Microdomain Effects on Transverse Cardiac Propagation

The effect of gap junctional coupling, sodium ion channel distribution, and extracellular conductivity on transverse conduction in cardiac tissue is explored using a microdomain model that incorporates aspects of the inhomogeneous cellular structure. The propagation velocities found in our model are compared to those in the classic bidomain model and indicate a strong ephaptic microdomain contribution to conduction depending on the parameter regime. We show that ephaptic effects can be quite significant in the junctional spaces between cells, and that the cell activation sequence is modified substantially by these effects. Further, we find that transverse propagation can be maintained by ephaptic effects, even in the absence of gap junctional coupling. The mechanism by which this occurs is found to be cablelike in that the junctional regions act like inverted cables. Our results provide insight into several recent experimental studies that indirectly indicate a mode of action potential propagation that does not rely exclusively on gap junctions.     

Microdomain Effects on Transverse Cardiac Propagation

The effect of gap junctional coupling, sodium ion channel distribution, and extracellular conductivity on transverse conduction in cardiac tissue is explored using a microdomain model that incorporates aspects of the inhomogeneous cellular structure. The propagation velocities found in our model are compared to those in the classic bidomain model and indicate a strong ephaptic microdomain contribution to conduction depending on the parameter regime. We show that ephaptic effects can be quite significant in the junctional spaces between cells, and that the cell activation sequence is modified substantially by these effects. Further, we find that transverse propagation can be maintained by ephaptic effects, even in the absence of gap junctional coupling. The mechanism by which this occurs is found to be cablelike in that the junctional regions act like inverted cables. Our results provide insight into several recent experimental studies that indirectly indicate a mode of action potential propagation that does not rely exclusively on gap junctions.     

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).     

Propagation of action potentials between parallel chains of cardiac muscle cells in PSpice simulation

Propagation of action potentials between parallel chains of cardiac muscle cells was simulated using the PSpice program. Excitation was transmitted from cell to cell along a strand of three or four cells not connected by low-resistance tunnels (gap-junction connexons) in parallel with one or two similar strands. Thus, two models were used: a 2 x 3 model (two parallel chains of three cells each) and a 3 x 4 model (three parallel chains of four cells each). The entire surface membrane of each cell fired nearly simultaneously, and nearly all the propagation time was spent at the cell junctions, thus giving a staircase-shaped propagation profile. The junctional delay time between contiguous cells in a chain was about 0.2-0.5 ms. A significant negative cleft potential develops in the narrow junctional clefts, whose magnitude depends on several factors, including the radial cleft resistance (Rjc). The cleft potential (Vjc) depolarizes the postjunctional membrane to threshold by a patch-clamp action. Therefore, one mechanism for the transfer of excitation from one cell to the next is by the electric field (EF) that is generated in the junctional cleft when the prejunctional membrane fires. Propagation velocity increased with elevation of Rjc. With electrical stimulation of the first cell of the first strand (cell A1), propagation rapidly spread down that chain and then jumped to the second strand (B chain), followed by jumping to the third strand (C chain) when present. The rapidity by which the parallel chains became activated depended on the longitudinal resistance of the narrow extracellular cleft between the parallel strands (Rol2). The higher the Rol2 resistance, the faster the propagation (lower propagation time) over the cardiac muscle sheet (2-dimensional). The transverse resistance of the cleft had no effect. When the first cell of the second strand (cell B1) was stimulated, propagation spread down the B chain and jumped to the other two strands (A and C) nearly simultaneously. When cell C1 was stimulated, propagation traveled down the C chain and jumped to the B chain, followed by excitation of the A chain. Thus, there was transverse propagation of excitation as longitudinal propagation was occurring. Therefore, transmission of excitation by the EF mechanism can occur between myocardial cells lying closely parallel to one another without the requirement of a specialized junction.     

Initiation and entrainment of multicellular automaticity via diffusion limited extracellular domains

Electrically excitable cells often spontaneously and synchronously depolarize in vitro and in vivo preparations. It remains unclear how cells entrain and autorhythmically activate above the intrinsic mean activation frequency of isolated cells with or without pacemaking mechanisms. Recent studies suggest that cyclic ion accumulation and depletion in diffusion-limited extracellular volumes modulate electrophysiology by ephaptic mechanisms (nongap junction or synaptic coupling). This report explores how potassium accumulation and depletion in a restricted extracellular domain induces spontaneous action potentials in two different computational models of excitable cells without gap junctional coupling: Hodgkin-Huxley and Luo-Rudy. Importantly, neither model will spontaneously activate on its own without external stimuli. Simulations demonstrate that cells sharing a diffusion-limited extracellular compartment can become autorhythmic and entrained despite intercellular electrical heterogeneity. Autorhythmic frequency is modulated by the cleft volume and potassium fluxes through the cleft. Additionally, inexcitable cells can suppress or induce autorhythmic activity in an excitable cell via a shared cleft. Diffusion-limited shared clefts can also entrain repolarization. Critically, this model predicts a mechanism by which diffusion-limited shared clefts can initiate, entrain, and modulate multicellular automaticity in the absence of gap junctions.     

Detecting and estimating rectification of gap junction conductance based on simulations of dual-cell recordings from a pair and a network of coupled cells

Gap junctions can exhibit rectification of conductance. Some reports use inequality of coupling coefficients as the first sign of the possible existence of rectification ( [Devor and Yarom, 2002], [Fan et al., 2005], [31], [Mann-Metzer and Yarom, 1999], [Nolan et al., 1999] and [Szabadics et al., 2001]). However, mathematical modeling and simulations of electrotonic coupling between an isolated pair of neurons showed conditions where the coupling coefficients were unreliable indicators of rectification. On the other hand, the transfer resistances were found to be reliable indicators of junctional rectification. The existing mathematical model of cell coupling ( [Bennett, 1966], [Devor and Yarom, 2002] and [Verselis and Veenstra, 2000]) was extended in order to measure rectification of the junctional conductances directly between dual-recorded neurons whether isolated or surrounded by a simulated 3-dimensional network of heterogeneous cells whose gap junctions offered parallel paths for current flow between the recorded neurons. The results showed that the transfer resistances could still detect rectification of the gap junction linking the dual-recorded neurons when embedded in a coupled cell network and that a mathematical model could estimate the conductances in both directions through this gap junction using only data that would be available from real dual-intracellular penetrations which allow electrophysiological recordings and intracellular staining. Rectification of gap junctions in unrecorded cells of a biologically realistic coupled cell network had negligible effects on the voltage responses of the dual-recorded neurons because of minimal current passing through these surrounding cells.     

Roles of subcellular Na+ channel distributions in the mechanism of cardiac conduction

The gap junction and voltage-gated Na⁺ channel play an important role in the action potential propagation. The purpose of this study was to elucidate the roles of subcellular Na⁺ channel distribution in action potential propagation. To achieve this, we constructed the myocardial strand model, which can calculate the current via intercellular cleft (electric-field mechanism) together with gap-junctional current (gap-junctional mechanism). We conducted simulations of action potential propagation in a myofiber model where cardiomyocytes were electrically coupled with gap junctions alone or with both the gap junctions and the electric field mechanism. Then we found that the action potential propagation was greatly affected by the subcellular distribution of Na⁺ channels in the presence of the electric field mechanism. The presence of Na⁺ channels in the lateral membrane was important to ensure the stability of propagation under conditions of reduced gap-junctional coupling. In the poorly coupled tissue with sufficient Na⁺ channels in the lateral membrane, the slowing of action potential propagation resulted from the periodic and intermittent dysfunction of the electric field mechanism. The changes in the subcellular Na⁺ channel distribution might be in part responsible for the homeostatic excitation propagation in the diseased heart.     

Fast calcium wave propagation mediated by electrically conducted excitation and boosted by CICR

We have investigated synchronization and propagation of calcium oscillations, mediated by gap junctional excitation transmission. For that purpose we used an experimentally based model of normal rat kidney (NRK) cells, electrically coupled in a one-dimensional configuration (linear strand). Fibroblasts such as NRK cells can form an excitable syncytium and generate spontaneous inositol 1,4,5-trisphosphate (IP(3))-mediated intracellular calcium waves, which may spread over a monolayer culture in a coordinated fashion. An intracellular calcium oscillation in a pacemaker cell causes a membrane depolarization from within that cell via calcium-activated chloride channels, leading to an L-type calcium channel-based action potential (AP) in that cell. This AP is then transmitted to the electrically connected neighbor cell, and the calcium inflow during that transmitted AP triggers a calcium wave in that neighbor cell by opening of IP(3) receptor channels, causing calcium-induced calcium release (CICR). In this way the calcium wave of the pacemaker cell is rapidly propagated by the electrically transmitted AP. Propagation of APs in a strand of cells depends on the number of terminal pacemaker cells, the L-type calcium conductance of the cells, and the electrical coupling between the cells. Our results show that the coupling between IP(3)-mediated calcium oscillations and AP firing provides a robust mechanism for fast propagation of activity across a network of cells, which is representative for many other cell types such as gastrointestinal cells, urethral cells, and pacemaker cells in the heart.     

Estimating conductances of dual-recorded neurons within a network of coupled cells

Simultaneous pre- and postsynaptic cell recordings are used to calculate gap junction conductance based on an equivalent electrical circuit of an electrically coupled pair of cells. This calculation is imprecise when recording from a cell pair that is coupled to neighboring cells providing indirect conductance paths between the recorded cells. Despite this imprecision, junctional conductance has been calculated for coupled cell networks during the past 40 years since a more accurate method was lacking. The present study simulated a three-dimensional network of electrically coupled heterogeneous neurons and used mathematical modeling to reduce the complexity to the simplest equations that could more accurately estimate the electrical properties of dual-recorded cells in the network. Analyses of the simulations showed that knowledge of the number of unrecorded cells directly linked to the recorded cells and of the voltage responses of these recorded cells were largely sufficient to accurately predict the direct junctional resistance linking the recorded cells as well as the input resistance of the recorded cells that would exist in the absence of junctional coupling. All model parameters could be obtained from real dual-intracellular penetrations which allow electrophysiological recordings and intracellular staining.     

Junctional transfer in cultured vascular endothelium: I. Electrical coupling

Vascular endothelial cultures are composed of flat, polygonal monolayer cells which retain many of the growth, metabolic and physiological characteristics of the intimal endothelium. However, intercellular gap and tight junctions, which are thought to perform important roles in normal intimal physiology, are reduced in complexity and extent in culture. We have used electrophysiological techniques to test confluent (3- to 5-day) primary cultures of calf aortic (BAEC) and umbilical cord vein (BVEC) endothelium for junctional transfer of small ions. Both cell types are extensively electrically coupled. The passive electrical properties of the cultured cells were calculated from the decrease in induced membrane potential deflections with distance from an intracellular, hyperpolarizing electrode. Data analyses were based on a thin-sheet model for current flow (Bessel function). The generalized space constants (lambda) were 208.6 microns (BAEC) and 288.9 microns (BVEC). The nonjunctional (6.14 and 8.72 X 10(8) omega) and junctional (3.67 and 3.60 X 10(6) omega) resistances were similar for the BAEC and BVEC, respectively. We detected no statistically significant differences in the resistance estimates for the two cell types. In vivo ultrastructural studies have suggested that aortic endothelium has more extensive gap junctions than venous endothelium. We have found that these ultrastructural differences are reduced in culture. The lack of any significant difference in electrical coupling capability suggests that cultured BAEC and BVEC have functionally similar junctional characteristics.     

Can the Sodium-Calcium Exchanger Initiate or Suppress Calcium Sparks in Cardiac Myocytes?

Positive feedback of Calcium (Ca)-induced Ca release is the mechanism of Ca spark formation in cardiac myocytes. To initiate this process, a certain amount of Ca in the cleft space is necessary. When the membrane potential becomes higher during excitation-contraction coupling, Ca can enter through both Ca current (I(CaL)) and sodium-calcium exchanger (NCX) and may activate ryanodine receptors to initiate a Ca spark. On the other hand, at the resting membrane potential (V(m) ~-80 mV), NCX removes Ca from the cell (forward mode). If Ca released from the sarcoplasmic reticulum is quickly removed via forward mode NCX before Ca-induced Ca release starts, the Ca release becomes nonspark Ca leak. This would also be influenced by the cleft/noncleft distribution of NCX, which is unknown. Using a physiologically detailed mathematical model of subcellular Ca cycling, we analyze how NCX strength and distribution alter Ca spark formation. During excitation-contraction coupling, most Ca sparks are induced by I(CaL) with very few due to NCX current. At the resting membrane potential if most NCX is localized to the cleft, spontaneous Ca sparks are significantly reduced.     

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.     

Calcium oscillations in a triplet of pancreatic acinar cells

We use a mathematical model of calcium dynamics in pancreatic acinar cells to investigate calcium oscillations in a ring of three coupled cells. A connected group of cells is modeled in two different ways: 1), as coupled point oscillators, each oscillator being described by a spatially homogeneous model; and 2), as spatially distributed cells coupled along their common boundaries by gap-junctional diffusion of inositol trisphosphate and/or calcium. We show that, although the point-oscillator model gives a reasonably accurate general picture, the behavior of the spatially distributed cells cannot always be predicted from the simpler analysis; spatially distributed diffusion and cell geometry both play important roles in determining behavior. In particular, oscillations in which two cells are in synchrony, with the third phase-locked but not synchronous, appears to be more dominant in the spatially distributed model than in the point-oscillator model. In both types of model, intercellular coupling leads to a variety of synchronous, phase-locked, or asynchronous behaviors. For some parameter values there are multiple, simultaneous stable types of oscillation. We predict 1), that intercellular calcium diffusion is necessary and sufficient to coordinate the responses in neighboring cells; 2), that the function of intercellular inositol trisphosphate diffusion is to smooth out any concentration differences between the cells, thus making it easier for the diffusion of calcium to synchronize the oscillations; 3), that groups of coupled cells will tend to respond in a clumped manner, with groups of synchronized cells, rather than with regular phase-locked periodic intercellular waves; and 4), that enzyme secretion is maximized by the presence of a pacemaker cell in each cluster which drives the other cells at a frequency greater than their intrinsic frequency.     

Estimation of the junctional resistance between electrically coupled receptor cells in Necturus taste buds

Junctional resistance between coupled receptor cells in Necturus taste buds was estimated by modeling the results from single patch pipette voltage clamp studies on lingual slices. The membrane capacitance and input resistance of coupled taste receptor cells were measured to monitor electrical coupling and the results compared with those calculated by a simple model of electrically coupled taste cells. Coupled receptor cells were modeled by two identical receptor cells connected via a junctional resistance. On average, the junctional resistance was approximately 200-300 M omega. This was consistent with the electrophysiological recordings. A junctional resistance of 200-300 M omega is close to the threshold for Lucifer yellow dye-coupling detection (approximately 500 M omega). Therefore, the true extent of coupling in taste buds might be somewhat greater than that predicted from Lucifer yellow dye coupling. Due to the high input resistance of single taste receptor cells (> 1 G omega), a junctional resistance of 200-300 M omega assures a substantial electrical communication between coupled taste cells, suggesting that the electrical activity of coupled cells might be synchronized.     

Morphofunctional integration between skeletal myoblasts and adult cardiomyocytes in coculture is favored by direct cell-cell contacts and relaxin treatment

The success of cellular cardiomyoplasty, a novel therapy for the repair of postischemic myocardium, depends on the anatomical integration of the engrafted cells with the resident cardiomyocytes. Our aim was to investigate the interaction between undifferentiated mouse skeletal myoblasts (C₂C₁₂ cells) and adult rat ventricular cardiomyocytes in an in vitro coculture model. Connexin43 (Cx43) expression, Lucifer yellow microinjection, Ca²⁺ transient propagation, and electrophysiological analysis demonstrated that myoblasts and cardiomyocytes were coupled by functional gap junctions. We also showed that cardiomyocytes upregulated gap junctional communication and expression of Cx43 in myoblasts. This effect required direct cell-to-cell contact between the two cell types and was potentiated by treatment with relaxin, a cardiotropic hormone with potential effects on cardiac development. Analysis of the gating properties of gap junctions by dual cell patch clamping showed that the copresence of cardiomyocytes in the cultures significantly increased the transjunctional current and conductance between myoblasts. Relaxin enhanced this effect in both the myoblast-myoblast and myoblast-cardiomyocyte cell pairs, likely acting not only on gap junction formation but also on the electrical properties of the preexisting channels. Our findings suggest that myoblasts and cardiomyocytes interact actively through gap junctions and that relaxin potentiates the intercellular coupling. A potential role for gap junctional communication in favoring the intercellular exchange of regulatory molecules, including Ca²⁺, in the modulation of myoblast differentiation is discussed. gap junctions; connexin43     

A model of slow conduction in bullfrog atrial trabeculae.

The success or failure of the propagation of electrical activity in cardiac tissue is dependent on both cellular membrane characteristics and intercellular coupling properties. This paper considers a linear arrangement of individual bullfrog atrial cells that are resistively coupled end to end to form a cylindrical strand. The strand, in turn, is encased by an endothelial sheath that provides a restricted extracellular space and an ion diffusion barrier to the outer bathing medium. This encased strand serves as an idealized model of an atrial trabeculum. Excitable membrane characteristics of the atrial cell are specified in terms of a Hodgkin-Huxley type of model that is quantitatively based on single-microelectrode voltage clamp data from bullfrog atrial myocytes. This membrane model can simulate the behavior of normal cells as well as of ischemic cells that exhibit depressed electrophysiological behavior (e.g., decreased resting potential, upstroke velocity, peak height, and action potential duration). Depressed activity can be easily simulated with variation of a single model parameter, the gain of the Na+/K+ pump current (INaK). Intercellular coupling properties are specified in terms of a lumped resistive T-type network between adjacent cells. The atrial strand model provides a means for studying the theoretical aspects of slow conduction in a "hybrid" strand that consists of a central region of cells having abnormal membrane or coupling properties, flanked on either side by normal atrial cells. Both uniform and discontinuous conduction are simulated by means of appropriate changes in the coupling resistance between cells. In addition, by varying either the degree of depressed electrical activity or the intercalated disc resistance in the central zone of the strand, slow conduction or complete conduction block in that region is demonstrated. Since the cellular model used in this study is based on experimental data and closely mimics both the atrial action potential and the underlying membrane currents, it has the potential to (1) accurately represent the current and voltage wave-forms occurring in the region of intercalated discs and (2) provide detailed information regarding the mechanisms in intercellular current spread in the region of slow conduction.     

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.     

Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts

We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the collection. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D, 2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts. The numerical experiments demonstrate that there is a region of instability of the form observed in the simplified model analysis.     

An electrophysiological study of the junctional membrane of epidermal cells in Tenebrio molitor

The insect epidermis is normally a coupled network with respect to the movement of inorganic ions through the junctional membranes connecting adjacent cells. The high ionic permeability of the junctional membrane may be reversibly abolished by either the iontophoretic injection of Ca into single cells or by replacing the Na in the external medium with Li. After Ca injection, a concomitant loss in ionic permeability of the junctional membrane and of the membrane potential of the injected cell was recorded within 3 min. Ionic coupling was restored by hyperpolarizing current pulses within a few minutes. Li substitution tripled the resistance of the junctional membrane within 30 min although the membrane potential remained stable during this period. After 60 min exposure to Li the membrane potential had decayed to zero and ionic coupling was unrecordable. Junctional membrane permeability and cell membrane potential were restored within 30 min re-exposure to normal saline. Since Li is thought to act by indirectly raising the free Ca level in the cytoplasm by its interaction with cytoplasmic Na, we suggest that a reduction in junctional permeability is a direct consequence of increased Ca activity in the cytoplasm of the epidermal cells.