Conduction in bullfrog atrial strands: simulations of the role of disc and extracellular resistance.

A number of fundamental properties of intercellular conduction in simulated cylindrical strands of cardiac tissue are examined. The paper is based on recent biophysical information describing the transmembrane ionic currents in bullfrog atrial cells as well as anatomical data on the structures (gap junctions) responsible for the coupling between cells in that tissue. A mathematical model of the single bullfrog atrial cell based on suction microelectrode single-cell voltage clamp data is employed, as well as a modified version of the well-known model of Heppner and Plonsey, to characterized the resistive connections between adjacent cells in a cardiac strand. In addition, the simulated cellular strand is assumed to be encased in a cylindrical, resistive endothelial sheath, thus forming an idealized atrial trabeculum; the trabeculum is immersed in an extensive volume conductor. It is possible to simulate both uniform and discontinuous conduction in this atrial strand model by appropriately changing the resistance of the intercalated discs that occur at cell boundaries. The conduction velocity achieved in the normal or control case is within the range of conduction velocities that have been measured for bullfrog atrial trabeculae using optical methods. Extracellular resistance is shown to have a significant effect on both conduction velocity and the critical value of disc resistance at which discontinuous conduction first occurs. Since the atrial cell model employed in this study is based on experimental data and can accurately simulate the atrial action potential, the transmembrane ionic currents generated by the model are capable of providing detailed information concerning the mechanisms of intercellular current spread, particularly in the region of the intercalated disc.     

Intercalated disk nanoscale structure regulates cardiac conduction

The intercalated disk (ID) is a specialized subcellular region that provides electrical and mechanical connections between myocytes in the heart. The ID has a clearly defined passive role in cardiac tissue, transmitting mechanical forces and electrical currents between cells. Recent studies have shown that Na⁺ channels, the primary current responsible for cardiac excitation, are preferentially localized at the ID, particularly within nanodomains such as the gap junction–adjacent perinexus and mechanical junction–associated adhesion-excitability nodes, and that perturbations of ID structure alter cardiac conduction. This suggests that the ID may play an important, active role in regulating conduction. However, the structures of the ID and intercellular cleft are not well characterized and, to date, no models have incorporated the influence of ID structure on conduction in cardiac tissue. In this study, we developed an approach to generate realistic finite element model (FEM) meshes replicating nanoscale of the ID structure, based on experimental measurements from transmission electron microscopy images. We then integrated measurements of the intercellular cleft electrical conductivity, derived from the FEM meshes, into a novel cardiac tissue model formulation. FEM-based calculations predict that the distribution of cleft conductances is sensitive to regional changes in ID structure, specifically the intermembrane separation and gap junction distribution. Tissue-scale simulations predict that ID structural heterogeneity leads to significant spatial variation in electrical polarization within the intercellular cleft. Importantly, we found that this heterogeneous cleft polarization regulates conduction by desynchronizing the activation of postjunctional Na⁺ currents. Additionally, these heterogeneities lead to a weaker dependence of conduction velocity on gap junctional coupling, compared with prior modeling formulations that neglect or simplify ID structure. Further, we found that disruption of local ID nanodomains can either slow or enhance conduction, depending on gap junctional coupling strength. Our study therefore suggests that ID nanoscale structure can play a significant role in regulating cardiac conduction.     

Simulation analysis of excitation conduction in the heart: Propagation of excitation in different tissues

The normal excitation and conduction in the heart are maintained by the coordination between the dynamics of ionic conductance of each cell and the electrical coupling between cells. To examine functional roles of these two factors, we proposed a spatially-discrete model of conduction of excitation in which the individual cells were assumed isopotential. This approximation was reasoned by comparing the apparent space constant with the measured junctional resistance between myocardial cells. We used the four reconstruction models previously reported for five kinds of myocardial cells. Coupling coefficients between adjacent cells were determined quantitatively from the apparent space constants. We first investigated to what extent the pacemaker activity of the sinoatrial node depends on the number and the coupling coefficient of its cells, by using a one-dimensional model system composed of the sinoatrial node cells and the atrial cells. Extensive computer simulation revealed the following two conditions for the pacemaker activity of the sinoatrial node. The number of the sinoatrial node cells and their coupling coefficients must be large enough to provide the atrium with the sufficient electric current flow. The number of the sinoatrial node cells must be large so that the period of the compound system is close to the intrinsic period of the sinoatrial node cell. In this simulation the same sinoatrial node cells produced action potentials of different shapes depending on where they were located in the sinoatrial node. Therefore it seems premature to classify the myocardial cells only from their waveforms obtained by electrical recordings in the compound tissue. Second, we investigated the very slow conduction in the atrioventricular node compared to, for example, the ventricle. This was assumed to be due to the inherent property of the membrane dynamics of the atrioventricular node cell, or to the small value of the coupling coefficient (weak intercellular coupling), or to the electrical load imposed on the atrioventricular node by the Purkinje fibers, because the relatively small atrioventricular node must provide the Purkinje fibers with sufficient electric current flow. Relative contributions of these three factors to the slow conduction were evaluated using the model system composed of only the atrioventricular cells or that composed of the atrioventricular and Purkinje cells. We found that the weak coupling has the strongest effect. In the model system composed of the atrioventricular cells, the propagation failure was not observed even for very small values of the coupling coefficient.(ABSTRACT TRUNCATED AT 400 WORDS)     

Simulated propagation of cardiac action potentials.

We have used numerical methods for solving cable equations, combined with previously published mathematical models for the membrane properties of ventricular and Purkinje cells, to simulate the propagation of cardiac action potentials along a unidimensional strand. Two types of inhomogeneities have been simulated and the results compared with experimentally observed disturbances in cardiac action potential propagation. Changes in the membrane model for regions of the strand were introduced to simulate regions of decreased excitability. Regional changes in the intercellular coupling were also studied. The results illustrate and help to explain the disturbances in propagation which have been reported to occur at regions of decreased excitability, regions with changing action potential duration, or regions with changing intercellular coupling. The propagational disturbances seen at all of these regions are discussed in terms of the changing electrical load imposed upon the propagating impulse.     

A model of the muscarinic receptor-induced changes in K(+)-current and action potentials in the bullfrog atrial cell.

A model is formulated for characterizing the behavior of the acetylcholine (ACh)-sensitive K+ membrane channel (muscarinic channel) in bullfrog atrial myocytes. Parameters of the muscarinic current model are chosen in fit available data from the literature on bullfrog atrial myocytes (3, 4, 45). This model is subsequently incorporated into a large mathematical model of the bullfrog myocyte that is based on quantitative whole-cell voltage clamp data (40). Simulations are conducted on the active atrial cell model in bathing media containing ACh at different concentrations to explore the effect of this muscarinic channel on the electrical behavior of the myocyte. The model predicts a progressive shortening of the action potential with increasing [ACh], as well as an indirect influence of the muscarinic K+ current on the other membrane currents of the atrial cell. Interpretation of the simulation results provides suggestions for the probable mechanisms underlying the shortening of the action potential due to activity of the muscarinic channel. Specifically, the model predicts that with an increase in ACh concentration: (a) the outward muscarinic current, IK,ACh(t), increases in magnitude but shortens in duration; (b) the calcium current, ICa(t), may increase in magnitude, but when it does so it decreases in duration compared with the control conditions; (c) the intracellular Ca2+ concentration [Ca2+]i waveform during the action potential decreases in both magnitude and duration. Because the contractile activity of the cell is controlled by the [Ca2+]i waveform, the model predicts a decrease in contractile strength with an increase in ACh concentration in the bathing medium; i.e., a negative inotropic effect.     

A cleft model for cardiac Purkinje strands.

Conduction of the action potential in cardiac muscle is complicated by its multicellular structure, with narrow intercellular clefts and cell-to-cell coupling. A model is developed from anatomical data to describe cardiac Purkinje strands of variable diameter and different internal arrangements of cells. The admittance of the model is solved analytically and fit to results of cable analysis. Using the extracted specific membrane and cell electrical parameters (Rm = 13 K omega cm2, Cm = 1.5 mu F/cm2, Ri = 100 mu cm, and Re = 50 omega cm), the model correctly predicted conduction velocity and filling of capacitance at the onset of a voltage step. The analysis permits more complete studies of the factors controlling conduction velocity; for instance, the effect on conduction velocity of a capacity in the longitudinal current circuit is discussed. Predictions of the impedance and phase angle were also made. Measurements of the frequency dependence of phase angle may provide a basis for separating cleft membrane properties from those of the surface membrane and may aid the measurement of nonlinear membrane properties in muscle.     

Unidirectional block between isolated rabbit ventricular cells coupled by a variable resistance.

We have used pairs of electrically coupled cardiac cells to investigate the dependence of successful conduction of an action potential on three components of the conduction process: (a) the amount of depolarization required to be produced in the nonstimulated cell (the "sink" for current flow) to initiate an action potential in the nonstimulated cell, (b) the intercellular resistance as the path for intercellular current flow, and (c) the ability of the stimulated cell to maintain a high membrane potential to serve as the "source" of current during the conduction process. We present data from eight pairs of simultaneously recorded rabbit ventricular cells, with the two cells of each pair physically separated from each other. We used an electronic circuit to pass currents into and out of each cell such that these currents produced the effects of any desired level of intercellular resistance. The cells of equal size (as assessed by their current threshold and their input resistance for small depolarizations) show bidirectional failure of conduction at very high values of intercellular resistance which then converts to successful bidirectional conduction at lower values of intercellular resistance. For cell pairs with asymmetrical cell sizes, there is a large range of values of intercellular resistance over which unidirectional block occurs with conduction successful from the larger cell to the smaller cell but with conduction block from the smaller cell to the larger cell. We then further show that one important component which limits the conduction process is the large early repolarization which occurs in the stimulated cell during the process of conduction, a process that we term "source loading."     

THE FINE STRUCTURE AND ELECTROPHYSIOLOGY OF HEART MUSCLE CELL INJURY

Injured frog heart cells electrically uncouple from their uninjured neighbors within 30 min after injury. This uncoupling process can be shown by the disappearance of an injury potential measured between such injured and uninjured cells. In the present study, the time course of the decline of injury potentials, and thus of electrical uncoupling, in bullfrog atrial trabeculae was determined. Tissue was fixed with glutaraldehyde and osmium tetroxide at various times after injury to determine the morphological changes which accompany this uncoupling process. In some cases, ruthenium red was included in the fixatives. Normal atrial cells are long and narrow, with intercellular junctions located along the lateral surfaces of the cells. Two types of intercellular junctions have been observed: cardiac adhesion plaques (CAPs), and close junctions. Close junctions occur only infrequently. Ruthenium red penetrates all around the cells, leaving only small areas within the CAPs unstained. After injury, the cells are very dense and the myofilaments disarranged. Both types of intercellular junction remain intact, and only slight changes within CAPs are observed. The results are discussed in relation to current concepts of intercellular communication.     

Effects of stochastic channel gating and distribution on the cardiac action potential

Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000 ms) was essentially caused by stochastic channel gating of I_Ks, persistent I_Na and I_Ca,L. In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling.     

Reflected reentry, delayed conduction, and electrotonic inhibition in segmentally depressed atrial tissues

Reflection is a subclass of reentrant cardiac arrhythmias in which reexcitation of the heart occurs as a result of to and fro electrotonically mediated transmission of impulses across a narrow zone of impaired conductivity. Although relatively well characterized in ventricular tissues, the reflection mechanism has not been studied in atrial tissues. In this study we examine the possibility of reflected reentry in segmentally depressed atrial tissues and evaluate conduction characteristics in these preparations. Narrow strips of atrial pectinate muscle or crista terminalis (canine and calf) were placed in a three-chambered bath and the central segment was superfused with an isotonic sucrose solution or an "ischemic" Tyrode's solution. Proximal to distal conduction across the 1.0- to 1.2-mm wide ischemic gap showed step delays as long as 210 ms. Reflected reentry was readily demonstrable when prominent step delays occurred during anterograde conduction of the impulse across the gap. Progressive acceleration of the stimulation rate resulted in progressively greater impairment of anterograde conduction until complete block occurred. The incidence and patterns of reflected reentry were therefore a sensitive function of the stimulation rate. Other features exhibited by these preparations include a slow recovery of excitability following the action potential, postrepolarization refractoriness, and electrotonic inhibition and summation. Our data suggest that the characteristics of conduction and reflection in segmentally depressed atrial tissues are qualitatively similar to those in ventricular tissues. The presence of electrotonic inhibition in atrial may also help to explain the functionally inexcitable zone seen in the vortex of the leading circle model of atrial flutter.     

Slow Conduction in Cardiac Muscle: A Biophysical Model

Mechanisms of slow conduction in cardiac muscle are categorized and the most likely identified. Propagating action potentials were obtained experimentally from a synthetically grown strand of cardiac muscle (around 50 μm by 30 mm) and theoretically from a one-dimensional cable model that incorporated varying axial resistance and membrane properties along its length. Action potentials propagated at about 0.3 m/s, but in some synthetic strands there were regions (approximately 100 μm in length) where the velocity decreased to 0.002 m/s. The electrophysiological behavior associated with this slow conduction was similar to that associated with slow conduction in naturally occurring cardiac muscle (notches, Wenckebach phenomena, and block). Theoretically, reasonable changes in specific membrane capacitance, membrane activity, and various changes in geometry were insufficient to account for the observed slow conduction velocities. Conduction velocities as low as 0.009 m/s, however, could be obtained by increasing the resistance (r_i) of connections between the cells in the cable; velocities as low as 0.0005 m/s could be obtained by a further increase in r_i made possible by a reduction in membrane activity by one-fourth, which in itself decreased conduction velocity by only a factor of 1/1.4. As a result of these findings, several of the mechanisms that have been postulated, previously, are shown to be incapable of accounting for delays such as those which occur in the synthetic strand as well as in the atrioventricular (VA) node.     

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.     

On the ionic mechanism underlying adrenergic-cholinergic antagonism in ventricular muscle

In atrial muscle, acetylcholine (ACh) decreases the slow inward current (Isi) and increases the time-independent outward K+ current. However, in ventricular muscle, ACh produces a marked negative inotropic effect only in the presence of positive inotropic agents that elevate cyclic adenosine monophosphate (AMP). A two-microelectrode voltage-clamp method was used on cultured reaggregates of cells from 16--20-d-old embryonic chick ventricles to determine the effects of ACh on Isi and outward current during beta-adrenergic stimulation. Only double penetrations displaying low-resistance coupling were voltage-clamped. Cultured reaggregates are advantageous because their small size (50-- 250 microns) permits better control of membrane potential and adequate space clamp. Tetrodotoxin (10(-6) M) and a holding potential of --50 to --40 mV were used to eliminate the fast Na+ current. Depolarizing voltage steps above --40 mV caused a slow inward current to flow that was sensitive to changes in [Ca]o and was depressed by verapamil (10(- 6) M). Maximal Isi was obtained at --10 mV and the reversal potential was about +25 mV. Isoproterenol (10(-6) M) increased Isi at all clamp potentials. Subsequent addition of ACh (10(-6) M) rapidly reduced Isi to control values (before isoproterenol) without a significant effect on the net outward current measured at 300 ms. The effects of ACh were reversed by muscarinic blockade with atropine (5 X 10(-6) M). We conclude that the anti-adrenergic effects of ACh in ventricular muscle are mediated by a reduction in Ca2+ influx during excitation.     

TRANSITIONAL CARDIAC CELLS OF THE CONDUCTIVE SYSTEM OF THE DOG HEART : Distinguishing Morphological and Electrophysiological Features

Cardiac cells with distinctive electrophysiological and morphological features were found at the junctional region between Purkinje and ventricular cells of the dog heart. The electrophysiological exploration of these "transitional" cells revealed action potentials markedly different in configuration from those generated by Purkinje or by ventricular cells. The impaled cardiac cells which generated transitional action potentials were identified in serial sections and studied with the light and the electron microscopes. The transitional cells were found to be characterized cytologically by: (a) their subendocardial location, (b) their small diameter, (c) the absence of T system and sarcoplasmic reticulum, and (d) the lack of intercalated discs under the light microscope and the sparsity of specialized intercellular junctions under the electron microscope. Purkinje, transitional, and ventricular cells were found to be joined by gap junctions permeable to lanthanum. A quantitative difference in the extent and distribution of specialized intercellular junctions may be one of the factors responsible for the slow velocity of conduction characteristic of the Purkinje-ventricular junctional region.     

Action potential propagation in inhomogeneous cardiac tissue: safety factor considerations and ionic mechanism

Heterogeneity of myocardial structure and membrane excitability is accentuated by pathology and remodeling. In this study, a detailed model of the ventricular myocyte in a multicellular fiber was used to compute a location-dependent quantitative measure of conduction (safety factor, SF) and to determine the kinetics and contribution of sodium current (I(Na)) and L-type calcium current [I(Ca(L))] during conduction. We obtained the following results. 1) SF decreases sharply for propagation into regions of increased electrical load (tissue expansion, increased gap junction coupling, reduced excitability, hyperkalemia); it can be <1 locally (a value indicating conduction failure) and can recover beyond the transition region to resume propagation. 2) SF and propagation across inhomogeneities involve major contribution from I(Ca(L)). 3) Modulating I(Na) or I(Ca(L)) (by blocking agents or calcium overload) can cause unidirectional block in the inhomogeneous region. 4) Structural inhomogeneity causes local augmentation of I(Ca(L)) and suppression of I(Na) in a feedback fashion. 5) Propagation across regions of suppressed I(Na) is achieved via a I(Ca(L))-dependent mechanism. 6) Reduced intercellular coupling can effectively compensate for reduced SF caused by tissue expansion but not by reduced membrane excitability.     

Electrotonic Coupling between Human Atrial Myocytes and Fibroblasts Alters Myocyte Excitability and Repolarization

Atrial fibrosis has been implicated in the development and maintenance of atrial arrhythmias, and is characterized by expansion of the extracellular matrix and an increased number of fibroblasts (Fbs). Electrotonic coupling between atrial myocytes and Fbs may contribute to the formation of an arrhythmogenic substrate. However, the role of these cell-cell interactions in the function of both normal and diseased atria remains poorly understood. The goal of this study was to gain mechanistic insight into the role of electrotonic Fb-myocyte coupling on myocyte excitability and repolarization. To represent the system, a human atrial myocyte (hAM) coupled to a variable number of Fbs, we employed a new ionic model of the hAM, and a variety of membrane representations for atrial Fbs. Simulations elucidated the effects of altering the intercellular coupling conductance, electrophysiological Fb properties, and stimulation rate on the myocyte action potential. The results demonstrate that the myocyte resting potential and action potential waveform are modulated strongly by the properties and number of coupled Fbs, the degree of coupling, and the pacing frequency. Our model provides mechanistic insight into the consequences of heterologous cell coupling on hAM electrophysiology, and can be extended to evaluate these implications at both tissue and organ levels.     

The atrioventricular node and bundle in the ferret heart: a light and quantitative electron microscopic study.

The cells of the atrioventricular (AV) junction in the ferret heart were examined using light microscopy, a wax-model reconstruction and quantitative electron microscopy to determine their organization and characteristics. A series of subdivisions of the specialized tissues of the AV junction was apparent at both the light and electron microscopic levels. A transitional zone was observed interposed between the atrial muscle cells and the AV node. The AV node consisted of a coronary sinus portion, a superficial portion and a deep portion. The AV bundle had a segment above the anulus fibrosus, a segment which penetrated the right fibrous trigone, a non-branching segment below the anulus fibrosus and a branched segment. At the ultrastructural level the AV junctional conduction tissues had fewer irregularly oriented myofibrils than did working atrial myocardial cells. T-tubules, present in atrial muscle cells, were not observed in the modified muscle cells of the AV node and bundle. Conventional intercalated discs also were not observed between the cells of the AV node or the AV bundle. Atrial myocardial cells had the highest percentage of the plasma membrane occupied by desmosomes, fasciae adherentes and gap junctions. The AV bundle cells had the highest percentage of appositional surface membrane and a relatively large fraction of plasma membrane occupied by gap junctions. Cells of the superficial portion of the AV node had the smallest percentage of the plasma membrane composed of gap junctions, desmosomes or fasciae adherentes, as well as the smallest fraction of the cell membrane apposed to adjacent cells. The stereological data indicate that the most useful distinguishing characteristic between atrial muscle cells and conduction cells was that a smaller percentage of the conduction cell sarcoplasm was occupied by mitochondria and myofibrils. The most useful characteristics that could be used to differentiate between the regions of the AV junctional conduction tissues were the amounts and types of surface membrane specializations in the respective cell types.     

Determinants of heterogeneity, excitation and conduction in the sinoatrial node: a model study

The sinoatrial node (SAN) is a complex structure that exhibits anatomical and functional heterogeneity which may depend on: 1) The existence of distinct cell populations, 2) electrotonic influences of the surrounding atrium, 3) the presence of a high density of fibroblasts, and 4) atrial cells intermingled within the SAN. Our goal was to utilize a computer model to predict critical determinants and modulators of excitation and conduction in the SAN. We built a theoretical "non-uniform" model composed of distinct central and peripheral SAN cells and a "uniform" model containing only central cells connected to the atrium. We tested the effects of coupling strength between SAN cells in the models, as well as the effects of fibroblasts and interspersed atrial cells. Although we could simulate single cell experimental data supporting the "multiple cell type" hypothesis, 2D "non-uniform" models did not simulate expected tissue behavior, such as central pacemaking. When we considered the atrial effects alone in a simple homogeneous "uniform" model, central pacemaking initiation and impulse propagation in simulations were consistent with experiments. Introduction of fibroblasts in our simulated tissue resulted in various effects depending on the density, distribution, and fibroblast-myocyte coupling strength. Incorporation of atrial cells in our simulated SAN tissue had little effect on SAN electrophysiology. Our tissue model simulations suggest atrial electrotonic effects as plausible to account for SAN heterogeneity, sequence, and rate of propagation. Fibroblasts can act as obstacles, current sinks or shunts to conduction in the SAN depending on their orientation, density, and coupling.     

A model of smooth muscle cell synchronization in the arterial wall

Vasomotion is a rhythmic variation in microvascular diameter. Although known for more than 150 years, the cellular processes underlying the initiation of vasomotion are not fully understood. In the present study a model of a single cell is extended by coupling a number of cells into a tube. The simulated results point to a permissive role of cGMP in establishing intercellular synchronization. In sufficient concentration, cGMP may activate a cGMP-sensitive calcium-dependent chloride channel, causing a tight spatiotemporal coupling between release of sarcoplasmic reticulum calcium, membrane depolarization, and influx of extracellular calcium. Low [cGMP] is associated only with unsynchronized waves. At intermediate concentrations, cells display either waves or whole cell oscillations, but these remain unsynchronized between cells. Whole cell oscillations are associated with rhythmic variation in membrane potential and flow of current through gap junctions. The amplitude of these oscillations in potential grows with increasing [cGMP], and, past a certain threshold, they become strong enough to entrain all cells in the vascular wall, thereby initiating sustained vasomotion. In this state there is a rhythmic flow of calcium through voltage-sensitive calcium channels into the cytoplasm, making the frequency of established vasomotion sensitive to membrane potential. It is concluded that electrical coupling through gap junctions is likely to be responsible for the rapid synchronization across a large number of cells. Gap-junctional current between cells is due to the appearance of oscillations in the membrane potential that again depends on the entrainment of sarcoplasmic reticulum and plasma membrane within the individual cell.     

Mechanisms of atrial-selective block of Na⁺ channels by ranolazine: II. Insights from a mathematical model

Block of Na(+) channel conductance by ranolazine displays marked atrial selectivity that is an order of magnitude higher that of other class I antiarrhythmic drugs. Here, we present a Markovian model of the Na(+) channel gating, which includes activation-inactivation coupling, aimed at elucidating the mechanisms underlying this potent atrial selectivity of ranolazine. The model incorporates experimentally observed differences between atrial and ventricular Na(+) channel gating, including a more negative position of the steady-state inactivation curve in atrial versus ventricular cells. The model assumes that ranolazine requires a hydrophilic access pathway to the channel binding site, which is modulated by both activation and inactivation gates of the channel. Kinetic rate constants were obtained using guarded receptor analysis of the use-dependent block of the fast Na(+) current (I(Na)). The model successfully reproduces all experimentally observed phenomena, including the shift of channel availability, the sensitivity of block to holding or diastolic potential, and the preferential block of slow versus fast I(Na.) Using atrial and ventricular action potential-shaped voltage pulses, the model confirms significantly greater use-dependent block of peak I(Na) in atrial versus ventricular cells. The model highlights the importance of action potential prolongation and of a steeper voltage dependence of the time constant of unbinding of ranolazine from the atrial Na(+) channel in the development of use-dependent I(Na) block. Our model predictions indicate that differences in channel gating properties as well as action potential morphology between atrial and ventricular cells contribute equally to the atrial selectivity of ranolazine. The model indicates that the steep voltage dependence of ranolazine interaction with the Na(+) channel at negative potentials underlies the mechanism of the predominant block of I(Na) in atrial cells by ranolazine.