Rhythms from Two Competing Periodic Sources Embedded in an Excitable Medium.

In an excitable medium, a stimulus generates a wave that propagates in space until it reaches the boundary or collides with another wave and annihilates. We study the dynamics generated by two periodic sources with different frequencies in excitable cardiac tissue culture using optogenetic techniques. The observed rhythms, which can be modeled using cellular automata and studied analytically, show unexpected regularities related to classic results in number theory. We apply the results to identify cardiac arrhythmias in people that are due to a putative mechanism of two competing pacemakers.

Universal mechanisms for self-termination of rapid cardiac rhythm.

Excitable media sustain circulating waves. In the heart, sustained circulating waves can lead to serious impairment or even death. To investigate factors affecting the stability of such waves, we have used optogenetic techniques to stimulate a region at the apex of a mouse heart at a fixed delay after the detection of excitation at the base of the heart. For long delays, rapid circulating rhythms can be sustained, whereas for shorter delays, there are paroxysmal bursts of activity that start and stop spontaneously. By considering the dependence of the action potential and conduction velocity on the preceding recovery time using restitution curves, as well as the reduced excitability (fatigue) due to the rapid excitation, we model prominent features of the dynamics including alternation of the duration of the excited phases and conduction times, as well as termination of the bursts for short delays. We propose that this illustrates universal mechanisms that exist in biological systems for the self-termination of such activities.

Double-wave reentry in excitable media.

A monolayer of chick embryo cardiac cells grown in an annular geometry supports two simultaneous reentrant excitation waves that circulate as a doublet. We propose a mechanism that can lead to such behavior. The velocity restitution gives the instantaneous velocity of a wave as a function of the time since the passage of the previous wave at a given point in space. Nonmonotonic restitution relationships will lead to situations in which various spacings between circulating waves are possible. In cardiology, the situation in which two waves travel in an anatomically defined circuit is referred to as double-wave reentry. Since double-wave reentry may arise as a consequence of pacing during cardiac arrhythmias, understanding the dynamic features of double-wave reentry may be helpful in understanding the physiological properties of cardiac tissue and in the design of therapy.

Bag1 Co-chaperone Promotes TRC8 E3 Ligase-dependent Degradation of Misfolded Human Ether a Go-Go-related Gene (hERG) Potassium Channels.

Cardiac long QT syndrome type 2 is caused by mutations in the human ether a go-go-related gene (hERG) potassium channel, many of which cause misfolding and degradation at the endoplasmic reticulum instead of normal trafficking to the cell surface. The Hsc70/Hsp70 chaperones assist the folding of the hERG cytosolic domains. Here, we demonstrate that the Hsp70 nucleotide exchange factor Bag1 promotes hERG degradation by the ubiquitin-proteasome system at the endoplasmic reticulum to regulate hERG levels and channel activity. Dissociation of hERG complexes containing Hsp70 and the E3 ubiquitin ligase CHIP requires the interaction of Bag1 with Hsp70, but this does not involve the Bag1 ubiquitin-like domain. The interaction with Bag1 then shifts hERG degradation to the membrane-anchored E3 ligase TRC8 and its E2-conjugating enzyme Ube2g2, as determined by siRNA screening. TRC8 interacts through the transmembrane region with hERG and decreases hERG functional expression. TRC8 also mediates degradation of the misfolded hERG-G601S disease mutant, but pharmacological stabilization of the mutant structure prevents degradation. Our results identify TRC8 as a previously unknown Hsp70-independent quality control E3 ligase for hERG.

Aldosterone, SGK1, and ion channels in the kidney.

Hyperaldosteronism, a common cause of hypertension, is strongly connected to Na+, K+, and Mg2+ dysregulation. Owing to its steroidal structure, aldosterone is an active transcriptional modifier when bound to the mineralocorticoid receptor (MR) in cells expressing the enzyme 11ß-hydroxysteroid dehydrogenase 2, such as those comprising the aldosterone-sensitive distal nephron (ASDN). One such up-regulated protein, the ubiquitous serum and glucocorticoid regulated kinase 1 (SGK1), has the capacity to modulate the surface expression and function of many classes of renal ion channels, including those that transport Na+ (ENaC), K+ (ROMK/BK), Ca2+ (TRPV4/5/6), Mg2+ (TRPM7/6), and Cl- (ClC-K, CFTR). Here, we discuss the mechanisms by which ASDN expressed channels are up-regulated by SGK1, while highlighting newly discovered pathways connecting aldosterone to nonselective cation channels that are permeable to Mg2+ (TRPM7) or Ca2+ (TRPV4).

Predicting the onset of period-doubling bifurcations in noisy cardiac systems.

Biological, physical, and social systems often display qualitative changes in dynamics. Developing early warning signals to predict the onset of these transitions is an important goal. The current work is motivated by transitions of cardiac rhythms, where the appearance of alternating features in the timing of cardiac events is often a precursor to the initiation of serious cardiac arrhythmias. We treat embryonic chick cardiac cells with a potassium channel blocker, which leads to the initiation of alternating rhythms. We associate this transition with a mathematical instability, called a period-doubling bifurcation, in a model of the cardiac cells. Period-doubling bifurcations have been linked to the onset of abnormal alternating cardiac rhythms, which have been implicated in cardiac arrhythmias such as T-wave alternans and various tachycardias. Theory predicts that in the neighborhood of the transition, the system's dynamics slow down, leading to noise amplification and the manifestation of oscillations in the autocorrelation function. Examining the aggregates' interbeat intervals, we observe the oscillations in the autocorrelation function and noise amplification preceding the bifurcation. We analyze plots--termed return maps--that relate the current interbeat interval with the following interbeat interval. Based on these plots, we develop a quantitative measure using the slope of the return map to assess how close the system is to the bifurcation. Furthermore, the slope of the return map and the lag-1 autocorrelation coefficient are equal. Our results suggest that the slope and the lag-1 autocorrelation coefficient represent quantitative measures to predict the onset of abnormal alternating cardiac rhythms.

Defining the pattern of initiation of monomorphic ventricular tachycardia using the beat-to-beat intervals recorded on implantable cardioverter defibrillators from the RAFT study: A computer-based algorithm.

Arrhythmia onset pattern may have important implications on morbidity, recurrent implantable cardioverter defibrillator (ICD) shocks, and mortality, given the proposed correlation between initiation pattern and arrhythmia mechanism. Therefore, we developed and tested a computer-based algorithm to differentiate the pattern of initiation based on the beat-to-beat intervals of the ventricular tachycardia (VT) episodes in ICD recordings from the Resynchronization-Defibrillation for Ambulatory Heart Failure Trial (RAFT). Intervals on intracardiac electrograms from ICDs were analyzed backwards starting from the marker of VT detection, comparing each interval with the average tachycardia cycle length. If the morphology of the beat initiating the VT was similar to the morphology of the VT itself, the episode was considered sudden. If the morphology of the beat initiating the VT was not similar to the morphology of the VT itself, the episode was considered non-sudden. The capability of the algorithm to classify the pattern of initiation based only on the beat-to-beat intervals allows for the classification and analysis of large datasets to further investigate the clinical importance of classifying VT initiation. If analysis of the VT initiation proves to be of clinical value, this algorithm could potentially be integrated into ICD software, which would make it easily accessible and potentially helpful in clinical decision-making.

Aldosterone Upregulates Transient Receptor Potential Melastatin 7 (TRPM7).

Transient receptor potential melastatin 7 (TRPM7) is a ubiquitously expressed Mg(2+)-permeable ion channel fused to a C-terminal α-kinase domain. Recently, aldosterone was shown to increase intracellular Mg(2+) levels and alter inflammatory signaling in TRPM7-expressing HEK293 cells. This study was undertaken to assess whether these effects were related to an aldosterone-mediated increase of TRPM7 current and/or plasma membrane localization. Using HEK293 cells stably expressing WT-TRPM7, we found that 18-h application of aldosterone significantly increased TRPM7 current and TRPM7 plasma membrane protein expression by 48% and 34%, respectively. The aldosterone-mediated increase of TRPM7 current was inhibited by eplerenone, a mineralocorticoid receptor (MR) blocker, and GSK-650394, an inhibitor of the serum- and glucocorticoid-regulated kinase 1 (SGK1). SGK1 blockade also prevented the aldosterone-induced increase of TRPM7 plasma membrane protein. It was further determined that K1648R-TRPM7, the phosphotransferase-inactive TRPM7 mutant, was unresponsive to aldosterone. Therefore, chronic aldosterone treatment increases the plasma membrane expression of TRPM7, which is associated with an increase of TRPM7 current. This process occurs via an MR-dependent, genomic signaling cascade involving SGK1 and a functioning TRPM7 α-kinase domain. We suggest that this mechanism may be of general relevance when interpreting the effects of aldosterone because the MR receptor is found in multiple tissues, and TRPM7 and SGK1 are ubiquitously expressed.

Inhibition of PRL-2·CNNM3 Protein Complex Formation Decreases Breast Cancer Proliferation and Tumor Growth.

The oncogenic phosphatase of regenerating liver 2 (PRL-2) has been shown to regulate intracellular magnesium levels by forming a complex through an extended amino acid loop present in the Bateman module of the CNNM3 magnesium transporter. Here we identified highly conserved residues located on this amino acid loop critical for the binding with PRL-2. A single point mutation (D426A) of one of those critical amino acids was found to completely disrupt PRL-2·human Cyclin M 3 (CNNM3) complex formation. Whole-cell voltage clamping revealed that expression of CNNM3 influenced the surface current, whereas overexpression of the binding mutant had no effect, indicating that the binding of PRL-2 to CNNM3 is important for the activity of the complex. Interestingly, overexpression of the CNNM3 D426A-binding mutant in cancer cells decreased their ability to proliferate under magnesium-deprived situations and under anchorage-independent growth conditions, demonstrating a PRL-2·CNNM3 complex-dependent oncogenic advantage in a more stringent environment. We further confirmed the importance of this complex in vivo using an orthotopic xenograft breast cancer model. Finally, because molecular modeling showed that the Asp-426 side chain in CNNM3 buries into the catalytic cavity of PRL-2, we showed that a PRL inhibitor could abrogate complex formation, resulting in a decrease in proliferation of human breast cancer cells. In summary, we provide evidence that this fundamental regulatory aspect of PRL-2 in cancer cells could potentially lead to broadly applicable and innovative therapeutic avenues.

Characterization of constitutive and acid-induced outwardly rectifying chloride currents in immortalized mouse distal tubular cells.

Thiazides block Na+ reabsorption while enhancing Ca2+ reabsorption in the kidney. As previously demonstrated in immortalized mouse distal convoluted tubule (MDCT) cells, chlorothiazide application induced a robust plasma membrane hyperpolarization, which increased Ca2+ uptake. This essential thiazide-induced hyperpolarization was prevented by the Cl- channel inhibitor 5-Nitro-2-(3-phenylpropylamino) benzoic acid (NPPB), implicating NPPB-sensitive Cl- channels, however the nature of these Cl- channels has been rarely described in the literature. Here we show that MDCT cells express a dominant, outwardly rectifying Cl- current at extracellular pH7.4. This constitutive Cl- current was more permeable to larger anions (Eisenman sequence I; I->Br-≥Cl-) and was substantially inhibited by >100mM [Ca2+]o, which distinguished it from ClC-K2/barttin. Moreover, the constitutive Cl- current was blocked by NPPB, along with other Cl- channel inhibitors (4,4'-diisothiocyanatostilbene-2,2'-disulfonate, DIDS; flufenamic acid, FFA). Subjecting the MDCT cells to an acidic extracellular solution (pH<5.5) induced a substantially larger outwardly rectifying NPPB-sensitive Cl- current. This acid-induced Cl- current was also anion permeable (I->Br->Cl-), but was distinguished from the constitutive Cl- current by its rectification characteristics, ion sensitivities, and response to FFA. In addition, we have identified similar outwardly rectifying and acid-sensitive currents in immortalized cells from the inner medullary collecting duct (mIMCD-3 cells). Expression of an acid-induced Cl- current would be particularly relevant in the acidic IMCD (pH<5.5). To our knowledge, the properties of these Cl- currents are unique and provide the mechanisms to account for the Cl- efflux previously speculated to be present in MDCT cells.

Varieties of reentrant dynamics.

Experiments were carried out in monolayer tissue cultures of embryonic chick heart cells imaged using a calcium sensitive fluorescent dye. The cells were grown in annular geometries and in annular geometries with an isthmus connecting antipodal region of the annulus. We observed a large number of spatially different patterns of propagation consisting of one or more circulating waves. As well, we also observed rhythms in which rotors embedded in the annuli generated propagating pulses. These results demonstrate that many different patterns of excitation can be present in cardiac tissue with simple geometries.

Demonstration of cardiac rotor and source mapping techniques in embryonic chick monolayers.

Excitable media, such as the heart, display propagating waves with different geometries including target patterns and rotors (spiral waves). Collision of two waves leads to annihilation of both. We present algorithms for data processing and analysis to identify the core of rotors. In this work, we show that as the spatial sampling resolution decreases it becomes increasingly difficult to identify rotors-there are instances of false negatives and false positives. These observations are relevant to current controversies concerning the role of rotors in the initiation, maintenance, and treatment of cardiac arrhythmias, especially atrial fibrillation. Currently some practitioners target the core of rotors for ablation, but the effectiveness of this procedure has been questioned. In view of the difficulties inherent in the identification of rotors, we conclude that methods to identify rotors need to first be validated prior to assessing the efficacy of ablation.

hERG quality control and the long QT syndrome.

Long-QT syndrome type-2 (LQT2) is characterized by reduced functional expression of the human ether-à-go-go related (hERG) gene product, resulting in impaired cardiac repolarization and predisposition to fatal arrhythmia. Previous studies have implicated abnormal trafficking of misfolded hERG as the primary mechanism of LQT2, with misfolding being caused by mutations in the hERG gene (inherited) or drug treatment (acquired). More generally, environmental and metabolic stresses present a constant challenge to the folding of proteins, including hERG, and must be countered by robust protein quality control (QC) systems. Disposal of partially unfolded yet functional plasma membrane (PM) proteins by protein QC contributes to the loss-of-function phenotype in various conformational diseases including cystic fibrosis (CF) and long-QT syndrome type-2 (LQT2). The prevalent view has been that the loss of PM expression of hERG is attributed to biosynthetic block by endoplasmic reticulum (ER) QC pathways. However, there is a growing appreciation for protein QC pathways acting at post-ER cellular compartments, which may contribute to conformational disease pathogenesis. This article will provide a background on the structure and cellular trafficking of hERG as well as inherited and acquired LQT2. We will review previous work on hERG ER QC and introduce the more novel view that there is a significant peripheral QC at the PM and peripheral cellular compartments. Particular attention is drawn to the unique role of the peripheral QC system in acquired LQT2. Understanding the QC process and players may provide targets for therapeutic intervention in dealing with LQT2.

Functional characterization of oscillatory and excitable media.

Cardiac and neural systems share common features of intrinsic oscillation in some cells as well as the ability to propagate excitation. One theoretical approach to study such systems is to develop realistic models for the tissue. This involves first developing detailed ionic "Hodgkin-Huxley"-type models of individual cells and then connecting the individual cells via synaptic and gap junctions in realistic geometries. An alternative approach is to characterize tissue in terms of functional properties such as phase resetting curves and restitution curves. Using simple models based on one-dimensional difference equations, the measured functional curves can be used to predict, analyze, and interpret nonlinear dynamical phenomena. This approach offers the prospects of providing simplified descriptions that offer insight into the experimental and clinical cardiac dynamics.

Spatial symmetry breaking determines spiral wave chirality.

Chirality represents a fundamental property of spiral waves. Introducing obstacles into cardiac monolayers leads to the initiation of clockwise-rotating, counterclockwise-rotating, and pairs of spiral waves. Simulations show that the precise location of the obstacle and the pacing frequency determine spiral wave chirality. Instabilities predicted by curves relating the action potential duration and the pacing frequency at different spatial locations predict sites of wave break initiation and, hence, spiral wave chirality.

N-myristoylation and Ca2+ binding of calcineurin B homologous protein CHP3 are required to enhance Na+/H+ exchanger NHE1 half-life and activity at the plasma membrane.

Calcineurin B homologous proteins (CHP) are N-myristoylated, EF-hand Ca(2+)-binding proteins that regulate multiple cellular processes, including intracellular pH homeostasis. Previous work has shown that the heart-enriched isoform, CHP3, regulates the plasmalemmal Na(+)/H(+) exchanger NHE1 isoform by enhancing its rate of oligosaccharide maturation and exocytosis as well as its half-life and transport activity at the cell surface (Zaun, H. C., Shrier, A., and Orlowski, J. (2008) J. Biol. Chem. 283, 12456-12467). However, the molecular basis for this effect is not well understood. In this report, we investigated whether the N-myristoylation and Ca(2+)-binding domains of CHP3 are important elements for regulating NHE1. Mutation of residues essential for either N-myristoylation (G2A) or calcium binding (D123A) did not prevent the interaction of CHP3 with NHE1, although the D123A mutant no longer showed elevated binding to NHE1 in the presence of Ca(2+) when assessed using in vitro binding assays. Disruption of either site also did not impair the ability of CHP3 to stimulate the biosynthetic processing and trafficking of NHE1 to the plasma membrane nor did it affect the H(+) sensitivity of the exchanger. However, they did significantly reduce the cell surface half-life and near maximal transport velocity of NHE1 to a similar extent. Simultaneous mutation of both sites (G2A/D123A) gave results identical to the individual substitutions. This finding suggests that both domains in CHP3 are interdependent and may function cooperatively as a Ca(2+)-myristoyl switch mechanism to selectively stabilize the NHE1·CHP3 complex at the cell surface in a conformation that promotes optimal transport activity.

The DNAJA2 substrate release mechanism is essential for chaperone-mediated folding.

DNAJA1 (DJA1/Hdj2) and DNAJA2 (DJA2) are the major J domain partners of human Hsp70/Hsc70 chaperones. Although they have overall similarity with the well characterized type I co-chaperones from yeast and bacteria, they are biologically distinct, and their functional mechanisms are poorly characterized. We identified DJA2-specific activities in luciferase folding and repression of human ether-a-go-go-related gene (HERG) trafficking that depended on its expression levels in cells. Mutations in different internal domains of DJA2 abolished these effects. Using purified proteins, we addressed the mechanistic defects. A mutant lacking the region between the zinc finger motifs (DJA2-Δm2) was able to bind substrate similar to wild type but was incapable of releasing substrate during its transfer to Hsc70. The equivalent mutation in DJA1 also abolished its substrate release. A DJA2 mutant (DJA-221), which had its C-terminal dimerization region replaced by that of DJA1, was inactive but retained its ability to release substrate. The release mechanism required the J domain and ATP hydrolysis by Hsc70, although the nucleotide dependence diverged between DJA2 and DJA1. Limited proteolysis suggested further conformational differences between the two wild-type co-chaperones and the mutants. Our results demonstrate an essential role of specific DJA domains in the folding mechanism of Hsc70.

Predicting discrete-time bifurcations with deep learning.

Many natural and man-made systems are prone to critical transitions-abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal for critical transitions by learning generic features of bifurcations from large simulated training data sets. So far, classifiers have only been trained to predict continuous-time bifurcations, ignoring rich dynamics unique to discrete-time bifurcations. Here, we train a deep learning classifier to provide an early warning signal for the five local discrete-time bifurcations of codimension-one. We test the classifier on simulation data from discrete-time models used in physiology, economics and ecology, as well as experimental data of spontaneously beating chick-heart aggregates that undergo a period-doubling bifurcation. The classifier shows higher sensitivity and specificity than commonly used early warning signals under a wide range of noise intensities and rates of approach to the bifurcation. It also predicts the correct bifurcation in most cases, with particularly high accuracy for the period-doubling, Neimark-Sacker and fold bifurcations. Deep learning as a tool for bifurcation prediction is still in its nascence and has the potential to transform the way we monitor systems for critical transitions.

Pacemaker interactions induce reentrant wave dynamics in engineered cardiac culture.

Pacemaker interactions can lead to complex wave dynamics seen in certain types of cardiac arrhythmias. We use experimental and mathematical models of pacemakers in heterogeneous excitable media to investigate how pacemaker interactions can be a mechanism for wave break and reentrant wave dynamics. Embryonic chick ventricular cells are cultured in vitro so as to create a dominant central pacemaker site that entrains other pacemakers in the medium. Exposure of those cultures to a potassium channel blocker, E-4031, leads to emergence of peripheral pacemakers that compete with each other and with the central pacemaker. Waves emitted by faster pacemakers break up over the slower pacemaker to form reentrant waves. Similar dynamics are observed in a modified FitzHugh-Nagumo model of heterogeneous excitable media with two distinct sites of pacemaking. These findings elucidate a mechanism of pacemaker-induced reentry in excitable media.

Chaotic dynamics in cardiac aggregates induced by potassium channel block.

Chaotic rhythms in deterministic models can arise as a consequence of changes in model parameters. We carried out experimental studies in which we induced a variety of complex rhythms in aggregates of embryonic chick cardiac cells using E-4031 (1.0-2.5 µM), a drug that blocks the hERG potassium channel. Following the addition of the drug, the regular rhythm evolved to display a spectrum of complex dynamics: irregular rhythms, bursting oscillations, doublets, and accelerated rhythms. The interbeat intervals of the irregular rhythms can be described by one-dimensional return maps consistent with chaotic dynamics. A Hodgkin-Huxley-style cardiac ionic model captured the different types of complex dynamics following blockage of the hERG mediated potassium current.