Cells coupled by voltage-dependent gap junctions: the asymptotic dynamical limit

We study the steady state and dynamical properties of a pair of cells coupled by a voltage-dependent gap junction. The cells have linear membrane properties, and the gap junction is modelled using a simple Markov chain with a voltage-dependent transition matrix. We first show that the voltage-independent case is globally convergent using energy dissipation as a Lyapunov function for the cells, and standard results on the convergence of homogeneous Markov chains for the junction. For the voltage-dependent case, we use the difference in cell and gap junction time scales to reduce the coupled equations for cells and the gap junction to a single equation for the gap junction, but with a transition matrix that depends upon the current gap junction state. We identify cooperativity as key property behind the global convergence of Markov chains and investigate convergence of the voltage-dependent system by establishing some conditions under which cooperativity is preserved.     

Biophysical properties of gap junction channels formed by mouse connexin40 in induced pairs of transfected human HeLa cells.

A clone of human HeLa cells stably transfected with mouse connexin40 DNA was used to examine gap junctions. Two separate cells were brought into physical contact with each other ("induced cell pair") to allow insertion of gap junction channels and, hence, formation of a gap junction. The intercellular current flow was measured with a dual voltage-clamp method. This approach enabled us to study the electrical properties of gap junction channels (cell pairs with a single channel) and gap junctions (cell pairs with many channels). We found that single channels exhibited multiple conductances, a main state (gamma j(main state)), several substates (gamma j(substates)), a residual state (gamma j (residual state)), and a closed state (gamma j(closed state)). The gamma j(main state) was 198 pS, and gamma j(residual state) was 36 pS (temperature, 36-37 degrees C; pipette solution, potassium aspartate). Both properties were insensitive to transjunctional voltage, Vj. The transitions between the closed state and an open state (i.e., residual state, substate, or main state) were slow (15-45 ms); those between the residual state and a substate or the main state were fast (1-2 ms). Under steady-state conditions, the open channel probability, Po, decreased in a sigmoidal manner from 1 to 0 (Boltzmann fit: Vj,o = -44 mV; z = 6). The temperature coefficient, Q10, for gamma j(main state) and gamma j(residual state) was 1.2 and 1.3, respectively (p < 0.001; range 15-40 degrees C). This difference suggests interactions between ions and channel structure in case of gamma j(residual state). In cell pairs with many channels, the gap junction conductance at steady state, gj, exhibited a bell-shaped dependency from Vj (Boltzmann fit, negative Vj, Vj,o = -45 mV, gj(min) = 0.24; positive Vj, Vj,o = 49 mV, gj(min) = 0.26; z = 6). We conclude that each channel is controlled by two types of gates, a fast one responsible for Vj gating and involving transitions between open states (i.e., residual state, substates, main state), and a slow one involving transitions between the closed state and an open state.     

Emergence of complex behaviour from simple circuit structures

The set of (feedback) circuits of a complex system is the machinery that allows the system to be aware of the levels of its crucial constituents. Circuits can be identified without ambiguity from the elements of the Jacobian matrix of the system. There are two types of circuits: positive if they comprise an even number of negative interactions, negative if this number is odd. The two types of circuits play deeply different roles: negative circuits are required for homeostasis, with or without oscillations, positive circuits are required for multistationarity, and hence, in biology, for differentiation and memory. In non-linear systems, a circuit can positive or negative (an 'ambiguous circuit', depending on the location in phase space. Full circuits are those circuits (or unions of disjoint circuits) that imply all the variables of the system. There is a tight relation between circuits and steady states. Each full circuit, if isolated, generates steady state(s) whose nature (eigenvalues) is determined by the structure of the circuit. Multistationarity requires the presence of at least two full circuits of opposite Eisenfeld signs, or else, an ambiguous circuit. We show how a significant part of the dynamical behaviour of a system can be predicted by a mere examination of its Jacobian matrix. We also show how extremely complex dynamics can be generated by such simple logical structures as a single (full and ambiguous) circuit.     

Differential regulation of distinct types of gap junction channels by similar phosphorylating conditions.

Studies on physiological modulation of intercellular communication mediated by protein kinases are often complicated by the fact that cells express multiple gap junction proteins (connexins; Cx). Changes in cell coupling can be masked by simultaneous opposite regulation of the gap junction channel types expressed. We have examined the effects of activators and inhibitors of protein kinase A (PKA), PKC, and PKG on permeability and single channel conductance of gap junction channels composed of Cx45, Cx43, or Cx26 subunits. To allow direct comparison between these Cx, SKHep1 cells, which endogenously express Cx45, were stably transfected with cDNAs coding for Cx43 or Cx26. Under control conditions, the distinct types of gap junction channels could be distinguished on the basis of their permeability and single channel properties. Under various phosphorylating conditions, these channels behaved differently. Whereas agonists/antagonist of PKA did not affect permeability and conductance of all gap junction channels, variable changes were observed under PKC stimulation. Cx45 channels exhibited an additional conductance state, the detection of the smaller conductance states of Cx43 channels was favored, and Cx26 channels were less often observed. In contrast to the other kinases, agonists/antagonist of PKG affected permeability and conductance of Cx43 gap junction channels only. Taken together, these results show that distinct types of gap junction channels are differentially regulated by similar phosphorylating conditions. This differential regulation may be of physiological importance during modulation of cell-to-cell communication of more complex cell systems.     

Gap junction channels: distinct voltage-sensitive and -insensitive conductance states.

All mammalian gap junction channels are sensitive to the voltage difference imposed across the junctional membrane, and parameters of voltage sensitivity have been shown to vary according to the gap junction protein that is expressed. For connexin43, the major gap junction protein in the cardiovascular system, in the uterus, and between glial cells in brain, voltage clamp studies have shown that transjunctional voltages (Vj) exceeding +/- 50 mV reduce junctional conductance (gj). However, substantial gj remains at even very large Vj values; this residual voltage-insensitive conductance has been termed gmin. We have explored the mechanism underlying gmin using several cell types in which connexin43 is endogenously expressed as well as in communication-deficient hepatoma cells transfected with cDNA encoding human connexin43. For pairs of transfectants exhibiting series resistance-corrected maximal gj (gmax) values ranging from < 2 to > 90 nS, the ratio gmin/gmax was found to be relatively constant (about 0.4-0.5), indicating that the channels responsible for the voltage-sensitive and -insensitive components of gj are not independent. Single channel studies further revealed that different channel sizes comprise the voltage-sensitive and -insensitive components, and that the open times of the larger, more voltage-sensitive conductance events declined to values near zero at large voltages, despite the high gmin. We conclude that the voltage-insensitive component of gj is ascribable to a voltage-insensitive substate of connexin43 channels rather than to the presence of multiple types of channels in the junctional membrane. These studies thus demonstrate that for certain gap junction channels, closure in response to specific stimuli may be graded, rather than all-or-none.     

Influence of dynamic gap junction resistance on impulse propagation in ventricular myocardium: a computer simulation study

The gap junction connecting cardiac myocytes is voltage and time dependent. This simulation study investigated the effects of dynamic gap junctions on both the shape and conduction velocity of a propagating action potential. The dynamic gap junction model is based on that described by Vogel and Weingart (J. Physiol. (Lond.). 1998, 510:177-189) for the voltage- and time-dependent conductance changes measured in cell pairs. The model assumes that the conductive gap junction channels have four conformational states. The gap junction model was used to couple 300 cells in a linear strand with membrane dynamics of the cells defined by the Luo-Rudy I model. The results show that, when the cells are tightly coupled (6700 channels), little change occurs in the gap junction resistance during propagation. Thus, for tight coupling, there are negligible differences in the waveshape and propagation velocity when comparing the dynamic and static gap junction representations. For poor coupling (85 channels), the gap junction resistance increases 33 MOmega during propagation. This transient change in resistance resulted in increased transjunctional conduction delays, changes in action potential upstroke, and block of conduction at a lower junction resting resistance relative to a static gap junction model. The results suggest that the dynamics of the gap junction enhance cellular decoupling as a possible protective mechanism of isolating injured cells from their neighbors.     

Gating of Connexin Channels by transjunctional-voltage: Conformations and models of open and closed states

Voltage is an important physiologic regulator of channels formed by the connexin gene family. Connexins are unique among ion channels in that both plasma membrane inserted hemichannels (undocked hemichannels) and intercellular channels (aggregates of which form gap junctions) have important physiological roles. The hemichannel is the fundamental unit of gap junction voltage-gating. Each hemichannel displays two distinct voltage-gating mechanisms that are primarily sensitive to a voltage gradient formed along the length of the channel pore (the transjunctional voltage) rather than sensitivity to the absolute membrane potential (V_m or V_i-o). These transjunctional voltage dependent processes have been termed V_j- or fast-gating and loop- or slow-gating. Understanding the mechanism of voltage-gating, defined as the sequence of voltage-driven transitions that connect open and closed states, first and foremost requires atomic resolution models of the end states. Although ion channels formed by connexins were among the first to be characterized structurally by electron microscopy and x-ray diffraction in the early 1980′s, subsequent progress has been slow. Much of the current understanding of the structure-function relations of connexin channels is based on two crystal structures of Cx26 gap junction channels. Refinement of crystal structure by all-atom molecular dynamics and incorporation of charge changing protein modifications has resulted in an atomic model of the open state that arguably corresponds to the physiologic open state. Obtaining validated atomic models of voltage-dependent closed states is more challenging, as there are currently no methods to solve protein structure while a stable voltage gradient is applied across the length of an oriented channel. It is widely believed that the best approach to solve the atomic structure of a voltage-gated closed ion channel is to apply different but complementary experimental and computational methods and to use the resulting information to derive a consensus atomic structure that is then subjected to rigorous validation. In this paper, we summarize our efforts to obtain and validate atomic models of the open and voltage-driven closed states of undocked connexin hemichannels.This article is part of a Special Issue entitled: Gap Junction Proteins edited by Jean Claude Herve.     

Limitations of the dual voltage clamp method in assaying conductance and kinetics of gap junction channels.

The electrical properties of gap junctions in cell pairs are usually studied by means of the dual voltage clamp method. The voltage across the junctional channels, however, cannot be controlled adequately due to an artificial resistance and a natural resistance, both connected in series with the gap junction. The access resistances to the cell interior of the recording pipettes make up the artificial resistance. The natural resistance consists of the cytoplasmic access resistances to the tightly packed gap junction channels in both cells. A mathematical model was constructed to calculate the actual voltage across each gap junction channel. The stochastic open-close kinetics of the individual channels were incorporated into this model. It is concluded that even in the ideal case of complete compensation of pipette series resistance, the number of channels comprised in the gap junction may be largely underestimated. Furthermore, normalized steady-state junctional conductance may be largely overestimated, so that transjunctional voltage dependence is easily masked. The model is used to discuss conclusions drawn from dual voltage clamp experiments and offers alternative explanations for various experimental observations.     

Gating properties of heterotypic gap junction channels formed of connexins 40, 43, and 45

Connexins (Cxs) 40, 43, and 45 are expressed in many different tissues, but most abundantly in the heart, blood vessels, and the nervous system. We examined formation and gating properties of heterotypic gap junction (GJ) channels assembled between cells expressing wild-type Cx40, Cx43, or Cx45 and their fusion forms tagged with color variants of green fluorescent protein. We show that these Cxs, with exception of Cxs 40 and 43, are compatible to form functional heterotypic GJ channels. Cx40 and Cx43 hemichannels are unable or effectively impaired in their ability to dock and/or assemble into junctional plaques. When cells expressing Cx45 contacted those expressing Cx40 or Cx43 they readily formed junctional plaques with cell-cell coupling characterized by asymmetric junctional conductance dependence on transjunctional voltage, V(j). Cx40/Cx45 heterotypic GJ channels preferentially exhibit V(j)-dependent gating transitions between open and residual states with a conductance of approximately 42 pS; transitions between fully open and closed states with conductance of approximately 52 pS in magnitude occur at substantially lower ( approximately 10-fold) frequency. Cx40/Cx45 junctions demonstrate electrical signal transfer asymmetry that can be modulated between unidirectional and bidirectional by small changes in the difference between holding potentials of the coupled cells. Furthermore, both fast and slow gating mechanisms of Cx40 exhibit a negative gating polarity.     

Voltage-dependent gating of single gap junction channels in an insect cell line.

De novo formation of cell pairs was used to examine the gating properties of single gap junction channels. Two separate cells of an insect cell line (clone C6/36, derived from the mosquito Aedes albopictus) were pushed against each other to provoke formation of gap junction channels. A dual voltage-clamp method was used to control the voltage gradient between the cells (Vj) and measure the intercellular current (Ij). The first sign of channel activity was apparent 4.7 min after cell contact. Steady-state coupling reached after 30 min revealed a conductance of 8.7 nS. Channel formation involved no leak between the intra- and extracellular space. The first opening of a newly formed channel was slow (25-28 ms). Each preparation passed through a phase with only one operational gap junction channel. This period was exploited to examine the single channel properties. We found that single channels exhibit several conductance states with different conductances gamma j; a fully open state (gamma j(main state)), several substates (gamma j(substates)), a residual state (gamma j(residual)) and a closed state (gamma j(closed)). The gamma j(main state) was 375 pS, and gamma j(residual) ranged from 30 to 90 pS. The transitions between adjacent substates were 1/7-1/4 of gamma j(main state). Vj had no effect on gamma j(main state), but slightly affected gamma j (residual). The lj transitions involving gamma j(closed) were slow (15-60 ms), whereas those not involving gamma j(closed) were fast (< 2 ms). An increase in Vj led to a decrease in open channel probability. Depolarization of the membrane potential (Vm) increased the incidence of slow transitions leading to gamma j(closed). We conclude that insect gap junctions possess two gates, a fast gate controlled by Vj and giving rise to gamma j(substates) and gamma j(residual), and a slow gate sensitive to Vm and able to close the channel completely.     

Transfection of mammalian cells with connexins and measurement of voltage sensitivity of their gap junctions

Vertebrate gap junction channels are formed by a family of more than 20 connexin proteins. These gap junction proteins are expressed with overlapping cellular and tissue specificity, and coding region mutations can cause human hereditary diseases. Here we present a summary of what has been learned from voltage clamp studies performed on cell pairs either endogenously expressing gap junctions or in which connexins are exogenously expressed. General protocols presented here are currently used to transfect mammalian cells with connexins and to study the biophysical properties of the heterologously expressed connexin channels. Transient transfection is accomplished overnight with maximal expression occurring at about 36 h; stable transfectants normally can be generated within three or four weeks through colony selection. Electrophysiological protocols are presented for analysis of voltage dependence and single-channel conductance of gap junction channels as well as for studies of chemical gating of these channels.     

Neonatal rat cardiomyocytes show characteristics of nonhomotypic gap junction channels

Neonatal rat cardiomyocytes mainly coexpress the connexins Cx40, Cx43, and to a small amount Cx45, leading to potential formation of mixed (heteromeric/heterotypic) gap junction channels. Using the dual-voltage clamp technique with switching clamp circuits, the authors investigated voltage sensitivity of gap junction channels between cell pairs of Cx40, Cx43, and Cx45 stably transfected HeLa cells and compared those data to data obtained from cell pairs of cultured neonatal rat cardiomyocytes. In accordance to previously published data, the relationship between normalized conductance and transjunctional voltage (g/V(j)) was quasisymmetrical for the transfected HeLa cells, indicating homotypic gap junction channels. Boltzmann curves fitted to data obtained from neonatal rat cardiomyocyte pairs expressing both Cx40 and Cx43 showed an asymmetrical inactivation pattern, which cannot be explained by the presence of pure populations of homotypic gap junction channels of either isoform. In conclusion the authors assume the additional presence of heterotypic and possibly even heteromeric gap junction channels in neonatal rat cardiomyocytes.     

Functional consequences of heterogeneous gap junction channel formation and its influence in health and disease

The capacity of multiple connexins to hetero-oligomerize into functional heterogeneous gap junction channels has been demonstrated in vivo, in vitro, and in nonmammalian expression systems. These heterogeneous channels display gating activity, channel conductances, selectivity and regulatory behaviors that are sometimes not predicted by the behaviors of the corresponding homogeneous channels. Such observations suggest that heteromerization of gap junction proteins offers an efficient cellular strategy for finely regulating cell-to-cell communication. The available evidence strongly indicates that heterogeneous gap junction assembly is important to normal growth and differentiation, and may influence the appearance of several disease states. Definitive evidence that heterogeneous gap junction channels differentially regulate electrical conduction in excitable cells is absent. This review examines the prevalence, regulation, and implications of gap junction channel hetero-oligomerization.     

Gap junction channels reconstituted in two closely apposed lipid bilayers

Intercellular communication mediated by gap junction channels plays an important role in many cellular processes. In contrast to other channels, gap junction channels span two plasma membranes resulting in an intracellular location for both ends of the junctional pore and the regulatory sites for channel gating. This configuration presents unique challenges for detailed experimental studies of junctional channel physiology and ligand-activation in situ. Availability of an appropriate model system would significantly facilitate future studies of gap junction channel function and structure. Here we show that the double-membrane channel can be reconstituted in pairs of closely apposed lipid bilayers, as experienced in cells. We have trapped the calcium-sensitive dye, arsenazo III (AIII), partially calcium-saturated (AIII-Ca), in one population of connexin32 reconstituted-liposomes, and EGTA in a second one. In such mixtures, the interaction of EGTA with AIII-Ca was measured by a large color shift from blue to red (decreased absorbance at 652 nm). The exchange of these compounds through gap junctions was proportional to these decrements. Results indicate that these connexon-mediated interliposomal channels are functional and are inhibited by the addition of alpha-glycyrrhetinic acid and by flufenamic acid, two gap junction communication inhibitors. Future use of this model system has the potential to improve our understanding of the permeability and modulation of junctional channels in its native intercellular assembly.     

Functional consequences of heterogeneous gap junction channel formation and its influence in health and disease

The capacity of multiple connexins to hetero-oligomerize into functional heterogeneous gap junction channels has been demonstrated in vivo¹, in vitro², and in nonmammalian expression systems. These heterogeneous channels display gating activity, channel conductances, selectivity and regulatory behaviors that are sometimes not predicted by the behaviors of the corresponding homogeneous channels. Such observations suggest that heteromerization of gap junction proteins offers an efficient cellular strategy for finely regulating cell-to-cell communication. The available evidence strongly indicates that heterogeneous gap junction assembly is important to normal growth and differentiation, and may influence the appearance of several disease states. Definitive evidence that heterogeneous gap junction channels differentially regulate electrical conduction in excitable cells is absent. This review examines the prevalence, regulation, and implications of gap junction channel hetero-oligomerization.     

Sharing signals: connecting lung epithelial cells with gap junction channels

Gap junction channels enable the direct flow of signaling molecules and metabolites between cells. Alveolar epithelial cells show great variability in the expression of gap junction proteins (connexins) as a function of cell phenotype and cell state. Differential connexin expression and control by alveolar epithelial cells have the potential to enable these cells to regulate the extent of intercellular coupling in response to cell stress and to regulate surfactant secretion. However, defining the precise signals transmitted through gap junction channels and the cross talk between gap junctions and other signaling pathways has proven difficult. Insights from what is known about roles for gap junctions in other systems in the context of the connexin expression pattern by lung cells can be used to predict potential roles for gap junctional communication between alveolar epithelial cells.     

Connexin32 gap junction channels in stably transfected cells: unitary conductance.

Pairs of SKHep1 cells, which are derived from a highly metastatic human hepatoma, were studied using the whole cell voltage clamp technique with patch-type electrodes containing CsCl as the major ionic species. In 12 of 81 cell pairs, current flow through junctional membranes was detectable; in the remaining 69 cell pairs, junctional conductance was less than the noise limit of our recording apparatus (worst case: 10 pS). Macroscopic junctional conductance (gj) in the small percentage of pairs where it was detectable ranged from 100 to 600 pS. Unitary junctional conductance (gamma j) determined in the lowest conductance pairs or after reducing conductance with a short exposure to the uncoupling agent halothane was 25-35 pS. To study properties of gap junction channels formed of connexin32, the parental SKHep1 cell line was stably transfected with a plasmid containing cDNA that encodes connexin32, the major gap junction protein of rat liver cells. In 85 of 98 pairs of voltage clamped connexin32-transfected SKHep1 cells, macroscopic gj was greater than 1 nS; gj increased with time after dissociation (from 1.8 +/- 0.6 [mean +/- SE; n = 7] nS at 2 h after plating to 9.3 +/- 2.2 [n = 9] nS, the maximal value, at 24 h). Unitary conductance of gap junction channels between pairs of transfected SKHep1 cells was measured in low conductance pairs and after reducing gj by exposure to halothane or heptanol. Histograms of gamma j values in transfected cells, in 10 experiments where greater than 100 transitions were measurable, displayed two peaks; 120-130 pS and 25-35 pS. The smaller size corresponded to channels that were occasionally detected in the parental cells. We therefore conclude that connexin32 forms gap junctions channels of the 120-130 pS size class.     

Gating properties of gap junction channels assembled from connexin43 and connexin43 fused with green fluorescent protein.

We used cell lines expressing wild-type connexin43 (Cx43) and Cx43 fused with enhanced green fluorescent protein (Cx43-EGFP) to examine mechanisms of gap junction channel gating. Previously it was suggested that each hemichannel in a cell-cell channel possesses two gates, a fast gate that closes channels to a nonzero conductance or residual state via fast (< approximately 2 ms) transitions and a slow gate that fully closes channels via slow transitions (> approximately 10 ms). Here we demonstrate that transjunctional voltage (V(j)) regulates both gates and that they are operating in series and in a contingent manner in which the state of one gate affects gating of the other. Cx43-EGFP channels lack fast V(j) gating to a residual state but show slow V(j) gating. Both Cx43 and Cx43-EGFP channels exhibit slow gating by chemical uncouplers such as CO(2) and alkanols. Chemical uncouplers do not induce obvious changes in Cx43-EGFP junctional plaques, indicating that uncoupling is not caused by dispersion or internalization of junctional plaques. Similarity of gating transitions during chemical gating and slow V(j) gating suggests that both gating mechanisms share common structural elements. Cx43/Cx43-EGFP heterotypic channels showed asymmetrical V(j) gating with fast transitions between open and residual states only when the Cx43 side was relatively negative. This result indicates that the fast V(j) gate of Cx43 hemichannels closes for relative negativity at its cytoplasmic end.