Ca2+ dynamics in a population of smooth muscle cells: modeling the recruitment and synchronization

Many experimental studies have shown that arterial smooth muscle cells respond with cytosolic calcium rises to vasoconstrictor stimulation. A low vasoconstrictor concentration gives rise to asynchronous spikes in the calcium concentration in a few cells (asynchronous flashing). With a greater vasoconstrictor concentration, the number of smooth muscle cells responding in this way increases (recruitment) and calcium oscillations may appear. These oscillations may eventually synchronize and generate arterial contraction and vasomotion. We show that these phenomena of recruitment and synchronization naturally emerge from a model of a population of smooth muscle cells coupled through their gap junctions. The effects of electrical, calcium, and inositol 1,4,5-trisphosphate coupling are studied. A weak calcium coupling is crucial to obtain a synchronization of calcium oscillations and the minimal required calcium permeability is deduced. Moreover, we note that an electrical coupling can generate oscillations, but also has a desynchronizing effect. Inositol 1,4,5-trisphosphate diffusion does not play an important role to achieve synchronization. Our model is validated by published in vitro experiments obtained on rat mesenteric arterial segments.     

Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.     

Model of intercellular calcium oscillations in hepatocytes: synchronization of heterogeneous cells.

Hepatocytes respond with repetitive cytosolic calcium spikes to stimulation by vasopressin and noradrenalin. In the intact liver, calcium oscillations occur in a synchronized fashion as periodic waves across whole liver lobules, but the mechanism of intercellular coupling remains unclear. Recently, it has been shown that individual hepatocytes can have very different intrinsic oscillation frequencies but become phase-locked when coupled by gap junctions. We investigate the gap junction hypothesis for intercellular synchronization by means of a mathematical model. It is shown that junctional calcium fluxes are effective in synchronizing calcium oscillations in coupled hepatocytes. An experimentally testable estimate is given for the junctional coupling coefficient required; it mainly depends on the degree of heterogeneity between cells. Intercellular synchronization by junctional calcium diffusion may occur also in other cell types exhibiting calcium-activated calcium release through InsP(3) receptors, if the gap junctional coupling is strong enough and the InsP(3) receptors are sufficiently sensitized by InsP(3).     

Endothelial coordination of cerebral vasomotion via myoendothelial gap junctions containing connexins 37 and 40

Control of cerebral vasculature differs from that of systemic vessels outside the blood-brain barrier. The hypothesis that the endothelium modulates vasomotion via direct myoendothelial coupling was investigated in a small vessel of the cerebral circulation. In the primary branch of the rat basilar artery, membrane potential, diameter, and calcium dynamics associated with vasomotion were examined using selective inhibitors of endothelial function in intact and endothelium-denuded arteries. Vessel anatomy, protein, and mRNA expression were studied using conventional electron microscopy high-resolution ultrastructural and confocal immunohistochemistry and quantitative PCR. Membrane potential oscillations were present in both endothelial cells and smooth muscle cells (SMCs), and these preceded rhythmical contractions during which adjacent SMC intracellular calcium concentration ([Ca(2+)](i)) waves were synchronized. Endothelium removal abolished vasomotion and desynchronized adjacent smooth muscle cell [Ca(2+)](i) waves. N(G)-nitro-l-arginine methyl ester (10 microM) did not mimic this effect, and dibutyryl cGMP (300 muM) failed to resynchronize [Ca(2+)](i) waves in endothelium-denuded arteries. Combined charybdotoxin and apamin abolished vasomotion and depolarized and constricted vessels, even in absence of endothelium. Separately, (37,43)Gap27 and (40)Gap27 abolished vasomotion. Extensive myoendothelial gap junctions (3 per endothelial cell) composed of connexins 37 and 40 connected the endothelial cell and SMC layers. Synchronized vasomotion in rat basilar artery is endothelium dependent, with [Ca(2+)](i) waves generated within SMCs being coordinated by electrical coupling via myoendothelial gap junctions.     

Multiple factors influence calcium synchronization in arterial vasomotion

The intercellular synchronization of spontaneous calcium (Ca(2+)) oscillations in individual smooth muscle cells is a prerequisite for vasomotion. A detailed mathematical model of Ca(2+) dynamics in rat mesenteric arteries shows that a number of synchronizing and desynchronizing pathways may be involved. In particular, Ca(2+)-dependent phospholipase C, the intercellular diffusion of inositol trisphosphate (IP(3), and to a lesser extent Ca(2+)), IP(3) receptors, diacylglycerol-activated nonselective cation channels, and Ca(2+)-activated chloride channels can contribute to synchronization, whereas large-conductance Ca(2+)-activated potassium channels have a desynchronizing effect. Depending on the contractile state and agonist concentrations, different pathways become predominant, and can be revealed by carefully inhibiting the oscillatory component of their total activity. The phase shift between the Ca(2+) and membrane potential oscillations can change, and thus electrical coupling through gap junctions can mediate either synchronization or desynchronization. The effect of the endothelium is highly variable because it can simultaneously enhance the intercellular coupling and affect multiple smooth muscle cell components. Here, we outline a system of increased complexity and propose potential synchronization mechanisms that need to be experimentally tested.     

Mechanisms of Propagation of Intercellular Calcium Waves in Arterial Smooth Muscle Cells

In rat mesenteric arteries, smooth muscle cells exhibit intercellular calcium waves in response to local phenylephrine stimulation. These waves have a velocity of ∼20 cells/s and a range of ∼80 cells. We analyze these waves in a theoretical model of a population of coupled smooth muscle cells, based on the hypothesis that the wave results from cell membrane depolarization propagation. We study the underlying mechanisms and highlight the importance of voltage-operated channels, calcium-induced calcium release, and chloride channels. Our model is in agreement with experimental observations, and we demonstrate that calcium waves presenting a velocity of ∼20 cells/s can be mediated by electrical coupling. The wave velocity is limited by the time needed for calcium influx through voltage-operated calcium channels and the subsequent calcium-induced calcium release, and not by the speed of the depolarization spreading. The waves are partially regenerated, but have a spatial limit in propagation. Moreover, the model predicts that a refractory period of calcium signaling may significantly affect the wave appearance.     

The Role of Cellular Coupling in the Spontaneous Generation of Electrical Activity in Uterine Tissue

The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not spontaneously active. It is known, however, that the expression of gap junctions increases dramatically in the approach to parturition, by more than one order of magnitude, which results in a significant increase in inter-cellular electrical coupling. In this paper, we build upon previous studies of the activity of electrically excitable smooth muscle cells (myocytes) and investigate the mechanism through which the coupling of these cells to electrically passive cells results in the generation of spontaneous activity in the uterus. Using a recently developed, realistic model of uterine muscle cell dynamics, we investigate a system consisting of a myocyte coupled to passive cells. We then extend our analysis to a simple two-dimensional lattice model of the tissue, with each myocyte being coupled to its neighbors, as well as to a random number of passive cells. We observe that different dynamical regimes can be observed over a range of gap junction conductances: at low coupling strength, corresponding to values measured long before delivery, the activity is confined to cell clusters, while the activity for high coupling, compatible with values measured shortly before delivery, may spread across the entire tissue. Additionally, we find that the system supports the spontaneous generation of spiral wave activity. Our results are both qualitatively and quantitatively consistent with observations from in vitro experiments. In particular, we demonstrate that the increase in inter-cellular electrical coupling observed experimentally strongly facilitates the appearance of spontaneous action potentials that may eventually lead to parturition.     

Detrusor smooth muscle cells of the guinea-pig are functionally coupled via gap junctions in situ and in cell culture

Intercellular communication between smooth muscle cells is crucial for contractile behaviour in normal and pathologically altered urinary bladder. Since the study of coupling is difficult in situ, we established cell cultures of bladder smooth muscle cells to analyse coupling mechanisms. Microinjection of Lucifer yellow demonstrated syncytia composed of only a few to several dozen cells. Electron-microscopic examination of freeze-fracture specimens and ultrathin sections revealed that the dye-coupling was based on typical gap junction formation between the cultured smooth muscle cells. Furthermore, we were able to demonstrate gap junctions within the tissue fragments from which the primary cultures were grown. By Western blotting, we found connexin-43-positive protein bands both in native tissue probes from the guinea-pig urinary bladder and in smooth muscle cell cultures. Extracellular electrical stimulation of single cells evoked calcium transients, as visualized by fura-2 ratiofluorimetry. Calcium waves propagated throughout the syncytia with a declining amplitude, showing that the calcium signal was not regenerative. Therefore, the calcium signal was probably transmitted by a diffusible factor. These findings correlated well with the dye-coupling that we found between detrusor smooth muscle cells in situ. The use of smooth muscle cell cultures therefore seems to be a feasible approach for studying coupling behaviour in vitro.     

Gap junction coupling and calcium waves in the pancreatic islet

The pancreatic islet is a highly coupled, multicellular system that exhibits complex spatiotemporal electrical activity in response to elevated glucose levels. The emergent properties of islets, which differ from those arising in isolated islet cells, are believed to arise in part by gap junctional coupling, but the mechanisms through which this coupling occurs are poorly understood. To uncover these mechanisms, we have used both high-speed imaging and theoretical modeling of the electrical activity in pancreatic islets under a reduction in the gap junction mediated electrical coupling. Utilizing islets from a gap junction protein connexin 36 knockout mouse model together with chemical inhibitors, we can modulate the electrical coupling in the islet in a precise manner and quantify this modulation by electrophysiology measurements. We find that after a reduction in electrical coupling, calcium waves are slowed as well as disrupted, and the number of cells showing synchronous calcium oscillations is reduced. This behavior can be reproduced by computational modeling of a heterogeneous population of β-cells with heterogeneous levels of electrical coupling. The resulting quantitative agreement between the data and analytical models of islet connectivity, using only a single free parameter, reveals the mechanistic underpinnings of the multicellular behavior of the islet.     

Morphology of smooth muscle cells in the rat thoracic duct

Summary The three-dimensional cytoarchitecture and ultrastructure of the smooth muscle cells in the wall of the rat thoracic duct were investigated by scanning and transmission electron microscopy. The muscle layer basically consists of a single layer of circularly arranged cells. The smooth muscle cell is fusiform or ribbon-like in shape, as in veins or venules with a similar or smaller diameter. Connections by spinous processes are observed between adjacent muscle cells along their length. Spot-like membrane contacts frequently occur in areas where facing membranes are closely apposed. These are thought to be gap junctions and may be responsible for electrical coupling and mechanical attachment. Large invaginations arranged regularly in rows on the surface of the smooth muscle cells can be observed. These invaginations are closely associated with a flattened sarcoplasmic reticulum, and caveolae tend to open into the invaginations.     

Electromechanical coupling between skeletal and cardiac muscle. Implications for infarct repair

Skeletal myoblasts form grafts of mature muscle in injured hearts, and these grafts contract when exogenously stimulated. It is not known, however, whether cardiac muscle can form electromechanical junctions with skeletal muscle and induce its synchronous contraction. Here, we report that undifferentiated rat skeletal myoblasts expressed N-cadherin and connexin43, major adhesion and gap junction proteins of the intercalated disk, yet both proteins were markedly downregulated after differentiation into myo-tubes. Similarly, differentiated skeletal muscle grafts in injured hearts had no detectable N-cadherin or connexin43; hence, electromechanical coupling did not occur after in vivo grafting. In contrast, when neonatal or adult cardiomyocytes were cocultured with skeletal muscle, approximately 10% of the skeletal myotubes contracted in synchrony with adjacent cardiomyocytes. Isoproterenol increased myotube contraction rates by 25% in coculture without affecting myotubes in monoculture, indicating the cardiomyocytes were the pacemakers. The gap junction inhibitor heptanol aborted myotube contractions but left spontaneous contractions of individual cardiomyocytes intact, suggesting myotubes were activated via gap junctions. Confocal microscopy revealed the expression of cadherin and connexin43 at junctions between myotubes and neonatal or adult cardiomyocytes in vitro. After microinjection, myotubes transferred dye to neonatal cardiomyocytes via gap junctions. Calcium imaging revealed synchronous calcium transients in cardiomyocytes and myotubes. Thus, cardiomyocytes can form electromechanical junctions with some skeletal myotubes in coculture and induce their synchronous contraction via gap junctions. Although the mechanism remains to be determined, if similar junctions could be induced in vivo, they might be sufficient to make skeletal muscle grafts beat synchronously with host myocardium.     

Structural and functional studies of myometrial gap junctions

Gap junctions are believed to be sites of metabolic and electrical coupling between cells. These contacts are present between myometrial cells immediately prior to and during parturition. We report the results of studies to investigate the control and the function of myometrial gap junctions. Injection of estradiol (500 micrograms/day) with or without progesterone into immature and ovariectomized mature rats demonstrated that estradiol stimulated whereas progesterone suppressed gap junction formation. Indomethacin treatment was also shown to potentiate the action of estradiol. Also, pregnant rats treated with oestradiol developed numerous myometrial gap junctions and aborted their fetuses. These results suggest that the steroid hormones and prostaglandins may control myometrial gap junction development. Diffusion studies of 3H-2-deoxyglucose in longitudinal myometrial strips revealed a significant increase in the diffusion coefficient in delivering versus ante-partum rat tissues. This indicates that there is increased metabolic transfer during parturition when gap junctions are present. The results of these studies show that steroid hormones and prostaglandins may regulate myometrial gap junctions and that metabolic, as well as electrical coupling, of uterine smooth muscle cells increase at parturition concomitant with the development of gap junctions.     

Immunocytochemical demonstration of the gap junction proteins connexin 43 and connexin 45 in the musculature of the rat small intestine

The immunohistochemical localization of connexin (Cx) 43 and Cx 45 in the musculature of the rat small intestine was studied at the ultrastructural level, with special reference to the interstitial cells of Cajal in the deep muscular plexus region (ICC-DMP). Cx 43 was localized at gap junctions formed between every group of cells, i.e., smooth muscle cell~smooth muscle cell, smooth muscle cell--ICC-DMP and ICC-DMP--ICC-DMP. In contrast, Cx 45 immunoreactivity was only detected at gap junctions between ICC-DMP--ICC-DMP. Since different types of Cx molecules have different properties for electrical and chemical coupling of cells, it is suggested that the homotypic network of ICC-DMP connected with Cx 45 gap junctions may function as an independent compartment segregated from the whole cellular network including the smooth muscle cells connected with Cx 43 gap junctions. It is further speculated that the ICC-DMP of the rat small intestine communicate with each other and with smooth muscle cells via the passage of messenger molecules through Cx 43, but they may use an additional mechanism, as yet unknown, for communications restricted to other ICC-DMP.     

Rhythmic coupling among cells in the suprachiasmatic nucleus

In mammals, the part of the nervous system responsible for most circadian behavior can be localized to a pair of structures in the hypothalamus known as the suprachiasmatic nucleus (SCN). Previous studies suggest that the basic mechanism responsible for the generation of these rhythms is intrinsic to individual cells. There is also evidence that the cells within the SCN are coupled to one another and that this coupling is important for the normal functioning of the circadian system. One mechanism that mediates coordinated electrical activity is direct electrical connections between cells formed by gap junctions. In the present study, we used a brain slice preparation to show that developing SCN cells are dye coupled. Dye coupling was observed in both the ventrolateral and dorsomedial subdivisions of the SCN and was blocked by application of a gap junction inhibitor, halothane. Dye coupling in the SCN appears to be regulated by activity-dependent mechanisms as both tetrodotoxin and the GABA(A) agonist muscimol inhibited the extent of coupling. Furthermore, acute hyperpolarization of the membrane potential of the original biocytin-filled neuron decreased the extent of coupling. SCN cells were extensively dye coupled during the day when the cells exhibit synchronous neural activity but were minimally dye coupled during the night when the cells are electrically silent. Immunocytochemical analysis provides evidence that a gap-junction-forming protein, connexin32, is expressed in the SCN of postnatal animals. Together the results are consistent with a model in which gap junctions provide a means to couple SCN neurons on a circadian basis.     

Effects of arterial wall stress on vasomotion

Smooth muscle and endothelial cells in the arterial wall are exposed to mechanical stress. Indeed blood flow induces intraluminal pressure variations and shear stress. An increase in pressure may induce a vessel contraction, a phenomenon known as the myogenic response. Many muscular vessels present vasomotion, i.e., rhythmic diameter oscillations caused by synchronous cytosolic calcium oscillations of the smooth muscle cells. Vasomotion has been shown to be modulated by pressure changes. To get a better understanding of the effect of stress and in particular pressure on vasomotion, we propose a model of a blood vessel describing the calcium dynamics in a coupled population of smooth muscle cells and endothelial cells and the consequent vessel diameter variations. We show that a rise in pressure increases the calcium concentration. This may either induce or abolish vasomotion, or increase its frequency depending on the initial conditions. In our model the myogenic response is less pronounced for large arteries than for small arteries and occurs at higher values of pressure if the wall thickness is increased. Our results are in agreement with experimental observations concerning a broad range of vessels.     

Model for synchronization of pancreatic beta-cells by gap junction coupling.

Pancreatic beta-cells coupled by gap junctions in sufficiently large clusters exhibit regular electrical bursting activity, which is described by the Chay-Keizer model and its variants. According to most reports, however, isolated cells exhibit disorganized spiking. We have previously (Sherman, A. J. Rinzel, and J. Keizer, 1988. Biophys. J. 54:411-425) modeled these behaviors by hypothesizing that stochastic channel fluctuations disrupt the bursts. We showed that when cells are coupled by infinite conductance gap junctions, so that the cluster is isopotential and may be viewed as a single "supercell," the fluctuations are shared over a larger membrane area and hence dampened. Bursting emerges when there are more than approximately 50 cells in the cluster. In the model the temporal organization of spikes into bursts increases the amplitude of intracellular calcium oscillations, which may be relevant for insulin secretion. We now extend the previous work by considering the case of a true "multicell" model with finite gap junctional conductance. Whereas the previous study assumed that the cells were synchronized, we can now study the process of synchronization itself. We show that, for sufficiently large clusters, the cells both synchronize and begin to burst with moderate, physiologically reasonable gap junctional conductance. An unexpected finding is that the burst period is longer, and calcium amplitude greater, than when coupling is infinitely strong, with an optimum in the range of 150-250 pS. Our model is in good agreement with recent experimental data of Perez-Armendariz, M., D. C. Spray, and M. V. L. Bennett. (1991. Biophys. J. 59:76-92) showing extensive gap junctions in beta-cell pairs with mean interfacial conductance of 213 +/- 113 pS. The optimality property of our model is noteworthy because simple slow-wave models without spikes do not show the same behavior.     

Role of the endothelium on arterial vasomotion

It is well-known that cyclic variations of the vascular diameter, a phenomenon called vasomotion, are induced by synchronous calcium oscillations of smooth muscle cells (SMCs). However, the role of the endothelium on vasomotion is unclear. Some experimental studies claim that the endothelium is necessary for synchronization and vasomotion, whereas others report rhythmic contractions in the absence of an intact endothelium. Moreover, endothelium-derived factors have been shown to abolish vasomotion by desynchronizing the calcium signals in SMCs. By modeling the calcium dynamics of a population of SMCs coupled to a population of endothelial cells, we analyze the effects of an SMC vasoconstrictor stimulation on endothelial cells and the feedback of endothelium-derived factors. Our results show that the endothelium essentially decreases the SMCs calcium level and may move the SMCs from a steady state to an oscillatory domain, and vice versa. In the oscillatory domain, a population of coupled SMCs exhibits synchronous calcium oscillations. Outside the oscillatory domain, the coupled SMCs present only irregular calcium flashings arising from noise modeling stochastic opening of channels. Our findings provide explanations for the published contradictory experimental observations.     

Signaling across myoendothelial gap junctions--fact or fiction?

Gap junctions interconnect vascular cells homocellularly, thereby allowing the spread of signals along the vessel wall, which serve to coordinate vessel behavior. In addition, gap junctions provide heterocellular coupling between endothelial and vascular smooth muscle cells, creating so-called myoendothelial gap junctions (MEGJs). Endothelial cells control vascular tone by the release of factors that relax vascular smooth muscle. Endothelial factors include nitric oxide, prostaglandins, and an additional dilator principle, which acts by smooth muscle hyperpolarization and is therefore named endothelium-derived hyperpolarizing factor (EDHF). Whether this principle indeed relies on a factor or on intact MEGJs, which allow direct current transfer from endothelial to smooth muscle cells, has recently been questioned. Careful studies revealed the presence of vascular cell projections that make contact through the internal elastic lamina, exhibit the typical GJ morphology, and express connexins in many vessels. The functional study of the physiological role of MEGJs is confined by the difficulty of selectively blocking these channels. However, in different vessels studied in vitro, the dilation related to EDHF was sensitive to experimental interventions that block MEGJs more or less specifically. Additionally, bidirectional electrical coupling between endothelial and smooth muscle cells was demonstrated in isolated small vessels. In marked contrast, similar approaches used in conjunction with intravital microscopy, which allows examination of vascular behavior in the intact animal, did not verify electrical or dye-coupling in different models investigated. The discrepancy between in vitro and in vivo investigations may be due to size and origin of the vessels studied using these distinct experimental approaches. Additionally, MEGJ coupling is possibly tightly controlled in vivo by yet unknown mechanisms that prevent unrestricted direct signaling between endothelial and smooth muscle cells.     

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans.

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.     

Gap junctions with amacrine cells provide a feedback pathway for ganglion cells within the retina.

In primates, one type of retinal ganglion cell, the parasol cell, makes gap junctions with amacrine cells, the inhibitory, local circuit neurons. To study the effects of these gap junctions, we developed a linear, mathematical model of the retinal circuitry providing input to parasol cells. Electrophysiological studies have indicated that gap junctions do not enlarge the receptive field centres of parasol cells, but our results suggest that they make other contributions to their light responses. According to our model, the coupled amacrine cells enhance the responses of parasol cells to luminance contrast by disinhibition. We also show how a mixed chemical and electrical synapse between two sets of amacrine cells presynaptic to the parasol cells might make the responses of parasol cells more transient and, therefore, more sensitive to motion. Finally, we show how coupling via amacrine cells can synchronize the firing of parasol cells. An action potential in a model parasol cell can excite neighbouring parasol cells, but only when the coupled amacrine cells also fire action potentials. Passive conduction was ineffective due to low-pass temporal filtering. Inhibition from the axons of the coupled amacrine cells also produced oscillations that might synchronize the firing of more distant ganglion cells.