We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we find that the stability of the completely synchronous state in such networks only depends on the number of signals each neuron receives, independent of all other details of the network topology. This is in contrast with linearly coupled bursting neurons where complete synchrony strongly depends on the network structure and number of cells. Through analysis and numerics, we show that the onset of synchrony in a network with any coupling topology admitting complete synchronization is ensured by one single condition.
Non-technical summary Long QT syndrome (LQTS) is a genetic disorder characterized by recurrent syncope and sudden cardiac death (SCD). Type 1 (LQT1) and Type 2 (LQT2) LQTS account for 90% of the genotyped mutations in patients with this disorder. These syndromes have been associated with different sympathetic modes for initiation of cardiac arrest. Using isolated cardiomyocytes and Langendorff-perfused hearts from transgenic rabbit models of LQT1 and LQT2, we have identified differential conditions and cellular mechanisms for the generation of early afterdepolarizations (EADs), abnormal depolarizations during the plateau and repolarization phase of action potentials and the hallmark of the arrhythmias in LQTS. These differences explain why different types of increased autonomic nervous system activity, i.e. sympathetic surge vs. high sympathetic tone, are associated with the initiation of polymorphic ventricular tachycardia in LQTS patients with different genetic background.Abstract Early after-depolarization (EAD), or abnormal depolarization during the plateau phase of action potentials, is a hallmark of long-QT syndrome (LQTS). More than 13 genes have been identified as responsible for LQTS, and elevated risks for EADs may depend on genotypes, such as exercise in LQT1 vs. sudden arousal in LQT2 patients. We investigated mechanisms underlying different high-risk conditions that trigger EADs using transgenic rabbit models of LQT1 and LQT2, which lack I Ks and I Kr (slow and fast components of delayed rectifying K + current), respectively. Single-cell patch-clamp studies show that prolongation of action potential duration (APD) can be further enhanced by lowering extracellular potassium concentration ([K + ] o ) from 5.4 to 3.6 mM. However, only LQT2 myocytes developed spontaneous EADs following perfusion with lower [K + ] o , while there was no EAD formation in littermate control (LMC) or LQT1 myocytes, although APDs were also prolonged in LMC myocytes and LQT1 myocytes. Isoprenaline (ISO) prolonged APDs and triggered EADs in LQT1 myocytes in the presence of lower [K + ] o . In contrast, continuous ISO perfusion diminished APD prolongation and reduced the incidence of EADs in LQT2 myocytes. These different effects of ISO on LQT1 and LQT2 were verified by optical mapping of the whole heart, suggesting that ISO-induced EADs are genotype specific. Further voltage-clamp studies revealed that ISO increases L-type calcium current (I Ca ) faster than I Ks (time constant 9.2 s for I Ca and 43.6 s for I Ks ), and computer simulation demonstrated a high-risk window of EADs in LQT2 during ISO perfusion owing to mismatch in the time courses of I Ca and I Ks , which may explain why a sympathetic surge rather than high sympathetic tone can be an effective trigger of EADs in LQT2 perfused hearts. In summary, EAD formation is genotype specific, such that EADs can be elicited in LQT2 myocytes simply by lowering [K + ] o , while LQT1 myocytes require sympathetic stimulation. Slower activation of I Ks than of I Ca by ISO may expla...
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