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1 School of Biomedical Engineering, University of Tennessee, Memphis, Tennessee 38163; 2 Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77251-1892; and 3 Department of Physiology and Biophysics, University of Calgary Medical School, Calgary, Alberta, Canada T2N 4N1
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ABSTRACT |
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We have extended
our compartmental model [Am. J. Physiol. 266 (Cell
Physiol. 35): C832-C852, 1994] of the single
rabbit sinoatrial node (SAN) cell so that it can simulate cellular
responses to bath applications of ACh and isoprenaline as well as the
effects of neuronally released ACh. The model employs three different types of muscarinic receptors to explain the variety of responses observed in mammalian cardiac pacemaking cells subjected to vagal stimulation. The response of greatest interest is the ACh-sensitive change in cycle length that is not accompanied by a change in action
potential duration or repolarization or hyperpolarization of the
maximum diastolic potential. In this case, an ACh-sensitive K+ current is not involved.
Membrane hyperpolarization occurs in response to much higher levels of
vagal stimulation, and this response is also mimicked by the model.
Here, an ACh-sensitive K+ current
is involved. The well-known phase-resetting response of the SAN cell to
single and periodically applied vagal bursts of impulses is also
simulated in the presence and absence of the
-agonist isoprenaline.
Finally, the responses of the SAN cell to longer continuous trains of
periodic vagal stimulation are simulated, and this can result in the
complete cessation of pacemaking. Therefore, this model is
1) applicable over the full range of intensity and pattern of vagal input and
2) can offer biophysically based
explanations for many of the phenomena associated with the autonomic
control of cardiac pacemaking.
action potential simulation; isoprenaline; muscarinic receptors; junctional receptor; extrajunctional receptor; phase sensitivity; phase-response curve; steady-state entrainment; cardiac pacemaker cell; whole cell voltage clamp; Hodgkin-Huxley model
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INTRODUCTION |
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DESPITE NEARLY FOUR DECADES of histological,
electrophysiological, pharmacological, and biochemical investigation,
relatively little is known regarding the ionic mechanisms underlying
the effects of vagal stimulation of the mammalian sinoatrial node (SAN)
cell. Cholinergic and adrenergic modulation of cardiac pacemaker activity continues to be a topic of considerable interest in cardiac electrophysiology and related mathematical modeling. The different types of experimental studies on the atropine-sensitive response of the
SAN to the neurotransmitter ACh can be grouped according to the nature
of input stimulus applied to the SAN cell in two different types of
preparations: 1) transient
iontophoretic pulses (5) or steady-state bath applications of ACh in
isolated myocyte preparations (22) and
2) transient or periodic vagal nerve
stimulation in isolated SAN preparations. In the second category, a
single burst stimulus consisting of 1-10 suprathreshold vagal
impulses has been applied to multicellular isolated SAN preparations,
as have periodic trains of bursts (54, 55, 84, 86). The collective evidence from both types of experiments suggests
1) a wide range in the response of
the SAN cell to ACh (0 < ACh
10 µM),
2) differences in the response of
the SAN cell to the type of ACh stimulation (i.e., vagally released ACh
vs. iontophoretic or bath application of ACh) (5, 11, 12), and
3) several ACh-sensitive receptor systems with different dose responses and dynamics in an SAN cell (23,
26, 39, 43, 72, 93). The relevant findings from both types of
experiment (isolated myocyte vs. isolated node) are summarized below;
the bath application of ACh to isolated myocytes is discussed first,
followed by vagal stimulation of the isolated SAN.
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ISOLATED MYOCYTE PREPARATIONS |
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Trautwein (93) studied the pharmacological response of dispersed
clusters of rabbit SAN cells to iontophoretically and bath-applied ACh.
These data show that relatively high doses of ACh
(10
6-10
3
M) activate a K+-sensitive ion
transfer mechanism and that this cholinergic effect is blocked by
atropine. More recently, it has been demonstrated that ACh activates
the GTPase activity of trimeric Gi proteins, initiating the dissociation of
- and 
-subunits. The

-subunits bind directly to KACh channels, causing an
increase in the muscarinic current IACh (77a). We
refer to this pathway as the "direct" pathway by which ACh
modulates the electrical activity of the SAN cell. Other studies
suggested that specific
-subunits inhibit the activation of the
KACh channel by 
-subunits (80a). The specific role
played by G proteins in modulating IK,ACh has not
been treated in our model.
A mathematical model of this muscarinic K+ current (IK,ACh) has been developed by Osterrieder et al. (72). This formulation for IK,ACh has been utilized in a number of models of the rabbit SAN cell, including those reported by Bristow and Clark (8), Michaels et al. (61), Dexter et al. (20, 21), Egan and Noble (31), Murphey and Clark (64), and Dokos et al. (28). Although additional subtypes of muscarinic receptors have been demonstrated, these models consider only the "direct" pathway mentioned above (6, 7, 63, 69). Because other muscarinic pathways play important physiological roles, a brief review of muscarinic receptor subtypes is included below based on the review of Nathanson (66).
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MUSCARINIC RECEPTOR SUBTYPES |
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Pharmacological and molecular cloning studies have shown that muscarinic ACh receptors comprise a family of at least five distinct genetic subtypes (M1-M5), which can be functionally separated into two groups: 1) M1, M3, and M5, which couple strongly to phosphoinositide hydrolysis, and 2) M2 and M4, which, among other actions, inhibit adenylate cyclase (ADC) activity (3, 32, 74). The M2 and M4 receptors couple preferentially to the Gi/o family of G proteins, whereas the M1, M3, and M5 receptors couple preferentially to the Gq family. Several groups have demonstrated that, of the five subtypes, the M2 receptor provides the most significant response to muscarinic agonists in the heart (32, 80). Current evidence suggests that the M2 receptor is negatively coupled to membrane-bound ADC through a pertussis toxin-sensitive G protein (46). Inhibition of ADC can result in reduced phosphorylation of L-type Ca2+ channels [reduced Ca2+ current (ICa)] and reduced hyperpolarization-activated current (If; see below). We call this the indirect muscarinic pathway. Additional evidence suggests that the M2-type receptor is also positively coupled to the KACh channel via pertussis toxin-sensitive Gi proteins as stated above (direct pathway).
Gallo et al. (32) employed the sensitive RT-PCR technique for assaying RNA content in M1-, M3-, and M4-muscarinic ACh receptors in guinea pig ventricle. They found that M1 is present, but not M3 or M4. Although the mammalian M5-muscarinic receptor gene has been identified by Bonner et al. (4), its level of expression in mammalian cardiac tissue is unknown. We therefore assume that the expression of the muscarinic cAMP-coupled M2 receptor in SAN tissue is much greater than any other type. Expression of the inositol 1,4,5-trisphosphate-coupled M1 receptor is considered comparatively small in SAN cells, which contain a relatively small volume of sarcoplasmic reticulum and contractile filaments. We therefore assume it to be negligible. The other receptors (M3-M5) are considered absent in nodal tissue, largely on the basis of the findings of Gallo et al. in guinea pig ventricle. Thus we assume that muscarinic receptors in the rabbit SAN cell are of the M2 type; however, they are coupled to Gi proteins that target different effector proteins, i.e., ADC in the indirect pathway and the KACh channel in the direct pathway. We therefore denote the receptors as M2/ADC and M2/KACh, respectively.
It is well known that in the presence of adrenergic tone the "indirect" effects of ACh on various membrane currents are also important, and they are mediated in part by the intracellular second-messenger cAMP. The major muscarinic ACh-sensitive receptor involved in this indirect pathway that modulates cAMP production appears to be an M2/ADC receptor (66). DiFrancesco et al. (23, 25-27) and Yatani et al. (96) provided experimental evidence showing that, at low doses, ACh inhibits the If (via the indirect muscarinic pathway), whereas at higher doses it activates IK,ACh (via the direct muscarinic pathway). Other investigators (39) have shown that If is enhanced when isoprenaline (Iso) is present in the bathing medium and that this indirect effect of Iso on If is mediated by changes in intracellular cAMP concentration ([cAMP]). Thus, when ACh is added to an SAN preparation, bradycardia is produced by activating M2/KACh muscarinic receptors or by resetting the voltage- and cAMP-dependent activation curve for If to more negative values (M2/ADC-mediated indirect pathway). Han et al. (43) presented evidence that nitric oxide (NO) is an obligatory mediator of the indirect effects of ACh in L-type Ca2+ current (ICa,L) in adult mammalian cardiac pacemaker tissue. Their findings (44) suggest that in mammalian primary pacemaker cells (in the presence of Iso), NO-mediated cholinergic inhibition of ICa,L is due to a cGMP-stimulated cAMP-specific phosphodiesterase (PDE), which hydrolyzes cAMP and thus inhibits cAMP-dependent phosphorylation of L-type Ca2+ channels. Direct and indirect effects of neurotransmitters on the strength and dynamics of several different ionic currents are discussed below.
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ISOLATED NODAL AND ATRIAL PREPARATIONS |
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In isolated sinus venosus preparations from frog and tortoise hearts, Hutter and Trautwein (48, 49) reported that vagal stimulation suppresses pacemaker potentials, greatly accelerates the repolarization of the action potential, and reduces its amplitude. Repetitive vagal stimulation at 20 Hz brought about cessation of pacemaking, hyperpolarization, and shortening of the poststimulus action potential. These experimental results formed the basis of the now classical K+ hypothesis, which holds that the effects of vagal stimulation can be attributed to an increase in membrane permeability to K+. However, similar experiments in isolated rabbit atrial preparations by Toda and West (91, 92) showed very little or no change in polarization in primary pacemaker cells. Their data suggested that the chief cholinergic effect was a reduction in the slope of diastolic depolarization. Later electrophysiological studies by Shibata et al. (82) on primary pacemaker cells within isolated rabbit SAN preparations showed that the only identifiable effect of physiological levels of vagal stimulation is a decrease in the slope of the pacemaker potential. This is not accompanied by a detectable hyperpolarization, any change in action potential duration, or any change in the rate of repolarization. However, a reduction in the maximum upstroke of the action potential (dV/dt) was also observed consistently in these studies (82). More recent multicellular experiments of this type, conducted on isolated toad sinus venosus (11) and guinea pig SAN (12) preparations, suggest that when ACh is neuronally released (rather than applied in the bath), two separate sets of muscarinic receptors may be activated.
Choate et al. (16) studied the structure and organization of cholinergic varicosities in the guinea pig SAN via electron microscopy and reported that the majority of parasympathetic varicosities form close appositions with the membranes of nearby pacemaker cells (cleft widths of ~75 nm). Synaptic vesicles were found at these regions of close apposition (16). These investigators conducted experiments on "arrested" toad sinus venosus (11) and guinea pig SAN (12) preparations and reported that vagally released or iontophoretically applied ACh elicited different electrophysiological responses in these pacemaker cells. Campbell et al. (12) propose that fundamentally different sets of ACh-sensitive receptors are utilized in each of these experimental situations. Specifically, they assume that vagally released ACh binds to junctional receptors that produce mainly a decrease in the inward Na+ current (INa) and the Na+ background current (IB,Na) (11, 12), whereas bath-applied ACh binds not only to these junctional (J type) receptors but also to more widely distributed extrajunctional receptors associated with the direct and indirect muscarinic pathways discussed previously. Cholinergic stimulation of these latter receptors produces a decrease in [cAMP] (M2/ADC mediated) and an increase in IK,ACh (M2/KACh mediated). A key observation made in these experiments was the lack of change in the vagally induced membrane hyperpolarization when Ba2+ was added to the bathing medium. Because Ba2+ is known to block IK,ACh, these investigators (11, 12) reasoned that ACh-sensitive receptors that respond to neuronally released ACh are fundamentally different from the extrajunctional muscarinic receptors of the direct and indirect pathways. Additional evidence shows that vagally induced hyperpolarization in the arrested membrane preparation is enhanced by the addition of Cs+ to the bathing medium (11, 12). This may be explained by the fact that Cs+ blocks K+ currents and strongly attenuates If, which normally opposes the hyperpolarization effect of vagal stimulation. Subsequent analyses of the conductance changes during vagal stimulation indicate a decrease in net inward current (increase in membrane resistance), and these findings have led to the suggestion that this junctional receptor decreases the total inward Na+ conductance (5, 30). In contrast, bath or iontophoretically applied ACh leads to membrane hyperpolarizations that are nearly abolished by Ba2+, prevented by Cs+, and lead to an increase in net inward current (decrease in membrane resistance).
The experimental findings of Campbell et al. (11, 12) represent a significant departure from the classical theories regarding the mechanisms involved in the response of the cardiac pacemaker cell to ACh. This work and the assumptions made regarding the roles of junctional vs. extrajunctional receptors need independent verification by other laboratories. In the interim, it is possible to provide an initial test of this hypothesis by assuming an appropriate distribution of junctional and extrajunctional ACh receptors and then simulating the consequences of different types of experimental protocols, including the bath application, iontophoretic injection, and vagal release of ACh.
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MODELING OBJECTIVES |
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Several lines of evidence suggest that at least three distinct types of ACh-sensitive pathways that are capable of modulating the electrical activity of the SAN sarcolemma: the indirect cAMP-mediated pathway, the direct pathway (IK,ACh), and the neuromuscular junction (J type) pathway. Accordingly, we have extended our original model of the single rabbit SAN cell (17) to simulate the cholinergic and adrenergic modulation of ionic currents INa, IB,Na, ICa,L, IK, INaK, and If (notation as in Ref. 17). The following elements have been added: 1) an ACh dependence of the expressions for INa and IB,Na associated with the junctional pathway, 2) an ACh-sensitive K+ current (IK,ACh) associated with the direct pathway, 3) expressions for the modulation of ADC production by Iso (stimulatory) and ACh (inhibitory) and the resulting cytosolic cAMP balance, 4) an equation describing the cAMP-mediated modulation of the activation variable (y) associated with If, and 5) equations that describe the cAMP dependence of ICa,L, IK, and INaK. The ACh-sensitive receptor associated with the cAMP modulation of ICa,L, IK, INaK, and If is the M2/ADC-type muscarinic receptor. These mathematical formulations are given in MODEL DEVELOPMENT. Their incorporation into the SAN cell model enables us to provide biophysically based explanations of the cAMP-mediated modulation of the electrophysiological activity in the rabbit SAN cell. The resultant model is henceforth referred to as the modified SAN cell model.
Our modeling focused initially on the effects of bath applications of ACh and Iso on the electrical activity of the SAN cell. Because cardiac pacemaker cells are also known to exhibit phase-resetting effects after the application of a brief stimulus (current or ACh) (59, 61, 84), we also attempted to simulate this type of functional response. Specifically, 1) the transient response of the SAN cell model was studied using a single vagal burst applied at various times during the cardiac cycle and the data were displayed in a transient phase-response curve (PRC); and 2) the steady-state responses to periodically applied vagal bursts were studied in terms of an entrainment curve (EC), which expresses the steady-state entrainment of SAN cell activity by the periodic stimulus pattern. Our computations show that 1) the typical pacemaker waveform changes that accompany ACh or Iso application to the bathing medium of the single SAN cell can be closely mimicked by this cell model, 2) the characteristics of the phase-sensitive effects (PRCs and ECs) are dependent on the amplitude and time course of the ACh waveform (upstroke velocity, peak height, and decay), 3) the sensitivity of the transient PRCs and the steady-state ECs are diminished by application of constant background levels of Iso, and 4) the model-generated responses of the SAN cell to prolonged (5 s) applications of vagal stimulation and bath-applied ACh (5 s) are intrinsically different. With regard to item 5, our modified model provides close agreement with the experimental data of Campbell et al. (12). Our computations also indicate that each muscarinic receptor type (M2/ADC, M2/KACh, and J) contributes to the PRC and suggest that the PRC may provide a means of testing the relative contribution of different receptor types, in response to different stimulation protocols (e.g., phasically related vagal stimulation or iontophoretic injection of ACh).
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MODEL DEVELOPMENT |
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The main goal of this study was to extend our model of the single
rabbit SAN cell (17), enabling it to mimic the important effects of the
second-messenger cAMP and to simulate the response of SAN cells to ACh
(12, 23, 26, 75, 82, 84) and Iso (19, 39) on the basis of experimental
findings. We consider the following effects (Fig.
1B):
1) ACh-mediated effects of the junctional (J type) receptors on
INa and
IB,Na,
2) the G protein-mediated, direct
effect of ACh on
IK,ACh via the
extrajunctional
M2/KACh muscarinic
receptor, and 3) the indirect
inhibitory effect of ACh on several membrane currents, acting through
the extrajunctional M2/ADC
receptor, resulting in an inhibition of the rate at which ADC
synthesizes cAMP. In the latter case, cAMP is assumed to have 1) a direct effect on the ionic
current If (23,
25, 26) and INaK
(19) and 2) an indirect effect
[via activation of the enzyme protein kinase A (PKA)] on
ICa,L and
IK. In the latter case, these integral membrane ion channel proteins are phosphorylated by PKA in response to changes in [cAMP].
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The original mathematical descriptions (17) of the ionic currents (i.e., INa, IB,Na, If, INaK, ICa,L, and IK) have been modified to include their known dependencies on ACh or cAMP, either directly (19, 25) or indirectly, via subsequent channel protein phosphorylation (52, 96). The modified expressions with their detailed descriptions are presented below.
Glossary
Because this model is a modification of our published SAN cell model (17), the Glossary from Ref. 17 will not be repeated. The definitions of the variables and the constants that have been added to our previous SAN cell model (17) are given here. The fundamental units are given in millivolts, nanoamperes, microsiemens, seconds, microfaradays, millimolar, and cubic millimeters. The values of specific constants are given in Tables 1-6 and in the text.isoprenaline
[cAMP], [ACh], and [Iso]
cAMP, ACh, and Iso concentrations
[cA
]
First time derivative of cytosolic [cAMP]
kADC
cAMP production rate
vPDE
cAMP degradation rate
PDE
Phosphodiesterase
KM,ACh
Half-activation [ACh]
KM,Iso
Half-activation [Iso]
FcAMP,CaL
Amplitude modulation of ICa,L conductance by cAMP
FcAMP,K
Amplitude modulation of IK conductance by cAMP
FcAMP,NaK
Amplitude modulation of maximum INaK by cAMP
V0.5
Half-activation potential of steady-state activation
(
)
IK,ACh
ACh- and voltage-sensitive K+ current
a
ACh- and voltage-dependent gating variable of IK,ACh
First time derivative of gating variable a
ACh-dependent opening rate constant
Voltage-dependent closing rate constant
K,ACh
Maximum IK,ACh
gK,ACh
Conductance of IK,ACh
ACh(t)
[ACh] as a function of time
m
Number of ACh stimuli
ti
Time of ith impulse at nerve terminations
M'
ACh stored in neural terminations due to a burst containing many closely spaced stimuli
M
Maximum ACh stored in the neural terminations
D
Diffusion coefficient of ACh in extracellular medium
x
Average distance between neural release site and receptor site on membrane surface
kh
First-order rate constant for irreversible enzymatic hydrolysis of ACh by tissue cholinesterase
fvagal
Frequency of vagal stimulation
Descriptions of the Membrane Currents Modulated by Autonomic Neurotransmitters
The electrical equivalent circuit for the modified SAN cell membrane is given in Fig. 1A. The general features of the intracellular second-messenger regulation pathways and the types of muscarinic receptors are shown in Fig. 1B. In the scheme shown in Fig. 1B, there are three types of ACh-sensitive receptors: neuronally controlled junctional receptors and two types of extrajunctional muscarinic receptors, 1) M2/ADC receptors coupled via Gi to the cytosolic enzyme cAMP and hence via PKA to a variety of other ion channels directly and 2) M2/KACh receptors coupled via Gi directly to the KACh channel. Figure 1B, inset, shows an SAN cell and the lumped representation of the vagus nerve fiber varicosity coupled with junctional receptors. We assume that the ACh released from neural varicosities activates primarily junctional receptors. However, a small amount of ACh is assumed to diffuse beyond the junctional region, subsequently activating a small portion of the extrajunctional receptor population. On the other hand, when ACh is applied in the bath, all the available ACh-sensitive receptors (regardless of type) have the potential to be activated, depending on the ACh concentration. Activated J-type receptors are assumed to modulate INa and IB,Na [analogous to the modeling studies of Edwards et al. (30)].Stimulation of
-adrenoceptors by Iso results in the activation of a
G protein (Gs) that stimulates ADC and enhances the
production of cAMP. Subsequently, cAMP may directly activate
If and
INaK and
indirectly activate
ICa,L and
IK (this latter
step involves activation of cAMP-dependent PKA before modulation of the
channel protein). In contrast to
-adrenergic stimulation, occupation of M2/ADC-muscarinic receptors by
ACh leads to activation of the inhibitory G protein
(Gi), which reduces the
catalytic activity of ADC and consequently decreases the intracellular
levels of cAMP (for review see Ref. 52). In the rabbit SAN cell, Han et al. (43) reported that the binding of ACh to muscarinic receptors results in stimulation of NO synthase (NOS) and the production of NO.
NO then stimulates guanylate cyclase, thus elevating cGMP levels,
which, in turn, activates a cAMP-specific PDE. This cGMP-activated cAMP-specific PDE hydrolyzes the Iso-elevated cAMP and decreases ICa,L (43, 44),
as well as IK,
If, and
INaK. Han et al.
further propose that NO is an obligatory mediator of the indirect
effect of ACh on
ICa,L in the
presence of Iso. The details of NO production as the result of ACh
binding to muscarinic receptors, as well as its effect on cGMP
production, are not well defined and require additional experimental study.
cAMP balance. In our model the rate of change of [cAMP] in the myoplasm results from differences in the rates of cAMP production and degradation. The rate of production (kADC) is modulated by [Iso] and [ACh], whereas the rate of degradation (vPDE · cGMP) represents the catalysis of cAMP by a cGMP-stimulated cAMP-specific PDE (2). We express this cAMP balance using the differential equation
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(1) |
3 mM) was
selected from the experimental dose-response relationships reported by
DiFrancesco et al. (23), whereas the Michaelis-Menten constant for Iso
(KM,Iso, 0.14 × 10
3 mM) was chosen
so that Iso is effective in a concentration range similar to that for
ACh. A normal value for the resting cytosolic ATP concentration was
assumed to be 3 mM, after Irisawa et al. (52). In their voltage-clamp
studies of single SAN cells, Anumonwo et al. (1) and Hagiwara and
Irisawa (39) used pipette (intracellular) solutions containing 5 mM
ATP. Using this work as a guide, we chose 3 mM as the mean ATP
concentration and assumed that 0.1% of this level is representative of
the mean [cAMP] in the rabbit SAN cell (i.e.,
[cAMP] = 3 × 10
3 mM). We also assumed a
constant cGMP concentration (i.e., [cGMP] = 2 × 10
3 mM). These
considerations effectively set the constant for the half-degradation
concentration of cAMP by PDE
(KPDE) to 6.0 × 10
3 mM. The rate
constants kADC
(8.0 × 10
3 mM/s) and
vPDE (20.0 × 10
3 mM/s) were
calculated when [cAMP] is at steady state; i.e.,
[cA
P] = 0, [cAMP] = 3 µM, [ACh] = [Iso] = 0. The parameter
PM2/ADC in Eq. 1 indicates the percentage of the
M2/ADC receptor population responding to applied ACh; i.e.,
PM2/ADC = 1 for bath-applied ACh, and
PM2/ADC = 0.02 for vagally
released ACh (vagal stimulation is assumed to affect the junctional
receptors primarily).
cAMP modulation of ICa,L and IK. When modeling the direct or indirect effects of cAMP on the ionic currents If and INaK or ICa,L and IK, respectively, we have assumed that the major input variable to modulate both of the aforementioned groups of ionic currents is [cAMP] and the output is the resultant change in the particular membrane current. As a consequence, although PKA is involved in the indirect regulation of ICa,L and IK, its effect is considered to be lumped into the conductance term in the ionic current description. Thus [cAMP] is considered to be the sole input variable in both myoplasmic pathways. Specifically, the effects of [ACh] and [Iso] on ICa,L and IK are produced via the cAMP-dependent modulation of L-type Ca2+ and K+ channel conductance (gCa,L and gK, in µS), respectively (9a, 18, 47, 52, 60, 75). Data from Petit-Jacques et al. (75) were used to guide the conductance change on ICa,L (Fig. 2A). Figure 2B shows the changes in the current-voltage relationship for ICa,L. Values for the above parameters (gCa,L and gK) associated with our model (see Tables A3 and A9 of Ref. 17) are annotated in the equations below with the subscript "control." These parameters vary with [cAMP] according to the following relationships
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(2) |
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(3) |
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(4) |
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(5) |
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cAMP modulation of If and
INaK.
If is modulated
in a fundamentally different manner, via a direct effect of
[cAMP] on the voltage dependence of its steady-state activation variable
. The ACh
dose-response data of DiFrancesco et al. (23, 26) provided the
information necessary for simulating the ACh-induced hyperpolarizing
shift in the half-activation potential
(V0.5, in mV) of
of
If. Thus
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(6) |
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(7) |
due to bath application of Iso.
Furthermore, we assumed that
changes with [cAMP] according to Eqs.
6 and 7. The
semilogarithmic graph in Fig.
3A shows
the relationship used for
V0.5 as a
function of [cAMP] superimposed on experimental data from
DiFrancesco and Tromba (26) and Hagiwara and Irisawa (39).
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-agonist-induced increase in
INaK observed in
the presence of high Ca2+
concentration
([Ca2+]i)
is mediated by a phosphorylation step via PKA. On the other hand, in
experiments on rat ventricular myocytes, Ishizuka and Berlin (53)
concluded that
INaK was not
modulated by
-adrenergic stimulation. Thus the effects of Iso on
INaK may be
species dependent (53).
ACh has also been reported to have an effect on
INaK. Iacono and
Vassalle (50) reported that ACh depresses the function of
INaK in the sheep
Purkinje fibers. Moreover, Yingst (97) reported that the cytosolic free
Ca2+ and certain intracellular
proteins (calnaktin, calmodulin, and protein kinase C) that are
associated with the changes in
[Ca2+]i
inhibit the
Na+-K+-ATPase.
In the absence of any quantitative evidence, we have assumed that, in
the rabbit SAN cell, cAMP directly stimulates INaK [in
accordance with Desilets and Baumgarten (19)] and that this cAMP
dependency may be modeled as follows
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(8) |
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(9) |
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(10) |
NaK
is the maximum pump current. We have also assumed that the kinetics of
the binding processes (e.g., binding of cAMP to a channel protein site)
are very fast relative to the activation of the particular ionic
current. Moreover, Gao et al. (33, 34) reported that
INaK is decreased
(rather than increased) by
-agonist-induced changes in the presence
of low
[Ca2+]i
(<150 nM). Accordingly, we have adopted two different equations for
the cAMP-dependent change in
INaK, depending
on whether
[Ca2+]i
is greater or less than 150 nM.
The resulting mathematical expressions (Eqs.
2-10) provide a description of the changes in
the magnitude and dynamics of the four modulated ionic membrane
currents (ICa,L,
IK,
If, and
INaK) in
response to changes in the bathing medium concentrations of ACh and Iso.
Direct modulation of IK,ACh.
We have utilized the general expression for
IK,ACh given by
Osterrieder, Noma, and Trautwein (ONT) (72) for
IK,ACh in the rabbit SAN cell. The gating variable
a(V,ACh)
in this model is governed by an opening rate constant (
) that is ACh
dependent and a closing rate constant (
) that is voltage dependent
(Fig. 3, B and
C). We have made two modifications
to the original model (72): 1) the
deactivation rate constant (
) was made faster, and
2) in our model the reversal
potential for
IK,ACh is the
calculated Nernst potential
(EK), whereas
the ONT model used a constant potential (
90 mV). These
modifications provided improved model-generated fits to the data
obtained in response to bath applications of ACh. The resulting
equations for
IK,ACh and its
ACh- and voltage-dependent gating variable
(a) are given in Table
1,1
and current-voltage relationships for
IK,ACh are shown
in Fig. 3D for a range of
[ACh] (0
[ACh]
10 µM).
IK,ACh is assumed to be activated fully by bath-applied ACh
(PM2/KACh = 1) and only to
a small degree by vagal stimulation (see Table 1).
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Neuroeffector Junction Model
Junction structure. The pattern of innervation within the rabbit SAN is not homogeneous (78), and parasympathetic nerve varicosities surround and interdigitate clusters of individual SAN cells. Canale et al. (13) suggested that an appreciable fraction of autonomic varicosities in the pacemaker region of the heart form close appositions or intimate contacts with adjacent cardiac cells but that most form en passant junctions, which lie some distance from the pacemaker cell. However, recent electron-microscopic investigations of the structure and organization of cholinergic and adrenergic varicosities in guinea pig SAN (16) indicate that the opposite may be true, i.e., only a very small proportion, rather than the majority of vesicles, form en passant contacts. At regions of close apposition, the varicosities lose part or all of their Schwann cell wrap and form neuromuscular-like junctions with the pacemaker cell. Of the 96 cholinergic varicosities studied (16), 82 were found to form close appositions to the SAN cell membrane (85.4%). The great majority of these (79 of 82) formed only single regions of apposition. The other 14 varicosities of the 96 did not form close contacts with the cell. The mean separation distance between the varicosity and the cell membrane for close contacts was 75 ± 4 nm, whereas the mean separation between the varicosity and the nearest cell was 140 ± 10 nm for noncontacting varicosities.
ACh release model. Rather than addressing the complex issue of junctional structure and the distribution of varicosities at various distances from the membrane of the SAN cell, we have taken a lumped approach consistent with our whole cell model and the microanatomic findings of Choate et al. (15, 16) and consider our cell to have a single neuroeffector junction with a junction distance of 75 nm. ACh concentration within the close-contact junction is assumed to be spatially uniform with respect to axial distance and varies only with radial distance (x) and time. As described by Bristow and Clark (8), we consider the ACh-release mechanism to be described by a single lumped Purves-type release model (76), wherein a burst of m stimuli to the vagus nerve produces a concentration ACh(t) at the outer surface of the junctional membrane given by
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(11) |
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(12) |
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(13) |
16 mol) is the amount of
ACh released per impulse, D (5.1469 × 10
11
cm2/s) is the diffusion
coefficient of ACh in the extracellular medium, x represents the average distance
between the neural release site (assumed to be 7.5 × 10
6 cm) and the receptor
site on the membrane surface, and
kh (50 s
1) is a first-order rate
constant for the irreversible enzymatic hydrolysis of ACh by the tissue cholinesterase.
Postjunctional model. Campbell et al. (12) proposed that vagally released ACh binds to junctional receptors, which results in a decrease in net inward current. In a related modeling study, Edwards et al. (30) assumed that the ionic currents INa and IB,Na are directly mediated by the neuroeffector junctional receptors (see also Refs. 5, 11, 12). We have made a similar assumption (i.e., vagal stimulation affects primarily J-type receptors, but see below). The ACh-mediated effects of the J-type receptors on the permeability of INa (PNa) and gB,Na are modeled as follows
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(14) |
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(15) |
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(16) |
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(17) |
Arrested SAN Cell
Figure 4A shows the hyperpolarizing effect of a burst of ACh stimuli [consisting of 1-9 impulses/burst; each stimulus 5 ms apart] applied to the arrested SAN cell. Sinus arrest (pacemaker inhibition) was produced by simulating ICa,L blockade by nifedipine (5, 15, 70). Noma and Irisawa (70) determined resting potential ranges for three types of arrested SAN cells: primary pacemaker cells [potential (V) =
39.6 ± 1 mV], driven nodal cells (V =
43.9 ± 1.7 mV), and
atrial cells (V =
56.0 ± 0.7 mV). Similar experimental results were obtained by Choate et al.
(15) on guinea pig SAN cells and Bramich et al. (5) on toad sinus
venosus cells, where the recorded rest potentials were
39.6 and
40 mV, respectively. Figure 4B
shows the model-generated ACh(t)
waveforms produced by "neurally" released ACh in trains
consisting of different numbers of stimuli. Figure
4C illustrates the corresponding
change in [cAMP]. The resting potential used in these
simulations was
39.8 mV. For these arrested membrane
simulations, intracellular Na+
concentration = 6.9 mM,
[Ca2+]i = 91 nM, and intracellular K+
concentration = 143 mM.
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The experimental findings of Bramich et al. (Figs. 1 and 2 in Ref. 5) on toad sinus venosus show fundamental differences between the time course of the hyperpolarization produced by vagal stimulation (7-12 V, 1.0-ms duration) and that produced by an iontophoretically applied ACh pulse. One of the important differences is that the decay of the hyperpolarization response is much faster with vagal stimulation. Bramich et al. attribute these differences to the activation of different types of ACh receptors. A previous arrested pacemaker study was conducted on the young kitten by Jalife and Moe (54). The vagal stimuli used in this study, however, were relatively intense (e.g., supramaximal stimuli of 10-15 V, 10-ms duration) and resulted in an asymmetric hyperpolarization response exhibiting a much slower decay of the hyperpolarization (Fig. 8 in Ref. 54). The associated vagal effect curves shown by Jalife and Moe indicate that ACh release was substantial and that ACh exerted an effect on pacemaker cycle length over several beats.
We have chosen a particular configuration of the three receptor types discussed previously to simulate the effects of vagal stimulation on the rabbit SAN cell. Specifically, we assume that junctional-type receptors are of the primary receptor type activated during vagal stimulation. However, we also allow for secondary activation of a small number of extrajunctional receptors via spillover from the primary vagal release site. When considering iontophoretic release of ACh from a micropipette, a different pattern is assumed, i.e., that extrajunctional receptors are the primary receptors activated. The membrane mechanisms that produce the fast decay of the hyperpolarization response are the relatively fast changes in IB,Na and INa, which are induced by ACh activation of the junctional receptor model (Fig. 4B). Thus a plausible explanation for the waveshape differences observed in experimental studies, e.g., between the vagal hyperpolarizing responses of Jalife and Moe (54) (asymmetric) and those of Bramich et al. (5) (more symmetrical), is that the fast-decaying hyperpolarization response is produced primarily by the junctional receptor response alone, whereas the asymmetric slowly decaying response represents the combined effect produced by junctional and extrajunctional receptors. With our assumed release and receptor configuration, the combined response could also be evoked under conditions of intense vagal stimulation.
Rigorous validation of our model assumptions requires data from an arrested pacemaker cell experiment that are not available. The differences between vagally and iontophoretically applied ACh responses in a mammalian species (preferably rabbit) need to be examined. An essential component of this investigation would include a sensitive means of grading vagal release of ACh [e.g., electric field stimulation (82)]. Data from such an experiment would provide a more definitive basis for the separation of receptor function. These issues are central to an understanding of parasympathetic nervous control of the heart, and until they are resolved via primary experimental evidence, modeling efforts must necessarily remain qualitative and somewhat speculative. Thus, with the model configured as discussed above, we proceed to simulate a wide variety of topics of fundamental importance to the vagal control of heart rate, including the phase sensitivity of the SAN cell to single and periodically applied vagal bursts, as well as the cell response to relatively long intervals of intense vagal stimulation.
Computational Aspects
Our rabbit SAN model assumes a cylindrical geometry [12 µm diameter, 32 µm long (95)] for the cell. The electrical equivalent circuit of the cell (Fig. 1) is described by a set of 29 first-order differential equations, 27 of which are given in Tables A1-A8 of Ref. 17. The modified equations for the ionic currents have been explained in the text, and the equations for the remaining two additional state variables ([cAMP] and a) are given in Eq. 1 and Table 1, respectively. The complete model consists of 12 equations that describe the ion fluxes across the sarcolemma; the remaining 17 are associated with 1) the material balance for three ionic species (Na+, K+, and Ca2+) in the cytosol and cleft space, 2) Ca2+ buffering, 3) formulations for the mechanisms for the uptake and release of Ca2+ by the sarcoplasmic reticulum, and 4) the material balance for [cAMP]i.The Runge-Kutta-Merson numerical integration algorithm (which includes an automatic step-size adjustment that is based on an error estimate) was used to solve these equations. The equations were coded in the C language, and SPARC workstations (SLC, ELC, and IPX) were used for all computations.
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RESULTS |
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Our published SAN cell model accurately simulates the experimental
action potential data recorded from isolated SAN myocytes (Fig. 7 in
Ref. 17). Figure 5 shows the simulated SAN
cell action potential and the underlying ionic currents for the control
case, where
ICa,L,
IK,
INaK, and
If are not
modulated (ACh = 0, Iso = 0, and
IK,ACh = 0).
Figure 5 is included for reference only; it is identical to Fig. 8 in
Ref. 17, which should be consulted for a detailed discussion of these
currents. Using the modified model, we have simulated the response of a
rabbit SAN cell under the following conditions:
1) a constant level of ACh or Iso
applied to the bathing medium (i.e., ACh or Iso = constant),
2) a discrete aperiodic ACh stimulus
[ACh(t)] elicited by a
single stimulus or a short burst of stimuli,
3) periodic application of a train of vagal stimuli containing one to nine stimuli, and
4) maintained vagal stimulation at
low and high rates. Stimulation protocols 2 and 3 have been
conducted in the presence of constant background levels of Iso in the
range 0
Iso
1 µM.
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Bath Applications of ACh and Iso
Bath-applied ACh.
Figure 6 shows the model-generated
inhibitory effects of ACh on the spontaneous activity of the SAN cell.
Figure 6A illustrates the action
potential, Fig. 6,
B-D,
shows the ionic membrane currents modulated by cAMP, and Fig. 6,
E and
F, shows the time course of
INa associated
with the junctional muscarinic receptor and the time course of
K+ current activated by the
M2/KACh-mediated response
(IK,ACh). At 10 and 100 nM ACh the cycle length of spontaneous activity is increased as
[ACh] is increased, because
1) the cAMP-dependent conductances
of ICa,L and
IK (Fig.
6B), the cAMP-dependent maximum value of INaK
(Fig. 6D), the ACh-dependent
permeability
(PNa) associated with
INa (Fig.
6E), and ACh-dependent conductance
of IB,Na are
decreased, 2) ACh inhibits
If by inducing a
hyperpolarizing shift in its activation gating variable
(Fig.
6C), and
3) the hyperpolarization resulting
from activation of
IK,ACh increases
progressively with higher [ACh] (23, 26) (Fig.
6F). This ACh-induced change in the
voltage dependence of
If is based on
the data of DiFrancesco et al. (23, 26). Their experiments showed that
low [ACh] (0 < [ACh] < 260 nM) inhibit
If via a direct (cAMP-mediated) effect. Much higher [ACh] (20-fold) are
needed to directly activate the ACh-dependent
K+ channel
(IK,ACh). At 1 and 10 µM ACh,
IK,ACh dominates
and spontaneous pacemaking is abolished (Fig.
6A; see Table
2 for changes in some membrane currents).
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