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Am J Physiol Heart Circ Physiol 292: H165-H174, 2007. First published July 28, 2006; doi:10.1152/ajpheart.01101.2005
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Computational evaluation of the roles of Na+ current, iNa, and cell death in cardiac pacemaking and driving

H. Zhang,1 Y. Zhao,1 M. Lei,2 H. Dobrzynski,2 J. H. Liu,3 A. V. Holden,4 and M. R. Boyett2

1Biological Physics Group, School of Physics and Astronomy and 2Division of Cardiovascular and Endocrine Sciences, The University of Manchester, Manchester, United Kingdom; 3College of Information Science and Engineering, Northeastern University, Shenyang, China; and 4Institute of Membrane and Systems Biology, The University of Leeds, Leeds, United Kingdom

Submitted 18 October 2005 ; accepted in final form 27 July 2006


   ABSTRACT
TOP
 ABSTRACT
MODEL DEVELOPMENT
 RESULTS
 CONCLUSIONS AND DISCUSSION
 GRANTS
 REFERENCES
 
Voltage-dependent sodium (Na+) channels are heterogeneously distributed through the pacemaker of the heart, the sinoatrial node (SA node). The measured sodium channel current (iNa) density is higher in the periphery but low or zero in the center of the SA node. The functional roles of iNa in initiation and conduction of cardiac pacemaker activity remain uncertain. We evaluated the functional roles of iNa by computer modeling. A gradient model of the intact SA node and atrium of the rabbit heart was developed that incorporates both heterogeneities of the SA node electrophysiology and histological structure. Our computations show that a large iNa in the periphery helps the SA node to drive the atrial muscle. Removal iNa from the SA node slows down the pacemaking rate and increases the sinoatrial node-atrium conduction time. In some cases, reduction of the SA node iNa results in impairment of impulse initiation and conduction that leads to the SA node-atrium conduction exit block. Decrease in active SA node cell population has similar effects. Combined actions of reduced cell population and removal of iNa from the SA node have greater impacts on weakening the ability of the SA node to pace and drive the atrium.

sodium current; sinoatrial node; aging; dysfunction; conduction block; computer simulation

THE CARDIAC PRIMARY PACEMAKER, the sinoatrial (SA) node, is heterogeneous, and cells from different parts of the SA node have different capacitance and ionic current densities (6–8, 17, 23–24, 26). The measured Na+ current (iNa) density is higher in the periphery but low or zero in the central SA node cells (8, 17). Possible contribution of iNa to the initiation and conduction of pacemaker potential is unclear because blocking of iNa by TTX has little or no effects on action potentials of leading pacemaker cells (4, 8, 17, 24, 28, 29, 31). However, there is a close link between iNa and the SA node dysfunction (5, 16, 39, 41). For example, mutation of Scn5a gene (encoding the Na+ channel) has been found in many patients with the sick sinus syndrome (SSS) (5), which is featured by intermittent sinus bradycardia and sinoatrial conduction block (8, 14, 15, 36, 37). In some other patients with long QT syndrome type 3 due to Scn5a mutations, sinus node dysfunction has also been found (41).

It is also possible that iNa is involved in the age-dependent deterioration in cardiac pacemaker functions. In humans and other mammals, the functions of the pacemaker of the heart declines with aging (2, 8, 20, 33, 38). The main features of the aged SA nodes are a slow pacemaking rate [i.e., increase in cycle length (CL)] and possible SA node-atrium conduction exit block or arrest of SA node pacemaking (i.e., termination of the SA node pacemaker activity) (2, 20, 33). There is experimental evidence for the associations between aging and a decreased population of the active SA node cells (i.e., an increased number of the dead SA node cells) (38). In humans, it was found about 16% reduction in the volume percentage of the SA node cells to the total SA node in the elderly compared with adults (38). As the pacing and driving ability of the SA node is dependent on its size (21), reduction of active SA node cell population may have negative effects on its pacemaker activity. For iNa, there is no direct evidence; however, several studies suggested a possible reduction of iNa in aged SA nodes (2, 4, 8). In the rabbit SA node, the measured upstroke velocity of the action potential in the center is lower than that in the periphery (8–9). With age, Alings and Bouman (2) found that, whereas the total area of SA node does not change, the region in which the upstroke velocity is low increases in area, i.e., the upstroke velocity in the periphery decreases to a value similar to that in the center. Such a decrease in the upstroke velocity in the periphery is possibly due to a reduction of the Na+ channel because the Na+ channel in the center of the SA node of the neonatal rabbit heart disappears by the time the animal is a young adult (4). How a reduction of iNa or a decrease in active SA node cell population, or a combination of both, affects the cardiac pacemaker activity is unclear yet.

In this study, we evaluated the functional roles of iNa and cell death in initiation and conduction of pacemaker action potentials by computer modeling. A gradient model of the intact SA node and its surrounding atrial muscle was developed that incorporated details of the SA node heterogeneous electrophysiology and histological geometry. The model of histological structure was based on discretization of a section of the rabbit SA node tissue cut through the leading pacemaker site to form a two-dimensional (2D) lattice. Each node of the lattice is represented by a model of a SA node cell or an atrial cell as appropriate (45–46). In the model, the SA node heterogeneous electrophysiology was based on the experimental data of the regional differences in the SA node cell size [cell capacitance (Cm)] and measured ionic current densities (45). Simulations have shown that block of the SA node iNa results in an increase of pacemaking CL (the time interval between two successive pacemaking action potentials) (equivalent to a decrease of pacemaking rate) and the SA node-atrium conduction time (SACT). Reduction of iNa can also produce the SA node-atrium conduction block, in which action potentials originating from the SA node can fail to conduct into the atrium, or termination of the SA node pacemaker activity. Decrease in active SA node cell population showed similar effects. When considered together, combined actions of a reduction in active cell population and removal of iNa from the SA node have a greater impact on slowing down the cardiac pacemaking rate and producing impairment of impulse initiation and conduction that leads to the SA node-atrium conduction exit block. These simulations resemble the main features of the dysfunction of the SA node in aged heart or SSS.

Glossary

AM
Atrial muscle

Cm
Cell membrane capacitance (in µF)

CFormula(i,j), CFormula(i,j)
Cell capacitance of atrial muscle cell (a) or sinoatrial (SA) node cell (s) in the two-dimensional (2D) tissue model with coordinates indexed by (i,j) in the 2D lattice

ga (i,j) gs (i,j)
Junctional coupling conductance between atrial muscle cells or SA node cells

gNa
Conductance of iNa

gNa,c, gNa,p
Conductance of iNa of central and peripheral SA node cell

gNas (i,j)
Conductance of iNa of SA node cell with coordinates indexed by (i,j)

iNa
TTX-sensitive Na+ current

iCa,L, iCa,T
L- and T-type Ca2+ currents

ito, isus
Transient outward and sustained components of 4-aminopyridine (AP)-sensitive current

iK,r, iK,s
Rapid and slow delayed rectifier K+ currents

ib,Na, ib,Ca, ib,K
Background Na+, Ca2+ and K+ currents

iNaCa
Na+/Ca2+ exchanger current

ip
Na+-K+ pump current

itot
Total membrane ionic channel current in a cell (in nA)

OS
Overshoot of cell membrane potential (in mV)

t
Time (in s)

V
Cell membrane potential (in mV)

Va(i,j), Vs(i,j)
Membrane potential of atrial muscle cell or SA node cell with coordinates indexed by (i,j)


   MODEL DEVELOPMENT
TOP
 ABSTRACT
 MODEL DEVELOPMENT
RESULTS
 CONCLUSIONS AND DISCUSSION
 GRANTS
 REFERENCES
 
Single cell model of the SA node. The electrical activities of SA node cells show regional differences (6–9, 22–24, 26, 32, 45). For example, action potentials recorded from the central cells have more positive take-off potential, slower upstroke velocity, and longer action potential duration, more positive maximum diastolic potential, and slower intrinsic pacemaker activity than those recorded from peripheral cells (8, 17, 23). Such heterogeneous electrical activities can be accounted for by gradient distributions of current densities of some ion channels in different regions of the SA node (8, 44–45). Experimental data obtained from single rabbit SA node myocytes have shown that the current density of iNa, L-type Ca2+ current iCa,L, 4-aminopyridine (AP)-sensitive transient outward current ito, rapidly activated rectifying potassium current iK,r, and hyperpolarization-activated current if correlate well with cell size (see Ref. 8 for review). A large cell, presumably from peripheral SA node (6), has greater current densities than a small cell, presumably from the central SA node. Such correlations were also observed from small balls cut from different regions of the rabbit SA node, where cells from the periphery have greater ion channel current densities than the cells from the center (8, 23). Based on the measured regional differences of ionic current densities, mathematical models of action potentials of the central and peripheral rabbit SA node cells have been developed by Zhang et al. (44–47). These models generated action potentials having the same characteristics as those recorded experimentally. In this study, we used the Zhang et al. (45) models to simulate the electrical action potentials of central and peripheral SA node cells. A general description of the single cell action potential models is given in Table 1, and details of the full equations were documented by Zhang et al. (45).


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  		Table 1. General equations for single cell action potential

 
Anatomical model of the intact SA node and surrounding atrial muscle. Initiation and conduction of the pacemaker activity depends not only on the properties of SA node cells, but also on the anatomical structure of the SA node (6, 8, 22, 26). The intact rabbit SA node is a complex structure, in which cells in the center are smaller and have fewer and more poorly organized myofilaments than do cells in the periphery (6, 8, 26). In our previous studies, we have combined different techniques (e.g., immunohisto-/cytochemistry and electrophysiology) to map the detailed structure and functions of the rabbit SA node at molecular, cellular, and tissue levels (12–13, 46). The rabbit SA node preparation was cut into a series of tissue sections through the atrial muscle of the crista terminalis and the intercaval region, where the SA node is located by a spatial resolution of 100 µm. These tissue slices were then labeled with different antibodies to characterize cell types and gap junctional coupling in the SA node. Details of the distribution of the various cell types and their electrophysiological properties, the connexin that determine the electrical coupling between cells, and spatial variations of cell arrangement and alignment across the SA node have been utilized to reconstruct a 3D anatomical model of the SA node (13), whereas spatial resolution of 100 µm is fine enough in the direction parallel to the crista terminalis, along which the SA cells are aligned (100 µm is close to the cell length of SA node cells, around 80 µm). However, in the cross section perpendicular to the crista terminalis, it requires higher resolution, which should be close or comparable to the cell diameter (around 10–15 µm). We chose one slice of the tissue sections to develop a 2D histological model of the SA node and atrium.

Figure 1A shows a low-magnification montage of a toluidene blue-stained tissue section through the atrial muscle of the crista terminalis, the periphery of the SA node, and the center of the SA node cut from the leading pacemaker site of the rabbit SA node. The center of the SA node is located in the intercaval region, and the periphery of the SA node rises up to the crista terminalis. Histology suggested that the SA node is not connected to the atrial muscle of the crista terminalis but is separated from it by connective tissue, which forms a barrier separating much of the periphery of the SA node from the crista terminalis. In Fig. 1A, the separating connective tissue was marked by a black curve. Data from this specific section suggested that there is only a small segment of contact between the SA node and the atrial muscle. Data from other sections showed similar results.


Figure 1
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  		Fig. 1. A: a toluidene blue-stained tissue section through the sinoatrial (SA) node (SAN) and its surrounding atrial muscle of the crista terminalis (CT) cut through the leading pacemaker site. B: a two-dimensional (2D) lattice model of the SA node and its surrounding atrium (A). SEP, atrium septum; Epi, epicardium; Endo, endocardium.

 
The SA node, like other cardiac tissues, comprises structured, anisotropic functional syncytia of electrically coupled cardiac cells (7, 14, 21, 26). Considering the discrete nature of cell spatial distribution and arrangement, in this study, we idealized the intact SA node and atrium as a network of electrically coupled SA node and atrial cells, which are bounded in an irregular spatial domain that can be modeled by the coupled ordinary differential equation network model. To classify the spatial structure of the SA node and surrounding atrium, the section of slice shown in Fig. 1A was discretized by a spatial resolution of 35 µm to generate a 2D discrete lattice with 91 x 28 nodes (see Fig. 1B). As the section was cut perpendicularly to the longitudinal direction of SA node myocytes, a spatial resolution of 35 µm is about two to three times of the diameter of a single myocyte (the diameter of single SA node myocyte is ~10–15 µm) (6, 8). Using the detailed information of molecular mapping (13), we classified each node in the lattice as either a SA node cell or an atrial cell.

Electrical activity of each node was modeled by a biophysically detailed model of action potentials and currents as appropriate. For a SA node cell, the action potential was modeled by the Zhang et al. (45) model. For an atrial cell, the action potential was modeled by the Earm-Hilgemann-Noble model (30). Both models are sets of nonlinear ordinary differential equations. Regional differences in electrical activity of the rabbit SA node were also incorporated into the model. Across the SA node, we assumed that cells in the center are small, whereas cells in the periphery are large. Correspondingly, there was a gradient change in the SA node cell capacitances: Cm changed from 20 pF in the center to 65 pF in the periphery. The ionic current densities in the SA node were functions of Cm as shown in the following equations of the 2D anatomical model of the intact SA node and surrounding atrium (where s denotes the SA node and a denotes the atrium). Across the atrium, homogeneous electrical activity was assumed.

Electrotonic interaction between cardiac cells was modeled by gap junctional coupling. Each node in the lattice was electrically coupled to its four nearest neighboring nodes. The junctional conductance was set to 25 nS for SA node-SA node cell or SA node-atrial cell, and 175 nS for atrial-atrial cells. These values of junctional conductance are comparable to the experimental data obtained from the rabbit SA node (2).

Numerical methods. The models (Eqs. 1–7 in Tables 1 and 2) were numerically solved by an explicit Euler method with a time step of 0.1 ms. The chosen time steps are sufficiently small for a stable and accurate solution. Numerical solution started from a gradient configuration of cell membrane potentials from +20 mV in the center to –70 mV in the periphery of the SA node across the 2D lattice. The potential and gating variables were set to their voltage-dependent quasi-steady states. In the atrial part, initial membrane potential was set to –90 mV, which is the equilibrium resting potential of the atrial cell model. Membrane potentials at each node of the 2D lattice were mapped into different colors, which changed from blue for –90 mV to red for +40 mV. Nodes of noncardiac cells (i.e., nodes outside of cardiac tissue) were set always to –90 mV. In simulations, action potentials were recorded for cells on the recording line as shown in Fig. 1B (cells spatially distributed from center toward periphery of SA node and atrium) and were plotted to display initiation and propagation of action potentials (space: vertically; time: horizontally). CL was measured as the time interval between two successive action potentials recorded from the SA node cell with coordination indexed by (90,15).


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  		Table 2. Two-dimensional anatomical model of the intact SA node and surrounding atrium

 

   RESULTS
TOP
 ABSTRACT
 MODEL DEVELOPMENT
 RESULTS
CONCLUSIONS AND DISCUSSION
 GRANTS
 REFERENCES
 
Figure 2 shows the initiation and conduction of pacemaker activity computed from the 2D model. In simulations, the electrical connection length between the SA node and atrium (L) was assumed to 1.3 mm or otherwise as stated in the text. Snapshots of membrane potentials across the 2D lattice were shown at 40 ms (Fig. 2A), 76 ms (Fig. 2B), and 144 ms (Fig. 2C) after the initial condition. The pacemaking action potential was first initiated in the center (Fig. 2A) and then propagated toward the periphery of the SA node. At the junction where the SA node is physically connected to the atrium, the SA node depolarized atrium generating excitation waves propagating in the atrium (Fig. 2B). However, repolarization took a reversed sequence. It started from the atrium and then periphery and center of the SA node (see Fig. 2C). The simulated sequences of depolarization (SA node center-SA node periphery-atrium) and repolarization (atrium-SA node periphery-SA node center) were similar to the experimental observations from the rabbit SA node and reflected the gradient nature of SA node electrical activity (8). In the intact SA node and atrium, peripheral cells are pacemaking faster than those of central cells; however, the pacemaking rate was determined by central cells rather than peripheral cells because of the electrotonic interaction between the SA node and atrium (8, 10, 21–22, 43–47). Through the electrotonic interaction, the atrium suppressed the pacemaker activity of the peripheral cells. Cells closer to atrium were depressed more than were the cells farther away. Consequently, central cells dominated the pacemaker activity and determined the pacemaking rate or the CL. In the simulation, the measured CL was 330 ms.


Figure 2
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  		Fig. 2. Snapshots of initiation and conduction of the pacemaker activity in 2D anatomical model of the intact SA node and atrium at various times after initial configuration (see Numerical Methods). A: 40 ms. B: 76 ms. C: 144 ms.

 
iNa current helps the node to drive the atrial muscle. To evaluate the functional roles of SA node iNa on initiation and conduction of the pacemaker activity, a series of simulations were performed under control and iNa removal from the SA node conditions. These results are shown in Fig. 3, which represented the space-time plot of action potentials of cells on the recording line under control (Fig. 3A) and SA node iNa removal by 50% (Fig. 3B) and 100% (Fig. 3C). In both control and iNa removal conditions, the action potential was first initiated in the center and then propagated toward the periphery and atrium. The repolarization started from the atrium and then periphery and center. Deduction of SA node iNa current did not alter the depolarization or repolarization sequences but slowed down pacemaker activity. A 50% and 100% reduction of SA node iNa increases the measured CL from 330 ms to 351 ms and 369 ms, respectively.


Figure 3
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  		Fig. 3. A–C: action potentials recorded from cells along the recording line with length (L) = 1.3 mm and various sodium channel current (iNa) removal. A: control. B: 50% iNa reduction. C: 100% iNa reduction. D–F: simulations under conditions similar to A–C, respectively, but with L = 1.4 mm. CL, cycle length; AM, atrial muscle; gNa, conductance of iNa.

 
Effects of SA node iNa removal on the initiation and conduction of pacemaker activity are dependent on the electrotonic interaction between the SA node and atrium. Figure 3, D–F show similar simulations but with L = 1.4 mm. An increase of L extended the physical contact area between the SA node and atrium, resulting in a stronger electrotonic interaction between these two tissues, which produced more depression of the pacemaker activity of the SA node; the SA node pacing became slower and failed to drive the atrium. Under control conditions, the measured CL was 343 ms, a 13-ms increase compared with the result when L was 1.3 mm. A 50% removal of iNa from the SA node increased CL to 363 ms. When SA node iNa was removed by 100%, the SA node, though pacing stably (the measured CL was 380 ms), failed to drive the atrium from beat to beat. SA node driving alternans occurred: a beat that succeeded in driving atrium was followed by a beat that failed to drive the atrium. This driving alternant phenomenon is similar to the SA node conduction exit block observed in aged or SSS SA node (15, 25, 36–37).

The increase in CL with SA node iNa removal was accompanied by changes in the characteristics of SA node action potentials determining the pacemaking rate. Figure 4 shows the effects of SA node iNa reduction on the maximal diastolic potential (MDP; open symbols in Fig. 4A), overshoot (OS); solid symbols in Fig. 4A), and maximal upstroke velocity (dV/dtmax; Fig. 4B) of action potential of cells on the recording line. In Fig. 4, the measured MDP, OS, and dV/dtmax were plotted against the distance of cells from the center of the SA node for control (100% gNa; solid triangles) and 100% SA node iNa reduction (gNa = 0; solid circles) conditions. In both cases, the measured quantities showed a similar spatial gradient from the center (0 mm) to the periphery of the SA node (around 2.1 mm) and the atrium, which is consistent with experimental observations (8). However, with SA node iNa removal, the measured OS and dV/dtmax were both significantly smaller compared with the control conditions, not only in the peripheral SA node cells as expected, but also in the center of the SA node cells (shown in Fig. 4, Ai and Bi, respectively). This is due to the electrotonic coupling between cells, which maps the reduction of OS and dV/dtmax in the periphery to the center of the SA node. SA node iNa removal also produced more hyperpolarized MDP as shown in Fig. 4Aii. Notably, such a more hyperpolarized MDP is transitional because reduced OS generates incomplete activation of repolarizing potassium current, resulting in an elevated MDP after the model reaches a stable solution. These changes together, especially the remarkable reduction in dV/dtmax, are attributable to the increased CL.


Figure 4
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  		Fig. 4. Spatial gradient of characteristics of action potentials of cells on the recording line for control ({blacktriangleup}), SA node iNa removal (bullet), and 10% reduction in active SA node cell population ({blacklozenge}). Quantities are plotted against the distance of cells from the center of the SA node. A: overshoot (OS, solid symbol) and maximal diastolic potential (MDP; open symbols). Ai and Aii: magnification of A in the central SA node region. B: maximal upstroke velocity (dV/dtmax). Bi: magnification of B in the central SA node region.

 
Decrease of iNa decreases dramatically the upstroke velocity of action potentials of the peripheral SA node cells (8, 17, 45). It has been conjectured that reduction of SA node iNa decreases the ability of the SA node to conduct the action potentials. We evaluated the functional roles of SA node iNa in conducting action potential by measuring the SACT under control, and iNa removal conditions used the same protocol (2). A sequence of high rate stimuli with a time interval of 250 ms was delivered to a group of four nodes in the atrium [cell(5,13), cell(6,13), cell(5,14), cell(6,14)]. The stimulus time interval was much shorter than the intrinsic pacemaking CL of the SA node; thus the stimuli-evoked excitation waves suppressed the pacemaker activity of the SA node and dominated the tissue excitation. After the seventh stimulus, the external stimulus was stopped, and after a time delay, the SA node resumed normal pacemaker activity. We measured the time interval ({delta}t) between the seventh stimulus and the time for the normal pacemaker activity to arrive at the stimulation site. The SACT was computed as 1/2({delta}t – CL).

Figure 5 plots the computed SACT under different levels of SA node iNa removal superimposed with experimental data obtained from the rabbit SA node (2). Reduction of SA node iNa increased the SACT monotonically. By 50% and 95% of SA node iNa removal, the SACT was increased by 15 ms and 35 ms, respectively, compared with control conditions (0% deduction). The computed SACT with iNa removal shows a similar increase pattern as observed in the aged rabbit SA node (2). This suggests that SA node iNa plays a significant role in conducting the pacemaker activity.


Figure 5
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  		Fig. 5. The computed SA node-atrium conduction time (SACT) with different percentages of SA node iNa removal ({blacksquare}) and experimental data obtained from the rabbit SA nodes in different age groups (adapted from Ref. 2).

 
Effects of cell death. A series of simulations was performed to investigate the possible actions of reduction in the active SA node cell population on the pacemaker activity. In simulations, CL was measured for 1%, 5%, 10%, and 15% reduction of the active SA node cells. Reduction of active SA node cells slowed down the pacemaking rate, which was demonstrated by an increase in the measured CL. By 1%, 5%, and 10% cell reduction, the measured CL was 332, 337, and 347 ms, respectively, an increase of 2, 7, and 17 ms to 330 ms when no dead cells were present. Similar to iNa removal, such an increase in CL was attributable to the reduced AM, dV/dtmax, and more hyperpolarized MDP of the SA node as shown in Fig. 4 (solid diamonds). By 15% reduction in the active SA node cells, the SA node terminated its pacemaker activity. A 15% reduction in the active cell population is close to the experimentally reported 16% cell death in elderly patients (38). However, it was unclear from that study (38) whether or not these patients had suffered arrest of SA node pacemaking (i.e., termination of the SA node pacemaker activity). A 10% reduction in active SA node cell population had negligible effect on the measured SACT (4-ms increase compared with the control conditions).

Combined actions of cell death and reduction of SA iNa current density were also studied. Figure 6 shows the initiation and conduction of the pacemaker activity for 10% cell death (Fig. 6A), 10% cell death together with 50% (Fig. 6B), or 100% (Fig. 6C) of SA node iNa removal. In all cases, combined actions of cell death and iNa removal had greater impact on slowing down the pacemaking rate compared with the actions of cell death only or actions of iNa removal only. The measured CLs for 50% and 100% removal iNa from the SA node were 366 and 382 ms, respectively, a significant increase of 36 ms and 54 ms compared with 330 ms under control conditions.


Figure 6
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  		Fig. 6. A–C: action potentials recorded from cells along the recording line with L = 1.3 mm and various levels of reductions in iNa and active cell populations in the SA node. A: 10% dead SA node cell population only. B: 50% iNa reduction and 10% dead SA node cell population. C: 100% iNa reduction and 10% dead SA node cell population. D–F: stimulations under conditions similar to A–C, respectively, but with L = 1.4 mm.

 
Electrotonic interaction between the SA node and atrium played an important role in determining the SA node pacing and driving. Figure 6, D–F, represented results obtained with L = 1.4 mm, together with a 10% loss of cell population and iNa removed by 0%, 50%, and 100%, respectively. In all cases, the SA node paced stably but failed to drive the atrium. The SA node action potentials penetrated into the atrium but failed to generate propagating waves. However, because of the electrical coupling between the SA node and atrium, the resting potential of atrial cells close to the SA node was elevated, which, in return, reduced the depressive actions of atrium to the SA node, resulting in a slightly faster pacemaking rate compared with the simulations shown in Fig. 6, A–C. The measured CLs were 337 ms, 352 ms, and 366 ms.

Effects of L. The electrotonic coupling between the SA node and atrium plays an important role in determining the initiation and conduction of the pacemaker activity in the SA node (6, 21–22, 45), especially under the conditions of reduction of the active SA node cell population and iNa current density. To characterize the effects of L, a series of simulations were performed with L changing systematically from 0 to 2.5 mm (the possible minimal and maximal connection length between the SA node and atrium in the model). The results are represented in Fig. 7, in which the computed CL was plotted against L under control conditions (solid circles) and combined actions of 10% cell death with 100% iNa removal (open triangles). Under control conditions, the contact area is large enough to provide sufficient electrical coupling for the SA node to pace and drive the atrium successfully only during the range of 1.1 mm ≤ L ≤ 1.5 mm. However, over this range (when 0 mm < L < 1.1 mm or 1.5 mm ≤ L ≤ 2.3 mm), though the SA node paces, it does not drive the atrium. When L is over 2.3 mm, the SA node failed to pace completely.


Figure 7
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  		Fig. 7. Measured CL against the connection length L between the SA node and atrium: bullet, control; {blacktriangleup}, 100% iNa block and 10% dead SA node cell population. With iNa removal and dead SA node cell population, SA node exit block/sinus arrest occurred when L was in the window within which the SA paces and drives atrium under control conditions.

 
When reductions of the active SA node cell population and iNa current density were considered, the measured CL increased with L in a similar way as under control conditions. Each case increased the CL compared with controls. Another important phenomenon was that there were some L windows in the range of 1.1 mm ≤ L ≤ 1.5 mm, within which the SA node failed to drive the atrium. The SA node resumed its pacing and driving with the specific connection length (L = 1.3 mm). Such transition happened because of complicated electrical interaction between the SA node and atrium. An increase of L extended the physical contact area between the SA node and atrium. On the one hand, it increased the area by which the SA node can excite the atrium, and on the other hand, it also increased the area by which the atrium depressed the SA node. These two processes interact with each other, and the balance between the two eventually determined whether the SA node is able to drive the atrium and was arrested. With L > 2.0 mm, the pacemaker activity of the SA node was abolished completely.


   CONCLUSIONS AND DISCUSSION
TOP
 ABSTRACT
 MODEL DEVELOPMENT
 RESULTS
 CONCLUSIONS AND DISCUSSION
GRANTS
 REFERENCES
 
Major conclusions. In this study, we have developed a 2D anatomical model of the intact SA node and atrium that incorporated details of anatomical and electrophysiological heterogeneities of the SA node. Using the model, we evaluated the functional roles of the SA node iNa in initiation and conduction of the pacemaker activity. The main findings of this study are the following. 1) SA node Na+ helps the SA node to pace and drive the atrium. Reduction of SA node iNa slows down the pacemaking rate and compromises the conduction of the pacemaker activity by increasing the sinoatrial node atrium conduction time. 2) Reductions of the SA node iNa current density and active SA node cell population may lead to SA node exit block or sinus arrest. This is seen in aged hearts or the hearts with SSS (2, 5, 14, 15, 36–37). 3) The functional roles of SA node iNa on the initiation and conduction of the pacemaker activity are dependent on the electrotonic interactions between the SA node and atrium, by which the surrounding atrium modulates the SA node pacemaker activity (10, 21–22, 43–47).

To conclude, the SA node Na+ current plays important roles in initiation and conduction of electrical pacemaker activity. Reduction of iNa results in impairment of impulse initiation and conduction. This study provides insights into understanding the ionic mechanisms underlying the genesis of SA node dysfunctions in SSS and aged hearts. This conclusion is consistent with recent experimental findings that mutations in genes encoding cardiac Na+ ion channels, e.g., Scn5A, have been detected in patients with SSS (5, 39).

Insights to the functional roles of iNa. The functional roles of SA node iNa on initiation and conduction of the pacemaker activity are an integrated action that cannot be fully understood on the basis of experimental information obtained at the level of the isolated single cell alone. The functional roles of iNa have remained controversial as previous studies have shown that iNa is only present in some transitional peripheral cells while absent in the primary central cells (8, 17, 24). There are two main concerns: 1) blocking iNa has very small or no effect on the action potential of primary SA node central cells; thus its contribution to pacemaking rate is limited; and 2) the window current of iNa peaks around –65 mV, which is more negative to the maximal diastolic potential of action potentials of most SA node cells. If present, iNa will not be fully activated during the time course of action potentials in some transitional cells. Thus its contribution to the conduction of the pacemaker activity is limited. These arguments are correct when the experimental data are interpreted at the isolated single cell level. However, when cell-to-cell electrical coupling is considered, the functional role of SA node iNa in initiation and conduction of the pacemaker activity is apparent. In our simulations, the measured CL increased with iNa removal from the SA node. So reduction of iNa slowed down the pacemaker activity of cells not only in the periphery but also in the center, where cells have no or small iNa current but dominate pacemaking rate. The mechanism behind this is due to the electrical interaction between the SA node and atrium via electrical coupling (10, 21–22, 43–47). This interaction is two way: the sinoatrial node excites and drives the atrial cells, initiating conduction of action potentials; and the atrial tissue acts as a "load" on the sinoatrial node. Since the atrial muscle is more hyperpolarized than the sinoatrial node and lacks a pacemaker potential, the electrotonic interaction between the sinoatrial node and atrial tissue will result in a hyperpolarizing current that suppresses the pacemaker activity of the SA node. Via cell-to-cell electrical coupling, such a hyperpolarizing current also depresses the pacemaker activity of central cells. Closer to the atrium, periphery cells are depressed more than central cells in pacemaking activity. The depressive electrical modulation of atrial muscle in situ on the pacemaker activity of the SA node was confirmed by Kirchhof et al. (22), who showed that, when the atrial muscle was cut away from the SA node, the pacemaker site shifted from the center to the periphery of the node with an accelerating pacemaking rate. However, in the intact SA node and atrium, the pacemaker activity was originated from the center with a slower pacemaking rate. When iNa is removed from the SA node, such a depressive action becomes greater not only in the periphery but also in the center. This is because there is less depolarizing inward current contributed by iNa to counterbalance the depressive electrical modulation generated by the interaction between the SA node and atrium. As a result, the overshoot of action potentials in the center is decreased and the maximal diastolic potential is more hyperpolarized (Fig. 4A). The diastolic depolarization velocity in the central SA node is also reduced (manifested by a decrease in the measured maximal upstroke velocity as shown in Fig. 4B). This is different from the observations in single cells (17, 45), with which a complete block of iNa reduces the maximal upstroke velocity of action potentials for a peripheral cell but not for a central cell (17, 45). In the intact tissue model, due to the electrotonic interaction between cells, block of iNa reduces the maximal upstroke velocity of action potentials not only for peripheral, but also for central cells (Fig. 4B). Consequentially, the overall SA node pacemaking rate is reduced. Reduced maximal upstroke velocity also contributes to slowing down the conduction of the pacemaker activity and results in an increased SACT. Slowing down in cardiac conduction by disruption of the cardiac sodium channel gene Scn5a has been observed experimentally (34).

Different models of the SA node. Our 2D model of the rabbit SA node was based on the experimental data of gradient distribution of ionic current densities and cell morphology (8). An alternative hypotheses on the SA node structure is the Mosaic model (42) in which it has been conjectured that the electrophysiological properties of pacemaker cells in the SA node are uniform throughout the SA node and the apparent regional differences in electrical activity in the SA node are the result of a progressive decrease in the percentage of intermingling atrial cells toward the center, giving rise to a progressive decrease in their hyperpolarizing influence from the periphery toward the center. However, computer simulations using the Mosaic model failed to generate action potentials for the center and periphery of SA node cells with characteristics consistent with those recorded experimentally (44). With possible atrial myocytes surrounding SA node cells (13, 42), the depressive electrical modulation of atrial cells on the pacemaker activity of SA node cells will be greater (44), and the iNa will be even more essential to provide an inward depolarizing current to overcome the greater depression to generate depolarization and spontaneous action potentials. Thus the functional roles of iNa will be also important in the Mosaic model in the initiation and conduction of pacemaker activity. Our conclusion on the functional roles of iNa, though based on the gradient model, is also applicable to the Mosaic model of the SA node tissue. The model-simulated effects of iNa blocking on initiation and conduction of the cardiac pacemaker are consistent with those observed experimentally from the genetically disrupted cardiac Na+ channel gene Scn5a of adult mice SA node (25).

Dysfunctions of the SA node. Sinus node dysfunction, clinically known as sick sinus syndrome (SSS), is a common cause of symptomatic arrhythmias and has the highest incidence in the elderly (15, 36). The main features of SSS are manifested by intermittent sinus bradycardia, slow SA node-atrium conduction, sinus pause, sinus arrest, sinus exit block, or alternating bradycardia and atrial tachycardia. The mechanism underlying the genesis of the SA node dysfunction is unclear and is believed to be associated with changes in the intrinsic properties of the SA node with age. Recently, several studies have found a causative link between SA node dysfunction and defects of the HCN4 gene (27, 37, 40), which codes the hyperpolarization-activated if channel {alpha}-subunit. As if is a major determinant responsible for the spontaneous depolarization of the SA node cell (11), malfunction of if channel due to HCN4 mutation could lead to defective cardiac pacemaking. Mutations of HCN4 gene have been found in patients with sinus node diseases, such as familial sinus bradycardia (27, 37) and sinus node dysfunction in conjunction with QT prolongation and polymorphic ventricular tachycardia, torsades de pointes (40).

There is correlation between the changes of the intrinsic properties of the SA node and age (2–3, 8, 18, 20, 33, 38). An age-related increase in the SA node size has been reported in humans (38), which is due to the increased volume of connective tissue. In contrast, the active cell population of the SA node actually decreases with age (38). Some changes in the electrophysiological properties of the SA node have also been observed. In the guinea pig model, a significant age-related loss of connexin 43 from the nodal structure was observed (18). Because connexins are the major proteins forming the intercellular electrical coupling of cardiac cells (19), a loss of connexin 43 is likely to have a significant impact on slowing down the conduction of the pacemaker activity and increase of SACT. The age-related remodeling of several major ionic channels has also been reported (1, 4, 35). In the rabbit heart, the measured ionic current density of iNa (4), if (1), and iCa,L (35) channels are remarkably greater in the newborn rabbit SA node than in the adult rabbit SA node. These changes may account for, at least partially, some age-related changes in the characteristics of pacemaker action potentials, such as the pacemaking rate and the maximal upstroke velocity (2). An age-related increase in action potential duration in the rabbit and cat SA node was reported by Alings et al. (2), which also raises the possibility that some other outward potassium currents may also be age dependent. The age-related SA node dysfunction may be due to the integral actions of changes in cellular ionic channels, intercellular electrical coupling, and tissue structures. In the present study, we only focused on the roles of iNa and active SA node cell population in cardiac pacemaking and driving. A detailed study considering all reported age-related changes in the intrinsic properties of the SA node on cardiac pacemaker activity remains the subject of further research.

Limitations of the study. The SA node has a complicated 3D anatomical structure and regional-dependent electrical properties (8, 13), which have important impacts on the conduction pathways that determines the activation pattern of action potential and the sinoatrial node-atrium conduction time. Our 2D model is based on a section of tissue cut from an adult rabbit SA node and atrium. It lacks the details of conduction pathways present in the 3D anatomical structure of the SA node and atrium. This may affect our computed SACT. In simulations, the computed SACT, though, is comparable but quantitatively larger than the experimental data reported by Alings et al. (2), especially in the young age range. This discrepancy is possibly due to the lack of details of conduction pathways in the 2D model and the location in the atrium used to measure the SACT. For all simulations, we did not consider the age-dependent changes in the size of the SA node (i.e., the young rabbit has significantly smaller SA node tissue size than the adult rabbit) (38). This may also affect our computed SACT, especially in the young age range.

The 2D model, presented in this study, though, is a simple reduction of the SA node 3D structure but forms an important step toward our final goal to develop a biophysically and anatomically detailed 3D model. In this study, we assumed a stepwise change in the gap junctional coupling conductance between the SA node and atrial regions. In future study, heterogeneous gap junctional coupling across the SA node region (6–8, 13) should be incorporated into the model when detailed experimental data become available.


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 ABSTRACT
 MODEL DEVELOPMENT
 RESULTS
 CONCLUSIONS AND DISCUSSION
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This work was supported by grants from the Engineering and Physical Science Research Council (GR/S03027/01), British Heart Foundation (PG/03/140/16236), Biological and Biotechnology Science Research Council (BBS/B1678X), EU-Network of Excellence (BioSim) (005137), and The Welcome Trust.


   ACKNOWLEDGMENTS
 
We thank the reviewers of the manuscript for useful suggestions.


   FOOTNOTES
 

Address for reprint requests and other correspondence: H. Zhang, Biological Physics Group, School of Physics and Astronomy (North Campus), Univ. of Manchester, Manchester, M60 1QD UK (e-mail: henggui.zhang{at}manchester.ac.uk)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
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 CONCLUSIONS AND DISCUSSION
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 REFERENCES
 

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M. Baruscotti and R. B. Robinson
Electrophysiology and pacemaker function of the developing sinoatrial node
Am J Physiol Heart Circ Physiol, November 1, 2007; 293(5): H2613 - H2623.
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