Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node

Mathematical models of the action potential in the periphery and center of the rabbit sinoatrial (SA) node have been developed on the basis of published experimental data. Simulated action potentials are consistent with those recorded experimentally: the model-generated peripheral action potential has a more negative takeoff potential, faster upstroke, more positive peak value, prominent phase 1 repolarization, greater amplitude, shorter duration, and more negative maximum diastolic potential than the model-generated central action potential. In addition, the model peripheral cell shows faster pacemaking. The models behave qualitatively the same as tissue from the periphery and center of the SA node in response to block of tetrodotoxin-sensitive Na(+) current, L- and T-type Ca(2+) currents, 4-aminopyridine-sensitive transient outward current, rapid and slow delayed rectifying K(+) currents, and hyperpolarization-activated current. A one-dimensional model of a string of SA node tissue, incorporating regional heterogeneity, coupled to a string of atrial tissue has been constructed to simulate the behavior of the intact SA node. In the one-dimensional model, the spontaneous action potential initiated in the center propagates to the periphery at approximately 0.06 m/s and then into the atrial muscle at 0.62 m/s.     

Simulation of atrial activity by a phase response curve based model of a two-dimensional pacemaker cells array: the transition from a normal activation pattern to atrial fibrillation

In this paper, we present an original model of the atria, based on our hypothesis that atrial cells have features of pacemaker cells, characterized by their normally longer intrinsic cycle lengths and different type of connection (stronger) than the, sino-atrial (SA) node pacemaker cells. The atrium is simulated by a two-dimensional array of pacemaker cells (25 × 25), composed of a region of SA node pacemaker cells (11 × 11) surrounded by atrial pacemaker cells. All pacemakers cells are characterized by only the most relevant functional properties, those which play the most direct role in the determination of the cardiac rate and in the mechanism of arrhythmias. These properties are: the intrinsic cycle length, τ, an `internal' feature of each pacemaker cell, and the phase-response curve (PRC), an `overall collective' function. The PRC embodies the interactions of each pacemaker cell with its neighboring cells, and thus represents the type of connection (strong, weak, etc.) of the pacemaker cell with its surroundings. In our model, the SA node region differs from the atrial region by cycle length distribution and PRCs. We studied the spatial interaction between SA node pacemaker cells and atrial pacemaker cells as a function of the regional variation of cells properties and as a function of the “electrical” coupling between cells (the PRC), in the SA node region, in the atrial region, and in a border zone between them. We investigated the influence of those parameters on the activation pattern, on the conduction time of the array, and on a pseudo-ECG signal. This study demonstrates that by representing the atrial cells as a population of `pacemaker-like' cells, similar to the SA node pacemaker cells, but differing markedly in their cycle lengths and cell-to-cell interaction (PRC), we can create a global picture of the atrial system by applying a simple physical-mathematical model. This approach enables us to explore physiological phenomena related to the genesis and maintenance of atrial activity. It also reveals the conditions which predispose to atrial arrhythmias and conduction disturbances (e.g. tachycardia, pacemaker shift, re-entry, fibrillation). In particular, it yields insight into the mechanism of transition from normal atrial activity to the disordered state of atrial fibrillation. Therefore, this study suggests a new way of looking at the development of cardiac arrhythmias of atrial origin. Received: 8 September 1997 / Accepted in revised form: 6 October 1998     

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.     

Presence of the Kv1.5 K(+) channel in the sinoatrial node.

The aim of this study was to establish, using immunolabeling, whether the Kv1.5 K(+) channel is present in the pacemaker of the heart, the sinoatrial (SA) node. In the atrial muscle surrounding the SA node and in the SA node itself (from guinea pig and ferret), Western blotting analysis showed a major band of the expected molecular weight, approximately 64 kD. Confocal microscopy and immunofluorescence labeling showed Kv1.5 labeling clustered in atrial muscle but punctate in the SA node. In atrial muscle, Kv1.5 labeling was closely associated with labeling of Cx43 (gap junction protein) and DPI/II (desmosomal protein), whereas in SA node Kv1.5 labeling was closely associated with labeling of DPI/II but not labeling of Cx43 (absent in the SA node) or Cx45 (another gap junction protein present in the SA node). Electron microscopy and immunogold labeling showed that the Kv1.5 labeling in atrial muscle is preferentially associated with desmosomes rather than gap junctions.     

Heterogeneous expression of Ca(2+) handling proteins in rabbit sinoatrial node.

We investigated the densities of the L-type Ca(2+) current, i(Ca,L), and various Ca(2+) handling proteins in rabbit sinoatrial (SA) node. The density of i(Ca,L), recorded with the whole-cell patch-clamp technique, varied widely in sinoatrial node cells. The density of i(Ca,L) was significantly (p<0.001) correlated with cell capacitance (measure of cell size) and the density was greater in larger cells (likely to be from the periphery of the SA node) than in smaller cells (likely to be from the center of the SA node). Immunocytochemical labeling of the L-type Ca(2+) channel, Na(+)-Ca(2+) exchanger, sarcoplasmic reticulum Ca(2+) release channel (RYR2), and sarcoplasmic reticulum Ca(2+) pump (SERCA2) also varied widely in SA node cells. In all cases there was significantly (p<0.05) denser labeling of cells from the periphery of the SA node than of cells from the center. In contrast, immunocytochemical labeling of the Na(+)-K(+) pump was similar in peripheral and central cells. We conclude that Ca(2+) handling proteins are sparse and poorly organized in the center of the SA node (normally the leading pacemaker site), whereas they are more abundant in the periphery (at the border of the SA node with the surrounding atrial muscle).     

Response Properties of a Sensory Hair Excised from Venus''s Flytrap

Multicellular sensory hairs were excised from the leaf of Venus's flytrap, and the sensory cells were identified by a destructive dissection technique. The sensory layer includes a radially symmetrical rosette of 20–30 apparently identical cells, and the sensory cells are organized in a plane normal to the long axis of the sensory hair. The sensory cells were probed with intracellular glass electrodes. The resting membrane potential was about -80 mv, and the response to a mechanical stimulus consisted of a graded response and an "action potential." The action potential appears to be similar to the action potential which propagates over the surface of the leaf. In the absence of stimulation, the upper and lower membranes of a single sensory cell behave in an electrically symmetrical fashion. Upon stimulation, however, the upper and lower membranes become electrically asymmetrical. Limiting values for the response asymmetry were calculated on the hypothesis of an electrical model consistent with the histology of the sensory cells.     

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.     

Effect of nonuniform interstitial space properties on impulse propagation: a discrete multidomain model

This work presents a discrete multidomain model that describes ionic diffusion pathways between connected cells and within the interstitium. Unlike classical models of impulse propagation, the intracellular and extracellular spaces are represented as spatially distinct volumes with dynamic/static boundary conditions that electrically couple neighboring spaces. The model is used to investigate the impact of nonuniform geometrical and electrical properties of the interstitial space surrounding a fiber on conduction velocity and action potential waveshape. Comparison of the multidomain and bidomain models shows that although the conduction velocity is relatively insensitive to cases that confine 50% of the membrane surface by narrow extracellular depths (≥2 nm), the action potential morphology varies greatly around the fiber perimeter, resulting in changes in the magnitude of extracellular potential in the tight spaces. Results also show that when the conductivity of the tight spaces is sufficiently reduced, the membrane adjacent to the tight space is eliminated from participating in propagation, and the conduction velocity increases. Owing to its ability to describe the spatial discontinuity of cardiac microstructure, the discrete multidomain can be used to determine appropriate tissue properties for use in classical macroscopic models such as the bidomain during normal and pathophysiological conditions.     

Ranolazine inhibits shear sensitivity of endogenous Na+ current and spontaneous action potentials in HL-1 cells

Na_V1.5 is a mechanosensitive voltage-gated Na⁺ channel encoded by the gene SCN5A, expressed in cardiac myocytes and required for phase 0 of the cardiac action potential (AP). In the cardiomyocyte, ranolazine inhibits depolarizing Na⁺ current and delayed rectifier (I_Kr) currents. Recently, ranolazine was also shown to be an inhibitor of Na_V1.5 mechanosensitivity. Stretch also accelerates the firing frequency of the SA node, and fluid shear stress increases the beating rate of cultured cardiomyocytes in vitro. However, no cultured cell platform exists currently for examination of spontaneous electrical activity in response to mechanical stimulation. In the present study, flow of solution over atrial myocyte-derived HL-1 cultured cells was used to study shear stress mechanosensitivity of Na⁺ current and spontaneous, endogenous rhythmic action potentials. In voltage-clamped HL-1 cells, bath flow increased peak Na⁺ current by 14 ± 5%. In current-clamped cells, bath flow increased the frequency and decay rate of AP by 27 ± 12% and 18 ± 4%, respectively. Ranolazine blocked both responses to shear stress. This study suggests that cultured HL-1 cells are a viable in vitro model for detailed study of the effects of mechanical stimulation on spontaneous cardiac action potentials. Inhibition of the frequency and decay rate of action potentials in HL-1 cells are potential mechanisms behind the antiarrhythmic effect of ranolazine.     

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.     

心房钠尿因子对豚鼠窦房结自律性的影响

用微电极技术研究表明,分别灌流心房钠尿因子(ANF)0.025和0.05μmol/L 7min 后,豚鼠窦房结细胞的自发节律无明显变化,而用0.1μmol/L 灌流时,其自发节律明显降低7%(P<0.01)。但当上述三种浓度 ANF 和异丙肾上腺素混合液灌流时,自发节律分别降低4,12和22%。这些结果表明,ANF 能抑制异丙肾上腺素的阳性变时效应。其机理可能与 ANF 阻滞窦房结细胞的 T 型钙通道电流有关。     

One-Dimensional Mathematical Model of the Atrioventricular Node Including Atrio-Nodal, Nodal, and Nodal-His Cells

Mathematical models are a repository of knowledge as well as research and teaching tools. Although action potential models have been developed for most regions of the heart, there is no model for the atrioventricular node (AVN). We have developed action potential models for single atrio-nodal, nodal, and nodal-His cells. The models have the same action potential shapes and refractoriness as observed in experiments. Using these models, together with models for the sinoatrial node (SAN) and atrial muscle, we have developed a one-dimensional (1D) multicellular model including the SAN and AVN. The multicellular model has slow and fast pathways into the AVN and using it we have analyzed the rich behavior of the AVN. Under normal conditions, action potentials were initiated in the SAN center and then propagated through the atrium and AVN. The relationship between the AVN conduction time and the timing of a premature stimulus (conduction curve) is consistent with experimental data. After premature stimulation, atrioventricular nodal reentry could occur. After slow pathway ablation or block of the L-type Ca²⁺ current, atrioventricular nodal reentry was abolished. During atrial fibrillation, the AVN limited the number of action potentials transmitted to the ventricle. In the absence of SAN pacemaking, the inferior nodal extension acted as the pacemaker. In conclusion, we have developed what we believe is the first detailed mathematical model of the AVN and it shows the typical physiological and pathophysiological characteristics of the tissue. The model can be used as a tool to analyze the complex structure and behavior of the AVN.     

Electrically excitable normal rat kidney fibroblasts: A new model system for cell-semiconductor hybrids

In testing various designs of cell-semiconductor hybrids, the choice of a suitable type of electrically excitable cell is crucial. Here normal rat kidney (NRK) fibroblasts are presented as a cell line, easily maintained in culture, that may substitute for heart or nerve cells in many experiments. Like heart muscle cells, NRK fibroblasts form electrically coupled confluent cell layers, in which propagating action potentials are spontaneously generated. These, however, are not associated with mechanical disturbances. Here we compare heart muscle cells and NRK fibroblasts with respect to action potential waveform, morphology, and substrate adhesion profile, using the whole-cell variant of the patch-clamp technique, atomic force microscopy (AFM), and reflection interference contrast microscopy (RICM), respectively. Our results clearly demonstrate that NRK fibroblasts should provide a highly suitable test system for investigating the signal transfer between electrically excitable cells and extracellular detectors, available at a minimum cost and effort for the experimenters.     

A spontaneously active focus drives a model atrial sheet more easily than a model ventricular sheet

Tachycardias can be produced when focal activity at ectopic locations in either the atria or the ventricles propagates into the surrounding quiescent myocardium. Isolated rabbit atrioventricular nodal cells were coupled by an electronic circuit to a real-time simulation of an array of cell models. We investigated the critical size of an automatic focus for the activation of two-dimensional arrays made up of either ventricular or atrial model cells. Over a range of coupling conductances for the arrays, the critical size of the focus cell group for successful propagation was smaller for activation of an atrial versus a ventricular array. Failure of activation of the arrays at smaller focus sizes was due to the inhibition of pacing of the nodal cells. At low levels of coupling conductance, the ventricular arrays required larger sizes of the focus due to failure of propagation even when the focus was spontaneously active. The major differences between activation of the atrial and ventricular arrays is due to the higher membrane resistance (lower inward rectifier current) of the atrial cells.     

雌二醇对家兔窦房结自律细胞的电生理学效应

本文旨在探讨雌二醇（17β-estradiol）对家兔窦房结自律细胞的电生理学效应及其作用机制。应用经典的细胞内玻璃微电极技术观察不同浓度雌二醇（1,10,100μmol／L）对家兔窦房结自律细胞动作电位的影响。结果显示：（1）雌二醇浓度依赖性地延长窦房结自律细胞动作电位复极化50％时间（APD50）和动作电位复极化90％时间（APD50）,降低窦房结自律细胞动作电位0期最大除极速率（Vmax）、动作电位幅值（amplitude of action potential,APA）,降低窦房结自律细胞放电频率（rate of pacemaker firing,RPF）、舒张期（4相）自动去极化速率[velocity of diastolic（phase4）depolarization,VDD]：而雌二醇对窦房结自律细胞的最大舒张电位（maximal diastolic potential,MDP）无明显影响。（2）雌激素受体阻断剂他莫昔芬（10μmol／L）不能阻断雌二醇（10μmol／L）对窦房结自律细胞动作电位的抑制效应。（3）一氧化氮合酶抑制剂L—NAME（100μmol／L）可完全阻断雌二醇（10μmol／L）对窦房结自律细胞动作电位的抑制效应。结果提示,雌二醇对家兔窦房结自律细胞的电生理活动具有明显的抑制作用,此作用可能是通过非基因组机制发挥,与一氧化氮作用有关。     

Electrophysiological changes induced by lysophosphatidylcholine, an ischaemic phospholipid catabolite, in rabbit atrial and ventricular cardiac cells.

The effects of palmitoyl-lysophosphatidylcholine (LPC) were studied on the cellular electrical activity of rabbit heart preparations. LPC (100 mumol/l) caused a considerable enhancement of the automaticity of the SA nodal and Purkinje fibers and frequently induced irregular firing in both supraventricular (SA node, atrium, AV junction) and ventricular (Purkinje fibers, papillary muscle) myocardial regions. The 'automatotropic' and arrhythmogenic effects of LPC were accompanied by a lengthening of the atrioventricular conduction time. In ventricular muscle fibers LPC (100 mumol/l) decreased the resting potential (RP), the maximum rate of depolarization (Vmax) and the amplitude (APA) and duration (APD) of the action potential, and often evoked action potentials of 'slow response' type. In atrial muscle cells, 100 mumol/l LPC was capable of inducing hyperpolarization, with concomitant increases in RP, Vmax, APA and APD; higher concentrations (300 and 600 mumol/l) of LPC resulted in decreases in RP, Vmax, APA and APD, i.e. phenomena similar to those observed with 100 mumol/l LPC in the ventricular myocardium. The results seem to support the assumption that lysolipids accumulating in the ischaemic myocardium may play a pathogenetic role in the development of both supraventricular and ventricular dysrhythmias accompanying coronary artery occlusion.     

How noise and coupling induce bursting action potentials in pancreatic {beta}-cells

Unlike isolated beta-cells, which usually produce continuous spikes or fast and irregular bursts, electrically coupled beta-cells are apt to exhibit robust bursting action potentials. We consider the noise induced by thermal fluctuations as well as that by channel-gating stochasticity and examine its effects on the action potential behavior of the beta-cell model. It is observed numerically that such noise in general helps single cells to produce a variety of electrical activities. In addition, we also probe coupling via gap junctions between neighboring cells, with heterogeneity induced by noise, to find that it enhances regular bursts.     

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.     

Ranolazine inhibits shear sensitivity of endogenous Na+ current and spontaneous action potentials in HL-1 cells

Na_V1.5 is a mechanosensitive voltage-gated Na⁺ channel encoded by the gene SCN5A, expressed in cardiac myocytes and required for phase 0 of the cardiac action potential (AP). In the cardiomyocyte, ranolazine inhibits depolarizing Na⁺ current and delayed rectifier (I_Kr) currents. Recently, ranolazine was also shown to be an inhibitor of Na_V1.5 mechanosensitivity. Stretch also accelerates the firing frequency of the SA node, and fluid shear stress increases the beating rate of cultured cardiomyocytes in vitro. However, no cultured cell platform exists currently for examination of spontaneous electrical activity in response to mechanical stimulation. In the present study, flow of solution over atrial myocyte-derived HL-1 cultured cells was used to study shear stress mechanosensitivity of Na⁺ current and spontaneous, endogenous rhythmic action potentials. In voltage-clamped HL-1 cells, bath flow increased peak Na⁺ current by 14 ± 5%. In current-clamped cells, bath flow increased the frequency and decay rate of AP by 27 ± 12% and 18 ± 4%, respectively. Ranolazine blocked both responses to shear stress. This study suggests that cultured HL-1 cells are a viable in vitro model for detailed study of the effects of mechanical stimulation on spontaneous cardiac action potentials. Inhibition of the frequency and decay rate of action potentials in HL-1 cells are potential mechanisms behind the antiarrhythmic effect of ranolazine.