INTRODUCTION

TOP ABSTRACT INTRODUCTION ISOLATED MYOCYTE PREPARATIONS MUSCARINIC RECEPTOR SUBTYPES ISOLATED NODAL AND ATRIAL... MODELING OBJECTIVES MODEL DEVELOPMENT RESULTS DISCUSSION REFERENCES

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.

	ISOLATED MYOCYTE PREPARATIONS

TOP ABSTRACT INTRODUCTION ISOLATED MYOCYTE PREPARATIONS MUSCARINIC RECEPTOR SUBTYPES ISOLATED NODAL AND ATRIAL... MODELING OBJECTIVES MODEL DEVELOPMENT RESULTS DISCUSSION REFERENCES

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 (10⁶-10³ 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 G_i proteins, initiating the dissociation of - and -subunits. The -subunits bind directly to K_ACh channels, causing an increase in the muscarinic current I_ACh (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 K_ACh channel by -subunits (80a). The specific role played by G proteins in modulating I_K,ACh has not been treated in our model.

A mathematical model of this muscarinic K⁺ current (I_K,ACh) has been developed by Osterrieder et al. (72). This formulation for I_K,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).

	MUSCARINIC RECEPTOR SUBTYPES

TOP ABSTRACT INTRODUCTION ISOLATED MYOCYTE PREPARATIONS MUSCARINIC RECEPTOR SUBTYPES ISOLATED NODAL AND ATRIAL... MODELING OBJECTIVES MODEL DEVELOPMENT RESULTS DISCUSSION REFERENCES

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 G_i/o family of G proteins, whereas the M₁, M₃, and M₅ receptors couple preferentially to the G_q 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 (I_Ca)] and reduced hyperpolarization-activated current (I_f; see below). We call this the indirect muscarinic pathway. Additional evidence suggests that the M₂-type receptor is also positively coupled to the K_ACh channel via pertussis toxin-sensitive G_i 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 G_i proteins that target different effector proteins, i.e., ADC in the indirect pathway and the K_ACh channel in the direct pathway. We therefore denote the receptors as M₂/ADC and M₂/K_ACh, 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 I_f (via the indirect muscarinic pathway), whereas at higher doses it activates I_K,ACh (via the direct muscarinic pathway). Other investigators (39) have shown that I_f is enhanced when isoprenaline (Iso) is present in the bathing medium and that this indirect effect of Iso on I_f is mediated by changes in intracellular cAMP concentration ([cAMP]). Thus, when ACh is added to an SAN preparation, bradycardia is produced by activating M₂/K_ACh muscarinic receptors or by resetting the voltage- and cAMP-dependent activation curve for I_f 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 (I_Ca,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 I_Ca,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.

	ISOLATED NODAL AND ATRIAL PREPARATIONS

TOP ABSTRACT INTRODUCTION ISOLATED MYOCYTE PREPARATIONS MUSCARINIC RECEPTOR SUBTYPES ISOLATED NODAL AND ATRIAL... MODELING OBJECTIVES MODEL DEVELOPMENT RESULTS DISCUSSION REFERENCES

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 (I_Na) and the Na⁺ background current (I_B,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 I_K,ACh (M₂/K_ACh 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 I_K,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 I_f, 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.

	MODELING OBJECTIVES

TOP ABSTRACT INTRODUCTION ISOLATED MYOCYTE PREPARATIONS MUSCARINIC RECEPTOR SUBTYPES ISOLATED NODAL AND ATRIAL... MODELING OBJECTIVES MODEL DEVELOPMENT RESULTS DISCUSSION REFERENCES

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 (I_K,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 I_Na, I_B,Na, I_Ca,L, I_K, I_NaK, and I_f (notation as in Ref. 17). The following elements have been added: 1) an ACh dependence of the expressions for I_Na and I_B,Na associated with the junctional pathway, 2) an ACh-sensitive K⁺ current (I_K,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 I_f, and 5) equations that describe the cAMP dependence of I_Ca,L, I_K, and I_NaK. The ACh-sensitive receptor associated with the cAMP modulation of I_Ca,L, I_K, I_NaK, and I_f 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/K_ACh, 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).

	MODEL DEVELOPMENT

TOP ABSTRACT INTRODUCTION ISOLATED MYOCYTE PREPARATIONS MUSCARINIC RECEPTOR SUBTYPES ISOLATED NODAL AND ATRIAL... MODELING OBJECTIVES MODEL DEVELOPMENT RESULTS DISCUSSION REFERENCES

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 I_Na and I_B,Na, 2) the G protein-mediated, direct effect of ACh on I_K,ACh via the extrajunctional M₂/K_ACh 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 I_f (23, 25, 26) and I_NaK (19) and 2) an indirect effect [via activation of the enzyme protein kinase A (PKA)] on I_Ca,L and I_K. In the latter case, these integral membrane ion channel proteins are phosphorylated by PKA in response to changes in [cAMP].

View larger version (34K): [in this window] [in a new window]   Fig. 1.   Components of rabbit sinoatrial node (SAN) cell model. A: electrical equivalent circuit of an SAN cell membrane modified by parallel addition of muscarinic K+ channel (IK,ACh). B: membrane-delimited and intracellular pathways coupled to autonomic innervation. ACh-mediated effects of junctional receptor (J) on Na+ current (INa) and background Na+ current (IB,Na) and extrajunctional muscarinic M2/KACh receptor on IK,ACh (direct muscarinic pathway) and cAMP-mediated effects of -adrenoceptor (adrenergic pathway) and M2/ADC receptor (indirect muscarinic pathway) on L-type Ca2+, K+, hyperpolarization-activated, and Na+-K+ currents (ICa,L, IK, If, and INaK, respectively) are shown. PDE, phosphodiesterase; PKA, protein kinase A; ADC, adenylate cyclase.

The original mathematical descriptions (17) of the ionic currents (i.e., I_Na, I_B,Na, I_f, I_NaK, I_Ca,L, and I_K) 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

isoprenaline

[cAMP], [ACh],    and [Iso]

cAMP, ACh, and Iso concentrations

[cA]

First time derivative of cytosolic [cAMP]

k_ADC

cAMP production rate

v_PDE

cAMP degradation rate

PDE

Phosphodiesterase

K_M,ACh

Half-activation [ACh]

K_M,Iso

Half-activation [Iso]

F_cAMP,CaL

Amplitude modulation of I_Ca,L conductance by cAMP

F_cAMP,K

Amplitude modulation of I_K conductance by cAMP

F_cAMP,NaK

Amplitude modulation of maximum I_NaK by cAMP

V_0.5

Half-activation potential of steady-state activation ()

I_K,ACh

ACh- and voltage-sensitive K⁺ current

a

ACh- and voltage-dependent gating variable of I_K,ACh

First time derivative of gating variable a

ACh-dependent opening rate constant

Voltage-dependent closing rate constant

_K,ACh

Maximum I_K,ACh

g_K,ACh

Conductance of I_K,ACh

ACh(t)

[ACh] as a function of time

m

Number of ACh stimuli

t_i

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

k_h

First-order rate constant for irreversible enzymatic hydrolysis of ACh by tissue cholinesterase

f_vagal

Frequency of vagal stimulation

Descriptions of the Membrane Currents Modulated by Autonomic Neurotransmitters

Stimulation of -adrenoceptors by Iso results in the activation of a G protein (G_s) that stimulates ADC and enhances the production of cAMP. Subsequently, cAMP may directly activate I_f and I_NaK and indirectly activate I_Ca,L and I_K (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 (G_i), 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 I_Ca,L (43, 44), as well as I_K, I_f, and I_NaK. Han et al. further propose that NO is an obligatory mediator of the indirect effect of ACh on I_Ca,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 (k_ADC) is modulated by [Iso] and [ACh], whereas the rate of degradation (v_PDE · cGMP) represents the catalysis of cAMP by a cGMP-stimulated cAMP-specific PDE (2). We express this cAMP balance using the differential equation

(1)

The Michaelis-Menten constant for ACh (K_M,ACh, 0.14 × 10³ mM) was selected from the experimental dose-response relationships reported by DiFrancesco et al. (23), whereas the Michaelis-Menten constant for Iso (K_M,Iso, 0.14 × 10³ 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 × 10³ mM). We also assumed a constant cGMP concentration (i.e., [cGMP] = 2 × 10³ mM). These considerations effectively set the constant for the half-degradation concentration of cAMP by PDE (K_PDE) to 6.0 × 10³ mM. The rate constants k_ADC (8.0 × 10³ mM/s) and v_PDE (20.0 × 10³ mM/s) were calculated when [cAMP] is at steady state; i.e., [cAP] = 0, [cAMP] = 3 µM, [ACh] = [Iso] = 0. The parameter P_M2/ADC in Eq. 1 indicates the percentage of the M₂/ADC receptor population responding to applied ACh; i.e., P_M2/ADC = 1 for bath-applied ACh, and P_M2/ADC = 0.02 for vagally released ACh (vagal stimulation is assumed to affect the junctional receptors primarily).

cAMP modulation of I_Ca,L and I_K. When modeling the direct or indirect effects of cAMP on the ionic currents I_f and I_NaK or I_Ca,L and I_K, 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 I_Ca,L and I_K, 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 I_Ca,L and I_K are produced via the cAMP-dependent modulation of L-type Ca²⁺ and K⁺ channel conductance (g_Ca,L and g_K, in µS), respectively (9a, 18, 47, 52, 60, 75). Data from Petit-Jacques et al. (75) were used to guide the conductance change on I_Ca,L (Fig. 2A). Figure 2B shows the changes in the current-voltage relationship for I_Ca,L. Values for the above parameters (g_Ca,L and g_K) 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

(2)

(3)

(4)

(5)

View larger version (22K): [in this window] [in a new window]   Fig. 2.   Modulation of ICa,L by cAMP. A: effect of cAMP on conductance of ICa,L represented by a normalized conductance change (FcAMP,CaL) shown with data from Petit-Jacques et al. (75). B: current-voltage characteristics of ICa,L changes induced by 50 nM, 100 nM, 250 nM, 1 µM, and 10 µM ACh. Holding potential was 50 mV. C, control (ACh = 0).

cAMP modulation of I_f and I_NaK. I_f 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 (V_0.5, in mV) of of I_f. Thus

(6)

where

(7)

Data from Hagiwara and Irisawa (39) were employed to formulate the depolarizing shift in 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 V_0.5 as a function of [cAMP] superimposed on experimental data from DiFrancesco and Tromba (26) and Hagiwara and Irisawa (39).

View larger version (26K): [in this window] [in a new window]   Fig. 3.   Model parameters involved in modulation of If by cAMP and IK,ACh by ACh. A: effect of cAMP on produces a voltage shift of half-activation potential (V0.5). ×, Data from DiFrancesco and Tromba (26), DiFrancesco et al. (23), and Hagiwara and Irisawa (39). x-Axis, logarithmic scale. B: ACh-dependent opening rate constant () of IK,ACh. x-Axis, logarithmic scale. C: voltage-dependent closing rate constant () of IK,ACh. D: current-voltage relation of IK,ACh [(/ + )K,ACh vs. V].

(8)

(9)

(10)

Direct modulation of I_K,ACh. We have utilized the general expression for I_K,ACh given by Osterrieder, Noma, and Trautwein (ONT) (72) for I_K,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 I_K,ACh is the calculated Nernst potential (E_K), 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 I_K,ACh and its ACh- and voltage-dependent gating variable (a) are given in Table 1,¹ and current-voltage relationships for I_K,ACh are shown in Fig. 3D for a range of [ACh] (0  [ACh]  10 µM). I_K,ACh is assumed to be activated fully by bath-applied ACh (P_M2/KACh = 1) and only to a small degree by vagal stimulation (see Table 1).

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)

where t_i represents the time occurrence of the ith impulse at the varicosity, and

(12)

The function M' represents the fact that the ACh stores in the varicosities may become depleted by a rapid vagal burst. This depletion phenomenon is modeled by Eq. 13; the amount of ACh per impulse varies according to the previous history of discharge, i.e.

(13)

where M (1.1862 × 10¹⁶ mol) is the amount of ACh released per impulse, D (5.1469 × 10¹¹ 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 × 10⁶ cm) and the receptor site on the membrane surface, and k_h (50 s¹) 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 I_Na and I_B,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 I_Na (P_Na) and g_B,Na are modeled as follows

(14)

(15)

(16)

(17)

Arrested SAN Cell

View larger version (26K): [in this window] [in a new window]   Fig. 4.   Temporal response of SAN model to a train of uniformly spaced vagal stimuli (i.e., 200 Hz). A: hyperpolarizing effects of a simulated burst of vagal stimulation [consisting of 1-9 pulses/burst (1-9)] on membrane potential when inward current (ICa,L) is blocked and ion concentrations are held constant at 6.9 mM intracellular Na+, 91 nM intracellular Ca2+, and 143 mM intracellular K+. B: ACh concentration changes due to vagal burst (containing 1-9 stimuli). C: changes in cAMP concentration during stimulus train.

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 I_B,Na and I_Na, 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

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 I_Ca,L, I_K, I_NaK, and I_f are not modulated (ACh = 0, Iso = 0, and I_K,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.

View larger version (31K): [in this window] [in a new window]   Fig. 5.   Model-generated spontaneous pacemaker activity and underlying membrane currents for rabbit SAN cell. A: membrane voltage; B-D: underlying membrane currents (as in Fig. 8 in Ref. 17).

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 I_Na associated with the junctional muscarinic receptor and the time course of K⁺ current activated by the M₂/K_ACh-mediated response (I_K,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 I_Ca,L and I_K (Fig. 6B), the cAMP-dependent maximum value of I_NaK (Fig. 6D), the ACh-dependent permeability (P_Na) associated with I_Na (Fig. 6E), and ACh-dependent conductance of I_B,Na are decreased, 2) ACh inhibits I_f by inducing a hyperpolarizing shift in its activation gating variable (Fig. 6C), and 3) the hyperpolarization resulting from activation of I_K,ACh increases progressively with higher [ACh] (23, 26) (Fig. 6F). This ACh-induced change in the voltage dependence of I_f is based on the data of DiFrancesco et al. (23, 26). Their experiments showed that low [ACh] (0 < [ACh] < 260 nM) inhibit I_f via a direct (cAMP-mediated) effect. Much higher [ACh] (20-fold) are needed to directly activate the ACh-dependent K⁺ channel (I_K,ACh). At 1 and 10 µM ACh, I_K,ACh dominates and spontaneous pacemaking is abolished (Fig. 6A; see Table 2 for changes in some membrane currents).

View larger version (35K): [in this window] [in a new window]   Fig. 6.   Effects of bath application of ACh on pacemaker activity and underlying currents. A: negative chronotropic effects of ACh on spontaneous steady-state activity of SAN cell model. B: ICa,L and IK. C: If. D: INaK and INaCa. E: INa. F: IK,ACh.

View larger version (28K): [in this window] [in a new window]   Fig. 7.   Bath applications of ACh. A: inhibitory effects of bath-applied ACh on steady-state spon