Zealand White rabbits weighing 2.5–3.5 kg. The
rabbits were anesthetized using 50 mg/kg pentobarbital
sodium and 500 U heparin intravenously, the heart was
rapidly extracted via thoracotomy with artificial respiration,
and the aorta was cannulated for Langendorff perfusion.
Single cells were isolated according to the methods of Hancox
et al. (12). Briefly, the cannulated heart was perfused sequentially at 37°C with a base solution 1 750 µM CaCl2 for 3 min,
the base solution 1 100 µM EGTA for 4 min, and the base
solution 1 240 µM CaCl2 1 enzyme for 6 min. The interatrial
septum was then excised and cut into thin strips and further
digested in the recirculated enzyme solution used above with
2% BSA for 10 min. Cells were isolated by triturating the
tissue strips and were then placed in a K-glutamate solution
with 3% BSA for 1 h at room temperature. To clean the
membrane further, cells were separated from the K-glutamate solution by centrifugation at 500 g for 3 min, the
supernatant was replaced with K-glutamate 1 1 mg/ml
protease, and the centrifugation tube was placed in a shaker
bath at 37°C for 5 min. The cells were again centrifuged at
500 g for 3 min, the supernatant was replaced with Kglutamate solution, and the cells were refrigerated until use.
The cells were placed in a chamber that was continuously
perfused with Tyrode solution at 2 ml/min at 35 6 0.5°C. Only
cells that were quiescent and had a rod-shaped appearance
were used in this study. Pipettes were pulled from borosilicate
glass that had a resistance of 3–6 MV when filled with the
internal solution. High-resistance seals were formed with the
cell membrane by applying light suction, and the membrane
under the pipette was disrupted by applying transient suction. The junctional potential was only corrected by zeroing
the potential before the pipette tip touched the cell membrane.
Solutions. The base solution contained (in mM) 130 NaCl,
4.5 KCl, 3.5 MgCl2, 0.4 NaH2PO4, 5.0 HEPES, and 10
dextrose, pH 7.25. The enzyme solution contained 1 mg/ml
collagenase (Worthington, type IIA), 0.07 mg/ml protease
(Sigma, type XIV) and base solution 1 240 µM CaCl2. The
K-glutamate solution had (in mM) 100 K-glutamate, 25 KCl,
10 KH2PO4, 0.5 EGTA, 1 MgSO4, 20 taurine, 5 HEPES, and
10 dextrose, pH 7.2. The normal Tyrode solution contained (in
mM) 148.8 NaCl, 4 KCl, 1.8 CaCl2, 0.53 MgCl2, 0.33 NaH2PO4,
5 HEPES, and 5 dextrose, pH 7.4. The pipette solution was
composed of (in mM) 135 KCl, 5 Na2-creatine phosphate, 5
MgATP, and 10 HEPES, pH 7.2.
Coupling a rabbit atrial cell to a computed SA nodal model.
The Wilders et al. (36) model for an isolated SA nodal cell
(SAN model) has been published in detail. This model includes mathematical representations of sarcolemmal ionic
channel currents and pump currents as well as a representation of intracellular calcium ion concentration and the release
and uptake of calcium by the sarcoplasmic reticulum. The
coupling circuit we are using has been previously described
for coupling a ventricular cell to a resistance-capacitance
circuit or to another ventricular cell (30). We recently extended this method to couple a real guinea pig ventricular cell
to a simulated Luo-Rudy (23, 24) ventricular cell model (37)
or to couple the SAN model to a real guinea pig or rabbit
ventricular cell (22, 34) with a sampling rate $10 kHz and
thus a time step for the model of #100 µs. We have also
evaluated the validity of the Wilders et al. (36) model as a
nodal cell model by coupling the SAN model cell to real SA
nodal cells (38) and comparing these results to the synchronization produced by coupling of two real SA nodal cells (33).
Briefly, as illustrated in Fig. 1, the hybrid cell pair system (1
real cell and 1 mathematical model solved in real time) has a
Gc that can be made a function of time. We record from a real
isolated cell in the ‘‘current clamp’’ mode with the ability to
pass a computed time-varying current into the cell based on
the coupling current that would have been present if the cell
Fig. 1. Experimental setup. A: general design of
coupling a mathematical model of a nodal cell to a
real rabbit atrial cell with a coupling conductance
(Gc, Siemens). B: experimental technique (see text).
SAN, sinoatrial node; V, voltage; I, current; A/D,
analog-to-digital converter; D/A, analog-to-digital
converter. V2 is potential of real cell, V t1Dt
is com1
puted potential of model cell for next time step, and
I tc is coupling current for present time step. Z2 is an
additional gain factor for the current applied to the
real cell to make the effective size of the real cell
multiplied by 1/Z2.
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of the AV node cells to which they are coupled (15). Thus
the interactions between the different cell types of the
atrium are complex and bidirectional, with the sequence of activation producing a situation near the SA
node in which the activation of the nodal cell leads (and
actually induces) the activation in the surrounding
fast-response cells, whereas near the AV node the
activation in the fast-response atrial cells propagates
into the region of the nodal cells. To examine the
interactions between a slow-response, automatic atrial
cell and a fast-response, quiescent atrial cell we have
extended our coupling clamp technique to couple together real, isolated atrial cells from the atrial septum
to a real-time solution of the Wilders et al. (36) SAN
model cell under conditions in which we vary Gc and
also the frequency for direct stimulation of the atrial
cell.
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ATRIAL CELL CONNECTED TO NODAL MODEL
were actually coupled by Gc to the SAN model cell, as shown
in Fig. 1B. Simultaneously, the computed coupling current is
being applied to the SAN model computations, after sampling
at each time step by the analog-to-digital converter. At the
end of each computational time step, the computed coupling
current is applied to the real cell by transferring a voltage
proportional to this current through a digital-to-analog converter through an amplifier with variable gain to the cell
through a voltage-to-current converter. The variable gain of
the amplifier of this coupling current signal can be used to
adjust the effective size of the real cell, but in the present
experiments, all of the real cells were used at their actual size
(i.e., Z2 5 1). All of our records then are recordings from the
real cell with simultaneously generated model solutions.
RESULTS
Fig. 2. A: results obtained when SAN model
cell (dotted line) is allowed to run without
electrical coupling to an atrial cell and when
an atrial cell (solid line) is stimulated at basic
cycle length (BCL) 5 600 ms without electrical coupling to SAN model cell. Timing relationships between SAN model action potentials and atrial cell action potentials are
arbitrary in this panel. B and C: simultaneously recorded membrane potentials (B)
and coupling current (C) during steady state
of interactions between a SAN model cell
(dotted line) and same atrial cell (solid line)
when no direct stimuli were applied to atrial
cell. BCL of entrained cell pair is 437 ms, and
there is a 52-ms delay between each action
potential of SAN model cell and coupled (0.4
nS) atrial cell. Experiment 01–07–97A, files
a057 and a073.
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Figure 2A illustrates action potentials recorded from
an isolated rabbit atrial cell (solid line) paced by
repetitive current pulses of 2-ms duration at a basic
cycle length (BCL) of 600 ms. The dotted line in Fig. 2A
shows the steady-state solution of membrane potential
for the SAN model cell when the model cell is uncoupled
(Gc 5 0) from the real cell. The atrial cell has a resting
membrane potential (RMP) of 279 mV, a peak amplitude of 130 mV, and a dV/dt of 160 V/s. The current
threshold for stimulation for the stimulus duration of 2
ms was 0.57 nA (defined as the smallest stimulus
magnitude that produced activation for each stimulus),
and the input resistance of the atrial cell for small
depolarizations was 364 MV. The SAN model cell has
intrinsic automaticity at a steady-state BCL of 388 ms,
a maximum diastolic potential of 266 mV, a peak
amplitude of 31 mV, and a dV/dt of 7 V/s. In our
previous work (34), we examined the critical Gc for
which the SAN model cell was able to successfully
develop automaticity (termed ‘‘pacing’’) and also to
repetitively excite (termed ‘‘driving’’) a rabbit ventricular cell in the absence of direct stimulation of the
ventricular cell. In this work, we found that there was
no value of Gc for which a SAN model cell of standard
size could successfully pace itself and drive a coupled
ventricular cell. In fact, we found that there was a
critical size of 5 (equivalent to a cluster of 5 SAN model
cells well coupled to each other) below which pacing
and driving could not occur, and for a critical size of 5
the required coupling conductance was 7.9 6 0.1 nS
(n 5 4). For the rabbit atrial cell, we found a very
different result, as illustrated in Fig. 2, B and C. We
followed a protocol in which the SAN model cell was
allowed to run uncoupled from the nonstimulated atrial
cell for a period of several seconds, and then we
examined the interactions between the SAN model cell
and the atrial cell after a coupling conductance of 0.4
nS had been turned for several seconds and the interactions had reached a stable pattern. Figure 2, B and C,
shows the membrane potential of the atrial cell (solid
line in Fig. 2B), the membrane potential of the SAN
model cell (dotted line in Fig. 2B), and the coupling
current (plotted in Fig. 2C with a positive value indicating a current from the SAN model cell to the atrial cell).
The coupled hybrid cell pair now has an increased BCL
of 437 ms (indicated by horizontal arrow in Fig. 2B),
with each action potential produced in the SAN model
cell accompanied, after a 52-ms delay, by a driven
action potential in the atrial cell. By the term ‘‘driven’’
here we mean brought to its activation threshold by the
coupling current flowing from the SAN model cell.
Compared with the uncoupled atrial action potentials
of Fig. 2A, the atrial action potentials of Fig. 2B rise
ATRIAL CELL CONNECTED TO NODAL MODEL
some of the action potentials from the SAN model cell
were conducted to the atrial cell and some were not.
For the same atrial cell used for Fig. 2 we then
investigated the interactions between the SAN model
cell and this atrial cell when we were also applying
periodic direct stimuli to activate the atrial cell. We
used the same protocol as for the experiments in which
no direct stimuli were applied to the atrial cell, with a
period of pacing of the SAN model cell without coupling
to the atrial cell and then the abrupt establishment of a
Gc at the time of maximum diastolic depolarization of a
SAN model cell action potential. We then continued to
record the interactions of the coupled hybrid cell pair
system for another 20 s of activity. To evaluate the
critical Gc for action potential propagation from the
atrial cell to the SAN model cell, we stimulated the
atrial cell with a pacing BCL of 300 ms to ‘‘overdrive’’
the SAN model cell when a sufficiently high Gc was
used. Figure 3A shows the superimposed solution of the
SAN model cell and the recorded atrial cell action
potentials directly stimulated at BCL 5 300 ms when
completely uncoupled. Figure 3B shows the steadystate pattern of entrainment that was produced when
the atrial cell, directly stimulated with BCL 5 300 ms,
was coupled to the SAN model cell with 0.3 nS. All
action potentials produced in the SAN model cell are
the result of propagation from the atrial cell, with a
resulting BCL for the SAN model cell of 300 ms. The
coupled action potentials of Fig. 3B, compared with
those of Fig. 2B (in which the nonstimulated atrial cell
was driven by the SAN model cell), clearly show the
reversal of the direction of conduction, with each activation of the atrial cell in Fig. 3B being followed by a
Fig. 3. A: results obtained when SAN
model cell (dotted line) is allowed to run
without electrical coupling to an atrial cell
and when an atrial cell (solid line) is
stimulated at BCL 5 300 ms without electrical coupling to SAN model cell. Timing
relationships between SAN model action
potentials and atrial cell action potentials
are arbitrary in this panel. B and C: simultaneously recorded membrane potentials
(B) and coupling current (C) during steadystate interactions between a SAN model
cell (dotted line) and same atrial cell (solid
line) when direct stimuli at BCL 5 300 ms
were applied to atrial cell. BCL of entrained cell pair is now 300 ms at a Gc of
0.3 nS. Experiment 01–07–97A, files a068
and a070.
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from a depolarized ‘‘resting potential’’ that is actually
not stable but slowly depolarizes during the diastolic
depolarization phase of the SAN model action potential
and then shows a prominent prepotential during the
activation of the SAN model cell, with final activation of
the atrial cell not occurring until a time during the
repolarization phase of the SAN model action potential.
When the atrial cell is driven by the SAN model cell (as
in Fig. 2B), the maximum dV/dt of the atrial cell is
reduced to 69 V/s and the peak amplitude is reduced to
121 mV. When each atrial cell activation does occur,
there is a ‘‘hump’’ on the falling phase of the SAN model
action potential as the electrotonic interaction is reversed in direction such that the atrial action potential
sends current back to the SAN model cell, as shown by
the periodic transient reversal of current flow in Fig.
2C. The coupling current shown in Fig. 2C is predominantly positive because the membrane potential of the
SAN model cell is less negative than that of the atrial
cell during the interval between action potentials and
the active depolarization phase of the action potential
of the SAN model cell also leads the corresponding
phase of the atrial cell, with a diastolic coupling current
on the order of 5–10 pA. We investigated the effects of a
range of coupling conductance values for this hybrid
cell pair, finding that for values .0.4 nS there was
conduction from the SAN model cell to this atrial cell
with a decreasing conduction delay as the coupling
conductance was increased. For coupling conductance
values ,0.3 nS, there was continued pacing of the SAN
model without successful driving of the coupled atrial
cell. For coupling conductance values between 0.3 and
0.4 nS, there was a partial synchronization such that
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ATRIAL CELL CONNECTED TO NODAL MODEL
Fig. 4. Results obtained for steady state of interactions between SAN model cell and an atrial cell
with a Gc of 0.2 nS. Top: coupling current. Bottom:
membrane potential of SAN model cell (dotted
line) and atrial cell (solid line). For this example,
atrial cell was stimulated directly at a BCL 5 300
ms through pipette and driven activity of atrial
cell, at this lower value of Gc, is not able to
entrain in a 1:1 fashion the SAN model cell but
does produce a periodic pattern of synchronized
activity (see text). A–F, action potentials. Experiment 01–07–97A, file a068.
conduct. Each atrial cell action potential A then begins
a new cycle of six atrial cell action potentials. To
demonstrate the periodicity of this phenomenon more
clearly, we plot in Fig. 5A four superimposed successive
periods of six stimulations (at BCL 5 300 ms), using the
labels A–F to identify the six action potentials of each
periodic set. The average conduction delays for action
potentials A–D were 27, 54, 70, and 92 ms, respectively,
for the four superimposed periods shown. This type of
periodicity resembles Wenckebach periodicity with respect to the progressive lengthening of conduction
delay and the subsequent conduction failure. The stable
periodicity of these interactions is further shown in Fig.
5, B and C, in which we show (Fig. 5B) the conduction
delay for the successive sets of action potentials A–D
throughout the period of coupling. This progressive
increase in delay and the periodic failure of conduction
also lead to a periodic pattern of the BCL of the SAN
model cell, as shown in Fig. 5C. During the time period
before coupling was established the SAN model cell has
an uncoupled BCL of 388 ms, whereas the directly
paced atrial cell has a BCL equal to the pacing BCL of
300 ms. During the time of coupling, the atrial cell
continues to have a constant BCL of 300 ms, but the
BCL of the SAN model cell oscillates, with some values
being longer than the uncoupled BCL and others being
shorter. Note that, as shown most clearly in Fig. 5A,
there are only five action potentials of the SAN model
cell associated with every six action potentials of the
atrial cell. The average BCL of the SAN model cell
during the time of coupling is 360 ms (the 1,800 ms of
the entire cyclic period divided by 5).
When we then maintained Gc at 0.2 nS but increased
the BCL for direct stimulation of the atrial cell to 600
ms, we got a very different pattern of synchronization of
the atrial cell to the SAN model cell, as illustrated in
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prepotential in the SAN model cell that then leads to a
delayed activation of the SAN model cell (with respect
to the activation of the atrial cell) such that the
activation of the SAN model cell occurs during the
repolarization phase of the atrial cell action potential.
The atrial cell action potential when the atrial cell
drives the SAN model cell has a peak amplitude of 127
mV and a maximum dV/dt of 157 V/s. The coupling
current of Fig. 3B now shows a prominent negative
phase associated with the action potential of the atrial
cell as current flows from the atrial cell to the SAN
model cell during this period.
When Gc was reduced below 0.3 nS, as the atrial cell
continued to be directly stimulated at BCL 5 300 ms,
an interesting pattern of entrainment developed. Figure 4 shows, for the same hybrid cell pair as for Figs. 2
and 3, the coupling current (top panel) and the simultaneously recorded membrane potentials (bottom panel)
for Gc of 0.2 nS. The results shown illustrate the
steady-state pattern in which a periodicity of 1.8 s (6
cycles of stimulation) is clearly present. The stimulated
atrial action potentials for two of these long cycles are
labeled A, B, C, D, E, F, A, B, C, D, E, F on the current
traces of the top panel and on the voltage traces of the
bottom panel in Fig. 4. Each atrial action potential A is
followed very closely in time by an action potential in
the SAN model cell. For successive action potentials A,
B, C, and D, the conduction delay from the atrial cell to
the SAN model cell progressively increases. For each
action potential E there is conduction failure from the
atrial cell to the SAN model cell, which is followed by a
spontaneously initiated action potential in the SAN
model cell that does not propagate to the atrial cell.
Each atrial cell action potential F occurs during the
repolarization phase of one of these spontaneous SAN
model cell action potentials and thus also does not
ATRIAL CELL CONNECTED TO NODAL MODEL
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Fig. 6. The top panel shows the coupling current, and
the bottom panel shows the membrane potentials of the
atrial cell and of the SAN model cell (same hybrid cell
pair as in Figs. 2–5). There is a clear periodicity that
repeats after every two atrial stimulations, even though
the atrial action potential cannot propagate directly to
the SAN model cell and the action potentials in the
SAN model cell cannot propagate directly to the atrial
cell. Two successive pairs of atrial action potentials are
labeled A and B in the bottom panel. Note that each
atrial action potential A is followed closely in time by a
SAN model cell action potential. Subsequent to the
action potentials A there is a spontaneous activation of
the SAN model cell that produces only a small depolarization in the atrial cell. Each action potential B occurs
during the refractory period of the SAN model cell and
thus produces only a small depolarization in the SAN
model cell. Between action potentials B and A of the
atrial cell, the SAN model cell produces another spontaneous action potential and then the subsequent atrial
Fig. 6. Results obtained during steady state of
interactions between SAN model cell and an
atrial cell with a Gc of 0.2 nS. Top: coupling
current. Bottom: membrane potential of SAN
model cell (dotted line) and atrial cell (solid line).
Atrial cell was stimulated directly at a BCL 5
600 ms through pipette, and driven activity of
atrial cell, at this lower value of Gc, is not able to
entrain in a 1:1 fashion activity of SAN model cell
but does produce a periodic pattern of synchronized activity. Horizontal arrows indicate time
segments replotted in Fig. 7 at faster time base.
Experiment 01–07–97A, file a057.
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Fig. 5. Periodicity of pattern of synchronization shown in Fig. 4. A: 4 superimposed
successive time periods of 1.8 s each (6
stimulus cycles) of data of Fig. 4, bottom,
including membrane potential of SAN
model cell (dotted lines) and atrial cell
(solid lines). Numbers above first 4 action
potentials refer to delays in conduction (in
ms) from atrial cell to SAN model cell. B:
conduction delay (ms). C: BCL (ms) for
action potentials recorded from a hybrid
cell pair with a Gc of 0.2 nS and a direct
stimulation applied to atrial cell at BCL 5
300 ms. Time of turning on Gc for panels B
and C is shown by horizontal arrow in C.
See text for details. Experiment 01–07–
97A, file a068.
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ATRIAL CELL CONNECTED TO NODAL MODEL
Fig. 7. Periodicity of pattern of synchronization shown in Fig. 6
demonstrated by superimposing 4 successive time periods of 2.4 s
each (4 stimulus cycles) of data of Fig. 6, bottom, including membrane
potential of SAN model cell (dotted lines) and that of atrial cell (solid
lines) with a time shift of 1,200 ms (2 stimulus cycles) between
successive segments plotted. Numbers shown on horizontal bar
indicate duration of successive cycles. Experiment 01–07–97A, file
a057.
Table 1. Critical parameters for atrial cells coupled to
the SAN model cell
Critical Gc , nS
Experiment
No.
Current
Threshold, nA
No stimulus
BCL 300 ms
12-23-96B
12-27-96B
12-31-96B
01-02-97A
01-02-97C
01-03-97A
01-07-97A
Mean
SE
0.60
0.70
0.50
0.50
0.68
0.56
0.62
0.59
0.03
0.60
0.70
0.40
0.50
0.75
0.50
0.40
0.55
0.05
0.30
0.30
0.35
0.35
0.35
0.30
0.30
0.32
0.01
SAN, sinoatrial node; Gc , coupling conductance; BCL, basic cycle
length.
We also evaluated the effects of altering the BCL for
stimulation of the atrial cell over a range of BCL values
from 300 to 600 ms at several values of Gc. Figure 8
shows the results for a hybrid cell pair consisting of an
atrial cell and the SAN model cell for which we applied
a protocol of selecting a value of BCL and a value of Gc
and then recording a time sequence in which we had
the two cells uncoupled for 5 s and then applied the
desired Gc for 25 s. From the simultaneous recordings
of the real atrial cell and the SAN model cell we then
determined the time of occurrence of each action potential and plotted the resulting values of BCL as a
function of time for the SAN model cell. For the atrial
cell, because the values of Gc chosen were lower than
the critical value for conduction from the SAN model
cell to the atrial cell, the BCL of the atrial cell was
always equal to the BCL for direct stimulation. Figure
8A shows the resulting values of BCL for a pacing BCL
of 300 ms and a Gc of 0.2 nS. The data shown here are
very similar to that shown in Fig. 5C for a different
hybrid cell pair in which we used the same protocol.
There is a clear periodicity of the BCL with a repeating
pattern occurring approximately every six cycles, such
that the expressed BCL of the SAN model cell varies
significantly from the intrinsic value of 388 ms. The
average BCL for the time period from 10 to 25 s as
shown was 356 ms. When we then increased the BCL
for stimulation of the atrial cell to 350 ms (still less
than the intrinsic BCL of the SAN model cell) there was
a 1:1 entrainment of the SAN model cell that stabilized
within 2 s of establishing the coupling (Fig. 8B). In Fig.
8C we show the results for a BCL of 400 ms for
stimulation of the atrial cell, which again resulted in a
1:1 entrainment of the SAN model cell at this BCL,
which is somewhat greater than the intrinsic BCL of
the SAN model cell. Note that the value of 0.2 for Gc is
sufficient for entrainment at BCL 5 350 and 400 ms
(which are values close to the intrinsic BCL of the SAN
model cell) but is too low for entrainment at BCL 5 300
ms. When we then increased the BCL for stimulation of
the atrial cell to 500 ms (Fig. 8D), we again saw an
approximately periodic phenomenon of alteration of the
BCL of the SAN model cell, including values of BCL
both above and below the intrinsic value for the SAN
model cell. The periodicity of this pattern repeats every
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action potential A is able to resynchronize the activity
of the SAN model cell, producing a repetitive period. To
show the periodicity and reproducibility of these cycles,
we have plotted in Fig. 7 four superimposed successive
segments (indicated by horizontal arrows in Fig. 6,
bottom) with a time shift of 1,200 ms (2 cycles of the
BCL 5 600 ms direct stimulation). There is a nearly
perfect superposition of these segments, with the BCL
of successive SAN model cell activations in a repeating
pattern of 404, 437, and 359 ms. There are now three
SAN model action potentials for each pair of atrial
action potentials, with an average BCL for the SAN
model cell of 400 ms (1,200 ms divided by 3).
We studied a total of seven atrial cells with this
protocol of assessing the dependence of entrainment on
Gc and the stimulus frequency (BCL 5 300 or 600 ms)
applied to the atrial cell. For these cells (see Table 1),
the current threshold for the atrial cells (using a
stimulus duration of 2 ms) was 0.59 6 0.03 nA (mean 6
SE), which is considerably less than the 2.6 6 0.2 nA (n
5 6) we previously reported (34) for rabbit ventricular
cells with the same duration stimulus pulse and the
same ionic solutions and temperature. Critical Gc values were determined with a resolution of 0.05 nS for
each cell. The critical Gc that allowed entrainment of
the SAN model cell to the atrial cell when no direct
stimulation was applied to the atrial cell was 0.55 6
0.05 nS, and the critical Gc that allowed entrainment of
the SAN model cell to the atrial cell when the atrial cell
was directly paced at BCL 5 300 ms was 0.32 6 0.01
nS. For each atrial cell we found periodic phenomena
similar to those shown above when Gc was set between
0.1 and 0.2 nS, below the value required for frequency
entrainment.
ATRIAL CELL CONNECTED TO NODAL MODEL
H2159
Fig. 8. Plots of successive BCL for a SAN model cell
coupled to an atrial cell with a Gc of 0.2 nS applied at a
time of 5 s during each overall recording period of 30 s.
BCL for direct stimulation of atrial cell was 300, 350,
400, 500, 550, and 600 ms for panels A–F, respectively.
Experiment 04–14–97B, cell 2.
BCL plots of Fig. 8. Figure 10 shows the simultaneously
recorded coupling current during the same intervals.
We have plotted the data of Figs. 9 and 10 in the same
format as for Fig. 8, with Figs. 9 and 10, A–F, corresponding to BCL values for stimulation of the atrial cell
of 300, 350, 400, 500, 550, and 600 ms, respectively. For
each panel, the horizontal arrows in Figs. 9 and 10
show the time intervals over which the periodicity of
the results are expressed. For Fig. 9A, the action
potentials show a Wenckebach-like pattern of progressively increasing delays from the atrial cell to the SAN
model cell very similar to that which we showed in Figs.
4 and 5 for a different atrial cell. The coupling current of
Fig. 10A also shows this periodicity, with the successive
atrial action potentials of the period indicated by the
Fig. 9. Plots of action potentials of a SAN model cell
(dotted lines) coupled to an atrial cell (solid lines) with a
Gc of 0.2 nS applied at a time of 5 s during each overall
recording period of 30 s (same cell pair as Fig. 8). Data
plotted are for time period of 20–25 s. BCL for direct
stimulation of atrial cell was 300, 350, 400, 500, 550,
and 600 ms for panels A–F, respectively. Horizontal
arrows indicate number of cycles for which pattern of
interactions repeats (see text). Experiment 04–14–97B,
cell 2.
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five to six cycles, and the mean BCL of the SAN model
cell is 408 ms. A further increase in the BCL for atrial
cell stimulation to 550 ms (Fig. 8E) also produces an
approximately periodic phenomenon, with a periodicity
of the pattern every four cycles and a mean BCL of the
SAN model cell of 402 ms. When we further increased
the BCL for atrial cell stimulation to 600 ms (Fig. 8F),
we then reestablished a nearly perfect periodic pattern
in which the SAN model cell BCL oscillates, both above
and below the intrinsic value for the SAN model cell,
with a repeating period of three cycles and a mean BCL
for the SAN model cell of 400 ms.
Figure 9 shows action potentials of the atrial cell
(solid lines) and the SAN model cell (dotted lines) for
the time periods of 20–25 s of the data protocols of the
H2160
ATRIAL CELL CONNECTED TO NODAL MODEL
Fig. 10. Plots of coupling current for a hybrid cell pair of
a SAN model cell coupled to an atrial cell with a Gc of 0.2
nS applied at a time of 5 s during each overall recording
period of 30 s (same cell pair as for Figs. 8 and 9). Data
plotted are for time period of 20–25 s. BCL for direct
stimulation of atrial cell was 300, 350, 400, 500, 550,
and 600 ms for panels A–F, respectively. Horizontal
arrows indicate number of cycles for which pattern of
interactions repeats (see text). Experiment 04–14–97B,
cell 2.
DISCUSSION
Our results can be summarized as follows. First, the
electrical interactions of a slow-response, automatic
nodal cell (as represented quantitatively by the Wilders
et al. model) with a real atrial cell are fundamentally
different from the electrical interactions of the same
SAN model cell with real ventricular cells. Specifically,
there are rather low values of Gc above which the atrial
cell, when directly stimulated, can reset the spontaneous activity of the SAN model cell and the SAN model
cell, when spontaneously activated, can propagate an
action potential to the atrial cell.
Second, if the atrial cell is not directly paced, there is
an average value for Gc of 0.55 nS required for the SAN
model cell to spontaneously generate action potentials
that can propagate to the atrial cell. This result is
fundamentally different from our previous studies (34)
in which we coupled the same SAN model cell to
isolated rabbit ventricular myocytes. In these studies
we found that we were required to raise the effective
size of the SAN model cell by a factor of 5 for the SAN
model cell to drive the isolated ventricular cell at any
value of Gc, and the mean required Gc was 7.9 nS.
Third, at a BCL for direct atrial cell stimulation of
300 ms, atrial cells require an average of only 0.32 nS
for Gc to ‘‘overdrive’’ a spontaneously pacing SAN model
cell. At BCL values closer to the intrinsic BCL of the
SAN model cell (388 ms), even less Gc is required for
overdrive of the SAN model cell to the atrial cell.
Fourth, when the BCL for direct pacing of the atrial
cell is larger than the intrinsic BCL for spontaneous
activity of the SAN model cell and Gc is lower than the
value required for the SAN model cell to activate the
atrial cell or for the atrial cell to propagate to the SAN
model cell, the resulting pattern of activations is a
complex, periodic modulation of the BCL of the SAN
model cell, with some cycles longer and others shorter
than the intrinsic BCL of the SAN model cell.
Finally, when the BCL for direct pacing of the atrial
cell is shorter than the intrinsic BCL for spontaneous
activity of the SAN model and Gc is lower than the
value required for the SAN model cell to activate the
atrial cell or for the atrial cell to propagate to the SAN
model cell, the resulting pattern is a periodic sequence
of progressive increases in the time difference between
the activations of the atrial cell and the SAN model cell,
which is then reset with a short time delay.
The major mechanism for the differences we have
observed in electrotonic interactions between this nodal
cell model and rabbit atrial cells versus electrotonic
interactions between the same nodal cell model and
rabbit ventricular cells is the very high membrane
resistivity of the atrial cells, compared with the ventricular cells, in the voltage range between the RMP and the
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horizontal arrow having approximately the same magnitude of negative coupling current (flowing from the
atrial cell the SAN model cell) but progressively greater
magnitudes of positive coupling current (flowing from
the SAN model cell to the atrial cell) as the activation of
the SAN model cell becomes progressively delayed with
respect to the activation of the atrial cell. For Fig. 10, B
and C (BCL 5 350 and 400 ms, respectively), there is a
clear entrainment of the two cell action potentials, as
shown in Fig. 9, and a constant, repetitive waveform of
the coupling current for each cycle. The action potential
and coupling current patterns of Figs. 9 and 10, D and
E, appear more complex, and the periodicity of the
repeating pattern is less exact, as indicated by the
dotted arrows that delimit five successive cycles for D
and four successive cycles for E. For Figs. 9F and 10F,
the pattern of action potential and coupling current
interactions is very similar to that shown in Figs. 6 and
7 for a different atrial cell, with three SAN model cell
action potentials for every two atrial cell action potentials.
ATRIAL CELL CONNECTED TO NODAL MODEL
(33) and found a critical Gc for frequency entrainment
of #0.5 nS for five cell pairs. Previous studies on the
interactions between the SA node and the surrounding
atrial cells have also demonstrated electrotonic effects.
Kirchhof et al. (20) showed that the BCL of the SA node
decreased from 348 to 288 ms after disconnection of the
surrounding atrium from the sinus node.
Our results show that the actual phenomenon produced when a nodal cell is interacting with a cell of the
fast-response type depends very critically on the activation properties of the fast-response cell. Previous theoretical studies of SA node-atrial interactions have used
various models of the fast-response cells of the atrium.
In a theoretical study published by one of us (18), the
mathematical model for the atrial cell was the BeelerReuter (2) model for ventricular cells (with a shortened
action potential duration), and thus it is quite certain
that we overestimated in the theoretical work the
electrical loading of the SA nodal cells and the critical
value of Gc for successful conduction from the SA node
out into the atrium. The ability to form cell pairs with
our coupling circuit, either with two real cells or with
one real cell and a cell model, is an obvious improvement over purely theoretical studies. However, the
realistic geometry of multidimensional current flow
among a large population of cells with spatial inhomogeneity in both membrane properties and Gc cannot yet
be experimentally recreated from isolated cells with
controlled or measured Gc. Our use of a direct connection between a central nodal cell model and a fastresponse atrial cell also ignores the presence of transitional cells that may play as yet undefined roles in
modulating action potential conduction and electrotonic interactions between central nodal cells and the
fast-response atrial cells.
This work was partially supported by National Heart, Lung, and
Blood Institute Grant HL-22562 (R. W. Joyner), the Emory Egleston
Children’s Research Center, The Netherlands Heart Foundation
Grant 92.310, and Netherlands Organization for Scientific Research
Grant 805–06–152.
Address for reprint requests: R. W. Joyner, Dept. of Pediatrics,
Emory Univ., 2040 Ridgewood Dr. NE, Atlanta, GA 30322.
Received 24 October 1997; accepted in final form 6 March 1998.
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11.
ATRIAL CELL CONNECTED TO NODAL MODEL