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J Gen PhysiolJ. Gen. PhysiolJ. Gen. PhysiolThe Journal of General Physiology0022-12951540-7748The Rockefeller University Press 9417138ArticlePacemaker Synchronization of Electrically Coupled Rabbit Sinoatrial 
Node Cells Verheijck E. Etienne *‡Wilders Ronald *‡Joyner Ronald W. §Golod David A. §Kumar Rajiv §Jongsma Habo J. ‡Bouman Lennart N. *van Ginneken Antoni C.G. *From the * Academic Medical Center, University of Amsterdam, Department of Physiology, 1100 DE Amsterdam, The Netherlands; ‡ Department of Medical Physiology and Sports Medicine, Utrecht University, 3584 CG Utrecht, The Netherlands; and § Todd Franklin 
Cardiac Research Laboratory, The Children's Heart Center, Department of Pediatrics, Emory University, Atlanta, Georgia 30322Address correspondence to Dr. E. Etienne Verheijck, Academic Medical Center, University of Amsterdam, Department of Physiology, PO 
Box 22700, 1100 DE Amsterdam, The Netherlands. Fax: 31 20 
6919319; E-mail: e.verheijck@amc.uva.nl


1 1 1998 111 1 95 112 31 7 1997 6 10 1997 1998This article is distributed under the terms of an Attribution–Noncommercial–Share Alike–No Mirror Sites license for the first six months after the publication date (see http://www.rupress.org/terms). After six months it is available under a Creative Commons License (Attribution–Noncommercial–Share Alike 4.0 Unported license, as described at http://creativecommons.org/licenses/by-nc-sa/4.0/).The effects of intercellular coupling conductance on the activity of two electrically coupled isolated 
rabbit sinoatrial nodal cells were investigated. A computer-controlled version of the “coupling clamp” technique 
was used in which isolated sinoatrial nodal cells, not physically in contact with each other, were electrically coupled at various values of ohmic coupling conductance, mimicking the effects of mutual interaction by electrical 
coupling through gap junctional channels. We demonstrate the existence of four types of electrical behavior of 
coupled spontaneously active cells. As the coupling conductance is progressively increased, the cells exhibit: (a) 
independent pacemaking at low coupling conductances, (b) complex dynamics of activity with mutual interactions, (c) entrainment of action potential frequency at a 1:1 ratio with different action potential waveforms, and 
(d) entrainment of action potentials at the same frequency of activation and virtually identical action potential 
waveforms. The critical value of coupling conductance required for 1:1 frequency entrainment was <0.5 nS in 
each of the five cell pairs studied. The common interbeat interval at a relatively high coupling conductance (10 
nS), which is sufficient to produce entrainment of frequency and also identical action potential waveforms, is determined most by the intrinsically faster pacemaker cell and it can be predicted from the diastolic depolarization 
times of both cells. Evidence is provided that, at low coupling conductances, mutual pacemaker synchronization 
results mainly from the phase-resetting effects of the action potential of one cell on the depolarization phase of 
the other. At high coupling conductances, the tonic, diastolic interactions become more important.

action potentialselectrophysiologycoupling clampgap junctionsperforated patch clamp
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introduction
In the sinoatrial (SA)1 node synchronization of the activation of electrically coupled, spontaneously pacing 
cells is a required attribute of normal action potential 
initiation. Individual isolated SA nodal cells display a 
large variety in action potential waveforms (Nakayama 
et al., 1984; Bouman and Jongsma, 1986, 1995). Moreover, individual cells may have irregular firing patterns, 
with a varying cycle length (Opthof, 1988; Wilders and 
Jongsma, 1993), which is most likely due to differences 
in the composition of membrane currents (Nathan, 
1986; Honjo et al., 1996). For the SA node to maintain 
a stable and regular discharge pattern, individual cells 
have to interact electrically such that their activation 
times are synchronized, producing action potentials at 
a regular rate. The mechanisms by which cells with different intrinsic rates of automaticity maintain this synchronization has been the subject of numerous studies 
using a variety of experimental and model systems.

Several experimental approaches have been used to 
study the electrical interactions between cardiac cells as 
a function of intercellular conductance without the 
complexity of a multidimensional syncytium. Studies 
using thin SA node strips (Jalife, 1984; Delmar et al., 
1986), with the central region of the strip sealed off in 
a compartment containing either ion-free sucrose solution or Tyrode solution containing heptanol, showed 
synchronization of the proximal and distal regions of 
the strand after electrical coupling had been established. However, specific measurements of cellular 
properties could not be made with this “sucrose gap” 
technique, because the tissue on either side of the gap 
was not isopotential. Other studies have used aggregates of spontaneously beating chick embryonic heart 
cells (Clapham et al., 1980; Scott, 1979) and showed 
synchronization of the aggregates after electrical coupling had been established between the two aggregates. 
Studies on cultured, spontaneously beating neonatal 
rat and embryonic chick heart cells have shown that 
beating irregularity decreases when more cells become 
coupled (Ypey et al., 1979; Jongsma et al., 1983). Clay 
and DeHaan (1979) showed that the coefficient of variation of the interbeat interval of embryonic chick ventricular cell aggregates was inversely proportional to 
the square root of the number of interconnected cells. 
Wilders (1993) reached the same conclusion in a 
model study on SA nodal cells of the rabbit.

Several attempts have been made to estimate the 
minimal amount of coupling conductance required for 
pacemaker synchronization. Anumonwo et al. (1992) 
observed a single-channel junctional conductance of 
∼50 pS in SA node cell pairs. Using this value, they estimated that approximately three gap junction channels 
between the cells would allow pacemaker synchronization. In a model study, Cai et al. (1994) determined 
that approximately four gap junction channels of 50 pS 
are needed for frequency entrainment. In a previous 
study (Wilders et al., 1996) in which we electrically coupled an SA node cell to the Wilders-Jongsma-van Ginneken model of an SA node cell (Wilders et al., 1991), 
we showed that the critical amount of coupling depends on the difference in the intrinsic interbeat interval of both cells. At an interbeat interval difference of 
∼10%, the critical coupling conductance became as 
low as 75 pS. Calculations performed by Noble (appendix to DeHaan, 1982) also indicate that two cells pacing 
at different frequencies could synchronize when connected by a gap junctional conductance of 100 pS.

We previously described an experimental “coupling 
clamp” system in which two isolated cells, not in physical contact with each other, can be electrically coupled 
at any desired value of intercellular conductance by 
means of an external circuit that continuously applies 
time-varying currents to each cell with a sign and magnitude that would have been present if the cells had 
been physically coupled (Tan and Joyner, 1990). The 
coupling clamp system allows the rapid independent 
measurement of the intrinsic cellular properties, and 
then the analysis of the effects of a wide range of intercellular conductance values on the electrical behavior 
of the cell pairs. In the present study, we have used a 
digital version of the coupling clamp technique to couple two real, freshly isolated SA node cells over a range 
of coupling conductances. Using this new coupling 
clamp technique, we determine the required coupling 
conductance for synchronization and the electrical behavior of these spontaneously active cells when coupled 
at levels below that for which complete synchronization 
occurs. We provide evidence that, at low coupling conductances, mutual pacemaker synchronization results 
mainly from the phase resetting effects of the action 
potential of one cell on the depolarization phase of the 
other. At higher coupling conductances, the tonic, diastolic interaction prevails.

materials and methods
Cell Isolation and Electrodes
Single SA nodal myocytes were isolated according to the method 
of DiFrancesco et al. (1986), with some modifications, as previously described in detail (Verheijck et al., 1995). Briefly, New 
Zealand albino rabbits of either sex weighing 1.8–2.5 kg were anaesthetized with 1 mg/kg Hypnorm (0.32 mg/ml fentanyl citrate 
and 10 mg/ml fluanisone, intramuscular; Janssen Pharmaceuticals, Tilburg, The Netherlands) under artificial ventilation. The 
thorax was opened and 0.1 ml heparin sodium (5,000 IU/ml) 
was injected into the left ventricle. The heart was excised and 
mounted on a Langendorff perfusion system. Blood was washed 
out with oxygenated normal Tyrode solution at 37°C for 10 min. 
Next, the heart was perfused with nominally Ca2+-free Tyrode solution for 5 min. The SA node area was excised and pinned down 
on a Sylgard layer in a Petri dish containing nominally Ca2+-free 
Tyrode solution. Subsequently, the SA node was cut into four 
strips (width ∼1 mm, length ∼2 mm) perpendicular to the crista 
terminalis. The strips were placed in a test tube containing oxygenated nominally Ca2+-free Tyrode solution at 37°C. The solution was refreshed two times. Next, the strips were incubated in 
10 ml of enzyme solution at 37°C for 10–14 min. During the incubation, the strips were gently triturated through a pipette with a 
tip diameter of 2.3 mm. At regular intervals, the solution was microscopically examined for the presence of dissociated myocytes. 
When single cells appeared, the strips were immediately transferred into a modified “Kraft-Brühe” (KB) solution (Isenberg 
and Klockner, 1982) and gently shaken. The modified KB solution was refreshed three times to remove the dissociation solution. Thereafter, the strips were again triturated in modified KB 
solution through a pipette (tip diameter 0.8–1.2 mm) for 5–10 
min. Single cells obtained during this step were stored at room 
temperature in modified KB solution for at least 45 min. Samples 
of the cell suspension (0.4 ml) were placed in recording chambers on the stages of two inverted microscopes (Diaphot; Nikon 
Inc., Melville, NY). The cells were allowed to settle for 5–10 min, 
after which superfusion with normal Tyrode solution (0.6 ml/
min) was started. For our coupling clamp experiments, we selected moderately sized spindle and elongated spindle-like cells 
(Denyer and Brown, 1987) that had not rounded up after readministration of calcium ions to the bathing solution and displayed regular spontaneous electrical activity. Electrophysiological recordings were performed at a temperature of 35 ± 0.5°C. 
The temperature of the bathing solution was monitored continuously with a thermistor probe and was maintained by a translucent heating plate underneath the bottom of the recording 
chamber.

Solutions
Normal Tyrode solution contained (mM) 140 NaCl, 5.4 KCl, 1.8 
CaCl2, 1.0 MgCl2, 5.0 HEPES, 5.5 glucose, pH adjusted to 7.4 with 
NaOH. The composition of nominally Ca2+-free Tyrode solution 
was the same as of normal Tyrode solution, except the CaCl2 was 
omitted. The enzyme solution contained collagenase B (0.28 U/
ml; Boehringer-Mannheim, Mannheim, Germany), pronase E 
(0.92 U/ml; Serva, Heidelberg, Germany), elastase (12.4 U/ml; 
Serva), and bovine serum albumin (1 mg/ml), in nominally 
Ca2+-free Tyrode solution. Modified KB solution contained 
(mM): 85 KCl, 30 K2HPO4, 5.0 MgSO4, 20 glucose, 5.0 pyruvic 
acid, 5.0 creatine, 30 taurine, 0.5 EGTA, 5.0 β-hydroxybutyric 
acid, 5.0 succinic acid, 2.0 Na2ATP, 50 g/liter polyvinylpyrrolidone, pH adjusted to 6.9 with KOH. The composition of the internal pipette solution was (mM) 125 K-gluconate, 20 KCl, 10 
HEPES, pH adjusted to 7.1 with KOH. The external solution was 
normal Tyrode solution.

Electrophysiological Recording
Simultaneous patch clamp recordings were made from two single 
isolated SA nodal myocytes, with the cells residing in two separate 
cell chambers in separate but essentially identical setups. Membrane potentials and currents were recorded using the amphotericin-perforated patch technique (Rae et al., 1991). With this 
technique, intracellular dialysis is prevented and the intracellular 
calcium concentration is allowed to change with time during the 
action potential. The recording period without significant 
changes in action potential shape of either cell of the cell pair 
was typically ∼15 min. Changes were considered significant if 
maximum diastolic potential or action potential amplitude changed 
by >3 mV, or if interbeat interval changed by >10 ms. Pipettes 
were pulled from borosilicate glass and heat polished. The pipettes had resistances of 3–5 MΩ when filled with the internal pipette solution. Shortly before the experiment, 6 mg amphotericin 
B (Sigma Chemical Co., St. Louis, MO) was dissolved in 100 μl 
DMSO, of which 10 μl were added to 3 ml internal pipette solution. 
Pipette tips were immersed in normal internal pipette solution 
for 1 s, and subsequently backfilled with the pipette solution to 
which amphotericin was added. Within 10 min after sealing to 
the membrane, a series resistance of 8–12 MΩ was obtained that 
remained stable throughout the experiment. This series resistance was compensated up to ∼90%. Apart from zeroing the potential before touching the cell surface by the pipette tip, no attempts were made to correct for junction potential. Recordings 
were made with custom-built dual amplifiers. Data were sampled 
directly into Macintosh Quadra 650 microcomputers (Apple 
Computer, Inc., Cupertino, CA) using custom-written data acquisition software, and stored on disk for off-line processing using 
custom-written data analysis software.

We defined the membrane capacitance for our cells as the amplitude of a small hyperpolarizing current pulse (typically 20–40 
pA) of 100-ms duration, divided by the initial slope of the transmembrane voltage in response to this current pulse. The current 
pulse was adjusted to produce a membrane hyperpolarization of 
∼10 mV, and was switched on shortly after the action potential 
had reached its maximum diastolic potential. Input resistance 
was defined as the amplitude of the steady state voltage response 
divided by the current amplitude, and input conductance as the 
reciprocal value of input resistance. Membrane capacitance of 
the cells used in our coupling clamp experiments was 40 ± 3 pF 
(mean ± SD, n = 10). Input resistance was 0.46 ± 0.12 GΩ 
(mean ± SD, n = 10), which is in general agreement with those 
observed by others (Irisawa et al., 1987; Denyer and Brown, 
1990).

Action Potential Parameters
The action potentials of the SA nodal cells used in our coupling 
clamp experiments were characterized by seven action potential 
parameters. These parameters were determined from 5–10 consecutive action potentials using custom-written data analysis software and are listed in Table I. Maximum diastolic potential 
(MDP) is the most negative value of membrane potential. Action 
potential amplitude is the amplitude of the action potential, 
measured as the peak positive potential minus the maximum diastolic potential. Interbeat interval (IBI) is the time between 50% 
depolarization on one upstroke and 50% depolarization on the 
next. Action potential duration at 50% repolarization (APD50) is 
the time between 50% depolarization and 50% repolarization of 
the action potential. Similarly, action potential duration at 90% 
repolarization (APD90) is the time between 50% depolarization 
and 90% repolarization of the action potential. Diastolic depolarization rate (DDR) is ΔV
m/Δt, where ΔV
m is the change in membrane potential (V
m) during a 75-ms time interval (i.e., Δt = 75 
ms) starting at a membrane potential that is 1 mV positive to the 
MDP. Maximum upstroke velocity (V
max) is the maximum rate of 
change of the membrane potential (i.e., the maximum value of 
dV
m/dt) attained during the upstroke of the action potential.


Coupling Two Isolated Sinoatrial Nodal Cells Together
The method used for electrical coupling of two isolated rabbit SA 
nodal cells is illustrated in Fig. 1. Fig. 1
A is a diagram of two cells, 
labeled ‘cell A' and ‘cell B,' which are electrically coupled by a 
coupling conductance (G
c; in siemens). If the membrane potentials (in volts) of the two cells are V
m,A and V
m,B, both functions of 
time, then the coupling current (Ic; in amperes) flowing from 
cell A to cell B, also a function of time, would be continuously 
given by Ic = G
c × (V
m,A − V
m,B). Thus, a current Ic (positive or 
negative) is continuously leaving cell A and entering cell B. The 
computer (labeled ‘PC') accomplishes this coupling by repetitively sampling, at a period of 130 μs, the membrane potentials 
of the two cells, computing the value of Ic, and then sending this 
value via a digital-to-analog (D/A) converter to each of the two 
voltage-to-current converters (labeled ‘V→ I'), as illustrated in 
Fig. 1
B. The value of Ic is sent directly to the voltage-to-current 
converter associated with cell A and is sent as an inverted signal 
to the voltage-to-current converter associated with cell B. The 
computer can thus couple the cells with any desired value of Gc 
and also rapidly turn this conductance on or off as a function of 
time. Note that the cell pairs studied always consisted of two cells 
being simultaneously studied in two separate microscope setups, 
thus precluding any electrical contact between the cells except 
that provided by the coupling circuit. Custom-written coupling 
clamp software was compiled as a DOS real mode application using Borland Pascal (version 7.0; Borland International, Scotts 
Valley, CA) and run on a 60-MHz Pentium processor computer 
equipped with a moderately fast 12-bit data acquisition board 
(model PCL-718; American Advantech, Sunnyvale, CA).


Since we measure the membrane capacitance (C
m; in farads) 
of each cell and we record the membrane potential as a function 
of time, we can compute the capacitative current (Icap; in amperes) of each cell (as a function of time) as C
m,A dV
m,A/dt and 
C
m,B dV
m,B/dt for cells A and B, respectively. For each cell, it must 
be true that the sum of the ionic membrane currents entering or 
leaving the cell (Iion), the coupling current, and the capacitative 
current must be zero at all times; i.e., Iion + Ic + Icap = 0. Therefore, we can compute the ionic membrane current of cells A and 
B as Iion,A = −C
m,A dV
m,A/dt − Ic and Iion,B = −C
m,B dV
m,B/dt + Ic, 
respectively, as functions of time. This computation makes no assumptions concerning the actual ionic conductances of the cell 
membrane, with the computed Iion being the sum at each time 
step of the inward and outward ionic currents across the cell 
membrane.

In our standard protocol, coupling is switched on after a 2-s period of recording at zero coupling conductance. Coupling stays 
on for 6 s, and is then switched off, ending the 10-s run with another 2-s period of uncoupling (see Figs. 2–5, below). The membrane potential of cells A and B and the coupling current are displayed during the run, thus providing real-time information on 
the coupling process. The computer program stores as an array 
the successive samples of the membrane potentials of the two 
cells. At the end of the run, these samples are transferred to disk, 
together with parameter settings. With this information, a second 
program can then off-line “replay” the experimental protocol, 
producing a disk file with a time sequence of the membrane potentials of the two cells, the coupling current, and any computed 
parameters of the cells (e.g., the capacitative currents and the 
membrane ionic currents) as functions of time.


It is likely that electrical interactions between SA nodal cells 
depend on cell size. As not all isolated SA nodal cells are similar 
in size, we have adopted a method of standardizing cell size before starting the coupling clamp experiments. We previously 
showed that major membrane ionic currents in isolated SA nodal 
cells are proportional to C
m (Wilders et al., 1996). Therefore, we 
used C
m to standardize cell size and set the effective “size” of either cell to 40 pF. The procedure we use is as follows. First, we on-line estimate C
m,A and C
m,B and compute size factors zA = C
m,A/40 
and zB = C
m,B/40 for cell A and cell B, respectively. During the 
experiment, the current inputs for cell A (Ic) and for cell B (−Ic) 
are replaced with Ic × zA and −Ic × zB, respectively. Thus, the 
current input for an 80-pF cell (size factor 2) is twice that for a 
40-pF cell, so that an 80-pF cell interacts like a 40-pF cell. In all 
experiments, the on-line estimates of C
m,A and C
m,B were 40 pF. 
Consequently, size factors zA and zB amounted to 1 in all experiments. Later off-line analysis revealed that the true values of C
m 
(listed in Table II) differed only slightly from their on-line estimates.


results
Increasing Coupling Conductance
Fig. 2 shows simultaneous recordings from two SA 
nodal cells, with the membrane potential recordings of 
the two cells distinguished by a solid (for cell A) or dotted (for cell B) line. Data for Fig. 2, as well as Figs. 3–7, 
are from experiment 950803-2 (Table II). Fig. 2
A (top) 
shows the experimental protocol in which the recordings were made without electrical coupling between 
the cells for two seconds, followed by a period of 6 s of 
electrical coupling at 0.10 nS, and then by a second period of uncoupling for 2 s. During the periods of uncoupling, the spontaneous activity of cell A is occurring 
at a shorter interbeat interval (310 ms) than the spontaneous activity of cell B (390 ms). The action potentials 
of the two cells are also somewhat different in shape, 
with cell A having a less negative maximum diastolic 
potential (−57 vs. −62 mV) and a less positive peak 
amplitude (26 vs. 28 mV) than cell B. Cell A also has a 
shorter action potential duration than cell B. The measured action potential parameters for these cells, when 
uncoupled, are listed in Table I, along with the parameter values for the cells of the other four cell pairs from 
which recordings were made. The Fig. 2
A (bottom) 
plots the coupling current for this cell pair. The coupling current is, of course, zero during the two periods 
of uncoupling, and is plotted as a positive current in 
the direction from cell A to cell B.


During the 6 s of coupling in Fig. 2
A, it is clear that 
the action potentials of cells A and B are not entrained 
to each other in a 1:1 manner. To aid in the interpretation, we have labeled the action potentials of cell A during the coupling period as sequential numbers 1–19. In 
addition, we have plotted in Fig. 2
B the data of the central time period of Fig. 2
A (as indicated by the horizontal two headed arrow) at a faster time base. Cell A action potential numbers 1–6 are occurring during the 
diastolic period of the action potentials of cell B and 
can be seen to be associated with the corresponding action potentials of cell B such that the delay between the 
action potentials of cell A and those of cell B is progressively increasing. Action potential number 7 of cell A 
produces a depolarization during the diastolic period 
of cell B and this depolarization actually delays the subsequent activation of cell B. The subsequent activation 
of cell B (indicated by the single vertical arrow head) 
occurs before action potential number 8 of cell A and 
actually shortens the cycle length between action potentials 7 and 8 of cell A. Action potentials 9 and 10 of 
cell A, however, reestablish the previous condition of 
cell A activating before cell B, although with increasing 
time delay between the activation of cell A and the activation of cell B. Action potential number 11 of cell A, 
however, repeats the process observed for action potential 7 of cell A, with a failure to directly produce an action potential in cell B, a delayed cycle length for cell 
B, or a reversal of the sequence of activation (cell B before cell A) for action potential number 12 of cell A 
(Fig. 2
A, vertical arrow head). This process then repeats 
again for action potentials numbered 15 and 16 of cell 
A, as indicated by the triple vertical arrow head. The 
lower panels of Fig. 2, A and B, show the simultaneously 
occurring coupling current. 

Figs. 3–5 show data from the same cell pair in the 
same presentation format as for Fig. 2, using values of 
coupling conductance of 0.15 nS (Fig. 3), 0.20 nS (Fig. 
4), and 10 nS (Fig. 5). For the period of coupling illustrated in Fig. 3, each of the action potentials (numbered 1–17) for cell A occur before an associated action potential of cell B, except action potentials numbered 8 and 9. For these two action potentials, the 
process described for Fig. 2 occurs, in which action potential number 8 of cell A produces a subthreshold depolarization during the diastolic period of cell B and 
this depolarization in cell B delays the subsequent activation of cell B. This subsequent activation of cell B occurs before action potential number 9 of cell A (Fig. 3
A, arrow), but action potential number 10 of cell A reestablishes the pattern of the action potential of cell A occurring before the associated action potential of cell B. 
Note that, at this higher value of coupling conductance 
(0.15 nS), this process occurs only once during the coupling period, as compared with the three occurrences 
during the coupling period when the coupling conductance was 0.1 nS (Fig. 2).

In Fig. 4 (G
c = 0.2 nS), a stable pattern of entrainment of the action potentials of cells A and B is established during the period of coupling. Note that the 
coupling current increases in magnitude from Fig. 2 to 
Fig. 3 to Fig. 4 as the coupling conductance increases. 
In Fig. 4, the action potentials of cells A and B are entrained at a common interbeat interval, but the shapes 
of the action potentials are still quite different for cell 
A and cell B, with cell B retaining a more negative maximum diastolic potential and a longer action potential 
duration. In other words, the cells show “frequency entrainment,” but not “waveform entrainment” (Cai et 
al., 1994). When the coupling conductance is further 
increased to 10 nS (Fig. 5), the action potentials of cells 
A and B are nearly synchronous during the period of 
coupling, with the action potential shapes now also 
nearly identical: the cells show both frequency and 
waveform entrainment. The coupling current is further 
increased in magnitude, although now the positive 
peak of the coupling current (from cell A to cell B) is 
much sharper during each cycle as the upstrokes of the 
two cells are synchronized. As before, there is a significant negative component of coupling current (flowing 
from cell B to cell A) due to the intrinsically longer 
APD of cell B. During diastolic depolarization, a sustained “tonic” component of coupling current, amounting to ∼10 pA, is flowing from cell A to cell B.

Activation Delay
If we define the successive activation times of either cell 
A or cell B as the times at which the membrane potential crosses zero in a positive direction, we can analyze 
the effects of the coupling conductance on the time-varying interbeat intervals and the activation delays between cells A and B for coupled action potentials. Fig. 6 
illustrates the effects of coupling conductance of either 
0.1 (part A) or 0.15 (part B) nS for the same cell pair 
used for Figs. 2–5. In Fig. 6
A, the IBI of the two cells 
fluctuates over a range of ∼25 ms during the initial period of uncoupling of the first 2 s. The horizontal arrow 
(Fig. 6
A) indicates the time period of coupling. Immediately after the coupling was established, there is a tendency of the IBI values of the two cells (cell A, •; cell B, 
□) to become nearly the same, but this tendency is interrupted by the interactions described in Fig. 2, with 
three occurrences of long IBI for cell B in a cyclical pattern. Note that the presence of a low value of coupling 
conductance (0.1 nS) actually increases the variability 
over time of the IBI for both cells A and B as compared 
with the fluctuations during the uncoupled periods. 
We plotted the activation delay (▴) between cell A and 
cell B only for the time period of coupling in the lower 
panel of Fig. 6
A. Since cell A has an intrinsically 
shorter IBI than cell B, we use the times of occurrence 
of activation of cell A as the index times for the determination of activation delay from cell A to cell B. There 
are three discontinuities in the plot of activation delay 
associated with action potentials of cell A, which were 
labeled as 7, 11, and 15 in the plot of Fig. 2 for this cell. 
For these action potentials, the associated response of 
cell B is a subthreshold depolarization and the subsequent action potentials in cell B clearly arise before the 
next action potentials in cell A. Therefore, the actual 
activation delay is negative (with respect to the activation times of cell A) for action potentials 8, 12, and 16 
of cell A. For Fig. 6
B, we plot the IBI and the activation 
delay for the data (from the same cell pair) plotted in 
Fig. 3 for a higher value of coupling conductance (0.15 
nS). Compared with the results of Fig. 6
A with the 
lower value of coupling conductance (0.1 nS), there is 
now more of a tendency for the IBI of the two cells to 
achieve a common value during the coupling period, 
with a predominant shortening of the IBI of the faster 
cell. However, there is a singular occurrence of the 
same process that occurred three times for Fig. 6
A, 
with a long IBI for the slower cell at a time of 5 s. This 
process also causes an apparent reversal in the direction of the activation for the beat after the long cycle 
length, thus producing a single negative value of activation delay.

Fig. 7 shows the IBI and the activation delay for the 
two higher values of coupling conductance for which 
the action potentials of cells A and B were entrained at 
a common IBI during the coupling period. For Fig. 7
A 
(coupling conductance, 0.2 nS), the two cells again 
show fluctuations of their IBI during the uncoupled periods, but during the coupling period the IBI of the two 
cells has a mean value slightly larger than that of the 
uncoupled IBI of cell A. Note that the common IBI is 
clearly not the arithmetic average of the IBI values for 
each of the cells. Fluctuations of IBI still occur during 
the coupling period with differences of up to 34 ms for 
IBI values of the two cells even for cycles that are associated in time as part of the entrainment process. The activation delay (Fig. 7
A, bottom) shows significant fluctuations from 24 to 64 ms with an average value of 43 ms. 
For Fig. 7
B (coupling conductance, 10 nS), the two 
cells have a common IBI during the coupling period 
that still varies somewhat with time, but for each cycle 
the IBI values for the two cells are nearly equal. The activation delay is now <1 ms for each cycle and shows 
very little fluctuation during the coupling period. For 
the first coupled action potential, cell B fires before cell 
A, resulting in a negative activation delay and a negative spike in coupling current at 2.2 s (Fig. 5
A, bottom).

Membrane Ionic Current
The presence of a high value of coupling conductance 
(10 nS) between cell A and cell B not only makes the 
action potential shapes and IBI of the two cells the same, 
but also produces very significant changes in the membrane ionic currents of the two cells. In Fig. 8, we have 
superimposed action potentials recorded from cell A 
and cell B at zero coupling conductance. The solid and 
dotted action potentials of cells A and B, respectively, 
have been aligned in time such that the upstrokes of 
the first action potential of each cell are simultaneous, 
with the zero time adjusted for each trace. The cycle 
length for cell A is shorter than the cycle length of cell 
B, producing a nonsynchronous occurrence of the 
second action potential for each cell, with the second 
action potential for cell A occurring before the second 
action potential of cell B. When we examine the total 
membrane ionic currents of the two cells (Iion,A as a 
solid line and Iion,B as a dotted line) shown in Fig. 8
B, 
with each ionic current trace aligned with the corresponding action potential trace for each cell, we see 
that the membrane ionic current of each cell is negative (inward) during the diastolic period of each cell action potential as expected, with comparable values of 
−3 to −4 pA. The large inward current during the upstroke of each action potential is truncated at the gain 
used for the plot. During the early repolarization phase 
of each action potential, the membrane current of 
each cell is outward, with a larger outward current for 
cell A than cell B due to the more “plateau”-like repolarization of the action potential of cell B. During the 
final repolarization phase of each action potential, the 
current is large and positive for both cells A and B, with 
a peak outward current of 77 pA for cell A and 60 pA 
for cell B.


In Fig. 9, we plot the action potentials of the same 
cell pair for the time period of coupling at 10 nS from 
4.7 to 5.4 s of Fig. 5. For part A, the action potentials 
are now synchronous in occurrence and with nearly 
identical shapes. The corresponding membrane ionic 
currents and the coupling current are plotted in part B, 
with the coupling current (Ic) plotted as a bold solid 
line. During the diastolic depolarization phase, the 
membrane current of cell A is now much more negative than the current for the diastolic depolarization for 
the same cell when uncoupled (see Fig. 8), even 
though the diastolic depolarization phase of cell A is 
prolonged by the presence of the coupling conductance. The membrane current of cell B is now actually 
positive during the diastolic depolarization phase of 
cell B, which seems somewhat paradoxical since the 
membrane potential of cell B is steadily depolarizing 
during this phase. Note that the coupling current is 
positive (in the direction from cell A to cell B) during 
the synchronized diastolic depolarization phases of the 
two cells. The presence of this coupling current of ∼9 
pA, being a transfer of charge from cell A to cell B, induces a larger inward membrane ionic current (∼−13 
pA) in cell A and an actual positive current (∼6 pA) in 
cell B, such that the capacitative currents of both cell A 
and cell B amount to −3 to −4 pA, corresponding with 
a diastolic depolarization rate of ∼80–90 mV/s.


The presence of electrical coupling also affects the 
membrane ionic currents during the repolarization 
phases of the action potentials. The coupled action potential has an early repolarization phase that is slower 
than the uncoupled early repolarization phase of cell A 
and faster than the uncoupled early repolarization 
phase of cell B. During this phase, the coupling current 
is negative (from cell B to cell A) and this induces a 
larger outward current in cell A than the value present 
when cell A was uncoupled and induces a smaller outward current in cell B (nearly zero) as compared with 
the value when cell B was uncoupled. Also, the peak 
outward ionic membrane currents for cells A and B, 
when coupled, are quite different than when uncoupled. The peak outward current for cell A increased 
from 77 to 97 pA and the peak outward current for cell 
B decreased from 60 to 48 pA.

Common Interbeat Interval
For the five cell pairs for which the basic data are summarized in Table II, there was a considerable intrinsic 
variability in the IBI of each cell when uncoupled. For 
two of the cell pairs, the IBI of the slower cell of the 
pair was within 10% of the IBI of the faster cell, while 
for one cell pair the IBI of the slower cell of the pair 
was ∼60% longer than that of the faster cell. The other 
two cell pairs had intermediate values of difference for 
the IBI of the faster and slower cell of the cell pair. 
Since each of the cell pairs had a common IBI at a coupling conductance of 10 nS (frequency and waveform 
entrainment), this intrinsic difference in IBI of the 
cells of the cell pairs gave us an opportunity to determine how the intrinsic difference in the IBI determined the common IBI when well coupled. Fig. 10
A 
plots, for each of the cell pairs, the common IBI (expressed as a percentage of the intrinsic IBI of the faster 
cell, IBIf), as a function of the intrinsic IBI of the slower 
cell (IBIs, also expressed as a percentage of the IBIf). If 
the common IBI were actually the average value of IBIf 
and IBIs, then all of the points would fall along the dotted line of the figure, which is plotted with a slope of 
0.5. It is clear that the points for which the IBIs of the 
cell pair was significantly greater than the IBIf of the 
cell pair deviate significantly from this relationship, 
with a clear tendency for the common IBI to be closer 
to the IBIf than to the IBIs. This phenomenon was also 
observed in our recent publication (Wilders et al., 
1996) in which we coupled two 40-pF model cells (using the Wilders-Jongsma-van Ginneken model of an isolated SA nodal cell; Wilders et al., 1991) together. In 
these model cell pairs, we systematically altered the 
maximum conductance for the hyperpolarizing activated current (If current) of one of the cells to make 
the intrinsic IBI of one of the cells to be shorter or 
longer than the standard IBI of the cell model (388 
ms), and then determined the common IBI of the two 
model cells when the two model cells were coupled by 
10 nS. The simulation results are shown in the open circles 
of Fig. 10
A and agree very closely with the phenomenon observed for coupling of two real SA nodal cells.


Critical Coupling Conductance
We also determined, for the simulation study of two 
model SA nodal cells (Wilders et al., 1996), the critical 
value of coupling conductance above which the two 
model cells had the same IBI (frequency entrainment) 
and the simulation results from our previous work are 
plotted in Fig. 10
B, ○ with the critical coupling conductance as the ordinate and the IBI of the slower beating cell as the abscissa as for part A. We determined the 
critical coupling conductance for three of the cell pairs 
of the current study. For each cell pair, we have plotted 
the critical coupling conductance as a vertical range 
specified by the highest value of coupling conductance 
tested for which the cells were not frequency entrained 
(lower bound) and the lowest value of coupling conductance tested for which the cells were frequency entrained (upper bound). The three ranges of critical 
coupling conductance determined from the pairs of 
cells fall generally within the relationship determined 
from the simulation study. For the remaining two cell 
pairs, determination of the critical coupling conductance could not be completed before the action potential configuration of one of the cells became unstable. 
At the lowest value of coupling conductance tested (0.5 
nS), these two cell pairs showed 1:1 frequency entrainment. So, for these two cell pairs, we can only state that 
the critical value of coupling conductance is ≤0.5 nS 
(Table II).

Diastolic Depolarization Time
To understand why the common IBI, when well coupled, for two cells that have intrinsically different values 
of IBI when uncoupled, is not simply the arithmetic average of the intrinsic IBI values, we have analyzed the 
diastolic process of the cell pairs during conditions of 
complete uncoupling and with a coupling conductance 
of 10 nS. To quantitate the diastolic trajectory for each 
cell, we define a diastolic depolarization time (DDT) as 
the time required for the potential to rise from the 
maximum diastolic potential to a value 20 mV positive 
to this potential (Fig. 11
A). We chose a value of 20 mV 
as an approximation of the threshold potential with respect to the maximum diastolic potential, since for 
these spontaneously beating cells the exact value of 
voltage threshold cannot be defined. For each cell pair, 
we compute the DDT for the intrinsic uncoupled beating of the slower cell (DDTs), for the intrinsic uncoupled beating of the faster cell (DDTf), and for the coupled, synchronized beating of the cell pair with 10 nS 
of coupling conductance (DDTc). Thus, the DDR for 
each cell would be:
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\begin{equation*}DDR={\Delta}V/DDT,\end{equation*}\end{document} 


where ΔV = 20 mV, and we can similarly define DDRs, 
DDRf, and DDRc. Since the DDR is determined by the 
capacitative current (Icap = C
m dV
m/dt) and this capacitative current is equal to Iion + Ic, but of opposite sign, 
the DDR for each cell is affected by the coupling current. As we showed in Fig. 5, there is a net coupling current during diastole for two coupled cells, which is in 
the direction from the cell that had the higher intrinsic 
DDR to the cell that had the lower intrinsic DDR. Since 
the magnitude of the coupling current is the same for the 
two cells (just being opposite in sign), we proposed the 
hypothesis that the change in DDR that occurred with 
coupling would be predicted as:
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\begin{equation*}DDR_{c}\;=\;(DDR_{s}\;+\;DDR_{f})/2.\end{equation*}\end{document} 
In other words, the decrease in depolarization rate of 
cell A induced by the coupling current leaving cell A is 
equal to the increase in depolarization rate of cell B induced by the coupling current entering cell B. This hypothesis then predicts that the observed DDTc would be:
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\begin{equation*}DDT_{c}\;=\;2\;{\times}\;(DDT_{f}\;{\times}\;DDT_{s})/(DDT_{f}\;+\;DDT_{s}),\end{equation*}\end{document} 
which follows from Eqs. 1 and 2. We measured DDTf, 
DDTs, and DDTc from each of the five cell pairs studied 
by using the averaged values of 10 successive action potentials during the coupled and uncoupled periods. 
Fig. 11
A shows the superimposed diastolic intervals of 
the same cells used for Figs. 2–7 with the corresponding DDT values indicated by horizontal arrows. Figs. 9 
and 11 show the results of this analysis for all five cell 
pairs for which we plot the observed diastolic time 
when coupled versus the value of DDTc for each cell 
pair that was predicted from the observed DDTf and 
DDTs. The dashed line has a slope of unity and corresponds to an exact agreement between the observed 
and predicted DDTc. The experimental data points are 
shown as the filled symbols. The open symbols were 
produced by applying the same analysis to our simulation model in which two model SA nodal cells were 
coupled by 10 nS. There is a very good agreement with 
this simple analytical formulation both for the simulated pair of cells and for our experimental data from 
the five cell pairs.

discussion
Coupling Clamp
In this study, the dynamic electrical interactions between two pacemaker cells that underlie pacemaker 
synchronization in the SA node were studied. We investigated the required coupling conductance for synchronization and the electrical behavior of the SA nodal 
cells when coupled at levels of coupling conductance 
above and below that for which 1:1 entrainment occurs. To this end, the digital coupling clamp technique 
(Wilders et al., 1996) was used, which allows us to set 
any desired coupling conductance and effective cell 
size. This two-cell system uniquely enabled us to study 
electrical interactions without the complexity of a multidimensional syncytium. It is clear that the intact SA 
node will not behave as a single cell. The rabbit SA 
node consists of small clusters of pacemaker cells embedded in a considerable amount of connective tissue 
(de Maziére et al., 1992). These cell clusters are not 
strongly coupled to each other. In this context, the extension of our experimental protocol is simply a matter 
of scaling. To the extent that one can regard all of the 
cells within a given cluster of, for instance, 100 cells as 
isopotential, the cluster simply acts as a single cell with 
a size 100 times that of one cell. This does not mean 
that all cells need to be absolutely isopotential on a very 
short time scale. However, a limitation of this analogy is 
that in the SA node two cell clusters are likely to be connected to other cell clusters in a complex spatial pattern and our present experimental model is limited to 
the considerations of a single coupled cell pair of cells 
(or cluster of cells). Nevertheless, we feel that it is useful to consider a simpler system in which factors such as 
coupling conductance and effective cell size can systematically be varied.

However, there are some additional limitations in the 
applicability of the coupling technique we used. It appears extremely difficult to perform simultaneous current clamp measurements on two isolated nodal cells. 
Determination of the critical coupling conductance required measurements of ∼20 min in which the action 
potential configuration of both cells of the cell pair had 
to remain stable. As a consequence, the success rate of 
this type of experiment is rather low. 

In the present experiments, we assume that the coupling conductance can be treated as a constant value, 
independent of the membrane potential of either cell. 
It has been shown, however, that cardiac gap junctions 
do not always behave like pure ohmic resistors but can 
also exhibit time- and voltage-dependent kinetics (Rook 
et al., 1988; Anumonwo et al., 1992). In principle, we 
could adapt the technique to incorporate these kinetics. However, in rabbit SA nodal cell pairs, the time and 
voltage dependence is only observed if transjunctional 
voltage clamp steps of large amplitude and long duration are applied (Anumonwo et al., 1992). Furthermore, in a model study we have demonstrated that the 
stochastic open-close kinetics of the gap junctional 
channels hardly affect the process of synchronization 
of SA node cells (Wilders, 1993). Therefore, we considered the coupling conductance to be an ohmic resistor. 
It has also been shown that junctional conductance can 
be modulated by the intracellular calcium and magnesium levels and intracellular pH (Noma and Tsuboi, 
1987; Spray and Burt, 1990). At this moment, no data is 
available to show that these levels change during the 
time course of a single action potential. Therefore, we 
did not attempt to incorporate the dependence of coupling conductance on these levels. Another limitation 
of the coupling clamp technique is that the cells are 
not only electrically coupled, but also serve as pathways 
through which exchange of intracellular messengers 
occur.

Mutual Entrainment
Sinoatrial node pacemaker cells behave as a population 
of electrically coupled oscillators, and their coordinated rhythm depends on the process of mutual entrainment (Winfree, 1967; Ypey et al., 1980). Mutual 
entrainment can be defined as a stable condition of 
electrical coupling between pacemaker cells with the 
result that the pacemaker cells have the same frequency (1:1 entrainment), or that their frequencies are 
harmonically related, but not necessarily with simultaneous discharges (Winfree, 1967). Since each cell 
would have a phasic influence on the other, it has been 
hypothesized that phase–response curves for each cell 
may give insight into their mutual interactions (Michaels 
et al., 1990; Ypey et al., 1982). It is assumed that the action potential of one cell acts as a depolarizing current 
pulse on the other cell and vice versa. By this mutual interaction, the two pacemakers would synchronize to a 
common IBI. Although the pacemakers fire with the 
same rhythm, they do not necessarily fire simultaneously. 
For the process of mutual entrainment to occur, there 
must always be some phase difference between them.

The process of mutual entrainment of rabbit SA 
node cells has been studied in SA node strips that were 
placed in a three-compartment tissue bath in which the 
central region was perfused with an ion-free sucrose solution permitting electrical insulation of the external 
segments (Jalife, 1984). In this “sucrose gap” study, it 
was shown that the dynamic interactions between two 
pacemakers resulted in mutual entrainment with both 
pacemakers beating at simple harmonic or complex ratios depending on the amount of coupling and the intrinsic interbeat intervals of the individual pacemakers.

In another study (Sano et al., 1978), the isolated SA 
node was partly divided into two parts by a cut in the 
middle portion. It was demonstrated that subthreshold 
depolarizing current pulses, when applied in the early 
portion of diastolic depolarization, prolong diastole, 
and when applied in the later portion, shorten it. Anumonwo et al. (1991) studied the phase resetting properties of single isolated SA node cells in response to 
brief current pulses and explained the mutual entrainment of SA node cells in terms of phase resetting. Theoretical studies explained the process of entrainment 
and synchronization of two (groups of) pacemaker 
cells (Cai et al., 1994; Ypey et al., 1980) and two-dimensional arrays of pacemaker cells (Cai et al., 1994), also 
in terms of phase–response curves. Analysis of phase–
response curves based on an SA node model have 
shown that a phase delay produced by a brief depolarizing current pulse within the first half of the intrinsic 
IBI was due to a transient decrease in the slow inward 
current and the fast sodium current, while phase advances produced by brief depolarizing current pulses 
within the second half of its intrinsic period were due 
to a transient increase in the same currents (Michaels 
et al., 1986).

Although interactions between pacemaker cells are 
actually continuous rather than pulse-wise, these studies have provided insight into phase resetting interactions between pacemaker cells. In the present study, we 
have observed that phase resetting indeed occurs between two isolated SA node pacemaker cells when they 
are electrically coupled. In Fig. 2
B and the accompanying Fig. 6
A, it was shown that, at coupling conductances below the critical value for 1:1 entrainment, action potential 7 of cell A (the intrinsically faster beating 
cell) produces a small depolarization during the early 
diastolic phase of cell B. The consequence of this “subthreshold” depolarization was to delay the activation of 
cell B. This phase resetting effect clearly demonstrates 
its importance in the process of mutual entrainment in 
pacemaker cells.

In the present study, we demonstrate the existence of 
a recurrent phenomenon that was present at levels of 
coupling conductance below that required for 1:1 entrainment. This phenomenon consisted of a progressive increase in the activation delay between the cell 
with a shorter intrinsic IBI and the cell with an intrinsically longer IBI that was interrupted by a single activation failure, which then resets this process. As the coupling conductance was progressively increased toward 
the critical value for 1:1 entrainment, the frequency of 
occurrence of this phenomenon was decreased. This 
phenomenon may be related to Wenckebach periodicity of conduction through the atrioventricular node 
(AV node), although the situation we are creating consists of two coupled cells, both of which are intrinsically 
automatic and thus, when conduction failure does occur, the distal cell is still able to display a spontaneously 
generated activation.

Common Interbeat Interval
One of the major determinants of the rate at which 
pacemaker cells fire their action potentials is the slope 
of diastolic depolarization. It is therefore generally assumed that the rhythm and frequency of the normal 
heartbeat is directed by the frequency of the SA node 
cell group with the steepest slope of diastolic depolarization (Bleeker et al., 1980). For synchronization to 
occur, the most important requirement is that the 
mechanism of mutual entrainment should advance or 
delay the influence of one pacemaker on another, so 
that equality of IBI results. In the present study, we observed that, at a high coupling conductance (G
c = 10 
nS, Fig. 10
A) at which both 1:1 frequency entrainment 
and waveform entrainment occurred, the common interbeat interval was always intermediate between the 
two intrinsic values of IBI, and closer to that of the intrinsically faster pacemaker cell. This phenomenon was 
also observed in our recent publication (Wilders et al., 
1996), in which we coupled two model SA node cells 
(Wilders et al., 1991), as well as a model SA node cell to 
a real SA node cell. This finding confirms the results of 
other experimental (Jalife, 1984; Anumonwo et al., 
1991) and theoretical (Cai et al., 1994; Michaels et al., 
1986; Ypey et al., 1980) studies. It should be noted, 
however, that the entrained interval measured in pairs 
of embryonic chick heart cells (DeHaan and Hirakow, 
1972) and pairs of neonatal rat heart cells (Jongsma et 
al., 1987) was not always intermediate between the two 
intrinsic values of IBI. This discrepancy is most likely 
the result of differences in membrane currents that 
govern the process of diastolic depolarization in natural pacemaker cells compared with that in embryonic 
chick heart cells and pairs of neonatal rat heart cells.

The intrinsic rate at which pacemaker cells fire their 
action potentials depends to a large extent on the slope 
of diastolic depolarization. Therefore, we hypothesized 
that the decrease in depolarization rate of the intrinsically faster pacemaker cell (produced by the coupling 
current leaving this cell) would be equal to the increase 
in depolarization rate of the intrinsically slower cell 
(produced by the same coupling current entering this 
cell). To test this hypothesis, we introduced the diastolic depolarization time and found an excellent correlation between the observed common DDT and the 
predicted common DDT (Fig. 11). From these data, it 
again becomes clear that not only the intrinsically 
faster beating cell determines the synchronization rate, 
but also the intrinsically slower beating cell is of importance in determining the common IBI. These data suggest that the heart rate is the result of a “democratic” 
process underlying synchronous firing of SA node cells, 
with each cell contributing to the overall mutual entrainment, which was also suggested by Michaels et al. 
(1987), although the fastest cell seems to be more important in determining the common frequency than 
the slowest.

Phasic and Tonic Interactions
When two pacemakers are electrically coupled, the 
time-dependent variations in the potential difference 
between them separate the effects of one pacemaker 
cell on the other cell into two major components: (a) 
the relatively continuous “tonic” interactions of the 
pacemakers during diastolic depolarization, and (b) 
the “phasic” influence resulting from electrotonic current flow during the discharge of the action potential. 
The progressive changes in the strength of the phasic 
interactions at a G
c of 0.1 nS (Fig. 2) results in 4:3 entrainment and resembles an atypical Wenckebach pattern of progressively increasing activation delay in a repetitive pattern. For the same cell pair, a G
c of 0.2 nS 
(Fig. 4) resulted in a 1:1 frequency entrainment. At this 
low G
c, a depolarizing Ic of ∼14 pA flows from the intrinsically faster beating cell to the intrinsically slower 
beating cell after the activation of the intrinsically 
faster beating cell, such that the follower (intrinsically 
slower) cell fires its action potential with an ∼50-ms latency. During diastolic depolarization, a tonic Ic of ∼2 
pA flows from the intrinsically faster beating cell to the 
intrinsically slower beating cell without having an important effect on the diastolic depolarization rate of either cell. It can easily be understood that synchronization at low coupling conductances is governed by large 
differences in membrane potential between both cells; 
e.g., at the moment one cell fires its action potential 
and the other is still in the diastolic period. With stronger coupling (G
c = 10 nS, Fig. 5), the phasic component becomes much shorter in duration and the depolarizing Ic flowing from the intrinsically faster beating 
cell to the intrinsically slower beating cell during the 
action potential upstroke increases to values of 15–30 
pA. However, the tonic period is prolonged and the 
tonic Ic is increased approximately five times to ∼9 pA 
(Figs. 5 and 9). Furthermore, during diastolic depolarization, membrane resistance is much higher (0.46 ± 
0.12 GΩ [mean ± SD, n = 10]) than the coupling resistance (0.1 GΩ, corresponding to a coupling conductance of 10 nS). Consequently, the increased tonic Ic, 
together with the high membrane resistance during 
diastole, will govern synchronization.

The major conclusions from our experimental observations is that at low G
c mutual pacemaker synchronization results mainly from the phase-resetting effects of 
the action potential of one cell on the depolarization 
phase of the other. At high G
c, the tonic, diastolic interaction prevails. Michaels et al. (1986) used a “pulsed 
coupling” protocol in which coupling only occurred 
during the action potential. They showed that at low 
coupling conductances 1:1 entrainment was quantitatively similar to that obtained when coupling was continuous. This finding is in agreement with our finding 
that at low coupling conductances the phasic component is most important in pacemaker entrainment. The 
distinction between phasic and tonic interactions with 
regard to their contribution to synchronization at different levels of coupling has previously been made 
(Ypey et al., 1980, 1982; Guevara, 1984; Wilders et al., 
1996).

Effects of Coupling Conductance on Membrane Ionic Current
Figs. 8 and 9 demonstrate that the entrainment of the 
two cells by a rather high value of coupling conductance (10 nS) produces significant changes in the 
membrane ionic currents (Iion) of each cell. By our definition of Iion, this current is the net current produced 
by the membrane channels and electrogenic pumps of 
the cell. In the uncoupled state, this current is equal to 
−C
m dV
m/dt and one can visualize a relationship such 
that the net membrane current therefore controls the 
time course of membrane potential. In the well coupled state, the different intrinsic action potential waveforms of the two cells are constrained to a common 
waveform, and thus this common waveform can be considered as an imposed waveform that has, in effect, voltage clamped each cell. During diastole in the coupled 
state, the rate of rise of potential has decreased for cell 
A (which had an intrinsically higher diastolic rate of 
rise) and increased for cell B (which had an intrinsically lower diastolic rate of rise). These alterations in 
the rate of rise of potential during diastole induce a 
more negative diastolic net membrane current for cell 
A and add a positive component to the net membrane 
current for cell B, which makes the net membrane current for cell B actually become positive during diastole. 
The positive net membrane current for cell B in the 
presence of a depolarizing membrane potential is not 
actually contradictory since the magnitude of the coupling current entering cell B during diastole is larger 
than the positive net membrane current of cell B during diastole. Similar arguments explain the alterations 
of net membrane current during the repolarization 
phases of the two cells. 

The coupling current, Ic, which is plotted in Fig. 9 is 
positive during diastole. Note, however, that this coupling current is flowing out of cell A and into cell B because of our convention of treating the coupling current from cell A to cell B as a positive current. With respect to the individual cells, this coupling current 
indeed acts like an outward membrane current for cell 
A (which slows the intrinsic diastolic depolarization 
rate) and acts like an inward membrane current for cell 
B (which speeds up the intrinsic diastolic depolarization rate). Since the waveforms of the two cells and the 
capacitances of the two cells are nearly the same during 
the coupled state, we can approximately state that C
m,A 
dV
m,A/dt = C
m,B dV
m,B/dt = −Iion,A − Ic = −Iion,B − Ic 
and, therefore, we derive that Iion,A − Iion,B = −2Ic during the coupled state. Thus, the amount of coupling 
current required to make the two waveforms the same 
depends on the degree to which the membrane properties of the cells (which determine the net membrane 
current as a function of voltage and time for each cell) 
are different. For two cells with nearly identical membrane properties (defined as identical relationships of 
Iion as a function of voltage and time), the intrinsic 
waveforms of the two cells would be nearly identical to 
each other when uncoupled and would achieve frequency entrainment with a very small amount of coupling current. Conversely, the greater the differences 
in intrinsic membrane properties of the two cells when 
uncoupled, the more coupling current (and thus the 
more coupling conductance) is required for entrainment.

Gap Junctions and Pacemaker Function
In the rabbit SA node, gap junctions were identified at 
the electron microscopic level by Masson-Pévet et al. 
(1979). They estimated that the gap junctions occupy 
∼0–2% of leading SA node cell membrane. This raised 
some doubt about whether these very small junctional 
connections would be sufficient to maintain synchrony 
between pacemaker cells. Anumonwo et al. (1992) 
demonstrated the presence of gap junctions between 
SA node cells, which consist of the protein connexin43. 
They found that the conductance of a single SA nodal 
gap junctional channel ranged between 40 and 60 pS at 
room temperature. At 37°C, this single channel conductance would be ∼75 pS (Bukauskas and Weingart, 
1993). In the present study, we show that pacemaker 
synchronization occurs at a coupling conductance as 
low as 0.17 nS at a 26% difference in intrinsic IBI of two 
pacemaker cells (Fig. 10
B, Table II). This would mean 
that two to three gap junctional channels are sufficient 
for 1:1 frequency entrainment. A smaller difference in 
intrinsic IBI between both cells results in an even lower 
critical G
c. In a previous study (Wilders et al., 1996), in 
which we electrically coupled a single isolated SA node 
cell to the Wilders-Jongsma-van Ginneken model of an 
SA node cell (Wilders et al., 1991), we observed that at 
an IBI difference of ∼10%, the critical G
c became as 
low as 75 pS, corresponding to the conductance of a 
single gap junctional channel. Calculations performed 
by Noble (appendix to DeHaan, 1982) also indicate 
that two cells pacing at different frequencies could synchronize due to the presence of a single gap junctional 
conductance channel.

In a recent model study, Cai et al. (1994) described 
interactions between cells of a cell pair in which a “central” SA node cell with an IBI of 347 ms was coupled to 
a “peripheral” SA node cell with an IBI of 276 ms, thus 
having a difference in IBI of 26% when expressed as a 
percentage of the IBI of the intrinsically faster beating 
cell. The required coupling conductance for 1:1 frequency entrainment of 220 pS, which they modelled as 
comparable to the value of 150–170 pS, we determined 
from our experimental study, as well as the value of 180 
pS predicted by our simulation results (Fig. 10
B). 

In 10 isolated pairs of rabbit SA node cells, a mean 
cell-to-cell resistance of ∼400 MΩ was observed (Anumonwo et al., 1992), corresponding with an intercellular coupling conductance of 2.5 nS. In the present 
study, we found that a G
c of 2 nS resulted in almost 
complete frequency and waveform entrainment. In the 
same cell pair as used in Figs. 2–9, we observed at a G
c 
of 2 nS a delay between the action potentials of only 3 
ms. The action potential waveforms of the two cells 
closely resembled each other at this value of coupling 
conductance. This value of G
c would necessitate ∼30 
gap junctional channels. In our experiments, the critical value of G
c required for 1:1 frequency entrainment 
ranged between 150 and 300 pS, corresponding with 
two to four gap junctional channels. This implies that 
the coupling conductance required for both frequency 
and waveform entrainment of SA nodal cells is one order of magnitude higher than that required for frequency entrainment alone. 

This work was supported in part by Netherlands Organization for Scientific Research grant 805–06–152, Netherlands Heart 
Foundation grant 92.310, and National Heart, Lung, and Blood Institute grant HL-22562.

1 
Abbreviations used in this paper: APD50, action potential duration at 
50% repolarization; DDR, diastolic depolarization rate; DDT, diastolic depolarization time; Gc, coupling conductance; IBI, interbeat 
interval; Ic, coupling current; Icap, capacitative current; Iion, membrane ionic current; KB, Kraft-Brühe; SA, sinoatrial.

Table I Action Potential Parameters of Rabbit Sinoatrial Node Cells Used in Coupling Clamp Experiments

Cell		MDP		APA		IBI		APD50
		APD90
		DDR		
V̇
max
	
		
mV
		
mV
		
ms
		
ms
		
ms
		
mV/s
		
V/s
	
950111A		−56		82		358		118		148		136		4.3	
950111B		−61		86		331		 77		104		101		4.4	
950117A		−56		84		236		 79		105		145		6.4	
950117B		−55		83		257		 68		 97		 93		6.7	
950131A		−45		66		344		 75		106		 59		2.9	
950131B		−59		78		424		 88		119		 68		3.4	
950803-1A		−61		90		279		 64		 81		117		9.3	
950803-1B		−68		93		442		119		148		 50		7.9	
950803-2A		−57		83		310		 60		 81		 95		7.0	
950803-2B		−62		90		390		115		143		 80		6.8	
Mean ± SD		−58 ± 6		84 ± 8		337 ± 69		86 ± 23		113 ± 26		94 ± 32		5.9 ± 2.1	
Model		−66		97		388		 92		125		 78		6.9	
MDP, maximum diastolic potential; APA, action potential amplitude; V̇
max, maximum upstroke velocity.
 

Figure 1 Diagram of the experimental system in which we electrically coupled two isolated sinoatrial node cells. (A) Overall experimental design in which our technique introduces a coupling 
conductance G
c between two patch-clamped isolated cells (cell A 
and cell B). (B) Simultaneous patch clamp recordings for cells A 
and B in the “current clamp” mode produce membrane potentials 
V
m,A and V
m,B, respectively, which are sampled by the computer 
(PC) via an A/D converter at each time step. The computer multiplies the difference in the two membrane potentials by a desired 
value of G
c, thus producing the equivalent Ic, which would have 
been present if the cells had indeed been electrically coupled. A 
voltage proportional to the desired Ic is output from the computer 
via a D/A converter and through a voltage-to-current converter 
(V→ I) as +Ic to cell A and through a separate set of converters as 
−Ic to cell B.

Figure 2 Simultaneous recording for 10 s of two isolated sinoatrial node cells, with the cells uncoupled during the first and last 2 s and 
coupled with a coupling conductance of 0.10 nS during the central 6 s. (A) Membrane potential (Vm) of cell A (solid line) and cell B (dotted 
line), and coupling current (Ic). The action potentials of cell A during the coupling period are numbered 1–19 for reference. The small 
vertical arrows indicate action potentials for which the action potential of cell B occurs before the corresponding action potential of cell A. 
(B) Data in A replotted for the time period indicated by the horizontal two headed arrow in A. Data from experiment 950803-2 (see Tables).

Figure 3 Simultaneous recording for 10 s of two isolated sinoatrial node cells, with the cells uncoupled during the first and last 2 s and 
coupled with a coupling conductance of 0.15 nS during the central 6 s. (A) Membrane potential (Vm) of cell A (solid line) and cell B (dotted 
line), and coupling current (Ic). The action potentials of cell A during the coupling period are numbered 1–17 for reference. The small 
vertical arrow indicates an action potential for which the action potential of cell B occurs before the corresponding action potential of cell 
A. (B) Data in A replotted for the time period indicated by the horizontal two headed arrow in A. Data from experiment 950803-2 (see Tables).

Figure 4 Simultaneous recording for 10 s of two isolated sinoatrial node cells, with the cells uncoupled during the first and last 2 s and 
coupled with a coupling conductance of 0.20 nS during the central 6 s. (A) Membrane potential (Vm) of cell A (solid line) and cell B (dotted 
line), and coupling current (Ic). (B) Data in A replotted for the time period indicated by the horizontal two headed arrow in A. Data from 
experiment 950803-2 (see Tables).

Figure 5 Simultaneous recording for 10 s of two isolated sinoatrial node cells, with the cells uncoupled during the first and last 2 s and 
coupled with a coupling conductance of 10 nS during the central 6 s. (A) Membrane potential (Vm) of cell A (solid line) and cell B (dotted 
line), and coupling current (Ic). (B) Data in A replotted for the time period indicated by the horizontal two headed arrow in A. Data from 
experiment 950803-2 (see Tables).

Table II Critical Coupling Conductance and Common Interbeat Interval of Rabbit Sinoatrial Node Cells. Coupling Clamp Data

Experiment		Membrane capacitance		Input resistance		Intrinsic interbeat 
internal		Critical
coupling
conductance		Common
interbeat
interval*
	
Cell A		Cell B	Cell A		Cell B	Cell A		Cell B	
		
pF
		
MΩ
		
ms
		
nS
		
ms
	
950111		44		36		420		650		358		331		≤0.50		342	
950117		37		45		250		480		236		257		0.125–0.15		245	
950131		40		39		300		460		344		424		 0.20–0.30		375	
950803-1		41		40		525		500		279		442		≤0.50		310	
950803-2		41		39		520		510		310		390		 0.15–0.17		333	
* At a coupling conductance of 10 nS.
 

Figure 6 Interbeat interval (IBI) for cells A and B (top, • and □, 
respectively) and the delay in activation of cell B with respect to 
the activation of cell A (bottom, ▴) for a coupling conductance Gc 
(horizontal arrow). (A) G
c = 0.10 nS. (B) G
c = 0.15 nS. The data in 
A and B come from the action potential recordings of Figs. 2 and 
3, respectively. Data from experiment 950803-2 (see Tables).

Figure 7 Interbeat interval (IBI) for cells A and B (top, • and □, 
respectively) and the delay in activation of cell B with respect to 
the activation of cell A (bottom, ▴) for a coupling conductance G
c 
(horizontal arrow). (A) G
c = 0.2 nS. (B) G
c = 10 nS. The data in A 
and B come from the action potential recordings of Figs. 4 and 5, 
respectively. Data from experiment 950803-2 (see Tables).

Figure 8 (A) Superimposed action potentials for the same cell 
pair used for Figs. 2–7 at zero coupling conductance, with the upstrokes of the first action potentials shown for each cell superimposed in time. (B) Calculated ionic membrane currents of cell A 
(Iion,A; solid line) and cell B (Iion,B; dotted line).

Figure 9 (A) Simultaneously recorded action potentials from 
the coupled period for the same cell pair used for Figs. 2–7 at a 
coupling conductance of 10 nS. (B) Calculated ionic membrane 
currents of cell A (Iion,A; solid line) and cell B (Iion,B; dotted line), and 
the coupling current (Ic; bold solid line). 

Figure 10 (A) Common interbeat interval (IBI) at a coupling 
conductance of 10 nS plotted (as a percentage of the IBI of the intrinsically faster beating cell, IBIf) versus the IBI of the slower beating cell of the cell pair (also as a percentage of the IBIf). Experimental results for the five cell pairs studied (•) and results obtained from a simulation of two pacing cells under the same 
conditions (○; see text). (B) Critical coupling conductance plotted versus the IBI of the slower beating cell of the cell pair (as a 
percentage of the IBIf). Ranges experimentally obtained for three 
cell pairs (solid symbols and lines) and results obtained from a simulation of two pacing cells under the same conditions (○; see text). 
Note the difference in abscissa scales between A and B.

Figure 11 (A) Diastolic depolarization phase for the same cell 
pair used for Figs. 2–9 either when the two cells were uncoupled or 
when the cells were coupled by 10 nS. The diastolic intervals 
(DDT) are from the slower cell of the cell pair when uncoupled 
(DDTs), the faster cell of the cell pair when uncoupled (DDTf), and 
the simultaneously recorded diastolic intervals of the two cells 
when coupled (DDTc). (B) Observed values of DDTc versus the values predicted from the uncoupled values of DDTs and DDTf using 
Eq. 3. The solid symbols show results for the five cell pairs studied, 
while the open symbols show results obtained from a simulation of 
two pacing cells under the same conditions (see text).
==== Refs
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