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

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

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 spontaneous activity of SAN cell model. B: experimental data of DiFrancesco (22) for comparison. Abscissa, normalized time relative to control period (P0) of pacemaking period, which is 261 ms (A) and 453 ms (B).

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) I_Ca,L, I_K (Fig. 8B), and I_NaK (Fig. 8F) are increased by the indirect effect of Iso that is mediated by increased cAMP levels and 2) I_f 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 I_Ca,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.

View larger version (30K): [in this window] [in a new window]   Fig. 8.   Bath applications of Iso: model output. A: positive chronotropic effects of Iso on spontaneous steady-state activity of SAN cell model compared. B: ICa,L and IK. C: T-type Ca2+ current (ICa,T). D: INa. E: If. F: INaK and INaCa. G: ICaP and background current (IB).

View larger version (26K): [in this window] [in a new window]   Fig. 9.   Bath applications of Iso: comparison with experimental data. Positive chronotropic effects of Iso on spontaneous steady-state activity of SAN cell model (A) are compared with data of Hagiwara et al. (41) (B). x-Axis is normalized by control period.

Response of SAN Model to Negative Chronotropic Stimuli

View larger version (27K): [in this window] [in a new window]   Fig. 10.   Negative chronotropic effects in SAN cell produced by a train of 6 stimuli (100 Hz). A: effects of a train of vagal "field" stimuli on an intracellular action potential recording (labeled 1) from a primary cell (82) compared with control activity (C). B: 1st derivative of action potentials (dV/dt) in A. C: model-generated changes in membrane potential due to stimulation of vagus nerve (1) and control records (C). D: model-generated changes in dV/dt due to stimulation of vagus nerve (1) and control data (C). E: simulated vagally released ACh waveform. Vagal stimulation (6 stimuli at 100 Hz) was delivered during time indicated by horizontal bar in A.

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.

(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 I_Ca,L and I_Na 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 I_Ca,L exerts considerable influence on the upstroke and peak regions of the action potential. After ACh application, I_Ca,L is diminished by a decrease in [cAMP], which is mediated by M₂/ADC receptor activation. Because I_Ca,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. I_f 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 I_Na (Fig. 11B) and I_B,Na. Our simulations show that, of the two currents, I_B,Na contributes to the phase sensitivity only to a minor degree. This observation agrees with the simulation results of Edwards et al. (30).

View larger version (22K): [in this window] [in a new window]   Fig. 11.   Model-generated transient phase-response curves (PRCs) with assumption that each muscarinic receptor subtype can be activated independently by a rectangular ACh pulse or a hyperpolarizing current pulse. A: PRCs when 100% of M2/ADC and junctional (J) receptors are activated independently by a rectangular ACh pulse (10 µM, 16 ms). B: normalized ICa,L and INa waveforms. C: PRCs when 100% of M2/KACh receptors are activated by an ACh pulse (10 µM, 16 ms) and when a hyperpolarizing current pulse (IStim, 18 pA, 16 ms) is applied independently. D: normalized membrane voltage activity. , phase; P, change in period.

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 I_Na 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).

View larger version (23K): [in this window] [in a new window]   Fig. 12.   PRCs of SAN cell to vagal input. A: PRCs ( vs. P) for increasing number of vagal impulses (i.e., 1-9) per burst. B: effect of background levels of Iso on PRCs of SAN cell. PRC obtained for a burst containing 9 vagal impulses, delivered 5 ms apart, under control conditions, is labeled Iso = 0 nM. Curves labeled 10 nM and 1 µM show effect on PRC when Iso background levels are increased. P was measured with respect to control cycle length at each background level. C: SAN cell membrane voltage normalized by cycle length.

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.

View larger version (26K): [in this window] [in a new window]   Fig. 13.   Model-generated steady-state entrainment curve of an SAN cell for vagal input with different background levels of Iso. Period of ACh stimuli vs. period of SAN pacemaker cell with distinct regions of vagal paradox at 1:1, 1:2, and 1:3 and general inhibitory effect of ACh are shown. Entrainment curves move downward and leftward with increasing Iso (25 nM, 50 nM, and 1 µM). Arrows, upper and lower limits of overlapping 1:1 entrainment zones for 0, 25, and 50 nM Iso. In 1:1 entrainment zone, from top, first 2 leftward arrows are for 0 nM Iso, 2 rightward arrows are for 25 nM Iso, and last two leftward arrows are for 50 nM Iso. Rightward arrows in 1:2 zone are for 25 nM Iso.

Differences in Responses of the SAN Cell Model to Vagally Released and Bath-Applied ACh

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 I_Ca,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 I_K,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/K_ACh receptors as a function of vagal stimulation frequency (see Table 1 and particularly the relationship for P_M2/KACh). Bath application of ACh (100 µM, 5 s), which is represented by a trapezoidal-type waveform with a rate constant of 5 s¹ 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/K_ACh, and J receptors are activated via the bath-applied ACh.

View larger version (60K): [in this window] [in a new window]   Fig. 14.   Model-generated responses of SAN cell to vagally released and bath-applied ACh. A-C: inhibitory effects of ACh are seen on spontaneous activity of SAN cell model for 2-, 10-, and 30-Hz vagal stimulation. D: inhibitory effects of 100 µM bath-applied ACh. Model-generated data are consistent with experimentally obtained data from guinea pig SAN (12).

	DISCUSSION

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

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 (I_K,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 I_Na and I_B,Na. The cAMP effects consist of modulations of the maximal conductances and, in some cases, changes in the time constants I_Ca,L, I_K, and I_NaK. In addition, the voltage-dependent activation characteristic (), which governs I_f, 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

Most of these models have assumed that the only vagally induced current involved in the parasympathetic control of the SAN is I_K,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 I_K,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 I_Na and I_B,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 I_Na and I_B,Na and achieved quite close agreement between model-generated and experimental data. Decreasing I_B,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 I_NaK. 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 (I_Ca,L, I_K, and I_f) as well as I_NaK.

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/K_ACh 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., I_Na and I_B,Na, rather than the muscarinic current I_K,ACh, as is assumed in many other models. In contrast, the M₂/K_ACh receptor associated with I_K,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

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/K_ACh, 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 I_Na and I_B,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 (G_s) and PKA stimulate I_Ca,L in guinea pig ventricular myocytes. Their results show that the effects of G_s and PKA are not additive. These results also suggest that G_s primes I_Ca,L for cAMP-dependent phosphorylation and thus potentiates the effects of PKA. The direct effects of G_s (or G_i) on I_Ca,L need experimental clarification.

7) Takano and Noma (90) reported that -receptor-operated Cl current (I_Cl) 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 I_Cl. For this reason, I_Cl 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 I_NaK in rabbit ventricular myocytes, and Gao et al. (33, 34) concluded that the -agonist-induced increase in I_NaK 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 I_Ca,L in isolated rabbit SAN cells can be mimicked by an NO donor and that ACh cannot reduce I_Ca,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 (I_up) 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 I_up. However, increases in [Ca²⁺]_i due to cAMP-induced I_Ca,L do increase I_up 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.