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(Circulation Research. 1996;79:631-646.)
© 1996 American Heart Association, Inc.

Articles

Gap Junctions in Vascular Tissues

Evaluating the Role of Intercellular Communication in the Modulation of Vasomotor Tone

George J. Christ, David C. Spray, Marwan El-Sabban, Lisa K. Moore, Peter R. Brink

the Departments of Urology (G.J.C.) and Neuroscience (D.C.S., M.E.-S., L.K.M.), Albert Einstein College of Medicine, Bronx, NY, and the Department of Physiology and Biophysics (P.R.B.), State University of New York at Stony Brook.

Correspondence to George J. Christ, PhD, Associate Professor and Director of Basic Research, Urology Research Laboratory, Room 716S, Forchheimer Building, Albert Einstein College of Medicine, 1300 Morris Park Ave, Bronx, NY 10461. E-mail christ@aecom.yu.edu.

	Abstract

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
Integration and coordination of responses among vascular wall cells are critical to the local modulation of vasomotor tone and to the maintenance of circulatory homeostasis. This article reviews the vast literature concerning the principles that govern the initiation and propagation of vasoactive stimuli among vascular smooth muscle cells, which are nominally the final effectors of vasomotor tone. In light of the abundance of new information concerning the distribution and function of gap junctions between vascular wall cells throughout the vascular tree, particular attention is paid to this integral aspect of vascular physiology. Evidence is provided for the important contribution of intercellular communication to vascular function at all levels of the circulation, from the largest elastic artery to the terminal arterioles. The thesis of this review is that the presence of gap junctions, in concert with the autonomic nervous system, pacemaker cells, myogenic mechanisms, and/or electrotonic current spread (both hyperpolarizing and depolarizing waves through gap junctions), confers a plasticity, adaptability, and flexibility to vasculature that may well account for the observed diversity in regulation and function of vascular tissues throughout the vascular tree. It is hoped that the summary information provided here will serve as a launching pad for a new discourse on the mechanistic basis of the integrative regulation and function of vasculature, which painstakingly accounts for the undoubtedly complex and manifold role of gap junctions in vascular physiology/dysfunction.

Key Words: gap junction • vascular physiology • vascular smooth muscle • intercellular communication

	Introduction

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
Coordination of responses among vascular wall cells is critical to the local modulation of vasomotor tone and to the maintenance of circulatory homeostasis. Because vascular smooth muscle is nominally the final effector of vessel tone, a central thrust of cardiovascular research has been to clarify the regulation and function of smooth muscle cells. However, despite the enormous amount of research that has been conducted, the mechanism(s) permitting coordinated response generation among smooth muscle cells in the vessel wall remains incompletely understood.

Thus, a review of the principles governing initiation and propagation of vasoactive stimuli among vascular smooth muscle cells seems relevant to a better understanding of circulatory control. The main thesis of this review is that although neuronal innervation and electrical excitability play major roles in vascular response generation, they are not the only mechanisms responsible for coordinated vessel tone. Particular emphasis is given to the role of intercellular communication through gap junctions (nexuses) among vascular smooth muscle cells in the regulation of vasomotor tone, although the role of endothelial cell–endothelial cell and endothelial cell–smooth muscle cell gap junctions is also considered. The focused attention on junctional communication in vascular smooth muscle seems justified given the recent and rapid expansion of information concerning the molecular and biophysical properties of gap junctions in these cells. Moreover, the reader should keep in mind that the gap junctional intercellular communication discussed here is distinct from other types of cell-to-cell interaction that are also important to vascular homeostasis, eg, paracrine interactions through the extracellular pathway.

Several contingencies have been identified for syncytial activation of vascular smooth muscle: (1) direct neuronal innervation of every or almost every smooth muscle cell (in this scenario, simultaneous activity of presynaptic nerve fibers would permit the synchronous activation of all cells independent of other mechanisms, ie, analogous to multiunit smooth muscle), (2) the presence of electrically excitable smooth muscle cells such that syncytial tissue responses could be achieved by regenerative electrical events triggered by fewer neuromuscular junctions and further modulated by the activity of pacemaker cells (ie, analogous to unitary smooth muscle organization), and (3) the passive movement of intercellular second messenger molecules/ions through gap junctions from directly activated cells to distally removed coupled cells, subsequent to activation of only a small fraction of smooth muscle cells (ie, a mixture of multiunit and unitary smooth muscle). These possibilities are considered in order.

	Neuronal Innervation of Vascular Smooth Muscle

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
The issue of neuronal innervation of the vasculature is critical to understanding how vasomotor tone might be coordinated. In the present review, the term neuronal innervation refers broadly to any component of the autonomic nervous system that contributes to the perivascular innervation of the systemic vasculature; ie, adrenergic, cholinergic, and nonadrenergic noncholinergic (eg, neuropeptides or nitric oxide) neurons are included in this terminology. Several excellent reviews have documented that the autonomic innervation of systemic blood vessels is largely confined to the adventitial-medial smooth muscle border^{1 2 3} and rarely penetrates the medial smooth muscle layer, although exceptions have been noted.^{4 5 6} Despite the large degree of complexity and variability concerning the innervation of both arterial and venous smooth muscle, some generalizations can be made. In particular, as pointed out by Burnstock^{4 5} and others,^{1 2 3} the autonomic neuroeffector junction in vascular smooth muscle differs both anatomically and physiologically from the classic neuromuscular junction of skeletal muscle (see Fig 1). Specifically, perivascular nerves coalesce at the adventitial-medial smooth muscle border to form a plexus consisting of an extensive network of branching terminal fibers. The terminal axons in this plexus are commonly devoid of a Schwann cell covering, are rich in varicosities (0.5 to 2 µm in diameter), and are separated by shorter intervaricose regions (0.1 to 0.3 µm in diameter).⁵ The varicosities are thought to represent the major sites for neurotransmitter release during neuronal activity; because individual axons may have numerous varicosities, impulses passing along an axon would be expected to successively depolarize a string of varicosities.

View larger version (62K): [in this window] [in a new window]   Figure 1. Depiction of the general anatomic arrangements and structural features of a small muscular artery. Top, Five or six layers of medial smooth muscle are shown to be separated from an endothelium-lined lumen by an internal elastic lamina; note that the internal lamina is depicted as being continuous for simplicity, although this is clearly not the case in vivo. Bottom, The same interrelationships are shown at higher magnification, after sectioning of the vessel in the plane perpendicular to the long axis of the vascular smooth muscle cell (shown as thick black line in the top panel). The thick lines through the media between the adventitial and endothelial (luminal) sides illustrate the bidirectional signaling that might occur in vivo by either the extracellular pathway (the line to the right) or the intercellular pathway (the line to the left).

Neuronal innervation of larger vessels is notably different from that of smaller vessels. For example, neuromuscular distances (which have been reported to range from 50 to 2000 nm), as well as the relative volume of smooth muscle being supplied by perivascular nerves, are usually much greater in large elastic arteries compared with smaller muscular arteries.^{2 3 4 5 7} In larger vessels, in particular, where there are many layers of smooth muscle (with innervation largely confined to the adventitial-medial smooth muscle border), a majority of the smooth muscle cells may not be directly innervated. In contrast, in small arterioles a larger proportion of smooth muscle cells may be directly innervated. Differential innervation patterns and neuromuscular distances in larger versus smaller blood vessels may have important implications with respect to neurotransmitter diffusion distances and the effective neurotransmitter concentrations achieved at the postsynaptic receptor sites.^{1 2 3}

In light of these anatomic relationships, neurotransmitter diffusion through the medial smooth muscle layer has been presumed to be the principal rate-limiting step required for activation of the smooth muscle cells, especially in progressively larger blood vessels.⁸ Several studies have examined the movement and disposition of neurotransmitters in the medial smooth muscle layer of blood vessels. For example, "overflow" of transmitter with histochemical evidence of diffusion to deeper layers of medial smooth muscle has been demonstrated in the dog dorsal pedal artery. Other reports have also indicated that neurotransmitter may diffuse through the medial smooth muscle layer in some blood vessels.^{2 9 10 11 12 13} Importantly, however, the necessity of the extracellular diffusion pathway to the syncytial activation of vascular smooth muscle has not been unequivocally established.

In contrast, in a very recent study, the kinetics of norepinephrine release from sympathetic nerves was directly measured electrochemically with a carbon fiber electrode in the isolated rat tail artery.¹⁴ This report demonstrated that, in this vessel, neurotransmitter diffusion was locally and temporally restricted to the arterial surface, with a time constant of 1 second. We conclude that although neural innervation and neurotransmitter activation of vascular smooth muscle clearly do provide an important mechanism for modulating vasomotor tone, there is no compelling evidence that nerve stimulation alone, in the absence of other mechanisms, could activate the majority of smooth muscle cells in the wall of larger elastic and muscular arteries.

	Electrical Properties of Vascular Smooth Muscle

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
The electrical properties of vascular smooth muscle cells have been well characterized both in vitro and in vivo. These cells express a variety of membrane ion channels,¹⁵ including K⁺ channels,^{16 17 18 19 20 21 22 23 24 25 26} Ca²⁺ channels,^{8 27 28 29 30 31 32 33 34} and perhaps Cl^- channels and Na⁺ channels as well.^{35 36 37 38 39 40 41 42 43} Despite the correlation between membrane potential and tension development shown in many vascular tissues, changes in membrane potential are neither necessary nor sufficient to elicit contractile responses in all blood.^{1 41 44 45 46 47 48} Although a more detailed discussion of the characteristics of the individual membrane ion channels on vascular smooth muscle cells is beyond the focus of the present review, studies to date support the supposition that the majority of smooth muscle does not exhibit action potentials.^{15 24}

Pacemaker Cells and Regenerative Electrical Events in Vascular Smooth Muscle
The initiation, propagation, and modification of contractile responses along blood vessels can clearly occur in the absence of neural modulation, especially in smaller caliber vessels, such as arterioles,^{49 50 51 52 53 54 55} as well as in larger caliber vessels, such as portal-mesenteric veins.⁵⁶ In the latter case, "spikelike" potentials were observed to decrementally spread along the vessel at a rate of 1 to 2 cm/s.⁵⁷ In fact, the presence of "pacemaker" cells has been hypothesized to participate in the initiation and coordination of vasomotor responses in vessels with spontaneous contractile activity.^{50 51} Thus, although excitatory junction potentials, spikelike potentials, and active membrane responses have been recorded in many blood vessels, particularly in those with spontaneous contractions,^{39 40 41 42 43 44 45 46 58 59 60 61 62 63 64 65 66 67} these potentials appear to be passively spread⁵⁹ in situ rather than actively propagated.^{68 69 70}

Electrotonic Current Spread in Vascular Smooth Muscle
Intercellular communication through gap junctions provides the mechanistic basis for strong electrical coupling between smooth muscle cells, so that even relatively small depolarizations can be passively spread over relatively large distances in vascular tissues.^{1 63 64} For example, neurotransmitter-induced excitatory junction potentials of 10 mV have been reported to spread with little attenuation both along the length of the blood vessel and from the adventitial-medial smooth muscle border to the inner smooth muscle layers.¹ Additionally, the rapid bidirectional spread of depolarization among vascular smooth muscle cells has been hypothesized to be important to vascular tone in rodents.^{71 72} The spread of hyperpolarizations of similar magnitude among smooth muscle cells has also been documented in isolated porcine coronary artery.⁷³ Although the physiological relevance of passive current spread in vivo still remains to be demonstrated, as noted above, hyperpolarization and depolarization have been correlated with vascular tissue relaxation and contraction, respectively, in vitro.^{71 72 73}

In fact, such passive current spread in blood vessels with many layers of medial smooth muscle is an important concept. For example, in larger vessels the space constant was observed to be much greater in the direction parallel to the blood vessel (as large as 1.5 to 3.0 mm) than in the direction perpendicular to the blood vessel (=0.1 mm)^{1 63 64} As a result of such anisotropy, the characteristics of electrotonic current flow will vary dramatically with the thickness and function of the vessel (Fig 2). Presumably, anisotropic space constants for current flow between smooth muscle cells are ascribable to tissue geometry and the distribution of gap junctions among vascular smooth muscle cells. The example that follows will serve to illustrate the potential significance of anisotropic electrotonic current spread in vascular tissues. Specifically, let us calculate the size of an "active vascular unit," which we will arbitrarily define as the number of cells within one space constant of the stimulated cell. Taking into account the aforementioned electrical anisotropy, as well as the geometry (width, 5 to 10 µm; length, 100 µm) and orientation (long axis of the smooth muscle cell largely perpendicular to the long axis of the blood vessel) of smooth muscle cells in the vessel wall (see Fig 2, bottom), the "active vascular unit" would clearly be very dependent on tissue geometry. In any case, because junctional permeability is an order of magnitude less than cytoplasmic diffusion, current flow will always be much greater along the long axis of the smooth muscle cell than perpendicular to the long axis of the cell. As such, depending on whether vessel geometry approximates a one-, two-, or three-dimensional case, the number of cells in the "active vascular unit" could range from a minimum of tens of cells to a maximum of hundreds of cells.^{74 75} Such large "active vascular units" have potentially important implications for vascular physiology (see below). However, the actual physiological relevance of such a phenomenon in situ remains to be determined but is amenable to both theoretical analysis and experimental verification.

View larger version (57K): [in this window] [in a new window]   Figure 2. Depiction of the general anatomic arrangements and structural features of a small muscular artery. Top, Five or six layers of medial smooth muscle are shown to be separated from an endothelium-lined lumen by an internal elastic lamina; note that the internal lamina is depicted as being continuous for simplicity, although this is clearly not the case in vivo. Bottom, Anisotropic intercellular communication is shown in blood vessels by a schematic diagram of the anisotropic character of intercellular diffusion. This panel depicts the expected orientation of the smooth muscle cells in the vessel wall after a sectioning of the vessel in a plane longitudinal to the long axis of the blood vessel, near the adventitial surface, where one might expect to find neuronal varicosities. This diagram illustrates the physical principles that may underlie the differential space constants observed for the passive spread of small depolarizations in the vessel wall in the planes that are parallel and perpendicular to the long axis of the blood vessel, respectively (see text). Thus, the anisotropic nature of intercellular diffusion may be related to the fact that cytoplasmic diffusion is an order of magnitude greater than junctional diffusion. Thus, the fewer junctional interfaces that must be traversed, the greater the effective intercellular diffusion distance.

	Intercellular Communication Among Vascular Wall Cells

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
The possibility that an intercellular pathway between adjacent smooth muscle cells may be relevant to tissue physiology dates back to the discovery of the gap junction (or nexus) in canine intestine by Barr and Dewey.⁷⁶ Shortly thereafter, Johansson and Ljung⁵⁶ suggested that myogenic intercellular propagation might similarly be important for signal spread in vasculature. In light of the many recent advances made in the understanding of the molecular and biophysical properties of gap junctions, the emphasis here will be on presenting the new experimental and theoretical evidence for the long suspected role of the nexus in vascular response generation. Presently, we review data that suggest that the presence of gap junctions between vascular wall cells in diverse vasculature (see Table 1) provides an anatomic substrate by which activation of only a small fraction of the total cell population might lead to rapid coordinated contractions.

View this table: [in this window] [in a new window]   Table 1. Expression of Connexins in Vascular Smooth Muscle

Defining Gap Junctions
Gap junctions are aggregates of intercellular channels, with each channel being formed by the union across the extracellular space of two hemichannels or connexons, one contributed by each cell of a pair (Fig 3). The connexons are generally believed to be hexameric complexes of homologous connexin proteins. A dozen individual cDNAs encoding distinct mammalian connexin proteins have been cloned and sequenced and are named according to their predicted molecular weights.^{77 78} Connexins show overlapping tissue-specific patterns of expression⁷⁹ ; three connexins, Cx43, Cx40, and Cx37, are expressed in vascular wall cells. As summarized in Tables 1 and 2, Cx43 and in some cases Cx40 are found in both smooth muscle and endothelial cells, with the presence of a third connexin, Cx37, also reported in endothelial cells. Thus, these intercellular channels provide an intercellular conduit through which ions and second messenger molecules may diffuse among vascular wall cells.

View larger version (142K): [in this window] [in a new window]   Figure 3. Schematic diagram of the salient features of two representative gap junction channels. This diagram highlights the fact that many physiologically relevant second messenger molecules or ionic species are gap junction permeant.

View this table: [in this window] [in a new window]   Table 2. Expression of Connexins in Endothelial Cells

Gap Junctions in the Cardiovascular System
In many tissues, including the heart, the physiological significance of intercellular communication in mediating conduction of ionic currents has been well established.^{67 77 80 81 82} A similar role for gap junctions in modulating vasomotor tone has long been suspected. In fact, the structural basis for gap junctions and their physiological correlates in vasculature have been studied for almost three decades^{4 5 7 56 83 84 85 86 87 88} and in the past few years have been complemented by experimental studies demonstrating their potential physiological relevance.^{1 71 72 73 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104} The focus here is on research conducted in arterial smooth muscle and endothelium of the systemic vasculature, ranging from the largest conduit arteries (eg, aorta), to smaller supplying arteries (eg, carotid or superior mesenteric arteries), down to arterioles. In addition, research on the venous system is considered occasionally for comparison.

Immunochemical and Molecular Biological Characterization of Gap Junctions Between Vascular Smooth Muscle Cells
As summarized in Table 1, immunochemical and molecular biological studies at both the cellular and intact tissue levels have indicated the presence of connexins in vascular smooth muscle from a wide range of blood vessels. Electron microscopy has further revealed that the diameter of junctional plaques between smooth muscle cells in the human corpus cavernosum and rat aorta in vivo ranges between 0.2 and 0.5 µm.^{89 99} In addition, immunogold staining with Cx43 antibodies revealed that the density of staining (expressed as the number of gold particles/µm²) in these same preparations is similar to that found in heart (30 gold particles/µm²), another cardiovascular tissue in which Cx43 is the predominant gap junction protein.⁸⁹ Immunofluorescence studies have also recently detected junctional plaques of similar size (0.5 µm) between vascular smooth muscle cells in rat and hamster resistance arteries, using both Cx43 and Cx40 antibodies.¹⁰² The immunostaining of these resistance vessels revealed a ubiquitous distribution of both connexins among the vascular smooth muscle cells. Furthermore, the overlapping patterns of immunofluorescence suggested the possibility that Cx40 and Cx43 might be colocalized to the same junctional plaques, even though these connexins do not appear to be functionally paired.^{105 106}

Vascular smooth muscle cells in vivo and in vitro thus appear to be interconnected by an extensive network of relatively small gap junction assemblies. Since both Cx43 and Cx40 appear to be prominent gap junction proteins found interconnecting vascular smooth muscle cells, it is conceivable that their distribution and location among vascular wall cells may confer important physiological properties to distinct vasculature.

Immunocytochemical and Molecular Biological Characterization of Gap Junctions Between Endothelial Cells
As summarized in Table 2, there are some important distinctions between the gap junctions found in endothelial cells and those found in vascular smooth muscle cells. Perhaps most notably, in addition to Cx43 and Cx40, endothelial cells also frequently express the gap junction protein Cx37. Consistent with the presence of additional junctional proteins in endothelial cells, semiquantitative immunochemical studies of rat aorta have revealed that the density of Cx43 immunogold labeling of gap junctions is much lower for junctional plaques between endothelial cells (9 gold particles/µm, authors' unpublished data, 1996) than for those between smooth muscle cells (30 gold particles/µm; see above), although the sizes of the junctional plaques were similar. Another recent report in rat and hamster resistance vessels used immunofluorescence techniques to demonstrate that Cx40 and Cx43 were distributed throughout the endothelial layer and also appeared to be colocalized to the same junctional plaques. The size of the junctional plaques detected between the endothelial cells in these rodent resistance vessels was nearly twice the size of junctional plaques composed of the same connexins detected between smooth muscle cells (ie, 0.9 versus 0.5 µm). It remains to be determined whether these apparent differences in plaque size are physiologically significant.

Histological Evidence for Gap Junctions Between Endothelial Cells and Smooth Muscle Cells
Myoendothelial gap junctions in arteries result from smooth muscle cell processes passing through fenestrae of the elastica interna to contact endothelial cells and may provide an efficient pathway for the direct transfer of low-molecular-weight molecules from endothelial cells to smooth muscle cells. However, in contrast to the situation concerning smooth muscle cell–smooth muscle cell and endothelial cell–endothelial cell gap junctions, immunocytochemical evidence for the presence of connexins at endothelial cell–smooth muscle cell junctions is not yet available. Nonetheless, ultrastructural evidence of gap junctions between endothelial cells and smooth muscle cells has been reported by several authors,^{90 93 107 108 109 110 111} and some recent studies do provide strong functional evidence for their existence.^{73 101 102 104} Clearly, the physiological significance, if any, of myoendothelial gap junctions remains to be determined.

	Physiological Evidence for a Potentially Important Role of Gap Junctions in Vascular Tissues

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
Thus far, a preponderance of morphological, structural, and molecular biological evidence has identified gap junctions between vascular wall cells throughout the vascular tree. At this point, it is relevant to review the experimental findings indicating that their disposition in the vessel wall is physiologically significant.

Possible Functional Roles for Gap Junctions in the Microcirculation
In this regard, it has been suggested that intercellular communication through gap junctions between smooth muscle and/or endothelial cells mediates the vasodilation and vasoconstriction responses observed to be conducted along the arteriolar wall in resistance vessels.^{92 100 103} One implication of such observations is that intercellular communication in the microcirculation provides a mechanism by which locally triggered vasodilatory responses can be conducted proximally (ie, upstream from the site of stimulation) into the feeding arteriole to induce increased blood flow into the stimulated vessel and thus increase perfusion of a more distal capillary bed.^{92 100 103} Such conducted vasomotor responses might play an important role in modulating the metabolically mediated hemodynamic responses characteristic of exercise. In fact, Duling and Berne¹¹² were the first to suggest that dilation along arterioles might play an important role in the local control of tissue blood flow and that intercellular communication through gap junctions between vascular wall cells (ie, smooth muscle and/or endothelial cells) is one mechanism that would permit such coordinated hemodynamic responses. Another recent study demonstrated that pressure changes in isolated arterioles were communicated to neighboring portions of the microcirculation.¹¹³ That is, a pressure change within an isolated segment of arteriole in situ elicited a myogenic response in the isolated segment as well as changes in arteriolar diameter at locations remote from the isolated segment, which were themselves insulated from the applied pressure changes.¹¹³

Other in situ evidence for metabolic coupling among vascular wall cells derives from recent studies in which tracers of various sizes and charges were used to assess the extent of intercellular communication among endothelial cells, among smooth muscle cells, and between endothelial and smooth muscle cells in hamster cheek pouch arterioles.^{102 104} These studies demonstrated that intracellular microinjection of junction-permeant dyes in vascular wall cells was always heptanol sensitive (ie, disruption of junctional communication with this lipophilic uncoupling agent prevented dye transfer [see below]). In short, these fluorescence studies were indicative of homologous coupling among both endothelial and smooth muscle cells but unidirectional, or asymmetric, heterologous intercellular communication from endothelial to smooth muscle cells. Because of the composition of connexins that exist in these two cell types (compare Tables 1 and 2) and because the tracers used have size and charge characteristics similar to those of known intracellular second messengers, these findings may have important implications for intercellular signaling in the vessel wall. Alternatively, the inherent volume mismatch between endothelial cells and smooth muscle cells, as well as potential artifacts arising from variations in the threshold for optical detection of fluorescent dye transfer, may also account for the observed asymmetries in junctional dye transfer.

Nevertheless, taken together, such observations suggest that longitudinal intercellular diffusion perpendicular to the long axis of the arteriolar smooth muscle cell, or coupling among endothelial cells, might account for both the coordination of metabolically initiated conducted vasomotor responses as well as the rapid myogenic propagation that originates from dynamic changes in pressure or the action of a locally released neurotransmitter within smaller blood vessels.^{1 103 112}

Possible Functional Roles for Gap Junctions in Macrovessels
In contrast to the rather compelling evidence for the importance of gap junctions to dynamic coordination of vascular signals at the arteriolar level, the physiological role of intercellular communication in larger arteries, both muscular and elastic, is not as intuitively obvious and has arguably more modest physiological relevance. However, one cannot exclude the possibility that integration of smooth muscle responses in the larger vessels may have some physiological relevance in vivo. For example, gap junctions might play a role in the regulation and function of larger vessels by integrating diverse neural and endothelial signals across the vessel wall. It has been suggested that such a mechanism would be important in modulating the homeostasis of the intervening medial smooth muscle layer⁵ and would, of course, have particular relevance to vessels with more than a few layers of smooth muscle (see Fig 1). Additionally, from a conceptual and theoretical standpoint, pharmacological studies of isolated vascular tissues, conducted under well-defined experimental conditions, provide an important opportunity to further study the contribution of intercellular communication to pharmacomechanical coupling and response generation (ie, both contraction and relaxation) in vasculature.

Physiological Evaluation of the Role of Gap Junctions in Larger Blood Vessels
As noted by Johansson and Ljung,⁸⁸ "Since only a limited number of muscle cells are supplied with vasomotor nerve `endings,' as indicated by the confinement of the adrenergic plexus to the outermost media in most vessels, myogenic spread of excitation may markedly increase the effectiveness of the nervous control by recruitment of non-innervated effector cells." In some elegant experiments conducted more than 20 years ago, Johansson and Ljung^{56 88} demonstrated that myogenic conduction between the hepatic and mesenteric segments was essential for the effective coordination of the contractile responses of the rat portal vein. Specifically, they convincingly demonstrated that myogenic conduction was responsible for the transfer of neurogenically induced excitation in the mesenteric segment to muscle cells in the hepatic segment that were not directly affected by the adrenergic transmitter. This first demonstrated the potentially important role played by intercellular communication in the vasculature, even in vessels in which some cells have a capacity for action potentials and in which spontaneous contractions are propagated.

Another example of the importance of passive intercellular diffusion to modulation of vascular responses was recently provided by Beny and Pacicca,⁷³ who presented in situ evidence for bidirectional electrical communication between smooth muscle and endothelial cells in the porcine coronary artery. They demonstrated smooth muscle cells hyperpolarized in response to both endothelium-dependent and endothelium-independent agents (eg, bradykinin and isoproterenol, respectively).

Pharmacological Evaluation of the Contribution of Gap Junctions to Response Generation in Isolated Vascular Tissues
The aorta is a sparsely innervated and electrically quiescent vascular tissue that may be largely dependent on intercellular communication through gap junctions for coordination of smooth muscle responses.⁸⁹ Recent experiments have shown that pretreatment of rat aortic rings with heptanol caused a profound and readily reversible diminution in the rate and magnitude of ₁-adrenergic contractions, without any detectable nonjunctional effects.^{34 37 89 95 99 114 115} The interpretation of this experimental observation was that the diminution in adrenergic contractility was related to a reversible disruption of intercellular communication by heptanol. The implication was that not all smooth muscle cells in this tissue were directly activated by exogenously applied drug but rather that only some fraction of cells were directly activated, and the remaining smooth muscle cells were recruited into the contractile response following the intercellular flux of second messenger molecules (eg, inositol trisphosphate or Ca²⁺). This conclusion was based on the explicit assumption that heptanol, a clearly pleiotropic lipophil, had relatively selective uncoupling actions at the concentrations used in these studies; the facts supporting this supposition have been outlined in great detail in a recent report.¹¹⁶ Other recent studies in rodent resistance arterioles are also consistent with this interpretation.⁷²

Interestingly, a greater heptanol concentration was found to be required to produce a similar diminution in the contractile responses of isolated rat aortic rings to the full ₁-adrenergic agonist phenylephrine compared with the partial ₁-adrenergic agonist oxymetazoline. This finding suggested that gap junctions may also modulate agonist efficacy.^{89 116} That is, the lesser sensitivity of phenylephrine to the uncoupling actions of heptanol was presumably related to the ability of phenylephrine to initiate intracellular events that were associated with significantly greater intercellular flux of relevant second messenger molecules/ionic species among coupled smooth muscle cells.¹¹⁷ Notably, additional pharmacological studies conducted on isolated rat aortic rings¹¹⁶ highlight the potential importance of gap junctions to contractile responses elicited by 5-hydroxytryptamine, endothelin-1, and prostaglandin F₂. Such observations indicate that gap junctions may modulate contractile responses following activation of diverse membrane receptor systems.^{114 115 116} In short, such observations provide strong experimental evidence that gap junctions participate in the modulation of contractile responses in isolated vascular tissues.

Other investigators have used an analogous research strategy, in distinct vasculature, to obtain similar results. In these studies, promotion of gap junction formation by tetraethylammonium was associated with heptanol-reversible increases in myotonic oscillations of rat tail artery at the tissue level. A similar heptanol-reversible enhancement of lucifer yellow dye transfer by tetraethylammonium treatment was seen in cultured mesenteric arterial smooth muscle cells. Last, when isolated tissues were precontracted with phenylephrine, the administration of 300 µmol/L heptanol caused a significant decrease in the magnitude of the acetylcholine-induced relaxation response. These data provide additional evidence that gap junctions participate in the modulation of both contraction and relaxation responses.

Perhaps the strongest evidence implicating a major role for gap junctions in human tissue physiology and function has been obtained in studies conducted on isolated tissue strips and cultured cells derived from corpus cavernosum smooth muscle.^{34 37 95 99} In these studies, treatment of isolated human corporal smooth muscle strips with heptanol (again, at presumably selective uncoupling concentrations) caused a profound and readily reversible diminution in the rate and magnitude of ₁-adrenergic receptor–mediated contractions, in the absence of any detectable nonjunctional effects.^{34 37 89 95 99 114 115} In this tissue, which has sparse autonomic innervation and little, if any, capacity for regenerative electrical events, intercellular communication through gap junctions has been postulated to provide a primary mechanism for the coordination of relaxation and contraction responses among the smooth muscle cells. Such intercellular communication is thought to be important in orchestrating the complex hemodynamic events associated with human penile erection and detumescence, respectively. An important correlate of such observations (in this and other vascular tissues) is that the magnitude of both contraction and relaxation would nominally be related to the number of cells recruited into the functional syncytial unit (see Fig 4). Taken together, all of the aforementioned studies provide evidence that both contraction and relaxation responses in many isolated vascular tissues are modulated, at least in part, by intercellular communication through gap junctions.

View larger version (47K): [in this window] [in a new window]   Figure 4. Intercellular communication has an impact on both contraction and relaxation responses. Organ bath experiments using the selective uncoupling agent heptanol are consistent with the hypothesis that the degree of vascular smooth muscle contraction and relaxation depends on both the strength of the activating stimulus and the extent of intercellular communication. This figure emphasizes that the magnitude of contraction and relaxation responses would be proportional to the number of activated cells. In all cases, the shaded cells represent activated cells, including both directly activated cells (ie, those nearest the neuronal source cell) and cells recruited into the response after activation by the intercellular transit of second messenger molecules or ions. Top left, A family of tracings (A through D) illustrating the change in tension or contractile force (in arbitrary units from baseline) over time (arbitrary units) as typically seen in vascular tissue in the organ bath chamber upon exogenous addition (arrow) of increasing concentrations of a contractile agent (eg, phenylephrine or norepinephrine; at half-log increments, for example). For each tracing, a corresponding panel (A through D) illustrates the nature of the relationship between cellular activation, intercellular communication, and the magnitude of the contractile or relaxant response. Extrapolating to the in vivo environment, response generation should also be proportionate to the strength of neuronal stimulation (denoted by the increasing size of the electrical stimulus shown in panels A through D). As illustrated, greater agonist concentrations or nerve stimulation result in a greater total number of activated cells (both directly and indirectly) and, thus, a proportionately greater contractile response. Top right, A family of tracings illustrating vascular tissues that are submaximally precontracted (eg, 80% of maximum) or under basal sympathetic tone, where addition of a vasorelaxant (arrows in uppermost left and right panels) or activation of endogenous vasorelaxing neurons would be expected to elicit a relaxation response in which the magnitude is stimulus dependent.

	Diffusion of Second Messenger Molecules Through Gap Junction Channels Connecting Vascular Wall Cells

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
The Relevance of Cellular Studies
Most studies with cultured cells suffer from the same intrinsic flaw, which is that not all aspects of the in vivo environment can be faithfully reproduced in culture. However, there is absolutely no question that when appropriately conducted, such studies can provide tremendous insights into the cellular events that modulate tissue physiology. This is especially true if the cellular studies are conducted under carefully defined experimental conditions on short-term cultured or enzymatically dissociated smooth muscle cells, where it has been shown that at least for some vascular smooth muscle cells, many of the physiological, pharmacological, biochemical, and morphological features expected in vivo are conserved in vitro.¹¹⁸ In this regard, much of the newly acquired molecular and biophysical information about gap junctions has necessarily been obtained on cultured or enzymatically dissociated cells. Such mechanistic studies seem justified in light of the likelihood that intercellular communication participates in the modulation of vasomotor tone and the fact that these studies cannot yet be conducted at the whole tissue level. Finally, the resolute intention of cellular studies in vitro is to elucidate the physiological boundary conditions for intercellular communication in vivo. The following discussion concentrates primarily on studies of cultured vascular smooth muscle cells, since these cells are better studied and, furthermore, inherently more stable in culture than endothelial cells.

Characterization of Gap Junction–Mediated Intercellular Communication Among Cultured Vascular Smooth Muscle Cells
Electrophysiological experiments have provided considerable appreciation of the biophysical characteristics of intercellular communication. The dual whole-cell voltage-clamp technique has demonstrated that many types of vascular smooth muscle cells in culture are well coupled by gap junctions,^{82 91 114 115} with a macroscopic junctional conductance typically between 5 and 20 nS.^{82 91 114} For cell types containing the gap junctional protein Cx43, treatment of cell pairs with the gap junctional–uncoupling agent halothane allows one to visualize unitary channel events, thus permitting estimation of individual channel conductance values. Alternatively, one can use ionic conditions that favor low levels of coupling such that unitary events can be visualized in the absence of lipophilic uncoupling agents.¹¹⁹ In general, in vascular smooth muscle cell pairs from humans (corpus cavernosum), rats (aortic), and rabbits (aortic, mesenteric, and femoral), both techniques revealed similar weakly voltage-dependent channel sizes of 30, 60, and 90 pS, respectively, electrophysiological characteristics consistent with the presence and predominance of Cx43.⁹¹ However, A7r5 cells (an embryonic rat aortic cell line) appear to have additional channel sizes, which may reflect the presence of an additional gap junction channel, nominally, Cx40.^{82 120}

Metabolic Coupling Among Vascular Smooth Muscle Cells
Consistent with electrophysiological findings, both current-carrying ions and second messenger molecules (Ca²⁺ ions and inositol trisphosphate) appear to diffuse through gap junctions between coupled human vascular smooth muscle cells in culture.³⁴ Furthermore, the intercellular diffusion of these second messenger molecules was completely and reversibly blocked by heptanol. The extent of metabolic coupling between adjacent smooth muscle cells has been most frequently studied using gap junction–permeant fluorescent dyes (eg, lucifer yellow, carboxyfluorescein, or fura 2). Such studies have shown significant intercellular coupling among diverse vascular smooth muscle cells^{82 89 91 114 115 121 122} ; moreover, these observations are consistent with similar experiments recently performed in vivo in resistance vessels.¹⁰²

The extent of metabolic coupling in cultured cells has also been shown to be altered by vasomodulators. For example, brief exposure of physiologically diverse cultured arterial smooth muscle cells (eg, human coronary, pig coronary, rat aorta, and rat mesentery) to serotonin was shown to increase junctional conductance and fluorescent dye coupling.⁹¹ The magnitude of the response and the underlying single-channel behavior varied depending on the vessel of origin. In this regard, one might hypothesize that the release of serotonin from aggregating platelets at vessel areas denuded of endothelium would exacerbate vasospastic phenomena. That is, by increasing junctional permeability, serotonin could significantly increase the number of recruited smooth muscle cells and thus enhance the size of the functional syncytial unit and the magnitude of the contractile response (Fig 4). Such a mechanism might partially explain the ability of serotonin to augment adrenergic vascular tone and underlie its proposed role in the etiology of certain vascular diseases, such as essential hypertension, coronary vasospasm, and Raynaud's disease.^{123 124 125 126 127}

Metabolic studies using cultured pulmonary vascular smooth muscle cells have also shown functional variability in dye coupling. More specifically, Bhattacharya et al¹²¹ found that pulmonary arterial smooth muscle was more highly coupled than venous smooth muscle, once again suggesting potentially important physiological differences in the extent of intercellular communication among distinct vascular smooth muscle cell types. Although the mechanism(s) responsible for such differences in intercellular coupling is not known, it is presumably related to quantitative and/or qualitative differences in the connexin(s) present in the different cell types and/or their regulation/function.

Second Messenger Regulation of Junctional Communication Between Vascular Smooth Muscle Cells
Several reports have examined the effects of second messenger molecules on the strength of intercellular coupling in cardiovascular tissues.^{91 99 115} In short, with respect to events coupled to Ca²⁺ mobilization and contractility, both modest increases (30%)¹¹⁵ and decreases (10% to 20%)⁹¹ in junctional conductance have been reported in vascular myocytes. Conversely, events coupled to activation of the cAMP pathway and relaxation generally tend to modestly diminish the degree of intercellular communication, as reflected by an 20% to 30% decrease in junctional conductance.^{91 92} Such observations suggest that the permeability of gap junction channels may be dynamically modulated during cellular activation in response to either contractile or relaxant stimulation. For example, in human vascular tissue, the observed changes in junctional conductance were accompanied by significant changes in the frequency distribution of the individual channel conductance values characteristic of Cx43.¹¹⁵ Thus, changes in the distribution of the channel conductances in response to activation of protein kinase A and/or C may have an impact on the extent of intercellular coupling and thus on the level of vascular smooth muscle tone. Such studies clearly underscore the potential complexity of junctional regulation in vascular tissues. However, to put such observations in proper perspective, it is important to point out that the experimentally determined characteristics of these channels indicate that 90% to 99% of the junctional channels would have to be closed/inactivated/removed in order to affect physiologically relevant changes in cell-to-cell coupling. Moreover, mathematical modeling predicts that downregulation of intercellular communication is much more likely to be physiologically relevant than upregulation¹¹⁷ (see below). Thus, the physiological relevance, if any, of these modest second messenger–mediated alterations in junctional coupling remains uncertain.

Permselectivity of Gap Junction Channels
A discussion of permselectivity was reserved for last, as it applies more to the biophysical properties of the channels themselves than to the cell type in which they are expressed. Since vascular wall cells express multiple connexins, it is conceivable that cells might modulate or modify the rate of intercellular transfer of specific cytosolic molecules by altering the number and or types of connexins within the membrane. There are a few mammalian connexins, and nonmammalian forms as well, where permselectivity has been determined. The data provide one overwhelming fact: gap junction channels are poorly selective. They are permissive with regard to both cations and anions. This is true for Cx32 and Cx26 in rat cells (anion-to-cation ratio, 0.6),¹²⁸ human Cx37 studied in transfected N2A cells (anion-to-cation ratio, 0.4),¹²⁹ chick Cx45 studied in transfected N2A cells (anion-to-cation ratio, 0.2),¹³⁰ and even invertebrate connexins (anion-to-cation ratio, 0.55).¹³¹ Although all gap junctions studied are poorly selective, some are more selective than others. Channels with greater anionic permissiveness might well be expected to enhance the efficiency of anionic second messenger diffusion from cell to cell relative to a connexin with lesser permissiveness. Thus, permselectivity and the total number of functional channel types present at any one time, along with their respective gating characteristics, are important parameters to evaluate in any nonexcitable cell type where syncytial behaviors are demonstrated. The smooth muscle and endothelial cells of vasculature are but two examples among many such tissue types.

	Modeling Intercellular Communication Mediated by Gap Junctions

Top Abstract Introduction Neuronal Innervation of Vascular... Electrical Properties of... Intercellular Communication... Physiological Evidence for a... Diffusion of Second Messenger... Modeling Intercellular... Neuronal Innervation, Signal... Pathophysiology of Gap Junctions Summary and Conclusions References

 
Intercellular Diffusion
At this juncture, it seems prudent to codify all of the aforementioned anatomic, pharmacological, molecular, and biophysical information about gap junctions. The goal is to use the available data to generate a model concerning the anticipated role of gap junctions in modulating vasomotor responses that will be amenable to experimental verification. As a starting point, the salient features of gap junctions composed of Cx43 in vascular smooth muscle are summarized in Table 3.

View this table: [in this window] [in a new window]   Table 3. Summary of Physiological Properties of Connexin43-Derived Gap Junction Channels Between Vascular Smooth Muscle Cells

In this regard, the discrete steplike pattern observed for the propagation of Ca²⁺ waves reported for epithelial and glial cells¹³² provides a simple system in which to evaluate the characteristics and modulation of intercellular second messenger propagation. Additionally, the architecture of many blood vessels is well described, and this makes them readily amenable to computer modeling analyses^{89 117} (Fig 5). Thus, the tissue monolayer model originally proposed by Brink and Ramanan¹³³ was used to assess the anticipated intercellular diffusion of second messenger molecules through gap junctions. The predicted intercellular diffusion profile for second messenger molecules/ions through gap junctions between the cells was then compared with the diffusion profile anticipated for the flow of neurotransmitter molecules in the extracellular space around the cells. The modeling studies suggested the following. First, if one assumes passive intercellular diffusion, then the profile for intercellular transit of second messenger molecules between vascular smooth muscles can approximate, but not exceed, the predicted diffusion profile for the drug or neurotransmitter in the extracellular space (Fig 6). In theory, then, the intercellular and extracellular passive diffusion pathways are roughly equivalent. However, experimental studies on isolated vascular tissues indicate that the physiologically important pathway is likely to be the intercellular pathway.^{34 38 89 95 99 114 115} Moreover, if one takes into account tissue tortuosity factors,¹³⁴ variations in neuromuscular distances,^{1 3 5 135} the small amount of neurotransmitter actually released during nervous activity, and the short half-lives of the physiologically relevant neurotransmitters,¹⁴ it is clear that the extracellular diffusion profile may fall off much more sharply than depicted (ie, be even steeper). Conversely, there is experimental evidence for the presence of regenerative gap junction–mediated intercellular inositol trisphosphate and/or Ca²⁺ waves in some cell types,¹³⁶ including human corporal smooth muscle.³⁴ Taken together, these data seem to suggest that intercellular signals would have larger space constants than extracellular neurotransmitters.

View larger version (75K): [in this window] [in a new window]   Figure 5. Depiction of how gap junctions might be expected to participate in coordination of vascular responses. For comparative purposes, panel A shows a phase contrast view of a cryostat section of frozen rat aorta, defining the different anatomic regions of this vessel (magnification x400). Panel B illustrates a model for gap junctional modulation of vascular tone in a small resistance blood vessel with several layers of medial smooth muscle, as described in a recent report.89 The generalized morphology shows axonal processes only at the adventitial-medial smooth muscle border. Thus, only the smooth muscle cells nearest the adventitial surface are near presynaptic nerve terminals (varicosities). Five layers of smooth muscle cells and a monolayer of endothelial cells are illustrated, with the cells interconnected by gap junctions. The outermost cells are directly activated by neurotransmitter released from the synaptic terminal. The shaded region indicates those cells with increased intracellular second messenger concentrations after direct neurotransmitter activation. Second messenger molecules would then diffuse through the cytoplasm and junctional channels into neighboring cells. Since all the cells of the surface are simultaneously activated, diffusion out of this layer into the next can be treated as a one-dimensional diffusion case. In the right panel, modeling intercellular diffusion through gap junctions is shown. At the top of the panel is a comparison of computer-generated curves for intercellular diffusion of second messenger molecules in vascular wall cells with differing junctional permeabilities. As schematically depicted, the three diffusion profiles (A, B, and C) reflect the intercellular diffusion of second messenger molecules from a constant source (cell 1 to as many as five cells distantly removed). The arrows in the diffusion profile emphasize the discontinuous nature of the curves and also highlight the differential intercellular second messenger concentrations expected across the junctional membrane of contiguous cells. For curve B, the junctional permeability is that expected of modestly coupled vascular wall cells (5x10-5 cm/s), whereas curves A (5x10-4 cm/s) and C (5x10-6 cm/s) show the effects of increasing or reducing junctional permeability by 10-fold, respectively. In this regard, recent studies demonstrate that 3- to 10-fold changes in junctional permeability (either upregulation or downregulation) would be expected to be associated with physiologically relevant changes in the number of cells recruited into the functional syncytial unit.125 As shown, cell width was assumed to be 10 µm for these calculations.

View larger version (12K): [in this window] [in a new window]   Figure 6. Comparison of computer-generated diffusion profiles for extracellular neurotransmitter diffusion (eg, norepinephrine) and intercellular diffusion of stable second messenger molecules (eg, Ca2+, inositol trisphosphate, and cAMP). The continuous line at the top represents the expected diffusion of neurotransmitter in the extracellular space, as described elsewhere.89 The other curve represents the expected intercellular diffusion profile for stable second messenger molecules in a linear series of cells labeled from 1 (top of graph) to 5. In this model, cell 1 is expected to have some arbitrary, but constant, concentration of second messenger molecules due to persistent receptor activation by agonist. Thus, the model depicts the expected passive diffusion of second messenger molecules from cell 1 to as many as five cells distantly removed. The arrows in the diffusion profile emphasize the discontinuous nature of the curves and also highlight the differential intercellular second messenger concentrations expected across the junctional membrane of contiguous cells. The junctional permeability used for this comparison was 5x10-4 cm/s, a junctional permeability characteristic of well-coupled vascular wall cells expressing the gap junction protein connexin43. Note that even though, in theory, the extracellular diffusion pathway might exceed that of the intercellular diffusion profile, the selective uncoupling actions of heptanol in vascular smooth muscle demonstrate that the intercellular pathway is the physiologically relevant one.89

Dynamic Changes in Cell-to-Cell Communication Through Gap Junctions
The discussion so far has centered around the evidence indicating that gap junctions participate in modulating vasomotor tone. The relevant issue is how gap junctions might affect vascular tone. In fact, until recently, there was no theoretical construct for understanding how dynamic changes in the extent of intercellular communication among coupled cells might participate in modulating vascular homeostasis and/or be involved in the pathogenesis of vascular disease (where the term dynamic changes in cell-to-cell communication refers to changes in junctional permeability that occur over the same time course as response generation). In fact, two observations suggested a dynamic role for gap junctions in the modulation of vascular tissue responses: (1) the demonstration of the rapid intercellular transit of physiologically relevant receptor-activated second messenger molecules through gap junctions between coupled cells in culture^{128 132 137 138 139 140 141} and (2) the fact that junctional permeability can be modulated by those same second messenger molecules to which the channels are freely diffusible.^{81 91 115 128 138} Thus, as discussed above, permeant second messenger molecules might provide an important link in the coordination of tissue responses by virtue of their ability to recruit cells not directly activated by locally restricted neuronal or endothelial signals as well as by their ability to directly modulate junctional permeability after changes in their own intracellular concentrations. Modeling studies suggested that for the dynamic modulation of junctional communication, downregulation was likely to be much more important than upregulation. These relationships are summarized in Fig 7. Recent patch-clamp studies^{115 142} have revealed that the mechanistic basis for this observation is related to the relatively high open probabilities and the long mean open times characteristic of Cx43-derived gap junction channels (Table 3).

View larger version (37K): [in this window] [in a new window]   Figure 7. Three-dimensional graph of the results of a model for the dynamic modulation of connexin43-mediated junctional permeability. The x axis represents the nascent probability (pn) that a channel is open. The y axis is the unitless parameter (C/k1/2) in a log scale, where C represents the concentration of the diffusing substance (ie, second messenger molecule) at the initial time of cellular activation, and k1/2 is the concentration of second messenger at which half of the hemichannels are occupied/phosphorylated by the substance. The z axis is the effective diffusion coefficient; Deff (the effective diffusion coefficient in units of 10-8 cm2/s) is a composite measure of the effects of both diffusion and membrane permeability. The upward-curving sheet is for substances that upmodulate gap junction channels in the junctional plaque (ie, cause an increase in the open probability of the channels), the bottom sheet is for downmodulators, and the sandwiched sheet is for substances that do not modulate gap junction channels. In short, the effects of upregulation and downregulation can be seen over a wide range of physiologically relevant conditions. However, consistent with the known biophysical characteristics of connexin43 (see Table 3), the graph indicates that downregulation is more prominent under more diverse physiological conditions (reproduced with permission125 ).