Pacemaker synchronization of electrically coupled rabbit sinoatrial node cells

Transcriptional regulation of the postnatal cardiac conduction system heterogeneity

The cardiac conduction system (CCS) is a network of specialized cardiomyocytes that coordinates electrical impulse generation and propagation for synchronized heart contractions. Although the components of the CCS, including the sinoatrial node, atrioventricular node, His bundle, bundle branches, and Purkinje fibers, were anatomically discovered more than 100 years ago, their molecular constituents and regulatory mechanisms remain incompletely understood. Here, we demonstrate the transcriptomic landscape of the postnatal mouse CCS at a single-cell resolution with spatial information. Integration of single-cell and spatial transcriptomics uncover region-specific markers and zonation patterns of expression. Network inference shows heterogeneous gene regulatory networks across the CCS. Notably, region-specific gene regulation is recapitulated in vitro using neonatal mouse atrial and ventricular myocytes overexpressing CCS-specific transcription factors, Tbx3 and/or Irx3. This finding is supported by ATAC-seq of different CCS regions, Tbx3 ChIP-seq, and Irx motifs. Overall, this study provides comprehensive molecular profiles of the postnatal CCS and elucidates gene regulatory mechanisms contributing to its heterogeneity.

Pacemaker Channels and the Chronotropic Response in Health and Disease

Loss or dysregulation of the normally precise control of heart rate via the autonomic nervous system plays a critical role during the development and progression of cardiovascular disease-including ischemic heart disease, heart failure, and arrhythmias. While the clinical significance of regulating changes in heart rate, known as the chronotropic effect, is undeniable, the mechanisms controlling these changes remain not fully understood. Heart rate acceleration and deceleration are mediated by increasing or decreasing the spontaneous firing rate of pacemaker cells in the sinoatrial node. During the transition from rest to activity, sympathetic neurons stimulate these cells by activating β-adrenergic receptors and increasing intracellular cyclic adenosine monophosphate. The same signal transduction pathway is targeted by positive chronotropic drugs such as norepinephrine and dobutamine, which are used in the treatment of cardiogenic shock and severe heart failure. The cyclic adenosine monophosphate-sensitive hyperpolarization-activated current (If) in pacemaker cells is passed by hyperpolarization-activated cyclic nucleotide-gated cation channels and is critical for generating the autonomous heartbeat. In addition, this current has been suggested to play a central role in the chronotropic effect. Recent studies demonstrate that cyclic adenosine monophosphate-dependent regulation of HCN4 (hyperpolarization-activated cyclic nucleotide-gated cation channel isoform 4) acts to stabilize the heart rate, particularly during rapid rate transitions induced by the autonomic nervous system. The mechanism is based on creating a balance between firing and recently discovered nonfiring pacemaker cells in the sinoatrial node. In this way, hyperpolarization-activated cyclic nucleotide-gated cation channels may protect the heart from sinoatrial node dysfunction, secondary arrhythmia of the atria, and potentially fatal tachyarrhythmia of the ventricles. Here, we review the latest findings on sinoatrial node automaticity and discuss the physiological and pathophysiological role of HCN pacemaker channels in the chronotropic response and beyond.

Swarmalators on a ring with uncorrelated pinning

We present a case study of swarmalators (mobile oscillators) that move on a 1D ring and are subject to pinning. Previous work considered the special case where the pinning in space and the pinning in the phase dimension were correlated. Here, we study the general case where the space and phase pinning are uncorrelated, both being chosen uniformly at random. This induces several new effects, such as pinned async, mixed states, and a first-order phase transition. These phenomena may be found in real world swarmalators, such as systems of vinegar eels, Janus matchsticks, electrorotated Quincke rollers, or Japanese tree frogs.

Emergent activity, heterogeneity, and robustness in a calcium feedback model of the sinoatrial node

The sinoatrial node (SAN) is the primary pacemaker of the heart. SAN activity emerges at an early point in life and maintains a steady rhythm for the lifetime of the organism. The ion channel composition and currents of SAN cells can be influenced by a variety of factors. Therefore, the emergent activity and long-term stability imply some form of dynamical feedback control of SAN activity. We adapt a recent feedback model-previously utilized to describe control of ion conductances in neurons-to a model of SAN cells and tissue. The model describes a minimal regulatory mechanism of ion channel conductances via feedback between intracellular calcium and an intrinsic target calcium level. By coupling a SAN cell to the calcium feedback model, we show that spontaneous electrical activity emerges from quiescence and is maintained at steady state. In a 2D SAN tissue model, spatial variability in intracellular calcium targets lead to significant, self-organized heterogeneous ion channel expression and calcium transients throughout the tissue. Furthermore, multiple pacemaking regions appear, which interact and lead to time-varying cycle length, demonstrating that variability in heart rate is an emergent property of the feedback model. Finally, we demonstrate that the SAN tissue is robust to the silencing of leading cells or ion channel knockouts. Thus, the calcium feedback model can reproduce and explain many fundamental emergent properties of activity in the SAN that have been observed experimentally based on a minimal description of intracellular calcium and ion channel regulatory networks.

The virtual sinoatrial node: What did computational models tell us about cardiac pacemaking?

Since its discovery, the sinoatrial node (SAN) has represented a fascinating and complex matter of research. Despite over a century of discoveries, a full comprehension of pacemaking has still to be achieved. Experiments often produced conflicting evidence that was used either in support or against alternative theories, originating intense debates. In this context, mathematical descriptions of the phenomena underlying the heartbeat have grown in importance in the last decades since they helped in gaining insights where experimental evaluation could not reach. This review presents the most updated SAN computational models and discusses their contribution to our understanding of cardiac pacemaking. Electrophysiological, structural and pathological aspects - as well as the autonomic control over the SAN - are taken into consideration to reach a holistic view of SAN activity.

Coupling and heterogeneity modulate pacemaking capability in healthy and diseased two-dimensional sinoatrial node tissue models

Both experimental and modeling studies have attempted to determine mechanisms by which a small anatomical region, such as the sinoatrial node (SAN), can robustly drive electrical activity in the human heart. However, despite many advances from prior research, important questions remain unanswered. This study aimed to investigate, through mathematical modeling, the roles of intercellular coupling and cellular heterogeneity in synchronization and pacemaking within the healthy and diseased SAN. In a multicellular computational model of a monolayer of either human or rabbit SAN cells, simulations revealed that heterogenous cells synchronize their discharge frequency into a unique beating rhythm across a wide range of heterogeneity and intercellular coupling values. However, an unanticipated behavior appeared under pathological conditions where perturbation of ionic currents led to reduced excitability. Under these conditions, an intermediate range of intercellular coupling (900-4000 MΩ) was beneficial to SAN automaticity, enabling a very small portion of tissue (3.4%) to drive propagation, with propagation failure occurring at both lower and higher resistances. This protective effect of intercellular coupling and heterogeneity, seen in both human and rabbit tissues, highlights the remarkable resilience of the SAN. Overall, the model presented in this work allowed insight into how spontaneous beating of the SAN tissue may be preserved in the face of perturbations that can cause individual cells to lose automaticity. The simulations suggest that certain degrees of gap junctional coupling protect the SAN from ionic perturbations that can be caused by drugs or mutations.

Active force generation contributes to the complexity of spontaneous activity and to the response to stretch of murine cardiomyocyte cultures

Abstract

Cardiomyocyte cultures exhibit spontaneous electrical and contractile activity, as in a natural cardiac pacemaker. In such preparations, beat rate variability exhibits features similar to those of heart rate variability in vivo. Mechanical deformations and forces feed back on the electrical properties of cardiomyocytes, but it is not fully elucidated how this mechano‐electrical interplay affects beating variability in such preparations. Using stretchable microelectrode arrays, we assessed the effects of the myosin inhibitor blebbistatin and the non‐selective stretch‐activated channel blocker streptomycin on beating variability and on the response of neonatal or fetal murine ventricular cell cultures against deformation. Spontaneous electrical activity was recorded without stretch and upon predefined deformation protocols (5% uniaxial and 2% equibiaxial strain, applied repeatedly for 1 min every 3 min). Without stretch, spontaneous activity originated from the edge of the preparations, and its site of origin switched frequently in a complex manner across the cultures. Blebbistatin did not change mean beat rate, but it decreased the spatial complexity of spontaneous activity. In contrast, streptomycin did not exert any manifest effects. During the deformation protocols, beat rate increased transiently upon stretch but, paradoxically, also upon release. Blebbistatin attenuated the response to stretch, whereas this response was not affected by streptomycin. Therefore, our data support the notion that in a spontaneously firing network of cardiomyocytes, active force generation, rather than stretch‐activated channels, is involved mechanistically in the complexity of the spatiotemporal patterns of spontaneous activity and in the stretch‐induced acceleration of beating.

Key points

Monolayer cultures of cardiac cells exhibit spontaneous electrical and contractile activity, as in a natural cardiac pacemaker. Beating variability in these preparations recapitulates the power‐law behaviour of heart rate variability in vivo. However, the effects of mechano‐electrical feedback on beating variability are not yet fully understood.

Using stretchable microelectrode arrays, we examined the effects of the contraction uncoupler blebbistatin and the non‐specific stretch‐activated channel blocker streptomycin on beating variability and on stretch‐induced changes of beat rate.

Without stretch, blebbistatin decreased the spatial complexity of beating variability, whereas streptomycin had no effects.

Both stretch and release increased beat rate transiently; blebbistatin attenuated the increase of beat rate upon stretch, whereas streptomycin had no effects.

Active force generation contributes to the complexity of spatiotemporal patterns of beating variability and to the increase of beat rate upon mechanical deformation. Our study contributes to the understanding of how mechano‐electrical feedback influences heart rate variability.

Automaticity in ventricular myocyte cell pairs with ephaptic and gap junction coupling

Spontaneous electrical activity, or automaticity, in the heart is required for normal physiological function. However, irregular automaticity, in particular, originating from the ventricles, can trigger life-threatening cardiac arrhythmias. Thus, understanding mechanisms of automaticity and synchronization is critical. Recent work has proposed that excitable cells coupled via a shared narrow extracellular cleft can mediate coupling, i.e., ephaptic coupling, that promotes automaticity in cell pairs. However, the dynamics of these coupled cells incorporating both ephaptic and gap junction coupling has not been explored. Here, we show that automaticity and synchronization robustly emerges via a Hopf bifurcation from either (i) increasing the fraction of inward rectifying potassium channels (carrying the I_K1 current) at the junctional membrane or (ii) by decreasing the cleft volume. Furthermore, we explore how heterogeneity in the fraction of potassium channels between coupled cells can produce automaticity of both cells or neither cell, or more rarely in only one cell (i.e., automaticity without synchronization). Interestingly, gap junction coupling generally has minor effects, with only slight changes in regions of parameter space of automaticity. This work provides insight into potentially new mechanisms that promote spontaneous activity and, thus, triggers for arrhythmias in ventricular tissue.

What keeps us ticking? Sinoatrial node mechano-sensitivity: the grandfather clock of cardiac rhythm

The rhythmic and spontaneously generated electrical excitation that triggers the heartbeat originates in the sinoatrial node (SAN). SAN automaticity has been thoroughly investigated, which has uncovered fundamental mechanisms involved in cardiac pacemaking that are generally categorised into two interacting and overlapping systems: the 'membrane' and 'Ca²⁺ clock'. The principal focus of research has been on these two systems of oscillators, which have been studied primarily in single cells and isolated tissue, experimental preparations that do not consider mechanical factors present in the whole heart. SAN mechano-sensitivity has long been known to be a contributor to SAN pacemaking-both as a driver and regulator of automaticity-but its essential nature has been underappreciated. In this review, following a description of the traditional 'clocks' of SAN automaticity, we describe mechanisms of SAN mechano-sensitivity and its vital role for SAN function, making the argument that the 'mechanics oscillator' is, in fact, the 'grandfather clock' of cardiac rhythm.

Synchronized Cardiac Impulses Emerge From Heterogeneous Local Calcium Signals Within and Among Cells of Pacemaker Tissue

OBJECTIVES

This study sought to identify subcellular Ca²⁺ signals within and among cells comprising the sinoatrial node (SAN) tissue.

BACKGROUND

The current paradigm of SAN impulse generation: 1) is that full-scale action potentials (APs) of a common frequency are initiated at 1 site and are conducted within the SAN along smooth isochrones; and 2) does not feature fine details of Ca²⁺ signaling present in isolated SAN cells, in which small subcellular, subthreshold local Ca²⁺ releases (LCRs) self-organize to generate cell-wide APs.

METHODS

Immunolabeling was combined with a novel technique to detect the occurrence of LCRs and AP-induced Ca²⁺ transients (APCTs) in individual pixels (chronopix) across the entire mouse SAN images.

RESULTS

At high magnification, Ca²⁺ signals appeared markedly heterogeneous in space, amplitude, frequency, and phase among cells comprising an HCN4⁺/CX43^- cell meshwork. The signaling exhibited several distinguishable patterns of LCR/APCT interactions within and among cells. Rhythmic APCTs that were apparently conducted within the meshwork were transferred to a truly conducting HCN4^-/CX43⁺ network of striated cells via narrow functional interfaces where different cell types intertwine, that is, the SAN anatomic/functional unit. At low magnification, the earliest APCT of each cycle occurred within a small area of the HCN4 meshwork, and subsequent APCT appearance throughout SAN pixels was discontinuous and asynchronous.

CONCLUSIONS

The study has discovered a novel, microscopic Ca²⁺ signaling paradigm of SAN operation that has escaped detection using low-resolution, macroscopic tissue isochrones employed in prior studies: synchronized APs emerge from heterogeneous subcellular subthreshold Ca²⁺ signals, resembling multiscale complex processes of impulse generation within clusters of neurons in neuronal networks.

Rad-GTPase contributes to heart rate via L-type calcium channel regulation

Sinoatrial node cardiomyocytes (SANcm) possess automatic, rhythmic electrical activity. SAN rate is influenced by autonomic nervous system input, including sympathetic nerve increases of heart rate (HR) via activation of β-adrenergic receptor signaling cascade (β-AR). L-type calcium channel (LTCC) activity contributes to membrane depolarization and is a central target of β-AR signaling. Recent studies revealed that the small G-protein Rad plays a central role in β-adrenergic receptor directed modulation of LTCC. These studies have identified a conserved mechanism in which β-AR stimulation results in PKA-dependent Rad phosphorylation: depletion of Rad from the LTCC complex, which is proposed to relieve the constitutive inhibition of CaV1.2 imposed by Rad association. Here, using a transgenic mouse model permitting conditional cardiomyocyte selective Rad ablation, we examine the contribution of Rad to the control of SANcm LTCC current (ICa,L) and sinus rhythm. Single cell analysis from a recent published database indicates that Rad is expressed in SANcm, and we show that SANcm ICa,L was significantly increased in dispersed SANcm following Rad silencing compared to those from CTRL hearts. Moreover, cRadKO SANcm ICa,L was not further increased with β-AR agonists. We also evaluated heart rhythm in vivo using radiotelemetered ECG recordings in ambulating mice. In vivo, intrinsic HR is significantly elevated in cRadKO. During the sleep phase cRadKO also show elevated HR, and during the active phase there is no significant difference. Rad-deletion had no significant effect on heart rate variability. These results are consistent with Rad governing LTCC function under relatively low sympathetic drive conditions to contribute to slower HR during the diurnal sleep phase HR. In the absence of Rad, the tonic modulated SANcm ICa,L promotes elevated sinus HR. Future novel therapeutics for bradycardia targeting Rad - LTCC can thus elevate HR while retaining βAR responsiveness.

Assembly of the Cardiac Pacemaking Complex: Electrogenic Principles of Sinoatrial Node Morphogenesis

Cardiac pacemaker cells located in the sinoatrial node initiate the electrical impulses that drive rhythmic contraction of the heart. The sinoatrial node accounts for only a small proportion of the total mass of the heart yet must produce a stimulus of sufficient strength to stimulate the entire volume of downstream cardiac tissue. This requires balancing a delicate set of electrical interactions both within the sinoatrial node and with the downstream working myocardium. Understanding the fundamental features of these interactions is critical for defining vulnerabilities that arise in human arrhythmic disease and may provide insight towards the design and implementation of the next generation of potential cellular-based cardiac therapeutics. Here, we discuss physiological conditions that influence electrical impulse generation and propagation in the sinoatrial node and describe developmental events that construct the tissue-level architecture that appears necessary for sinoatrial node function.

Rhythm Drivers, Physical Properties, Mechanisms of Formation

A mathematical model of the pacemaker is presented in the form of a nonlinear system of ordinary differential equations and in the form of a system of partial differential equations for distributed pacemakers. For the numerical study of the properties of the pacemaker, a modified axiomatic Wiener-Rosenbluth method was used using the properties of uniform almost periodic functions. Physical foundations, mechanisms of formation, properties of point and distributed pacemakers are described in detail.

Development of the Cardiac Conduction System

The cardiac conduction system initiates and propagates each heartbeat. Specialized conducting cells are a well-conserved phenomenon across vertebrate evolution, although mammalian and avian species harbor specific components unique to organisms with four-chamber hearts. Early histological studies in mammals provided evidence for a dominant pacemaker within the right atrium and clarified the existence of the specialized muscular axis responsible for atrioventricular conduction. Building on these seminal observations, contemporary genetic techniques in a multitude of model organisms has characterized the developmental ontogeny, gene regulatory networks, and functional importance of individual anatomical compartments within the cardiac conduction system. This review describes in detail the transcriptional and regulatory networks that act during cardiac conduction system development and homeostasis with a particular emphasis on networks implicated in human electrical variation by large genome-wide association studies. We conclude with a discussion of the clinical implications of these studies and describe some future directions.

Dynamic Properties of Heart Fragments from Different Regions and Their Synchronization

The dynamic properties of the heart differ based on the regions that effectively circulate blood throughout the body with each heartbeat. These properties, including the inter-beat interval (IBI) of autonomous beat activity, are retained even in in vitro tissue fragments. However, details of beat dynamics have not been well analyzed, particularly at the sub-mm scale, although such dynamics of size are important for regenerative medicine and computational studies of the heart. We analyzed the beat dynamics in sub-mm tissue fragments from atria and ventricles of hearts obtained from chick embryos over a period of 40 h. The IBI and contraction speed differed by region and atrial fragments retained their values for a longer time. The major finding of this study is synchronization of these fragment pairs physically attached to each other. The probability of achieving this and the time required differ for regional pairs: atrium-atrium, ventricle-ventricle, or atrium-ventricle. Furthermore, the time required to achieve 1:1 synchronization does not depend on the proximity of initial IBI of paired fragments. Various interesting phenomena, such as 1:n synchronization and a reentrant-like beat sequence, are revealed during synchronization. Finally, our observation of fragment dynamics indicates that mechanical motion itself contributes to the synchronization of atria.

A practical method for estimating coupling functions in complex dynamical systems

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99, 064101. (doi:10.1103/PhysRevLett.99.064101)) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Engineered Cardiac Pacemaker Nodes Created by TBX18 Gene Transfer Overcome Source-Sink Mismatch

Every heartbeat originates from a tiny tissue in the heart called the sinoatrial node (SAN). The SAN harbors only ≈10 000 cardiac pacemaker cells, initiating an electrical impulse that captures the entire heart, consisting of billions of cardiomyocytes for each cardiac contraction. How these rare cardiac pacemaker cells (the electrical source) can overcome the electrically hyperpolarizing and quiescent myocardium (the electrical sink) is incompletely understood. Due to the scarcity of native pacemaker cells, this concept of source-sink mismatch cannot be tested directly with live cardiac tissue constructs. By exploiting TBX18 induced pacemaker cells by somatic gene transfer, 3D cardiac pacemaker spheroids can be tissue-engineered. The TBX18 induced pacemakers (sphTBX18) pace autonomously and drive the contraction of neighboring myocardium in vitro. TBX18 spheroids demonstrate the need for reduced electrical coupling and physical separation from the neighboring ventricular myocytes, successfully recapitulating a key design principle of the native SAN. β-Adrenergic stimulation as well as electrical uncoupling significantly increase sphTBX18s' ability to pace-and-drive the neighboring myocardium. This model represents the first platform to test design principles of the SAN for mechanistic understanding and to better engineer biological pacemakers for therapeutic translation.

Resonant model-A new paradigm for modeling an action potential of biological cells

Organ level simulation of bioelectric behavior in the body benefits from flexible and efficient models of cellular membrane potential. These computational organ and cell models can be used to study the impact of pharmaceutical drugs, test hypotheses, assess risk and for closed-loop validation of medical devices. To move closer to the real-time requirements of this modeling a new flexible Fourier based general membrane potential model, called as a Resonant model, is developed that is computationally inexpensive. The new model accurately reproduces non-linear potential morphologies for a variety of cell types. Specifically, the method is used to model human and rabbit sinoatrial node, human ventricular myocyte and squid giant axon electrophysiology. The Resonant models are validated with experimental data and with other published models. Dynamic changes in biological conditions are modeled with changing model coefficients and this approach enables ionic channel alterations to be captured. The Resonant model is used to simulate entrainment between competing sinoatrial node cells. These models can be easily implemented in low-cost digital hardware and an alternative, resource-efficient implementations of sine and cosine functions are presented and it is shown that a Fourier term is produced with two additions and a binary shift.

Electrical coupling and its channels

As the physiology of synapses began to be explored in the 1950s, it became clear that electrical communication between neurons could not always be explained by chemical transmission. Instead, careful studies pointed to a direct intercellular pathway of current flow and to the anatomical structure that was (eventually) called the gap junction. The mechanism of intercellular current flow was simple compared with chemical transmission, but the consequences of electrical signaling in excitable tissues were not. With the recognition that channels were a means of passive ion movement across membranes, the character and behavior of gap junction channels came under scrutiny. It became evident that these gated channels mediated intercellular transfer of small molecules as well as atomic ions, thereby mediating chemical, as well as electrical, signaling. Members of the responsible protein family in vertebrates-connexins-were cloned and their channels studied by many of the increasingly biophysical techniques that were being applied to other channels. As described here, much of the evolution of the field, from electrical coupling to channel structure-function, has appeared in the pages of the Journal of General Physiology.

Heterogeneity of calcium clock functions in dormant, dysrhythmically and rhythmically firing single pacemaker cells isolated from SA node

Current understanding of how cardiac pacemaker cells operate is based mainly on studies in isolated single sinoatrial node cells (SANC), specifically those that rhythmically fire action potentials similar to the in vivo behavior of the intact sinoatrial node. However, only a small fraction of SANC exhibit rhythmic firing after isolation. Other SANC behaviors have not been studied. Here, for the first time, we studied all single cells isolated from the sinoatrial node of the guinea pig, including traditionally studied rhythmically firing cells ('rhythmic SANC'), dysrhythmically firing cells ('dysrhythmic SANC') and cells without any apparent spontaneous firing activity ('dormant SANC'). Action potential-induced cytosolic Ca²⁺ transients and spontaneous local Ca²⁺ releases (LCRs) were measured with a 2D camera. LCRs were present not only in rhythmically firing SANC, but also in dormant and dysrhythmic SANC. While rhythmic SANC were characterized by large LCRs synchronized in space and time towards late diastole, dysrhythmic and dormant SANC exhibited smaller LCRs that appeared stochastically and were widely distributed in time. β-adrenergic receptor (βAR) stimulation increased LCR size and synchronized LCR occurrences in all dysrhythmic and a third of dormant cells (25 of 75 cells tested). In response to βAR stimulation, these dormant SANC developed automaticity, and LCRs became coupled to spontaneous action potential-induced cytosolic Ca²⁺ transients. Conversely, dormant SANC that did not develop automaticity showed no significant change in average LCR characteristics. The majority of dysrhythmic cells became rhythmic in response to βAR stimulation, with the rate of action potential-induced cytosolic Ca²⁺ transients substantially increasing. In summary, isolated SANC can be broadly categorized into three major populations: dormant, dysrhythmic, and rhythmic. We interpret our results based on simulations of a numerical model of SANC operating as a coupled-clock system. On this basis, the two previously unstudied dysrhythmic and dormant cell populations have intrinsically partially or completely uncoupled clocks. Such cells can be recruited to fire rhythmically in response to βAR stimulation via increased rhythmic LCR activity and ameliorated coupling between the Ca²⁺ and membrane clocks.

Applications of Dynamic Clamp to Cardiac Arrhythmia Research: Role in Drug Target Discovery and Safety Pharmacology Testing

Dynamic clamp, a hybrid-computational-experimental technique that has been used to elucidate ionic mechanisms underlying cardiac electrophysiology, is emerging as a promising tool in the discovery of potential anti-arrhythmic targets and in pharmacological safety testing. Through the injection of computationally simulated conductances into isolated cardiomyocytes in a real-time continuous loop, dynamic clamp has greatly expanded the capabilities of patch clamp outside traditional static voltage and current protocols. Recent applications include fine manipulation of injected artificial conductances to identify promising drug targets in the prevention of arrhythmia and the direct testing of model-based hypotheses. Furthermore, dynamic clamp has been used to enhance existing experimental models by addressing their intrinsic limitations, which increased predictive power in identifying pro-arrhythmic pharmacological compounds. Here, we review the recent advances of the dynamic clamp technique in cardiac electrophysiology with a focus on its future role in the development of safety testing and discovery of anti-arrhythmic drugs.

Regularity of beating of small clusters of embryonic chick ventricular heart-cells: experiment vs. stochastic single-channel population model

The transmembrane potential is recorded from small isopotential clusters of 2-4 embryonic chick ventricular cells spontaneously generating action potentials. We analyze the cycle-to-cycle fluctuations in the time between successive action potentials (the interbeat interval or IBI). We also convert an existing model of electrical activity in the cluster, which is formulated as a Hodgkin-Huxley-like deterministic system of nonlinear ordinary differential equations describing five individual ionic currents, into a stochastic model consisting of a population of ∼20 000 independently and randomly gating ionic channels, with the randomness being set by a real physical stochastic process (radio static). This stochastic model, implemented using the Clay-DeFelice algorithm, reproduces the fluctuations seen experimentally: e.g., the coefficient of variation (standard deviation/mean) of IBI is 4.3% in the model vs. the 3.9% average value of the 17 clusters studied. The model also replicates all but one of several other quantitative measures of the experimental results, including the power spectrum and correlation integral of the voltage, as well as the histogram, Poincaré plot, serial correlation coefficients, power spectrum, detrended fluctuation analysis, approximate entropy, and sample entropy of IBI. The channel noise from one particular ionic current (I_Ks), which has channel kinetics that are relatively slow compared to that of the other currents, makes the major contribution to the fluctuations in IBI. Reproduction of the experimental coefficient of variation of IBI by adding a Gaussian white noise-current into the deterministic model necessitates using an unrealistically high noise-current amplitude. Indeed, a major implication of the modelling results is that, given the wide range of time-scales over which the various species of channels open and close, only a cell-specific stochastic model that is formulated taking into consideration the widely different ranges in the frequency content of the channel-noise produced by the opening and closing of several different types of channels will be able to reproduce precisely the various effects due to membrane noise seen in a particular electrophysiological preparation.

Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking

We used the Dynamic Clamp technique for i) comparative validation of conflicting computational models of the hyperpolarization-activated funny current, If, and ii) quantification of the role of If in mediating autonomic modulation of heart rate. Experimental protocols based on the injection of a real-time recalculated synthetic If current in sinoatrial rabbit cells were developed. Preliminary results of experiments mimicking the autonomic modulation of If demonstrated the need for a customization procedure to compensate for cellular heterogeneity. For this reason, we used a cell-specific approach, scaling the maximal conductance of the injected current based on the cell's spontaneous firing rate. The pacemaking rate, which was significantly reduced after application of Ivabradine, was restored by the injection of synthetic current based on the Severi-DiFrancesco formulation, while the injection of synthetic current based on the Maltsev-Lakatta formulation did not produce any significant variation. A positive virtual shift of the If activation curve, mimicking the Isoprenaline effects, led to a significant increase in pacemaking rate (+17.3 ± 6.7%, p < 0.01), although of lower magnitude than that induced by real Isoprenaline (+45.0 ± 26.1%). Similarly, a negative virtual shift of the activation curve significantly lowered the pacemaking rate (-11.8 ± 1.9%, p < 0.001), as did the application of real Acetylcholine (-20.5 ± 5.1%). The Dynamic Clamp approach, applied to the If study in cardiomyocytes for the first time and rate-adapted to manage intercellular variability, indicated that: i) the quantitative description of the If current in the Severi-DiFrancesco model accurately reproduces the effects of the real current on rabbit sinoatrial cell pacemaking rate and ii) a significant portion (50-60%) of the physiological autonomic rate modulation is due to the shift of the If activation curve.

The functions of atrial strands interdigitating with and penetrating into sinoatrial node: a theoretical study of the problem

The sinoatrial node (SAN)-atrium system is closely involved with the activity of heart beating. The impulse propagation and phase-locking behaviors of this system are of theoretical interest. Some experiments have revealed that atrial strands (ASs) interdigitate with and penetrate into the SAN, whereby the SAN-atrium system works as a complex network. In this study, the functions of ASs are numerically investigated using realistic cardiac models. The results indicate that the ASs penetrating into the central region of the SAN play a major role in propagating excitation into the atrium. This is because the threshold SAN-AS coupling for an AS to function as an alternative path for propagation is lower at the center than at the periphery. However, ASs penetrating into the peripheral region have a great effect in terms of enlarging the 1:1 entrainment range of the SAN because the automaticity of the SAN is evidently reduced by ASs. Moreover, an analytical formula for approximating the enlargement of the 1:1 range is derived.

Potential effects of intrinsic heart pacemaker cell mechanisms on dysrhythmic cardiac action potential firing

The heart's regular electrical activity is initiated by specialized cardiac pacemaker cells residing in the sinoatrial node. The rate and rhythm of spontaneous action potential firing of sinoatrial node cells are regulated by stochastic mechanisms that determine the level of coupling of chemical to electrical clocks within cardiac pacemaker cells. This coupled-clock system is modulated by autonomic signaling from the brain via neurotransmitter release from the vagus and sympathetic nerves. Abnormalities in brain-heart clock connections or in any molecular clock activity within pacemaker cells lead to abnormalities in the beating rate and rhythm of the pacemaker tissue that initiates the cardiac impulse. Dysfunction of pacemaker tissue can lead to tachy-brady heart rate alternation or exit block that leads to long atrial pauses and increases susceptibility to other cardiac arrhythmia. Here we review evidence for the idea that disturbances in the intrinsic components of pacemaker cells may be implemented in arrhythmia induction in the heart.

From two competing oscillators to one coupled-clock pacemaker cell system

At the beginning of this century, debates regarding “what are the main control mechanisms that ignite the action potential (AP) in heart pacemaker cells” dominated the electrophysiology field. The original theory which prevailed for over 50 years had advocated that the ensemble of surface membrane ion channels (i.e., “M-clock”) is sufficient to ignite rhythmic APs. However, more recent experimental evidence in a variety of mammals has shown that the sarcoplasmic reticulum (SR) acts as a “Ca²⁺-clock” rhythmically discharges diastolic local Ca²⁺ releases (LCRs) beneath the cell surface membrane. LCRs activate an inward current (likely that of the Na⁺/Ca²⁺ exchanger) that prompts the surface membrane “M-clock” to ignite an AP. Theoretical and experimental evidence has mounted to indicate that this clock “crosstalk” operates on a beat-to-beat basis and determines both the AP firing rate and rhythm. Our review is focused on the evolution of experimental definition and numerical modeling of the coupled-clock concept, on how mechanisms intrinsic to pacemaker cell determine both the heart rate and rhythm, and on future directions to develop further the coupled-clock pacemaker cell concept.

Stochasticity intrinsic to coupled-clock mechanisms underlies beat-to-beat variability of spontaneous action potential firing in sinoatrial node pacemaker cells

Recent evidence indicates that the spontaneous action potential (AP) of isolated sinoatrial node cells (SANCs) is regulated by a system of stochastic mechanisms embodied within two clocks: ryanodine receptors of the "Ca(2+) clock" within the sarcoplasmic reticulum, spontaneously activate during diastole and discharge local Ca(2+) releases (LCRs) beneath the cell surface membrane; clock crosstalk occurs as LCRs activate an inward Na(+)/Ca(2+) exchanger current (INCX), which together with If and decay of K(+) channels prompts the "M clock," the ensemble of sarcolemmal-electrogenic molecules, to generate APs. Prolongation of the average LCR period accompanies prolongation of the average AP beating interval (BI). Moreover, the prolongation of the average AP BI accompanies increased AP BI variability. We hypothesized that both the average AP BI and AP BI variability are dependent upon stochasticity of clock mechanisms reported by the variability of LCR period. We perturbed the coupled-clock system by directly inhibiting the M clock by ivabradine (IVA) or the Ca(2+) clock by cyclopiazonic acid (CPA). When either clock is perturbed by IVA (3, 10 and 30 μM), which has no direct effect on Ca(2+) cycling, or CPA (0.5 and 5 μM), which has no direct effect on the M clock ion channels, the clock system failed to achieve the basal AP BI and both AP BI and AP BI variability increased. The changes in average LCR period and its variability in response to perturbations of the coupled-clock system were correlated with changes in AP beating interval and AP beating interval variability. We conclude that the stochasticity within the coupled-clock system affects and is affected by the AP BI firing rate and rhythm via modulation of the effectiveness of clock coupling.

Direct negative chronotropic action of desflurane on sinoatrial node pacemaker activity in the guinea pig heart

BACKGROUND

Desflurane inhalation is associated with sympathetic activation and concomitant increase in heart rate in humans and experimental animals. There is, however, little information concerning the direct effects of desflurane on electrical activity of sinoatrial node pacemaker cells that determines the intrinsic heart rate.

METHODS

Whole-cell patch-clamp experiments were conducted on guinea pig sinoatrial node pacemaker cells to record spontaneous action potentials and ionic currents contributing to sinoatrial node automaticity, namely, hyperpolarization-activated cation current (If), T-type and L-type Ca currents (ICa,T and ICa,L, respectively), Na/Ca exchange current (INCX), and rapidly and slowly activating delayed rectifier K currents (IKr and IKs, respectively). Electrocardiograms were recorded from ex vivo Langendorff-perfused hearts and in vivo hearts.

RESULTS

Desflurane at 6 and 12% decreased spontaneous firing rate of sinoatrial node action potentials by 15.9% (n = 11) and 27.6% (n = 10), respectively, which was associated with 20.4% and 42.5% reductions in diastolic depolarization rate, respectively. Desflurane inhibited If, ICa,T, ICa,L, INCX, and IKs but had little effect on IKr. The negative chronotropic action of desflurane was reasonably well reproduced in sinoatrial node computer model. Desflurane reduced the heart rate in Langendorff-perfused hearts. High concentration (12%) of desflurane inhalation was associated with transient tachycardia, which was totally abolished by pretreatment with the β-adrenergic blocker propranolol.

CONCLUSIONS

Desflurane has a direct negative chronotropic action on sinoatrial node pacemaking activity, which is mediated by its inhibitory action on multiple ionic currents. This direct inhibitory action of desflurane on sinoatrial node automaticity seems to be counteracted by sympathetic activation associated with desflurane inhalation in vivo.

Synchronization of sinoatrial node pacemaker cell clocks and its autonomic modulation impart complexity to heart beating intervals

BACKGROUND

A reduction of complexity of heart beating interval variability that is associated with an increased morbidity and mortality in cardiovascular disease states is thought to derive from the balance of sympathetic and parasympathetic neural impulses to the heart. However, rhythmic clocklike behavior intrinsic to pacemaker cells in the sinoatrial node (SAN) drives their beating, even in the absence of autonomic neural input.

OBJECTIVE

To test how this rhythmic clocklike behavior intrinsic to pacemaker cells interacts with autonomic impulses to the heart beating interval variability in vivo.

METHODS

We analyzed beating interval variability in time and frequency domains and by fractal and entropy analyses: (1) in vivo, when the brain input to the SAN is intact; (2) during autonomic denervation in vivo; (3) in isolated SAN tissue (ie, in which the autonomic neural input is completely absent); (4) in single pacemaker cells isolated from the SAN; and (5) after autonomic receptor stimulation of these cells.

RESULTS

Spontaneous beating intervals of pacemaker cells residing in the isolated SAN tissue exhibit fractal-like behavior and have lower approximate entropy compared with those in the intact heart. Isolation of pacemaker cells from SAN tissue, however, leads to a loss in the beating interval order and fractal-like behavior. β-Adrenergic receptor stimulation of isolated pacemaker cells increases intrinsic clock synchronization, decreases their action potential period, and increases system complexity.

CONCLUSIONS

Both the average beating interval in vivo and beating interval complexity are conferred by the combined effects of clock periodicity intrinsic to pacemaker cells and their response to autonomic neural input.

Dynamic clamp as a tool to study the functional effects of individual membrane currents

Today, the patch-clamp technique is the main technique in electrophysiology to record action potentials or membrane current from isolated cells, using a patch pipette to gain electrical access to the cell. The common recording modes of the patch-clamp technique are current clamp and voltage clamp. In the current clamp mode, the current injected through the patch pipette is under control while the free-running membrane potential of the cell is recorded. Current clamp allows for measurements of action potentials that may either occur spontaneously or in response to an injected stimulus current. In voltage clamp mode, the membrane potential is held at a set level through a feedback circuit, which allows for the recording of the net membrane current at a given membrane potential.A less common configuration of the patch-clamp technique is the dynamic clamp. In this configuration, a specific non-predetermined membrane current can be added to or removed from the cell while it is in free-running current clamp mode. This current may be computed in real time, based on the recorded action potential of the cell, and injected into the cell. Instead of being computed, this current may also be recorded from a heterologous expression system such as a HEK-293 cell that is voltage-clamped by the free-running action potential of the cell ("dynamic action potential clamp"). Thus, one may directly test the effects of an additional or mutated membrane current, a synaptic current or a gap junctional current on the action potential of a patch-clamped cell. In the present chapter, we describe the dynamic clamp on the basis of its application in cardiac cellular electrophysiology.

Remifentanil has a minimal direct effect on sinoatrial node pacemaker activity in the Guinea pig heart

BACKGROUND

Whereas remifentanil administration is associated with severe bradycardia, it has yet to be fully investigated whether the negative chronotropic action of remifentanil is mediated by its direct action on sinoatrial (SA) node pacemaker activity in the heart versus indirect results of enhanced vagal activity.

METHODS

We examined the effects of remifentanil and fentanyl on the spontaneous action potentials of guinea pig SA node cells at concentrations of 5, 10, 100, and 1000 nM using the amphotericin B-perforated whole-cell patch-clamp technique. Isolated guinea pig hearts were perfused in a Langendorff mode with 5, 10, 100, and 1000 nM remifentanil.

RESULTS

The spontaneous firing rate and diastolic depolarization rate (DDR) of the SA node action potentials were 189.1 ± 14.8 /min and 74.1 ± 2.9 mV/s (n = 8), respectively, under control conditions, and were not significantly affected by exposure to 5 nM (P = 1.0 for both spontaneous firing rate and DDR; n = 6), 10 nM (P = 0.62 for spontaneous firing rate, P = 0.99 for DDR; n = 6), or 100 nM (P = 0.23 for spontaneous firing rate, P = 0.38 for DDR; n = 6) remifentanil. However, 1000 nM remifentanil modestly but significantly decreased the spontaneous firing rate (P = 0.0087) and DDR (P = 0.0072, n = 6). Remifentanil did not affect the heart rate of isolated Langendorff-perfused guinea pig hearts at concentrations of 5 nM (P = 0.98), 10 nM (P = 0.35), or 100 nM (P = 0.24) but significantly reduced the heart rate at 1000 nM (P < 0.0001). Fentanyl did not affect the spontaneous firing rate and DDR at concentrations of 5 nM (P = 1.0 for both spontaneous firing rate and DDR) and 10 nM (P = 0.62 for spontaneous firing rate, P = 0.79 for DDR), but it significantly reduced both at 100 nM (P = 0.00038 for spontaneous firing rate, P = 0.0080 for DDR) and 1000 nM (P < 0.0001 for both spontaneous firing rate and DDR).

CONCLUSIONS

Clinically relevant concentrations (nanomolar order concentrations) of remifentanil do not produce significant direct effects on intrinsic cardiac automaticity; thus, suggesting that remifentanil-induced bradycardia in the clinical setting is independent of its direct cardiac effects.

Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

Exploring the implicit interlayer regulatory mechanism between cells and tissue: stochastic mathematical analyses of the spontaneous ordering in beating synchronization

The present study focused on beating synchronization, and tried to elucidate the interlayer regulatory mechanisms between the cells and clump in beating synchronization with using the stochastic simulations which realize the beating synchronizations in beating cells with low cell-cell conductance. Firstly, the fluctuation in interbeat intervals (IBIs) of beating cells encouraged the process of beating synchronization, which was identified as the stochastic resonance. Secondly, fluctuation in the synchronized IBIs of a clump decreased as the number of beating cells increased. The decrease in IBI fluctuation due to clump formation implied both a decline of the electrophysiological plasticity of each beating cell and an enhancement of the electrophysiological stability of the clump. These findings were identified as the community effects. Because IBI fluctuation and the community effect facilitated the beating stability of the cell and clump, these factors contributed to the spontaneous ordering in beating synchronization. Thirdly, the cellular layouts in clump affected the synchronized beating rhythms. The synchronized beating rhythm in clump was implicitly regulated by a complicated synergistic effect among IBI fluctuation of each beating cell, the community effect and the cellular layout. This finding was indispensable for leading an elucidation of mechanism of emergence. The stochastic simulations showed the necessity of considering the synergistic effect, to elucidate the interlayer regulatory mechanisms in biological system.

MATLAB implementation of a dynamic clamp with bandwidth of >125 kHz capable of generating I Na at 37 °C

We describe the construction of a dynamic clamp with a bandwidth of >125 kHz that utilizes a high-performance, yet low-cost, standard home/office PC interfaced with a high-speed (16 bit) data acquisition module. High bandwidth is achieved by exploiting recently available software advances (code-generation technology and optimized real-time kernel). Dynamic-clamp programs are constructed using Simulink, a visual programming language. Blocks for computation of membrane currents are written in the high-level MATLAB language; no programming in C is required. The instrument can be used in single- or dual-cell configurations, with the capability to modify programs while experiments are in progress. We describe an algorithm for computing the fast transient Na(+) current (I Na) in real time and test its accuracy and stability using rate constants appropriate for 37 °C. We then construct a program capable of supplying three currents to a cell preparation: I Na, the hyperpolarizing-activated inward pacemaker current (I f) and an inward-rectifier K(+) current (I K1). The program corrects for the IR drop due to electrode current flow and also records all voltages and currents. We tested this program on dual patch-clamped HEK293 cells where the dynamic clamp controls a current-clamp amplifier and a voltage-clamp amplifier controls membrane potential, and current-clamped HEK293 cells where the dynamic clamp produces spontaneous pacing behavior exhibiting Na(+) spikes in otherwise passive cells.

Functional cardiac tissue engineering

Heart attack remains the leading cause of death in both men and women worldwide. Stem cell-based therapies, including the use of engineered cardiac tissues, have the potential to treat the massive cell loss and pathological remodeling resulting from heart attack. Specifically, embryonic and induced pluripotent stem cells are a promising source for generation of therapeutically relevant numbers of functional cardiomyocytes and engineering of cardiac tissues in vitro. This review will describe methodologies for successful differentiation of pluripotent stem cells towards the cardiovascular cell lineages as they pertain to the field of cardiac tissue engineering. The emphasis will be placed on comparing the functional maturation in engineered cardiac tissues and developing heart and on methods to quantify cardiac electrical and mechanical function at different spatial scales.

Pluripotent stem cell-derived cardiac tissue patch with advanced structure and function

Recent advances in pluripotent stem cell research have provided investigators with potent sources of cardiogenic cells. However, tissue engineering methodologies to assemble cardiac progenitors into aligned, 3-dimensional (3D) myocardial tissues capable of physiologically relevant electrical conduction and force generation are lacking. In this study, we introduced 3D cell alignment cues in a fibrin-based hydrogel matrix to engineer highly functional cardiac tissues from genetically purified mouse embryonic stem cell-derived cardiomyocytes (CMs) and cardiovascular progenitors (CVPs). Procedures for CM and CVP derivation, purification, and functional differentiation in monolayer cultures were first optimized to yield robust intercellular coupling and maximize velocity of action potential propagation. A versatile soft-lithography technique was then applied to reproducibly fabricate engineered cardiac tissues with controllable size and 3D architecture. While purified CMs assembled into a functional 3D syncytium only when supplemented with supporting non-myocytes, purified CVPs differentiated into cardiomyocytes, smooth muscle, and endothelial cells, and autonomously supported the formation of functional cardiac tissues. After a total culture time similar to period of mouse embryonic development (21 days), the engineered cardiac tissues exhibited unprecedented levels of 3D organization and functional differentiation characteristic of native neonatal myocardium, including: 1) dense, uniformly aligned, highly differentiated and electromechanically coupled cardiomyocytes, 2) rapid action potential conduction with velocities between 22 and 25 cm/s, and 3) significant contractile forces of up to 2 mN. These results represent an important advancement in stem cell-based cardiac tissue engineering and provide the foundation for exploiting the exciting progress in pluripotent stem cell research in the future tissue engineering therapies for heart disease.

Phase-locking behaviors in an ionic model of sinoatrial node cell and tissue

Phase-locking behaviors in sinoatrial node (SAN) are closely related to cardiac arrhythmias. An ionic model considering structural heterogeneity of SAN is numerically investigated. The bifurcations between phase-locking zones are interpreted by the map derived from the phase resetting curve. Furthermore, the validity of the circle map in describing phase locking of the actual SAN system is evaluated and explained. We reveal also how the phase-locking behaviors in heterogeneous tissue depend on the location of stimulating site and the coupling strength of the tissue. All these results may be of suggestive uses for understanding and controlling practical SAN dynamics.

Functional role of CLC-2 chloride inward rectifier channels in cardiac sinoatrial nodal pacemaker cells

A novel Cl(-) inward rectifier channel (Cl,ir) encoded by ClC-2, a member of the ClC voltage-gated Cl(-) channel gene superfamily, has been recently discovered in cardiac myocytes of several species. However, the physiological role of Cl,ir channels in the heart remains unknown. In this study we tested the hypothesis that Cl,ir channels may play an important role in cardiac pacemaker activity. In isolated guinea-pig sinoatrial node (SAN) cells, Cl,ir current was activated by hyperpolarization and hypotonic cell swelling. RT-PCR and immunohistological analyses confirmed the molecular expression of ClC-2 in guinea-pig SAN cells. Hypotonic stress increased the diastolic depolarization slope and decreased the maximum diastolic potential, action potential amplitude, APD(50), APD(90), and the cycle-length of the SAN cells. These effects were largely reversed by intracellular dialysis of anti-ClC-2 antibody, which significantly inhibited Cl,ir current but not other pacemaker currents, including the hyperpolarization-activated non-selective cationic "funny" current (I(f)), the L-type Ca(2+) currents (I(Ca,L)), the slowly-activating delayed rectifier I(Ks) and the volume-regulated outwardly-rectifying Cl(-) current (I(Cl,vol)). Telemetry electrocardiograph studies in conscious ClC-2 knockout (Clcn2(-/-)) mice revealed a decreased chronotropic response to acute exercise stress when compared to their age-matched Clcn2(+/+) and Clcn2(+/-) littermates. Targeted inactivation of ClC-2 does not alter intrinsic heart rate but prevented the positive chronotropic effect of acute exercise stress through a sympathetic regulation of ClC-2 channels. These results provide compelling evidence that ClC-2-encoded endogenous Cl,ir channels may play an important role in the regulation of cardiac pacemaker activity, which may become more prominent under stressed or pathological conditions.

Causes of transient instabilities in the dynamic clamp

The dynamic clamp is a widely used method for integrating mathematical models with electrophysiological experiments. This method involves measuring the membrane voltage of a cell, using it to solve computational models of ion channel dynamics in real-time, and injecting the calculated current(s) back into the cell. Limitations of this technique include those associated with single electrode current clamping and the sampling effects caused by the dynamic clamp. In this study, we show that the combination of these limitations causes transient instabilities under certain conditions. Through physical experiments and simulations, we show that dynamic clamp instability is directly related to the sampling delay and the maximum simulated conductance being injected. It is exaggerated by insufficient electrode series resistance and capacitance compensation. Increasing the sampling rate of the dynamic clamp system increases dynamic clamp stability; however, this improvement, is constrained by how well the electrode series resistance and capacitance are compensated. At present, dynamic clamp sampling rates are justified solely on the temporal dynamics of the models being simulated; here we show that faster rates increase the stable range of operation for the dynamic clamp system. In addition, we show that commonly accepted levels of resistance compensation nevertheless significantly compromise the stability of a dynamic clamp system.

Electrical Synapses Between AII Amacrine Cells: Dynamic Range and Functional Consequences of Variation in Junctional Conductance

AII amacrine cells form a network of electrically coupled interneurons in the mammalian retina and tracer coupling studies suggest that the junctional conductance ( Gj) can be modulated. However, the dynamic range of Gjand the functional consequences of varying Gjover the dynamic range are unknown. Here we use whole cell recordings from pairs of coupled AII amacrine cells in rat retinal slices to provide direct evidence for physiological modulation of Gj, appearing as a time-dependent increase from about 500 pS to a maximum of about 3,000 pS after 30–90 min of recording. The increase occurred in recordings with low- but not high-resistance pipettes, suggesting that it was related to intracellular washout and perturbation of a modulatory system. Computer simulations of a network of electrically coupled cells verified that our recordings were able to detect and quantify changes in Gjover a large range. Dynamic-clamp electrophysiology, with insertion of electrical synapses between AII amacrine cells, allowed us to finely and reversibly control Gjwithin the same range observed for physiologically coupled cells and to examine the quantitative relationship between Gjand steady-state coupling coefficient, synchronization of subthreshold membrane potential fluctuations, synchronization and transmission of action potentials, and low-pass filter characteristics. The range of Gjvalues over which signal transmission was modulated depended strongly on the specific functional parameter examined, with the largest range observed for action potential transmission and synchronization, suggesting that the full range of Gjvalues observed during spontaneous run-up of coupling could represent a physiologically relevant dynamic range.

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 (IP3)-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 IP3receptor 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 IP3-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.

Left-right olfactory asymmetry results from antagonistic functions of voltage-activated calcium channels and the Raw repeat protein OLRN-1 in C. elegans

BACKGROUND

The left and right AWC olfactory neurons in Caenorhabditis elegans differ in their functions and in their expression of chemosensory receptor genes; in each animal, one AWC randomly takes on one identity, designated AWCOFF, and the contralateral AWC becomes AWCON. Signaling between AWC neurons induces left-right asymmetry through a gap junction network and a claudin-related protein, which inhibit a calcium-regulated MAP kinase pathway in the neuron that becomes AWCON.

RESULTS

We show here that the asymmetry gene olrn-1 acts downstream of the gap junction and claudin genes to inhibit the calcium-MAP kinase pathway in AWCON. OLRN-1, a protein with potential membrane-association domains, is related to the Drosophila Raw protein, a negative regulator of JNK mitogen-activated protein (MAP) kinase signaling. olrn-1 opposes the action of two voltage-activated calcium channel homologs, unc-2 (CaV2) and egl-19 (CaV1), which act together to stimulate the calcium/calmodulin-dependent kinase CaMKII and the MAP kinase pathway. Calcium channel activity is essential in AWCOFF, and the two AWC neurons coordinate left-right asymmetry using signals from the calcium channels and signals from olrn-1.

CONCLUSION

olrn-1 and voltage-activated calcium channels are mediators and targets of AWC signaling that act at the transition between a multicellular signaling network and cell-autonomous execution of the decision. We suggest that the asymmetry decision in AWC results from the intercellular coupling of voltage-regulated channels, whose cross-regulation generates distinct calcium signals in the left and right AWC neurons. The interpretation of these signals by the kinase cascade initiates the sustained difference between the two cells.

The relevance of non-excitable cells for cardiac pacemaker function

Age-dependent changes in the architecture of the sinus node comprise an increasing ratio between fibroblasts and cardiomyocytes. This change is discussed as a potential mechanism for sinus node disease. The goal of this study was to determine the mechanism through which non-excitable cells influence the spontaneous activity of multicellular cardiomyocyte preparations. Cardiomyocyte monolayers (HL-1 cells) or embryonic stem cell-derived cardiomyocytes were used as two- and three-dimensional cardiac pacemaker models. Spontaneous activity and conduction velocity (theta) were monitored by field potential measurements with microelectrode arrays (MEAs). The influence of fibroblasts (WT-fibs) was determined in heterocellular cultures of different cardiomyocyte and fibroblast ratios. The relevance of heterocellular gap junctional coupling was evaluated by the use of fibroblasts deficient for the expression of Cx43 (Cx43(-/-)-fibs). The beating frequency and of heterocellular cultures depended negatively on the fibroblast concentration. Interspersion of fibroblasts in cardiomyocyte monolayers increased the coefficient of the interbeat interval variability. Whereas Cx43(-/-)-fibs decreased theta significantly less than WT-fibs, their effect on the beating frequency and the beat-to-beat variability seemed largely independent of their ability to establish intercellular coupling. These results suggest that electrically integrated, non-excitable cells modulate the excitability of cardiac pacemaker preparations by two distinct mechanisms, one dependent and the other independent of the heterocellular coupling established. Whereas heterocellular coupling enables the fibroblast to depolarize the cardiomyocytes or to act as a current sink, the mere physical separation of the cardiomyocytes by fibroblasts induces bradycardia through a reduction in frequency entrainment.

Inferring phase equations from multivariate time series

An approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate important properties of the phase equations including natural frequencies and interaction functions between the oscillators. Our approach requires the measurement of an experimental observable of the oscillators; in contrast with previous methods it does not require measurements in isolated single or two-oscillator setups. This noninvasive technique can be advantageous in biological systems, where extraction of few oscillators may be a difficult task. The method is most efficient when data are taken from the nonsynchronized regime. Applicability to experimental systems is demonstrated by using a network of electrochemical oscillators; the obtained phase model is utilized to predict the synchronization diagram of the system.

Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.

Connexin-mediated cardiac impulse propagation: connexin 30.2 slows atrioventricular conduction in mouse heart

In mouse heart, four connexins (Cxs), Cx30.2, Cx40, Cx43, and Cx45, form gap junction (GJ) channels for electric and metabolic cell-to-cell signaling. Extent and pattern of Cx isoform expression together with cytoarchitecture and excitability of cells determine the velocity of excitation spread in different regions of the heart. In the SA node, cell-cell coupling is mediated by Cx30.2 and Cx45, which form low-conductance (approximately 9 and 32 pS, respectively) GJ channels. In contrast, the working cardiomyocytes of atria and ventricles express mainly Cx40 and Cx43, which form GJ channels of high conductance (approximately 180 and 115 pS, respectively) that facilitate the fast conduction necessary for efficient mechanical contraction. In the AV node, cell-cell coupling is mediated by abundantly expressed Cx30.2 and Cx45 and Cx40, which is expressed to a lesser extent. Cx30.2 and Cx45 may determine higher intercellular resistance and slower conduction in the SA- and AV-nodal regions than in the ventricular conduction system or the atrial and ventricular working myocardium. Cx30.2 and its putative human ortholog, Cx31.9, under physiologic conditions form unapposed hemichannels in nonjunctional plasma membrane; these hemichannels have a conductance of approximately 20 pS and are permeable to cationic dyes up to approximately 400 Da in molecular mass. Genetic ablation of Cxs confirmed that Cx40 and Cx43 are important in determining the high conduction velocities in atria and ventricles, whereas the deletion of the Cx30.2 complementary DNA led to accelerated conduction in the AV node and reduced the Wenckebach period. We suggest that these effects are caused by (1) a dominant-negative effect of Cx30.2 on junctional conductance via formation of low-conductance homotypic and heterotypic GJ channels, and (2) open Cx30.2 hemichannels in non-junctional membranes, which shorten the space constant and depolarize the excitable membrane.

Parametric sensibility study of the sinoatrial node math model

The results of the parametric sensibility study to the sinoatrial node math model was presented. The model was proposed by H. Zhang, A. V. Holden and M.R. Boyett. The sensitivity analysis indicates that the sodium and potassium ionic concentrations need to be controlled in order to maintain the normal behavior of the node. The calcium concentrations changes simulated don't produce significant effects over the operation of the node. One response surface model was developed as a simplification of original model. The diastolic depolarization rate was redefined in order to allow its measure in potential waves for peripheral node cells.