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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
|
|
(11) |
|
(12) |
|
(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
|
(14) |
|
(15) |
|
(16) |
|
(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.
|
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.
| |
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.
|
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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|
|
|
|
Bath applications of Iso.
The effects of Iso on the cycle length of the SAN cell are shown in
Figs. 8A
and 9A.
Higher Iso concentrations produce a decrease in the cycle length, since
1)
ICa,L,
IK (Fig.
8B), and
INaK (Fig. 8F) are increased by the indirect
effect of Iso that is mediated by increased cAMP levels and
2)
If is activated
to a greater extent as a result of the cAMP-dependent depolarizing
shift of its voltage-dependent activation curve
(
; Fig.
8E). Moreover, with a faster rate of
diastolic depolarization, more
ICa,T (Fig.
8C) is recruited, which contributes
to a faster pacing rate (see Table 5 for
changes in some membrane currents). With higher doses of Iso, the MDP and peak overshoot levels increase slightly. Figure
9B shows the action potential data
from Hagiwara et al. (41) at 1 µM bath Iso. A comparison of these
indexes from the model-generated action potential and the experimental
data of Hagiwara et al. (41) (Table 6) shows quite close
agreement between the data and the model. When 1 µM Iso is applied,
1) the cycle lengths of the
model-generated and experimental data (41) decrease by 24% and 22% of
their free-running (control) values, respectively,
2) the upstroke velocity increases
(model by 37.5% and data from Ref. 41 by 52%),
3) the peak overshoot increases
slightly, and 4) the MDP becomes slightly more negative than control. Thus these model-generated and
experimentally recorded responses to bath-applied Iso (1 µM) are very
similar. Although direct comparisons cannot be made, such changes in
action potential upstroke velocity, peak height, and MDP with
bath-applied Iso also closely resemble the experimental results
obtained by Brown et al. (10) on isolated rabbit SAN strips in response
to bath application of epinephrine (for review see Ref. 35). However, a
more detailed comparison of the model-generated and experimentally
recorded waveforms reveals that the specific changes induced in action
potential duration and diastolic depolarization rate by bath
application of 1 µM Iso are only qualitatively mimicked by the model.
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|
Response of SAN Model to Negative Chronotropic Stimuli
Application of a brief train of stimuli to the vagus nerve via extracellular electrodes (field stimulation; 6 stimuli at an interspike pulse frequency of 100 Hz) under conditions of
-adrenergic blockade
produces a transient slowing of pacemaker rate (negative chronotropic
effect) in an isolated rabbit SAN preparation (82). Experimental data
from Shibata et al. (Fig. 3 in Ref. 82) are shown in Fig.
10, A and
B. An identical stimulus protocol was
applied to our model of the single SAN cell by using the vagal release model (Eq. 11), and the results are
shown in Fig. 10, C and
D. The pacing rate is slowed by 32%
in the experimental data and by 36% in the model-generated results.
This vagal train stimulation also induces a reduction in the slope of
the phase 4 depolarization during the last one-third to one-half of
this phase (cf. Fig. 10, A and
C). In response to the vagal
stimulus burst, a reduction in the maximum
dV/dt
is also observed in the experimental data; however, the model predicts
only a slight reduction in the maximum dV/dt
(cf. Fig. 10, B and
D). The vagally released ACh
waveform accompanying the stimulus train is illustrated in Fig.
10E. Note from Fig. 10
1) the lack of hyperpolarization of
the MDP in the model-generated and experimental data waveforms and
2) the lack of a measurable change
in the action potential duration or the repolarization phase of the
action potential. These findings are also in general agreement with
those of Toda and West (91, 92). If the vagal effect is mediated solely
by a muscarinic K+ current, then
it would be expected that the repolarization of the action potential
would be affected and hyperpolarization of the MDP would occur. The
absence of these electrophysiological changes points directly to other
mechanisms, perhaps including additional muscarinic receptor subtypes
and novel postjunctional conductance mechanisms. It is also important
to note that Shibata et al. did observe the classical hyperpolarization
effects associated with vagal stimulation at excessive nonphysiological
rates of vagal stimulation. Although this confirms previous findings
(54, 58, 86), it may also call into question the stimulation protocols used to study "vagal effect" in many of these
studies.
|
Response of the SAN Cell Model to Single and Periodically Applied Vagal Stimuli
PRCs. The dynamic behavior of cardiac pacemaker cells in response to brief electrophysiological perturbations (e.g., synaptic currents) is strongly phase sensitive. Mathematical "phase-resetting" techniques have been employed to analyze the dynamic behavior of this oscillatory system (experimental studies in Refs. 29, 51, 54, 55, 59, 77, 84, and 86-89 and modeling-based studies in Refs. 8, 21, 37, 38, 61, 62, 64, and 83; for an introduction to these analytic methods see Refs. 36 and 83). The phase sensitivity of our SAN cell model to simulated cholinergic neural stimuli can be demonstrated in terms of transient PRCs and steady-state ECs (see below). It is well known that the adrenergic positive chronotropic effect develops only after pronounced latency. Spear et al. (86) reported a latency of 1-1.5 s (several heartbeats) in rabbit SAN. Consequently, phase-sensitive effects are unlikely, and therefore only changes in background levels of adrenergic tone are considered here.
PRCs are constructed by plotting the phase (
) of the applied
stimulus vs. the resulting change in the cycle length (
P) of SAN
cell activity. These quantities are normalized relative to the period
of the free-running SAN cell activity
(P0). The stimulus is applied at
a time ts, which
is varied from the beginning of the action potential upstroke
(tup) to a
maximum value of P0 (the control
period of the free-running SAN cell activity). These quantities are
defined as follows
|
(18) |
|
(19) |
Phase sensitivity of the component receptors.
To gain information concerning the contribution of each class of
muscarinic response to the phase sensitivity of the SAN cell, we first
simulated the activation of each receptor type separately, by means of
a single rectangular pulse of ACh (10 µM, 16 ms), and then
constructed the associated PRCs (Fig. 11,
A and
C). Although this stimulus waveform
is highly idealized, it represents a brief impulselike perturbation
that can reveal the phase sensitivity of the receptor type without
adding time dependence of its own. In Fig.
11A the
M2/ADC receptor exhibits a
relatively constant delay over the interval 0 <
< 0.35 and tapers off beyond that region. For comparison, the ionic
membrane currents
ICa,L and INa are shown on
the normalized time scale in Fig. 11B
on two different ordinate scales. The region where this
receptor-mediated phenomenon has its effect is also the region where
ICa,L exerts
considerable influence on the upstroke and peak regions of the action
potential. After ACh application,
ICa,L is
diminished by a decrease in [cAMP], which is mediated by
M2/ADC receptor activation.
Because ICa,L is
decreased, membrane potential is not brought to the firing threshold as
quickly as in the control case, and consequently the period (cycle
length) is lengthened.
If is also
diminished by ACh activation of the
M2/ADC receptor and contributes
to this effect. Figure 11A also
shows the PRC associated with activation of the J-type receptor, which,
when activated, decreases
INa (Fig. 11B) and
IB,Na. Our
simulations show that, of the two currents, IB,Na contributes
to the phase sensitivity only to a minor degree. This observation
agrees with the simulation results of Edwards et al. (30).
|
P < 0) and phase delay
(
P > 0).
Figure 11A shows that rectangular
pulse stimulation of the M2/ADC-
and J-type receptors produces primarily phase delay (although the
J-type PRC shows a very small region of phase advance). The underlying
mechanism is a reduction in an inward current(s). In contrast, the PRCs
produced in response to rectangular current or ACh pulses (activation
of IK,ACh) are essentially biphasic, with phase
advance for stimuli delivered earlier in the cycle and phase delay if
delivered later. The underlying mechanism is the introduction of a
stimulation-based current (either a hyperpolarizing current pulse or
IK,ACh) that is
not present in the free-running cell under control conditions. Of the
three types of responses, only the activation of
IK,ACh can produce a strong biphasic PRC to
rectangular pulse stimulation. These responses also exhibit maximum
sensitivity in different portions of the cardiac cycle. The
M2/ADC-mediated response has its
effect in the action potential range of
, whereas the J- and
M2/KACh-mediated responses have their major
effects in the pacemaker region. The peak response of the J receptor
occurs at smaller values of
than the peak for
IK,ACh (M2/KACh). In
response to the same input ACh pulse, the peak change in period
produced by IK,ACh dominates that of the other two
receptor types (note ordinate scales). However, this is an idealized
case, wherein all three receptor types are equally weighted (equal
access to ACh).
The waveshape of any stimulus has a pronounced effect on the shape of
the PRC. A simple demonstration is obtained by lengthening the stimulus
pulse (current or ACh). As it is made longer, its duration becomes a
more significant fraction of P0,
the shape of the PRC is altered, and the relationships between the PRC
and the underlying currents (as in Fig. 11,
A and
B) are shifted and become less
clear. More realistic ACh waveforms may be better characterized by
other functions of time (e.g., a Gaussian). Such waveforms often occupy
a much more significant fraction of the free-running cycle length
(P0) than the brief pulse and,
consequently, produce PRCs that are more spread out in phase and are
primarily monophasic (delay only).
Experimentally derived PRCs from isolated atrial or SAN preparations
with vagal supply intact tend to be monophasic rather than biphasic.
Originally, Jalife and Moe (54) demonstrated two types of PRCs in the
young kitten: monophasic (only phase delay) and biphasic (a small
segment of phase advance and a large segment of phase delay). Later
studies by Jalife et al. (55, 84) on rabbits show only monophasic PRCs
associated with vagal stimulation. Important differences in these early
and late studies are the preparations and stimulation methods used: the
isolated atrium-vagus nerve preparation with supramaximal stimulation
of the right vagal trunk (54) vs. the isolated sinus node preparation and more localized postganglionic vagal field stimulation (55, 84). In
the former case, supramaximal stimulation produces higher ACh levels at
the cell membrane; therefore, IK,ACh is likely to be activated more strongly. If ACh levels are sufficiently high, the
PRC would be IK,ACh dominated and biphasic. Thus
this maximum response of all the parasympathetic elements of the nerve
trunk would tend to flood the node with ACh and mask the more subtle rate change responses obtained in the field stimulation experiments of
Shibata et al. (82). These latter responses are presumably mediated by
a non-K+ current mechanism.
Transient PRCs obtained with single-burst stimulation.
Figure
12A
shows the model-generated PRCs constructed by utilizing an increasing
number of stimuli delivered within the brief vagal burst. In Fig.
12A, within the family of curves in
the range 0 <
< 0.54 there is a gradual increase in the cycle
length with increasing phase, which terminates with the maximum slowing
of the cycle length at maximum
(
max). This is
followed by a relatively rapid decline in cycle length with increasing
phase over the interval 0.54 <
< 0.80. This peak at
max coincides with the early phase of diastolic
depolarization (Fig. 12C), where
INa normally
begins to increase. The "no-effect zone" follows in the interval
0.80 <
< 1. The family of PRCs shown in Fig.
12A grades with increasing numbers of
ACh impulses per burst (i.e., 1-9), causing progressively more
inhibition. The response begins to exhibit a decrease in peak response
beyond three impulses per burst. The intraburst stimulus frequencies
used in these simulations were chosen to be similar to those employed
in experimental investigations of the phase sensitivity of cardiac
pacemaker cells (29, 51, 54, 55, 59, 62, 84, 86-89).
|
< P0.
As stated by Demir et al. (17), our model is intended to mimic the
electrophysiological responses of a representative transitional cell
from a region bordering the primary pacemaking region. Cells from this
region are assumed to exhibit anatomic and electrophysiological properties that are quite similar to those of the primary pacemaker region (17). Kodama and Boyett (57) showed that the rabbit SAN contains
a number of cell types [nominally true pacemaker, transitional
and junctional (near border with atrium) cells]. The action
potentials recorded from these cells differ considerably, reflecting a
different contribution/expression of ionic currents. It would seem
logical to assume that these cells also have different PRCs, although
there are very few data to support this assumption. One study that does
give preliminary indications that this may be the case is the study of
Slenter et al. (84), who constructed PRCs from action potential data
obtained from two different nodal cell types within an isolated rabbit
SAN preparation. These investigators employed localized field
stimulation [train of 11 pulses, each 0.1-ms duration at 200 Hz
(84)], and microelectrode recordings were obtained from two sites
(one in the dominant pacemaker region and the other in the transitional
septal border region of the SAN). Mean PRCs were constructed for each
cell type and are shown in Fig. 5A of
Ref. 84 (black dots, dominant pacemaker cell; open circles, septal
border cell; n = 13). A direct
comparison cannot be made between our PRC of Fig.
12A and the PRCs of Slenter et al.,
since the latter are obtained from a preparation where the two cells
studied are coupled via a multicellular medium. The septal border cell
exhibits latent pacemaker activity and is in effect driven by the
dominant pacemaker cell. The two cells, when uncoupled, would exhibit
different PRCs. Our single SAN cell model has a PRC that is similar to
that of the dominant pacemaker cell. The field stimulation protocol
utilized in Ref. 84 corresponds (approximately) to that utilized by
Shibata et al. (82), and although the pacemaker rate changed,
pronounced hyperpolarization effects (lowering of MDP) were not
observed (see Fig. 3C in Ref. 84). As
previously discussed, this would implicate reduction of pacing rate via
the reduction of an inward current, perhaps by a J-type receptor
mechanism. It seems possible also that the "dominant pacemaker"
PRC of Slenter et al. is a J receptor-dominated PRC.
In comparing Fig. 12A with Fig.
5A of Ref. 84 (black dots), there is
reasonable agreement regarding the extent of the no-effect interval and
the particular phase at which peak delay occurs, but there is also a
distinct lack of agreement in the peak magnitude achieved and the
magnitude of phase delay associated with smaller values of phase, i.e.,
0 <
< 0.4. Our model-generated PRC (Fig. 12A) is mainly due to J- and
M2/ADC-type receptors, which
contribute to the "shoulder" of the PRC in this range. We
consider the role played by IK,ACh in single-burst
stimulation to be minimal. Under other stimulation protocols, where ACh
levels are higher, IK,ACh contributes more strongly
and its peak response occurs at higher values of phase (e.g., 0.54 <
< 1.0). At high [ACh], however, IK,ACh dominates the responses of the other two
receptors, drastically changing the shape of the PRC.
Inhibition curves. In 1934, Brown and Eccles (8a, 9) investigated the effects of phasic vagal stimulation on heart period in the cat. They presented their data in the form of inhibition curves (ICs), which represent the effect of a single vagal stimulation on the heart period in which it occurs, as well as subsequent heart periods, until the effect of the stimulus dies. Many modeling studies have included IC representations (for a review see Ref. 83). Because the information contained in the IC and PRC is, to a certain extent, redundant, ICs are not included in this study. Instead, our transient and steady-state results are presented in the form of PRCs and ECs, respectively. Because our transient PRCs in Fig. 12A are monophasic, the associated ICs would be monophasic as well.
ECs.
The steady-state response of the SAN cell to trains of periodically
applied ACh stimuli is often plotted in terms of ECs (55). In the
construction of our plots, we assume that transient responses caused by
sudden application of ACh pulses decline completely within 75 cycles.
While the repetitive pulses are applied, the average value of the
period calculated over the following 25 cycles (after 75 cycles) is
plotted in the steady-state EC shown in Fig. 13.
|
[Iso]
1 µM) the various entrainment zones each tend to
overlap and are easily connected by a straight line. For the Iso-free case (0 nM), P0 is indicated on
the diagram. Arrows are used to delineate the upper and lower limits of
the 1:1 entrainment zone at three different concentrations (0, 25, and
50 nM). In the Iso-free case, two leftwardly directed arrows are used
to mark the peak and minimum values of period within the entrainment
zone. Note that the lower arrow of the pair lies at the point
(P0,P0),
which is consistent with the fact that the PRC of Fig. 12 is monophasic (delay only). It is only with more pronounced vagal stimulation (higher
levels of ACh; biphasic PRC) that the heart can be accelerated (period < P0). Thus it is only with
strong vagal stimulation, characterized by an
IK,ACh-dominated biphasic PRC, that the phenomenon known as "vagal paradox" (59) is observed.
Differences in Responses of the SAN Cell Model to Vagally Released and Bath-Applied ACh
As discussed in MODEL DEVELOPMENT, experimental evidence by Bywater et al. (11) and Campbell et al. (12) suggests that there are significant differences in the response of cardiac pacemaking cells to bath-applied and neuronally released ACh. Our simulations are based on the following assumptions: 1) vagally released ACh activates primarily junctional receptors, whereas the extrajunctional M2/ADC- and M2/KACh-mediated responses are activated only to a minor degree; and 2) bath application of ACh can activate all types (subsets) of muscarinic receptors. Moreover, we assume that the cytosolic cAMP changes resulting from the indirect (M2/ADC mediated) effect of ACh are slower than the membrane current changes produced by activation of the junctional receptors or the direct (M2/KACh mediated) type of muscarinic responses. We test these assumptions by comparing the model-generated response to a variety of vagally released and bath-applied ACh waveforms with experimentally obtained data (12).The effects of a vagal burst consisting of nine impulses delivered
repetitively for 5 s were calculated for low (2 Hz), medium (10 Hz),
and high (30 Hz) frequencies. These results were then compared with
those resulting from the bath application of a trapezoid-shaped pulse
of ACh (100 µM, 5 s). These computations are shown in Fig. 14. Overall, they are quite similar to
the experimental results reported by Campbell et al. (12) in guinea pig
SAN. Figure 14A shows that during the
2-Hz vagal stimulation the SAN cell beats slowly and the peak overshoot
of the action potentials decreases as a result of the cAMP-mediated
decrease in ICa,L
in response to ACh. The intermediate (10 Hz) vagal frequency
stimulation of the SAN cell (Fig.
14B) causes pacing to stop. Membrane
potential settles to a value that lies positive relative to the MDP. As vagal stimulation continues, pacing ultimately resumes, illustrating the phenomenon of "vagal escape." Figure
14C shows the effect of high-frequency
(30 Hz) vagal stimulation. Pacing stops and the membrane potential of
the quiescent "preparation" is depolarized relative to the MDP.
For vagal stimulation frequencies >25 Hz, we assume that there is a
"spillover" of neurally released ACh; i.e., at these higher
frequencies [ACh] in the junctional region is more
pronounced, and a larger fraction of the receptors coupled to
IK,ACh are activated because of the diffusion of
ACh to the extrajunctional receptors. In this case, an algorithm is
used to increase the fraction of M2/KACh
receptors as a function of vagal stimulation frequency (see Table 1 and
particularly the relationship for
PM2/KACh). Bath
application of ACh (100 µM, 5 s), which is represented by a
trapezoidal-type waveform with a rate constant of 5 s
1 for the removal of ACh,
produces arrest of spontaneous activity at membrane potential levels
that are hyperpolarized relative to the MDP (Fig. 14). After the
bath-applied ACh is "removed," ~3.5 s are required to return to
the control spontaneous beating rate. In this latter simulation, we
assumed that, during the 5-s interval indicated, 100% of the
M2/ADC,
M2/KACh, and J receptors are activated via
the bath-applied ACh.
|
| |
DISCUSSION |
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|
|
|---|
Our rabbit SAN cell model can quite accurately simulate the responses
of a rabbit SAN pacemaker cell to cholinergic and adrenergic agonists.
This is made possible by a simplified mathematical characterization of
the intracellular biochemical pathways mediating these effects, specifically 1) the direct effect of
ACh on the muscarinic G protein-mediated K+ channels
(IK,ACh),
2) the indirect effects of bath
applications of ACh and Iso on [cAMP], and
3) the effect of neuronally released ACh on junctional receptors, which in turn modulate the inward currents
INa and
IB,Na. The cAMP
effects consist of modulations of the maximal conductances and, in some
cases, changes in the time constants
ICa,L,
IK, and
INaK. In
addition, the voltage-dependent activation characteristic
(
), which governs
If, is shifted by
[cAMP]. Simulation of cholinergic stimulation of the model is made possible by assuming that vagally released ACh activates mainly
junctional receptors, whereas bath-applied ACh affects junctional and
extrajunctional receptors equally. This model was subjected to a wide
range of tests, including 1) bath
applications of ACh and Iso (Figs. 6-9),
2) aperiodic and periodic vagal
stimuli (Figs. 10-13), and 3)
prolonged vagal stimulation at different frequencies (Fig. 14). In all
cases, there was qualitative agreement with experimental data. During
all these tests the fundamental SAN cell model parameters remained
fixed, and only the modes of applying ACh to the putative, distinct ACh
receptor types were changed. Taken together, these simulations
demonstrate that our model is capable of representing a wide range of
experimental data that are typical of single- and multiple-cell (e.g.,
isolated SAN and intact animal) preparations.
Comparison of Models
Several (8, 20, 21, 28, 31, 61, 64, 72) models of the muscarinic IK,ACh in rabbit SAN cell have been developed. The ONT model (72) includes a description of the kinetics of ACh binding to a muscarinic receptor that controls the activation of an inwardly rectifying K+ current. Subsequently, this IK,ACh model has been used by several groups (61, 64). Egan and Noble (31) employed the data of Sakmann et al. (79) to develop an expression for IK,ACh and subsequently incorporated it into a modified version of the model of Noble and Noble (68). Egan and Noble concluded that, with ACh application, inhibition of a slow inward current was needed in addition to an increase in IK,ACh. In their simulations, they decreased the conductance of the slow inward current in response to ACh application and increased the conductance for IK,ACh. Dokos et al. (28) also utilized the IK,ACh equations of the ONT model, which were incorporated into the SAN model of DiFrancesco and Noble (24).Most of these models have assumed that the only vagally induced current involved in the parasympathetic control of the SAN is IK,ACh. However, the recent experimental data of Edwards et al. (30) question this assumption. Using an organic Ca2+ blocker to produce cardiac arrest and a Ba2+ concentration sufficient to block IK,ACh, they report that the hyperpolarizing effects of vagal stimulation are not changed significantly from control conditions. Furthermore, measurements of membrane conductance changes during stimulation lead to the suggestion that vagally released ACh decreases the inward currents INa and IB,Na (5, 30). Recently, Edwards et al. and Bramich et al. (5) modified the SAN model of Noble and Noble (68) for the purpose of simulating pacemaker action potentials from the sinus venosus region of the toad heart. They tested the hypothesis that vagal inhibition of pacemaker cells results from a suppression of INa and IB,Na and achieved quite close agreement between model-generated and experimental data. Decreasing IB,Na alone did not produce acceptable results (30). Our simulation results are consistent with these findings.
Our model differs from those mentioned above in several respects.
1) It is based on our model of the rabbit SAN cell, which, in turn, was formulated on quantitative voltage-clamp data on single isolated myocytes. The cell is placed in a "representation" of its normal milieu (surrounded by other cells and separated from them by a very small cleft space).
2) The modified model contains a material balance expression for intracellular cAMP, and this balance is used to modulate the activity of several ionic current levels and INaK. The cAMP balance can be modulated by Iso and ACh via functional relationships that loosely represent the appropriate G protein-mediated pathways for modulating the ongoing activity of membrane-bound ADC. We assume that the muscarinic receptor that acts to decrease the level of cytosolic cAMP is the M2/ADC receptor (indirect muscarinic pathway). Thus, unlike the models mentioned above, it provides descriptions for the adrenergic and cholinergic modulation of specific ion channels (ICa,L, IK, and If) as well as INaK.
3) The ACh sensitivity of the SAN cell is modeled in terms of three receptor-mediated pathways: the indirect (M2/ADC mediated) pathway discussed above, the classical direct (M2/KACh mediated) pathway, which is described in our model using a modified ONT model (72), and a neuromuscular junction formulation, which describes the vagal innervation of the SAN cell. The latter is based on the recent microanatomic findings of Choate et al. (16) in guinea pig SAN, which show that a very large portion of the parasympathetic varicosities form a single organized neuroeffector contact with a pacemaker cell. This possibility has not been included in previous models of vagal nerve terminal endings and neurotransmitter release.
4) The coupling of the vagal neuroeffector junction with specific ion channels follows the lead of Edwards et al. We have assumed that the junctional receptors modulate inward currents, i.e., INa and IB,Na, rather than the muscarinic current IK,ACh, as is assumed in many other models. In contrast, the M2/KACh receptor associated with IK,ACh is considered to be an extrajunctional receptor that is exposed to the cleft space medium and its contents. Therefore, it is not considered to be an integral part of the specialized postjunctional membrane of the neuroeffector junction.
5) We have assumed that junctional-type receptors represent the major receptor type activated during vagal stimulation. However, provision is made for the activation of a small number of extrajunctional receptors via spillover from the primary vagal release site. When considering iontophoretic release of ACh from a pipette, a different receptor configuration is assumed, i.e., that extrajunctional receptors are the primary receptors activated. These assumptions are based on the experimental findings of Bramich et al. (5), who show that there are fundamental differences in the time course of the hyperpolarization response produced by vagal stimulation and by an iontophoretically applied ACh pulse.
One benefit that accrues from the assumption of this particular form of junctional model is that it provides a mechanism for explaining directly relevant experimental data (82) that demonstrate the sensitive, perhaps more physiological, control of pacemaker rate by ACh. As indicated in the introduction, the experimental data of Shibata et al. (82) provide evidence against a K+ current mechanism for reducing rate at low [ACh]. Partly for that reason, the junctional mechanism utilized in this study reduces rate by reducing an inward current. Figure 10 shows that the model fits these data quite closely.
Figures 7 and 9 show that our model provides acceptable fits to bath-applied ACh and Iso. In addition, Figs. 11 and 12 show that the model is able to simulate the dynamic phase-sensitive behavior of the SAN cell to single and periodically applied vagal bursts in the presence and absence of Iso. In the present study, comparisons with experimentally derived PRCs from rabbit SAN (84) are qualitative. Often PRCs have different peak magnitudes and shapes, which in the current model may be explained in terms of the relative densities (or efficacy) of receptors or the ion channels/G proteins associated with them.
Clearly, an issue that needs clarification is the relative expression levels/patterns of the different extrajunctional and junctional receptors that are present in the SAN cell as well as the specific currents that are influenced. Figure 11 suggests that individually these entities differ in their phase sensitivity and that, when they are excited in combination, can have effects that determine the shape of the PRC. Differences in the shape of the PRC obtained under different stimulation protocols could prove to be useful in determining the relative strengths of receptor types expressed in a given SAN cell.
The model-generated results simulating SAN cell responses to prolonged periodic stimulation at different frequencies agree quite well with microelectrode recordings from isolated, multicellular guinea pig SAN preparations made with the vagus nerve intact (12). The simulation asks the question, If all the cells within the SAN were identical and were innervated identically, would the single representative cell adequately represent the electrical activity of the isolated SAN? Figure 14 shows that the major features of the experimental data from guinea pig SAN (12) are indeed mimicked by this vagally driven single-cell model. This includes the demonstration of the complete cessation of SAN cell activity with 1) 30-Hz vagal stimulation for 5 s and 2) bath-applied 100 µM ACh for a similar time period. The time course of the effects and the cell membrane potential in the quiescent (arrested) state agree very well with the data. At lower stimulation frequencies the phenomenon of vagal escape is observed (Fig. 14B, 10 Hz; resumption of beating activity in the face of continued vagal stimulation).
Model Limitations
Some important limitations of this model of autonomic regulation of the rabbit SAN cell are as follows.1) The microanatomic distribution of nerve varicosities has not been described in detail for rabbit SAN. In an early study using random sections, Hartzell (45) reported that the distribution of varicosities in the amphibian heart is random. More recent microanatomic studies using serial sections by Klemm et al. (56) describe only organized junctions in the amphibian heart. Other serial section studies describe neuromuscular junctions in the mammalian (guinea pig) heart (16). Although detailed microanatomic studies have not been reported for the rabbit heart, we have assumed the existence of such junctions. Accordingly, we have formulated a simplified model of the parasympathetic neural terminations. More detailed microanatomic information regarding the geometry and distribution of these putative junctions on the rabbit SAN cell membrane is essential for verification of the microanatomic details and the structure of our junctional model.
2) Further experimental data are needed to firmly establish the identity of the junctional and extrajunctional muscarinic receptors, designated as J and M2/ADC and M2/KACh, respectively. Our assumptions may therefore need to be modified as results relevant to other possibilities become available. For example, specific spatial distributions of the relevant ion channels, ADCs, and G proteins in junctional and/or nonjunctional regions of cardiac pacemaker cell membranes remain to be demonstrated. In addition, the pathways described may interact in ways that are at present poorly understood.
3) On the basis of the vagal stimulation experiments of Campbell et al. (12), our model suggests an important role for a neuroeffector junction receptor that is functionally connected to INa and IB,Na. In the model this mechanism is important for the sensitive vagal control of heart rate in the absence of hyperpolarization (no enhancement of the MDP) as in the data of Shibata et al. (82). The proposed functional mechanism needs experimental verification in a variety of mammalian species and thorough examination as to receptor type and ionic current mechanisms.
4) We have assumed that our SAN cell is representative of a transitional cell located close to the primary pacemaking region of the SAN. Within that local region, we have assumed that all SAN cells are identical. The experimental data of Kodama and Boyett (57) show that there are regional differences in electrophysiological behavior within the rabbit SAN. Additional quantitative voltage-clamp data are needed that would provide information on the ionic mechanisms (e.g., expression of different types of ionic membrane currents and their relative strengths) underlying the regional differences in recorded action potentials. The effects of vagally released and bath-applied ACh may also be different in the different SAN cell types, since they have different complements of ionic membrane currents. There are regional differences in the distribution of parasympathetic nerves as well (78).
5) The mathematical descriptions utilized in the model to simulate the G protein-mediated effects of muscarinic agonists on ion channels and the synthesis/degradation of cAMP are useful, but crude, approximations. As more quantitative data describing the physical biochemistry, substrate, and Ca2+ dependence of these enzymes in the myoplasm become available, these aspects of our model will need to be updated and refined.
6) Cavalie et al. (14) reported that a stimulatory G protein (Gs) and PKA stimulate ICa,L in guinea pig ventricular myocytes. Their results show that the effects of Gs and PKA are not additive. These results also suggest that Gs primes ICa,L for cAMP-dependent phosphorylation and thus potentiates the effects of PKA. The direct effects of Gs (or Gi) on ICa,L need experimental clarification.
7) Takano and Noma (90) reported
that
-receptor-operated
Cl
current
(ICl) was
insignificant in atrial and SAN cells but was prominent in rabbit
ventricular myocytes. However, the earlier findings of Seyama (81) on
rabbit SAN cells suggested the presence of
ICl. For this
reason, ICl has
been neglected in the model, but additional data are needed to clarify
this issue.
8) Additional data describing the
effects of Iso on the
Na+-K+
pump are needed. Desilets and Baumgarten (19) reported that Iso
directly stimulates
INaK in rabbit
ventricular myocytes, and Gao et al. (33, 34) concluded that the
-agonist-induced increase in
INaK in the
presence of high
[Ca2+]i
(>150 nM) is mediated by the cAMP-dependent PKA in guinea pig ventricular myocytes. In contrast, Ishizuka and Berlin (53) found that
-adrenergic stimulation does not regulate the
Na+-K+
pump function in rat ventricular myocytes. Our approach is based on the
data of Desilets and Baumgarten. Additional experiments aimed at
clarifying this issue in rabbit SAN are needed.
9) Quantitative measurements of [cAMP] are needed in isolated SAN cells.
10) Recently, Han et al. (43) demonstrated that the cholinergic inhibition of ICa,L in isolated rabbit SAN cells can be mimicked by an NO donor and that ACh cannot reduce ICa,L if NOS is inhibited. In this scheme, NO-activated guanylyl cyclase elevates intracellular cGMP, which reduces myoplasmic cAMP levels by action of a cGMP-stimulated cAMP-specific PDE. Thus cGMP inhibits cAMP-dependent phosphorylation of the L-type Ca2+ channel. Our model accounts for the effect of cGMP on [cAMP], but since details regarding how NOS is activated after application of muscarinic agonists are lacking, the cGMP concentration is assumed to be constant and NO is not modeled as a dynamic second messenger. As new data become available, better models of this potentially important regulatory pathway will be developed.
11) The activity of the sarcoplasmic
reticulum uptake current
(Iup) is known
to be increased when the regulatory protein phospholamban is
phosphorylated by
-adrenergic stimulation or by
Ca2+-calmodulin (71). We have not
modeled the specific phospholamban-mediated effect on
Iup. However,
increases in
[Ca2+]i
due to cAMP-induced
ICa,L do increase
Iup in the model.
12) Given the broad scope of this modeling study, a detailed sensitivity analysis has not been included. The model is robust in the sense that with a single, fixed set of model parameters the model, in response to a variety of input waveforms [ACh(t) concentration waveforms in the presence or absence of Iso], is capable of mimicking a wide variety of experimental data from this field. Nevertheless, the robustness of the model should be further validated in terms of a formal parameter sensitivity analysis (for an introduction see Ref. 73). Such an analysis would help specify a measure of the influence of an individual model parameter on the complete set of model variables (i.e., the system state vector). The individual parameters could then be ranked according to their sensitivity for better manipulation in achieving good least-squares fits to data. In some instances, quantitative data are unavailable for validation of component parts of the model or are available only in part (e.g., junctional and extrajunctional receptor data). In this context the sensitivity analysis would be useful in exploring putative model behavior within the physiological range of important (sensitive) parameters.
Despite these limitations, our modified SAN cell model (17) offers the first unified approach to modeling adrenergic and cholinergic effects on SAN pacemaker activity. The mathematical expressions that characterize the junctional and extrajunctional muscarinic receptors, as well as the direct and indirect (cAMP mediated) regulatory pathways, result in a model that can provide specific, biophysically based postulates for the cholinergic and adrenergic modulation of the ionic membrane currents of the SAN cell. This model provides a starting point for a more comprehensive model of the autonomic control of heart rate in the rabbit. In its present form, this model provides a useful tool for the characterization of a wide range of experimental data; moreover, it can be used as a "predictive tool" for further experimental and theoretical studies of the autonomic control of heart rate.
| |
ACKNOWLEDGEMENTS |
|---|
The authors acknowledge the contributions and helpful comments of Liwei Peng (Baylor College of Medicine) and thank the W. M. Keck Center for Computational Biology for support.
| |
FOOTNOTES |
|---|
This work was supported in part by National Science Foundation Grant BNS-8716568 awarded to J. W. Clark. W. R. Giles is a Medical Scientist of the Alberta Heritage Foundation for Medical Research. Grants from the Canadian Medical Research Council and the Heart and Stroke Foundation of Canada supported the experimental work in W. R. Giles' laboratory. J. W. Clark held an Alberta Heritage Foundation for Medical Research Visiting Professor Award during the initial phase of this work.
1
Only changes from the previous model equations
(17) are presented. Expressions for the intracellular cAMP balance,
changes made in our previous model (17) that are needed to simulate modulation of
ICa,L,
IK,
If, and
INaK by cAMP
(i.e., gCa,L,
gK,
, and
NaK are
modified), and modulation of INa and
IB,Na by ACh
(i.e., PNa and
gB,Na are
changed) are presented in MODEL
DEVELOPMENT. Formulations utilized for simulating the time course of [ACh] in the computations of transiently and
periodically applied vagal stimuli are also given in the text. Table 1
describes the muscarinic K+
current
(IK,ACh). Data
and simulations for bath-applied ACh and Iso concentrations are
compared in Tables 2-6. Units used in the simulations are
millivolts, nanoamperes, microsiemens, seconds, mircofaradays,
millimolar, and cubic millimeters. It is assumed that the temperature
for these computations is 37°C. Other specific units in this
modified SAN model are given in Tables 1-6.
Address for reprint requests and other correspondence: J. W. Clark, Dept. of Electrical and Computer Engineering, Rice University, PO Box 1892, Houston, TX 77251-1892 (E-mail: jwc{at}rice.edu).
Received 5 June 1995; accepted in final form 19 October 1998.
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