Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh–Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue.     

Cardiac mitochondrial network excitability: insights from computational analysis

In the heart, mitochondria form a regular lattice and function as a coordinated, nonlinear network to continuously produce ATP to meet the high-energy demand of the cardiomyocytes. Cardiac mitochondria also exhibit properties of an excitable system: electrical or chemical signals can spread within or among cells in the syncytium. The detailed mechanisms by which signals pass among individual elements (mitochondria) across the network are still not completely understood, although emerging studies suggest that network excitability might be mediated by the local diffusion and autocatalytic release of messenger molecules such as reactive oxygen species and/or Ca(2+). In this short review, we have attempted to described recent advances in the field of cardiac mitochondrial network excitability. Specifically, we have focused on how mitochondria communicate with each other through the diffusion and regeneration of messenger molecules to initiate and propagate waves or oscillations, as revealed by computational models of mitochondrial network.     

Reaction-diffusion equations for simulation of calcium signalling in cell systems.

Numerous experimental and theoretical studies have recently pointed to the importance of calcium signals and their propagation as waves of various kinds inside cells. This phenomenon has been particularly noted in fertilized egg cells. Ca2+ plays a fundamental role in these cells as it is capable of stimulating, by means of a first, large wave, the beginning of an organism's life at fertilization, immediately after sperm penetration. Furthermore, calcium is involved in numerous subsequent processes that are essential for the development of the future embryo, e.g. in contraction of cortical cytoplasm, protein synthesis and cell differentiation. Calcium waves, which are generated by self-oscillating pacemakers and propagate in excitable media, have been observed in some types of egg cells after fertilization. These waves adopt different shapes according to their emission frequency, wavelength, velocity and curvature, and they can occur as solitary waves, target waves or spiral waves. The mathematical models that study the progress of these waves have been developed by means of partial differential equations of the "reaction-diffusion" type. This study will discuss some significant models of intracellular Ca2+ dynamics. Some preliminary considerations will then be made in order to develop a model that describes the propagation of Ca2+ waves in ascidian eggs.     

Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction

Complex anatomical and physiological structure of an excitable tissue (e.g., cardiac tissue) in the body can represent different electrical activities through normal or abnormal behavior. Abnormalities of the excitable tissue coming from different biological reasons can lead to formation of some defects. Such defects can cause some successive waves that may end up to some additional reorganizing beating behaviors like spiral waves or target waves. In this study, formation of defects and the resulting emitted waves in an excitable tissue are investigated. We have considered a square array network of neurons with nearest-neighbor connections to describe the excitable tissue. Fundamentally, electrophysiological properties of ion currents in the body are responsible for exhibition of electrical spatiotemporal patterns. More precisely, fluctuation of accumulated ions inside and outside of cell causes variable electrical and magnetic field. Considering undeniable mutual effects of electrical field and magnetic field, we have proposed the new Hindmarsh–Rose (HR) neuronal model for the local dynamics of each individual neuron in the network. In this new neuronal model, the influence of magnetic flow on membrane potential is defined. This improved model holds more bifurcation parameters. Moreover, the dynamical behavior of the tissue is investigated in different states of quiescent, spiking, bursting and even chaotic state. The resulting spatiotemporal patterns are represented and the time series of some sampled neurons are displayed, as well.     

Spontaneous action potentials produced by Na and Cl channels in maturing Rana pipiens oocytes

The electrical excitability of maturing Rana pipiens oocytes was studied using intracellular recording and voltage-clamp techniques. Naturally ovulated oocytes, removed from the body cavity within a few hours after ovulation, possess voltage-sensitive Na and Cl channels that can produce action potentials (ap's). Young oocytes (sometime during metaphase I to first polar body stage) can generate trains of spontaneous action potentials: no chemical treatment or current injection is required. This is the first report of spontaneous repetitive firing in an egg cell membrane. As the oocyte matures, the duration of each ap increases because the outward Cl- current decreases. Middle-aged oocytes (about first polar body stage to metaphase II) have continuously positive membrane potentials (Vm's). Mature, activatable (metaphase II) oocytes have negative Vm's when impaled but can produce a long-lived ap when depolarizing current is injected. The ap's differ fundamentally from ap's in other excitable cells, including eggs: the Na+ current develops slowly and does not inactivate; most of the outward current is carried by Cl-, not by K+; the Cl channel is lost or is rendered insensitive to voltage as the oocyte matures.     

Real-time computer simulations of excitable media: JAVA as a scientific language and as a wrapper for C and FORTRAN programs.

We describe a useful setting for interactive, real-time study of mathematical models of cardiac electrical activity, using implicit and explicit integration schemes implemented in JAVA. These programs are intended as a teaching aid for the study and understanding of general excitable media. Particularly for cardiac cell models and the ionic currents underlying their basic electrical dynamics. Within the programs, excitable media properties such as thresholds and refractoriness and their dependence on parameter values can be analyzed. In addition, the cardiac model applets allow the study of reentrant tachyarrhythmias using premature stimuli and conduction blocks to induce or to terminate reentrant waves of electrical activation in one and two dimensions. The role of some physiological parameters in the transition from tachycardia to fibrillation also can be analyzed by varying the maximum conductances of ion channels associated with a given model in real time during the simulations. These applets are available for download at http://arrhythmia.hofstra.edu or its mirror site http://stardec.ascc.neu.edu/~fenton.     

Electrical excitability of taste cells. Mechanisms and possible physiological significance

Neuronal, muscle and some endocrine cells are electrically excitable. While in muscle and endocrine cells AP stimulates and synchronizes intracellular processes, neurons employ action potentials (APs) to govern discontinuous synapses located distantly. Meanwhile, such axonless sensory cells as photoreceptors and hair cells exemplify afferent output, which is not driven by APs; instead, gradual receptor potentials elicited by sensory stimuli control the release of afferent neurotransmitter glutamate. Mammalian taste cells of the type II and type III are electrically excitable and respond to stimulation by firing APs. Since taste cells also have no axons, physiological significance of the electrical excitability for taste transduction and encoding sensory information is unclear. Perhaps, AP facilitates transmitter release, ATP in type II cells and 5-HT in type III cells, although via different mechanisms. The ATP release is mediated by connexin hemichannels, does not require a Ca²⁺ trigger, and largely gated by membrane voltage. 5-HT secretion is driven by intracellular Ca²⁺ and involves VG Ca²⁺ channels. Here, we discuss ionic mechanisms of excitability of taste cells and speculate on a likely role of APs in mediating their afferent output.     

钠离子通道疾病及其抑制剂生物学功能研究进展

电压门控型钠离子通道(Voltage-gated sodium channel,VGSC)广泛分布于兴奋性细胞,是电信号扩大和传导的主要介质,在神经细胞以及心肌细胞兴奋传导等方面发挥重要作用。钠离子通道结构和功能的异常会改变细胞的兴奋性,从而导致多种疾病的发生,如神经性疼痛、癫痫,以及心律失常等。目前临床上多采用钠离子通道抑制剂治疗上述疾病。近些年,研究人员陆续从动物的毒液中分离纯化出具有调控钠离子通道功能的神经毒素。这些神经毒素多为化合物或小分子多肽。现已有医药研发公司将这些天然的神经毒素进行定向设计改造成钠离子通道靶向药物用于临床疾病的治疗。此外,来源于七鳃鳗Lampetra japonica口腔腺的富含半胱氨酸分泌蛋白(Cysteine-rich buccal gland protein,CRBGP)也首次被证明能够抑制海马神经元和背根神经元的钠离子电流。以下针对钠离子通道疾病及其抑制剂生物学功能的最新研究进展进行分析归纳。     

High-Frequency Stimulation of Excitable Cells and Networks

High-frequency (HF) stimulation has been shown to block conduction in excitable cells including neurons and cardiac myocytes. However, the precise mechanisms underlying conduction block are unclear. Using a multi-scale method, the influence of HF stimulation is investigated in the simplified FitzhHugh-Nagumo and biophysically-detailed Hodgkin-Huxley models. In both models, HF stimulation alters the amplitude and frequency of repetitive firing in response to a constant applied current and increases the threshold to evoke a single action potential in response to a brief applied current pulse. Further, the excitable cells cannot evoke a single action potential or fire repetitively above critical values for the HF stimulation amplitude. Analytical expressions for the critical values and thresholds are determined in the FitzHugh-Nagumo model. In the Hodgkin-Huxley model, it is shown that HF stimulation alters the dynamics of ionic current gating, shifting the steady-state activation, inactivation, and time constant curves, suggesting several possible mechanisms for conduction block. Finally, we demonstrate that HF stimulation of a network of neurons reduces the electrical activity firing rate, increases network synchronization, and for a sufficiently large HF stimulation, leads to complete electrical quiescence. In this study, we demonstrate a novel approach to investigate HF stimulation in biophysically-detailed ionic models of excitable cells, demonstrate possible mechanisms for HF stimulation conduction block in neurons, and provide insight into the influence of HF stimulation on neural networks.     

Use of aminopterin in selecting electrically active neuroblastoma cells

A marked increase in electrical excitability and process formation occurs in the N-18 clone of mouse neuroblastoma as these cells go from the logarithmic phase of growth to the stationary state in confluent cultures. Even more excitable cells can be selected by growth in culture medium containing 10⁻⁵ M aminopterin which kills about 90% of the cells. Clone 1A-103 does not develop significant processes or exhibit marked electrical excitability under any of the culture conditions studied. Thus, our results show that one or more of the steps required for generation of the action potential is sensitive to regulation in cultured cells. Methods are presented for obtaining populations of either electrically passive cells or electrically excitable cells which can easily be maintained for several weeks. Clones differ markedly in their capacity to extend processes and their ability to generate action potentials.     

Wavelet formation in excitable cardiac tissue: the role of wavefront-obstacle interactions in initiating high-frequency fibrillatory-like arrhythmias.

High-frequency arrhythmias leading to fibrillation are often associated with the presence of inhomogeneities (obstacles) in cardiac tissue and reduced excitability of cardiac cells. Studies of antiarrhythmic drugs in patients surviving myocardial infarction revealed an increased rate of sudden cardiac death compared with untreated patients. These drugs block the cardiac sodium channel, thereby reducing excitability, which may alter wavefront-obstacle interactions. In diseased atrial tissue, excitability is reduced by diminished sodium channel availability secondary to depolarized rest potentials and cellular decoupling secondary to intercellular fibrosis. Excitability can also be reduced by incomplete recovery between successive excitations. In all of these cases, wavefront-obstacle interactions in a poorly excitable medium may reflect an arrhythmogenic process that permits formation of reentrant wavelets leading to flutter, fibrillation, and sudden cardiac death. To probe the relationship between excitability and arrhythmogenesis, we explored conditions for new wavelet formation after collision of a plane wave with an obstacle in an otherwise homogeneous excitable medium. Formulating our approach in terms of the balance between charge available in the wavefront and the excitation charge requirements of adjacent medium, we found analytically the critical medium parameters that defined conditions for wavefront-obstacle separation. Under these conditions, when a parent wavefront collided with a primitive obstacle, the resultant fragments separated from the obstacle boundaries, subsequently curled, and spawned new "daughter" wavelets. We identified spatial arrangements of obstacles such that wavefront-obstacle collisions leading to spawning of new wavelets could produce high-frequency wavelet trains similar to fibrillation-like arrhythmias.     

Identification of an endogenous glutamatergic transmitter system controlling excitability and conductivity of atrial cardiomyocytes

As an excitatory transmitter system, the glutamatergic transmitter system controls excitability and conductivity of neurons. Since both cardiomyocytes and neurons are excitable cells, we hypothesized that cardiomyocytes may also be regulated by a similar system. Here, we have demonstrated that atrial cardiomyocytes have an intrinsic glutamatergic transmitter system, which regulates the generation and propagation of action potentials. First, there are abundant vesicles containing glutamate beneath the plasma membrane of rat atrial cardiomyocytes. Second, rat atrial cardiomyocytes express key elements of the glutamatergic transmitter system, such as the glutamate metabolic enzyme, ionotropic glutamate receptors (iGluRs), and glutamate transporters. Third, iGluR agonists evoke iGluR-gated currents and decrease the threshold of electrical excitability in rat atrial cardiomyocytes. Fourth, iGluR antagonists strikingly attenuate the conduction velocity of electrical impulses in rat atrial myocardium both in vitro and in vivo. Knockdown of GRIA3 or GRIN1, two highly expressed iGluR subtypes in atria, drastically decreased the excitatory firing rate and slowed down the electrical conduction velocity in cultured human induced pluripotent stem cell (iPSC)-derived atrial cardiomyocyte monolayers. Finally, iGluR antagonists effectively prevent and terminate atrial fibrillation in a rat isolated heart model. In addition, the key elements of the glutamatergic transmitter system are also present and show electrophysiological functions in human atrial cardiomyocytes. In conclusion, our data reveal an intrinsic glutamatergic transmitter system directly modulating excitability and conductivity of atrial cardiomyocytes through controlling iGluR-gated currents. Manipulation of this system may open potential new avenues for therapeutic intervention of cardiac arrhythmias.Subject terms: Cell biology, Molecular biology     

Voltage-gated calcium channels and disease

Voltage-gated calcium channels are a family of integral membrane calcium-selective proteins found in all excitable and many nonexcitable cells. Calcium influx affects membrane electrical properties by depolarizing cells and generally increasing excitability. Calcium entry further regulates multiple intracellular signaling pathways as well as the biochemical factors that mediate physiological functions such as neurotransmitter release and muscle contraction. Small changes in the biophysical properties or expression of calcium channels can result in pathophysiological changes leading to serious chronic disorders. In humans, mutations in calcium channel genes have been linked to a number of serious neurological, retinal, cardiac, and muscular disorders.     

Development of electrical excitability in embryonic neurons: Mechanisms and roles

Xenopus spinal neurons serve as a nearly ideal population of excitable cells for study of developmental regulation of electrical excitability. On the one hand, the firing properties of these neurons can be directly examined at early stages of differentiation and membrane excitability changes as neurons mature. Underlying changes in voltage-dependent ion channels have been characterized and the mechanisms that bring about these changes are being defined. On the other hand, these neurons have been shown to be spontaneously active at stages when action potentials provide significant calcium entry. Calcium entry provokes further elevation of intracellular calcium via release from intracellular stores. The resultant transient elevations of intracellular calcium encode differentiation in their frequency. Recent studies have shown that different neuronal subpopulations enlist distinct mechanisms for regulation of excitability and recruit specific programs of differentiation by particular patterns of activity. © 1998 John Wiley & Sons, Inc. J Neurobiol 37: 190–197, 1998     

Expression and properties of acetylcholine receptors in several clones of mouse neuroblastoma X L cell somatic hybrids

Three clones of somatic cell hybrids between neuroblastoma and L cells, NL-1F, NL-308 and NL-309 (3), have been studied for their electrical excitability and chemosensitivity to acetylcholine (Ach) applied by iontophoresis. Parental and hybrid lines were all treated and tested in media containing mM db-cAMP. The percentage of excitable N X L hybrid cells was as high or higher than that of their neuroblastoma parents. The percentage of cells sensitive to Ach was several-fold higher for the three N X L clones than for the neuroblastoma or L cell parents. While the neuroblastoma parents gave only depolarizing cholinergic responses, the N X L hybrid cells displayed slow hyperpolarizing (H) responses which resembled the H-cholinergic response obtained from L cells. The H-response of the N X L hybrids has properties which indicate the involvement of a muscarinic receptor. A correlation between expression of muscarinic receptors and excitability to electrical current (i.e., action potential ionophores), not found in the neuroblastoma parents, was present in the hybrids. However, a few N X L hybrid cells expressed muscarinic receptors independently from electrical excitability, as is the case for the L cell parent. The three N X L clones are discussed as potentially useful models to study interaction of Ach with muscarinic receptors.     

Calcium wave propagation by calcium-induced calcium release: An unusual excitable system

We discuss in detail the behaviour of a model, proposed by Goldbeteret al. (1990.Proc. natn. Acad. Sci. 87, 1461–1465), for intracellular calcium wave propagation by calcium-induced calcium release, focusing our attention on excitability and the propagation of waves in one spatial dimension. The model with no diffusion behaves like a generic excitable system, and threshold behaviour, excitability and oscillations can be understood within this general framework. However, when diffusion is included, the model no longer behaves like a generic excitable system; the fast and slow variables are not distinct and previous results on excitable systems do not necessarily apply. We consider a piecewise linear simplification of the model, and construct travelling pulse and periodic plane wave solutions to the simplified model. The analogous behaviour in the full model is studied numerically. Goldbeter's model for calciuminduced calcium release is an excitable system of a type not previously studied in detail.     

Opposite Effects of Low and High Doses of Aβ42 on Electrical Network and Neuronal Excitability in the Rat Prefrontal Cortex

Changes in neuronal synchronization have been found in patients and animal models of Alzheimer''s disease (AD). Synchronized behaviors within neuronal networks are important to such complex cognitive processes as working memory. The mechanisms behind these changes are not understood but may involve the action of soluble β-amyloid (Aβ) on electrical networks. In order to determine if Aβ can induce changes in neuronal synchronization, the activities of pyramidal neurons were recorded in rat prefrontal cortical (PFC) slices under calcium-free conditions using multi-neuron patch clamp technique. Electrical network activities and synchronization among neurons were significantly inhibited by low dose Aβ42 (1 nM) and initially by high dose Aβ42 (500 nM). However, prolonged application of high dose Aβ42 resulted in network activation and tonic firing. Underlying these observations, we discovered that prolonged application of low and high doses of Aβ42 induced opposite changes in action potential (AP)-threshold and after-hyperpolarization (AHP) of neurons. Accordingly, low dose Aβ42 significantly increased the AP-threshold and deepened the AHP, making neurons less excitable. In contrast, high dose Aβ42 significantly reduced the AP-threshold and shallowed the AHP, making neurons more excitable. These results support a model that low dose Aβ42 released into the interstitium has a physiologic feedback role to dampen electrical network activity by reducing neuronal excitability. Higher concentrations of Aβ42 over time promote supra-synchronization between individual neurons by increasing their excitability. The latter may disrupt frontal-based cognitive processing and in some cases lead to epileptiform discharges.     

Development of one experimental module to study the modulation of the propagation velocity of chemical excitation waves in gel by weak external force (gravity)

Biological and chemical systems in which the pattern of flow of energy and matter imposes self-organization can be seen as examples of excitable media. One property of such media is the presence of excitation waves. The Belouzov-Zabotinsky(B-Z) reaction system and the retinal spreading depression wave are examples of experimental models of excitable media in which the influence of gravity can be studied. In this paper we describe one especial module constructed to test the influence of gravity in gels of the B-Z system. In the gel condition, convection effects are minimized. The results will be directly comparable to retinal experiments programmed by the same group and complete a series of investigations of systematic comparison of the modulation of chemical and biological excitation waves by weak external forces.     

Reliable Activation of Immature Neurons in the Adult Hippocampus

Neurons born in the adult dentate gyrus develop, mature, and connect over a long interval that can last from six to eight weeks. It has been proposed that, during this period, developing neurons play a relevant role in hippocampal signal processing owing to their distinctive electrical properties. However, it has remained unknown whether immature neurons can be recruited into a network before synaptic and functional maturity have been achieved. To address this question, we used retroviral expression of green fluorescent protein to identify developing granule cells of the adult mouse hippocampus and investigate the balance of afferent excitation, intrinsic excitability, and firing behavior by patch clamp recordings in acute slices. We found that glutamatergic inputs onto young neurons are significantly weaker than those of mature cells, yet stimulation of cortical excitatory axons elicits a similar spiking probability in neurons at either developmental stage. Young neurons are highly efficient in transducing ionic currents into membrane depolarization due to their high input resistance, which decreases substantially in mature neurons as the inward rectifier potassium (Kir) conductance increases. Pharmacological blockade of Kir channels in mature neurons mimics the high excitability characteristic of young neurons. Conversely, Kir overexpression induces mature-like firing properties in young neurons. Therefore, the differences in excitatory drive of young and mature neurons are compensated by changes in membrane excitability that render an equalized firing activity. These observations demonstrate that the adult hippocampus continuously generates a population of highly excitable young neurons capable of information processing.