A mathematical model of electrotonic interactions between ventricular myocytes and fibroblasts

Functional intercellular coupling has been demonstrated among networks of cardiac fibroblasts, as well as between fibroblasts and atrial or ventricular myocytes. In this study, the consequences of these interactions were examined by implementing the ten Tusscher model of the human ventricular action potential, and coupling it to our electrophysiological models for mammalian ventricular fibroblasts. Our simulations reveal significant electrophysiological consequences of coupling between 1 and 4 fibroblasts to a single ventricular myocyte. These include alterations in plateau height and/or action potential duration (APD) and changes in underlying ionic currents. Two series of simulations were carried out. First, fibroblasts were modeled as a spherical cell with a capacitance of 6.3 pF and an ohmic membrane resistance of 10.7 G Omega. When these "passive" fibroblasts were coupled to a myocyte, they caused slight prolongation of APD with no changes in the plateau, threshold for firing, or rate of initial depolarization. In contrast, when the same myocyte-fibroblast complexes were modeled after addition of the time- and voltage-gated K(+) currents that are expressed in fibroblasts, much more pronounced effects were observed: the plateau height of the action potential was reduced and the APD shortened significantly. In addition, each fibroblast exhibited significant electrotonic depolarizations in response to each myocyte action potential and the resting potential of the fibroblasts closely approximated the resting potential of the coupled ventricular myocyte.     

Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium

In the mammalian heart, myocytes and fibroblasts can communicate via gap junction, or connexin-mediated current flow. Some of the effects of this electrotonic coupling on the action potential waveform of the human ventricular myocyte have been analyzed in detail. The present study employs a recently developed mathematical model of the human atrial myocyte to investigate the consequences of this heterogeneous cell–cell interaction on the action potential of the human atrium. Two independent physiological processes which alter the physiology of the human atrium have been studied. i) The effects of the autonomic transmitter acetylcholine on the atrial action potential have been investigated by inclusion of a time-independent, acetylcholine-activated K⁺ current in this mathematical model of the atrial myocyte. ii) A non-selective cation current which is activated by natriuretic peptides has been incorporated into a previously published mathematical model of the cardiac fibroblast. These results identify subtle effects of acetylcholine, which arise from the nonlinear interactions between ionic currents in the human atrial myocyte. They also illustrate marked alterations in the action potential waveform arising from fibroblast–myocyte source–sink principles when the natriuretic peptide-mediated cation conductance is activated. Additional calculations also illustrate the effects of simultaneous activation of both of these cell-type specific conductances within the atrial myocardium. This study provides a basis for beginning to assess the utility of mathematical modeling in understanding detailed cell–cell interactions within the complex paracrine environment of the human atrial myocardium.     

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.     

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.     

In Silico Screening of the Key Cellular Remodeling Targets in Chronic Atrial Fibrillation

Chronic atrial fibrillation (AF) is a complex disease with underlying changes in electrophysiology, calcium signaling and the structure of atrial myocytes. How these individual remodeling targets and their emergent interactions contribute to cell physiology in chronic AF is not well understood. To approach this problem, we performed in silico experiments in a computational model of the human atrial myocyte. The remodeled function of cellular components was based on a broad literature review of in vitro findings in chronic AF, and these were integrated into the model to define a cohort of virtual cells. Simulation results indicate that while the altered function of calcium and potassium ion channels alone causes a pronounced decrease in action potential duration, remodeling of intracellular calcium handling also has a substantial impact on the chronic AF phenotype. We additionally found that the reduction in amplitude of the calcium transient in chronic AF as compared to normal sinus rhythm is primarily due to the remodeling of calcium channel function, calcium handling and cellular geometry. Finally, we found that decreased electrical resistance of the membrane together with remodeled calcium handling synergistically decreased cellular excitability and the subsequent inducibility of repolarization abnormalities in the human atrial myocyte in chronic AF. We conclude that the presented results highlight the complexity of both intrinsic cellular interactions and emergent properties of human atrial myocytes in chronic AF. Therefore, reversing remodeling for a single remodeled component does little to restore the normal sinus rhythm phenotype. These findings may have important implications for developing novel therapeutic approaches for chronic AF.     

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.     

Propagation through electrically coupled cells. How a small SA node drives a large atrium.

Each normal cardiac cycle is started by an action potential that is initiated in the sino-atrial (SA) node by automaticity of the SA nodal cells. This action potential then propagates from the SA node into the surrounding atrial cells. We have done numerical simulations of electrically coupled cells to understand how a small SA node can be spontaneously active and yet be sufficiently electrically coupled to the surrounding quiescent atrial cells to initiate an action potential in the atrial cells. Our results with a simple model of two coupled cells and a more complex model of a two-dimensional sheet of cells suggest that some degree of electrical uncoupling of the cells within the SA node may be an essential design feature of the normal SA-atrial system.     

Stretch-activated non-selective cation channel: a causal link between mechanical stretch and atrial natriuretic peptide secretion

The polypeptide hormone atrial natriuretic peptide (ANP) plays vital roles in maintaining blood volume and arterial blood pressure. The recognition of clinical benefits of ANP both in healthy and diseased heart identifies ANP as a potential candidate for therapeutic strategy in the treatment of heart disease. ANP is synthesized and stored in cardiac myocytes and it is released through the exocytosis of ANP granules both constitutively and in response to stimuli. It is well known that mechanical stretch is the predominant stimulus for ANP secretion. However, the mechanistic link between mechanical stimuli and exocytosis of ANP vesicles in single atrial myocyte has not yet been demonstrated. Over the last decade, compelling evidence suggested that stretch-activated ion channels might function as mechanosensors. We showed previously that direct stretch of single atrial myocyte using two micro-electrodes activated a non-selective cation channel (SAC). So far it is not known whether activation of SAC is involved in stretch-induced ANP secretion. The present article aims to give an overview of the mechanism of mechanical stretch-stimulated ANP secretion and describes an innovative technique to detect ANP secretion from isolated rat atrial myocytes with high time-resolution. Combined with capacitance measurement and patch-clamp technique in conjunction with in situ ANP bioassay, we were able to demonstrate that SAC in rat atrial myocytes acts as a mechanosensor to transduce stretch signals into the ANP secretion pathway.     

Expression,purification and functional characterization of a recombinant scorpion venom peptide BmTXKbeta

BmTXKbeta, a scorpion toxin isolated from the Chinese scorpion Buthus martensii Karsch (BmK), was expressed as a GST fusion protein in BL21 (DE3) strain. The recombinant GST-BmTXKbeta protein was purified by affinity chromatography. When treated with enterokinase, the GST-BmTXKbeta fusion protein released an approximate 6.5kDa protein which was the expected size for correctly processed. About 2mg purified recombinant BmTXKbeta protein (rBmTXKbeta) was produced from 1l bacterial culture, using this expression and purification system. The function of rBmTXKbeta was studied on the rabbit atrial myocyte by whole-cell patch clamp technique. The results showed that rBmTXKbeta inhibited the transient outward current (I(to)) of rabbit atrial myocyte with recovery after washout and the inhibition was concentration-dependent. The rBmTXKbeta prolonged the action potential duration of rabbit atrial myocyte in a concentration-dependent manner, whereas it did not affect the action potential amplitude.     

Coupling between contraction rhythm and calcium oscillation in a cultured cardiac myocyte: Fluctuation behaviour and its modelling

Isolated and cultured neonatal cardiac myocytes show self-sustaining cyclic contraction, and have the properties of a nonlinear oscillator. We study the dynamics of mechanical contraction and cellular free Ca²⁺ in a single myocyte for the purposes of gaining an insight into the way in which excitation and contraction processes are inter-related. The concentration of intracellular Ca²⁺ in the myocyte is also found to vary periodically associated with its rhythmic contraction. The Ca²⁺ dynamics maintains its self-oscillatory nature when the spontaneous contraction is abolished by pharmacological treatment using 2,3-butanedione monoxime. However, fluctuation analysis of the Ca²⁺ oscillation intervals reveals that there occurs a characteristic change in the fluctuation behaviour due to the suppression of contraction; the mean value and fluctuation magnitude of the oscillation intervals and the persistency of the fluctuation correlations at short timescales all increase after pharmacological treatment. We develop a new nonlinear model based on Bonhoeffer - van der Pol oscillators to elucidate the mechanisms behind the observed effects of cardiac contraction on the Ca²⁺ oscillation. The model is composed of three coupled nonlinear differential equations that can describe the dynamics of both excitation (cellular free Ca²⁺) and contraction. Almost all the experimental findings are successfully reproduced by adjusting a parameter in the model responsible for excitation - contraction coupling.     

Loading effect of fibroblast-myocyte coupling on resting potential, impulse propagation, and repolarization: insights from a microstructure model

The numerous nonmyocytes present within the myocardium may establish electrical connections with myocytes through gap junctions, formed naturally or as a result of a cell therapy. The strength of the coupling and its potential impact on action potential characteristics and conduction are not well understood. This study used computer simulation to investigate the load-induced electrophysiological consequences of the coupling of myocytes with fibroblasts, where the fibroblast resting potential, density, distribution, and coupling strength were varied. Conduction velocity (CV), upstroke velocity, and action potential duration (APD) were analyzed for longitudinal and transverse impulse propagation in a two-dimensional microstructure tissue model, developed to represent a monolayer culture of cardiac cells covered by a layer of fibroblasts. The results show that 1) at weak coupling (<0.25 nS), the myocyte resting potential was elevated, leading to CV up to 5% faster than control; 2) at intermediate coupling, the myocyte resting potential elevation saturated, whereas the current flowing from the myocyte to the fibroblast progressively slowed down both CV and upstroke velocity; 3) at strong couplings (>8 nS), all of the effects saturated; and 4) APD at 90% repolarization was usually prolonged by 0-20 ms (up to 60-80 ms for high fibroblast density and coupling) by the coupling to fibroblasts. The changes in APD depended on the fibroblast resting potential. This complex, coupling-dependent interaction of fibroblast and myocytes also has relevance to the integration of other nonmyocytes in the heart, such as those used in cellular therapies.     

The Role of Cellular Coupling in the Spontaneous Generation of Electrical Activity in Uterine Tissue

The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not spontaneously active. It is known, however, that the expression of gap junctions increases dramatically in the approach to parturition, by more than one order of magnitude, which results in a significant increase in inter-cellular electrical coupling. In this paper, we build upon previous studies of the activity of electrically excitable smooth muscle cells (myocytes) and investigate the mechanism through which the coupling of these cells to electrically passive cells results in the generation of spontaneous activity in the uterus. Using a recently developed, realistic model of uterine muscle cell dynamics, we investigate a system consisting of a myocyte coupled to passive cells. We then extend our analysis to a simple two-dimensional lattice model of the tissue, with each myocyte being coupled to its neighbors, as well as to a random number of passive cells. We observe that different dynamical regimes can be observed over a range of gap junction conductances: at low coupling strength, corresponding to values measured long before delivery, the activity is confined to cell clusters, while the activity for high coupling, compatible with values measured shortly before delivery, may spread across the entire tissue. Additionally, we find that the system supports the spontaneous generation of spiral wave activity. Our results are both qualitatively and quantitatively consistent with observations from in vitro experiments. In particular, we demonstrate that the increase in inter-cellular electrical coupling observed experimentally strongly facilitates the appearance of spontaneous action potentials that may eventually lead to parturition.     

二十二碳六烯酸对心房颤动大鼠心房肌生理改变及双孔钾通道TASK-1蛋白表达的影响

目的：探讨二十二碳六烯酸（DHA）对大鼠心房颤动（AF）模型心房肌生理特性的影响及相关机制研究。方法：80只乙酰胆碱-氯化钙混合液敏感的SD大鼠分为对照组（CTL组）、DHA处理组（DHA组）、房颤组（AF组）和房颤+DHA处理组（DHA+AF组）,观察房颤持续时间;采用全细胞膜片钳技术记录大鼠心房肌细胞动作电位时程（APD）和双孔钾通道TASK-1电流,Western blot测定大鼠心房组织TASK-1蛋白表达。结果：大鼠尾静脉注射乙酰胆碱-氯化钙混合液后,房颤持续时间随实验天数增加而逐渐延长,DHA干预缩短房颤持续时间。与CTL组相比,AF组大鼠心房肌细胞复极50%时的动作电位时程（APD₅₀）和复极90%时的动作电位时程（APD₉₀）明显缩短,心房肌细胞TASK-1电流密度升高,蛋白表达升高（P<0.05）。与AF组相比,DHA+AF组大鼠心房肌细胞APD₅₀和APD₉₀明显延长,TASK-1电流密度和蛋白表达降低（P<0.05）。结论：DHA具有延长房颤大鼠心房肌细胞APD的作用,可能与其下调心房肌TASK-1蛋白的表达从而降低心房肌细胞TASK-1电流密度有关。     

Impact of sarcoplasmic reticulum calcium release on calcium dynamics and action potential morphology in human atrial myocytes: a computational study

Electrophysiological studies of the human heart face the fundamental challenge that experimental data can be acquired only from patients with underlying heart disease. Regarding human atria, there exist sizable gaps in the understanding of the functional role of cellular Ca2+ dynamics, which differ crucially from that of ventricular cells, in the modulation of excitation-contraction coupling. Accordingly, the objective of this study was to develop a mathematical model of the human atrial myocyte that, in addition to the sarcolemmal (SL) ion currents, accounts for the heterogeneity of intracellular Ca2+ dynamics emerging from a structurally detailed sarcoplasmic reticulum (SR). Based on the simulation results, our model convincingly reproduces the principal characteristics of Ca2+ dynamics: 1) the biphasic increment during the upstroke of the Ca2+ transient resulting from the delay between the peripheral and central SR Ca2+ release, and 2) the relative contribution of SL Ca2+ current and SR Ca2+ release to the Ca2+ transient. In line with experimental findings, the model also replicates the strong impact of intracellular Ca2+ dynamics on the shape of the action potential. The simulation results suggest that the peripheral SR Ca2+ release sites define the interface between Ca2+ and AP, whereas the central release sites are important for the fire-diffuse-fire propagation of Ca2+ diffusion. Furthermore, our analysis predicts that the modulation of the action potential duration due to increasing heart rate is largely mediated by changes in the intracellular Na+ concentration. Finally, the results indicate that the SR Ca2+ release is a strong modulator of AP duration and, consequently, myocyte refractoriness/excitability. We conclude that the developed model is robust and reproduces many fundamental aspects of the tight coupling between SL ion currents and intracellular Ca2+ signaling. Thus, the model provides a useful framework for future studies of excitation-contraction coupling in human atrial myocytes.     

Anti-fibrotic effects of fresh and cryopreserved human amniotic membrane in a rat liver fibrosis model

The human amniotic membrane (hAM), thanks to its favorable properties, including anti-inflammatory, anti-fibrotic and pro-regenerative effects, is a well-known surgical material for many clinical applications, when used both freshly after isolation and after preservation. We have shown previously that hAM patching is a potential approach to counteract liver fibrosis. Indeed, when fresh hAM was used to cover the liver surface of rats with liver fibrosis induced by the bile duct ligation (BDL) procedure, the progression and severity of fibrosis were significantly reduced. Since cryopreservation enables safety and long-term storage of hAM but may influence its functional properties, here we compared the anti-fibrotic effects of fresh and cryopreserved hAM in rats with BDL-induced liver fibrosis. After BDL, the rat liver was covered with a piece of fresh or cryopreserved hAM, or left untreated. Six weeks later, the degree of liver fibrosis was assessed histologically using the Knodell and the METAVIR scoring systems. Digital image analysis was used to quantify the percentage of the areas of each liver section displaying ductular reaction, extracellular matrix (ECM) deposition, activated myofibroblasts and hepatic stellate cells (HSCs). Liver collagen content was also determined by spectrophotometric technique. The degree of liver fibrosis, ductular reaction, ECM deposition, and the number of activated myofibroblasts and HSCs were all significantly reduced in hAM-treated rats compared to control animals. Fresh and cryopreserved hAM produced the same anti-fibrotic effects. These findings indicate that cryopreservation maintains the anti-fibrotic properties of hAM when used as a patch to reduce the severity of liver fibrosis.     

Modelling the Effect of Gap Junctions on Tissue-Level Cardiac Electrophysiology

When modelling tissue-level cardiac electrophysiology, a continuum approximation to the discrete cell-level equations, known as the bidomain equations, is often used to maintain computational tractability. Analysing the derivation of the bidomain equations allows us to investigate how microstructure, in particular gap junctions that electrically connect cells, affect tissue-level conductivity properties. Using a one-dimensional cable model, we derive a modified form of the bidomain equations that take gap junctions into account, and compare results of simulations using both the discrete and continuum models, finding that the underlying conduction velocity of the action potential ceases to match up between models when gap junctions are introduced at physiologically realistic coupling levels. We show that this effect is magnified by: (i) modelling gap junctions with reduced conductivity; (ii) increasing the conductance of the fast sodium channel; and (iii) an increase in myocyte length. From this, we conclude that the conduction velocity arising from the bidomain equations may not be an accurate representation of the underlying discrete system. In particular, the bidomain equations are less likely to be valid when modelling certain diseased states whose symptoms include a reduction in gap junction coupling or an increase in myocyte length.     

The Role of Distal Dendritic Gap Junctions in Synchronization of Mitral Cell Axonal Output

One of the first and most important stages of odor processing occurs in the glomerular units of the olfactory bulb and most likely involves mitral cell synchronization. Using a detailed model constrained by a number of experimental findings, we show how the intercellular coupling mediated by intraglomerular gap junctions (GJs) in the tuft dendrites could play a major role in sychronization of mitral cell action potential output in spite of their distal dendritic location. The model suggests that the high input resistance and active properties of the fine tuft dendrites are instrumental in generating local spike synchronization and an efficient forward and backpropagation of action potentials between the tuft and the soma. The model also gives insight into the physiological significance of long primary dendrites in mitral cells, and provides evidence against the use of reduced single compartmental models to investigate network properties of cortical pyramidal neurons.     

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.