INTRODUCTION

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THE ATRIUM CONTAINS 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 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 fast-upstroke 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 (G_c). 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 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 G_c and also the frequency for direct stimulation of the atrial cell.

	METHODS

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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 + 750 µM CaCl₂ for 3 min, the base solution + 100 µM EGTA for 4 min, and the base solution + 240 µM CaCl₂ + 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 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 K-glutamate 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 ± 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 M 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 + 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 G_c 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 were actually coupled by G_c 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 = 1). All of our records then are recordings from the real cell with simultaneously generated model solutions.

View larger version (20K): [in this window] [in a new window]   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, Vt+t1 is computed potential of model cell for next time step, and Itc 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.

	RESULTS

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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 (G_c = 0) from the real cell. The atrial cell has a resting membrane potential (RMP) of 79 mV, a peak amplitude of +30 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 M. The SAN model cell has intrinsic automaticity at a steady-state BCL of 388 ms, a maximum diastolic potential of 66 mV, a peak amplitude of 31 mV, and a dV/dt of 7 V/s. In our previous work (34), we examined the critical G_c 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 G_c 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 ± 0.1 nS (n = 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 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 +21 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 some of the action potentials from the SAN model cell were conducted to the atrial cell and some were not.

View larger version (33K): [in this window] [in a new window]   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) = 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.

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 G_c 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 G_c 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 G_c was used. Figure 3A shows the superimposed solution of the SAN model cell and the recorded atrial cell action potentials directly stimulated at BCL = 300 ms when completely uncoupled. Figure 3B shows the steady-state pattern of entrainment that was produced when the atrial cell, directly stimulated with BCL = 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 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 +27 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.

View larger version (36K): [in this window] [in a new window]   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 = 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 steady-state interactions between a SAN model cell (dotted line) and same atrial cell (solid line) when direct stimuli at BCL = 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.

When G_c was reduced below 0.3 nS, as the atrial cell continued to be directly stimulated at BCL = 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 G_c 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 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 = 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).

View larger version (43K): [in this window] [in a new window]   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 = 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.

View larger version (38K): [in this window] [in a new window]   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 = 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.

When we then maintained G_c 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 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 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 = 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).

View larger version (36K): [in this window] [in a new window]   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 = 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.

View larger version (34K): [in this window] [in a new window]   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.

We studied a total of seven atrial cells with this protocol of assessing the dependence of entrainment on G_c and the stimulus frequency (BCL = 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 ± 0.03 nA (mean ± SE), which is considerably less than the 2.6 ± 0.2 nA (n = 6) we previously reported (34) for rabbit ventricular cells with the same duration stimulus pulse and the same ionic solutions and temperature. Critical G_c values were determined with a resolution of 0.05 nS for each cell. The critical G_c 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 ± 0.05 nS, and the critical G_c that allowed entrainment of the SAN model cell to the atrial cell when the atrial cell was directly paced at BCL = 300 ms was 0.32 ± 0.01 nS. For each atrial cell we found periodic phenomena similar to those shown above when G_c was set between 0.1 and 0.2 nS, below the value required for frequency entrainment.

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 G_c. 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 G_c and then recording a time sequence in which we had the two cells uncoupled for 5 s and then applied the desired G_c 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 G_c 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 G_c 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 G_c is sufficient for entrainment at BCL = 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 = 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 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.

View larger version (38K): [in this window] [in a new window]   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.

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 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 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 = 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.

View larger version (51K): [in this window] [in a new window]   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.

View larger version (34K): [in this window] [in a new window]   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

Top Abstract Introduction Methods Results Discussion References

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 G_c 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 G_c 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 G_c, and the mean required G_c 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 G_c 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 G_c 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 G_c 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 G_c 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 voltage threshold for action potential initiation. In a comparative study of activation properties of atrial cells versus ventricular cells (11) we found that the anatomical "size" of the atrial cells is somewhat smaller than that of the ventricular cells, with the membrane area of the two cell types, as measured by the cell capacitance of isolated cells, being ~30% less in atrial cells than in ventricular cells. The input resistance of rabbit atrial cells was much higher (341 vs. 16.5 M), and the amount of depolarization from the resting potential required to initiate an action potential was lower (24 vs. 36 mV) than for rabbit ventricular cells. The actual input resistance for the SAN model cell is in the range of 400-500 M assessed during diastole, which is consistent with our finding that the required conductance for the SAN model cell to drive an atrial cell is somewhat higher (0.55 nS) than the required conductance for the atrial cell, when directly stimulated at BCL = 300 ms, to overdrive the SAN model cell (0.32 nS). However, the process by which an intrinsically quiescent cell, when directly stimulated at a BCL less than the intrinsic BCL of a coupled spontaneously active cell, is able to overdrive the spontaneously active cell is more complex than the process by which two quiescent cells propagate an action potential after one of the cells is stimulated. As we showed in Figs. 8-10, the critical conductance for overdriving depends on the difference between the intrinsic BCL of the automatic cell and the driven BCL of the intrinsically quiescent cell. For the same G_c of 0.2 nS, the cell pair showed overdrive entrainment when the BCL for stimulation of the atrial cell was 350 or 400 ms, but when the BCL for stimulation of the same atrial cell was 300 ms the cell pair demonstrated a Wenckebach-like periodicity with a repetitive pattern of progressively increasing conduction delays. This phenomenon of the frequency dependence of Wenckebach periodicity is well established for conduction through the AV node (15) and may be related to the relative paucity of gap junctions within the AV node (7, 10, 25) as well as to the slow recovery of excitability of the nodal cells (4, 5, 9, 40).

Our results are consistent with recent studies from other laboratories that have used the coupling clamp technique to couple together isolated cells and cell models. Watanabe et al. (35) coupled together isolated SA node cells (or cell clusters) to a resistance-capacitance circuit designed to represent the input impedance of isolated atrial cells. They found a threshold G_c of 0.58 nS for conduction from the isolated SA node cell to the atrial cell model. Spitzer et al. (29) coupled isolated AV node cells to a resistance-capacitance model of an atrial cell and showed that a G_c of 1 nS allowed the AV node cell to continue pacing and to produce depolarizations in the atrial model cell that would have been suprathreshold for a real atrial cell. They also coupled a cluster of AV node cells to a real atrial cell and showed pacing of the nodal cells and driving of the atrial cell at a G_c of 20 nS. They also did experiments on coupling together a pair of AV node cells and showed synchronization of activity at a G_c of 2 nS. We have done similar experiments on coupling together a pair of SA node cells (33) and found a critical G_c 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 Beeler-Reuter (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 G_c 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 G_c cannot yet be experimentally recreated from isolated cells with controlled or measured G_c. Our use of a direct connection between a central nodal cell model and a fast-response 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.