The authors have no proprietary or commercial interest in any of the materials discussed in this article.

Excitable cells can exhibit complex patterns of oscillations, such as spiking and bursting. In cardiac cells, pathological voltage oscillations, called early afterdepolarizations (EADs), have been widely observed under disease conditions, yet their dynamical mechanisms remain unknown. Here, we show that EADs are caused by Hopf and homoclinic bifurcations. During period pacing, chaos always occurs at the transition from no EAD to EADs as the stimulation frequency decreases, providing a novel explanation for the irregular EAD behavior frequently observed in experiments.Complex oscillatory behaviors, such as spiking and bursting dynamics in pancreatic β-cells [1], neurons [1][2][3][4][5], and optical lasers [6], are common phenomena in excitable systems. These complex dynamics are generally described by systems with fast and slow time scales, where the full system behavior can be described by slow dynamics evolving the fast subsystem through a series of bifurcations [1,2]. Cardiac myocytes can exhibit pathological excitations called early afterdepolarizations (EADs), which are voltage oscillations during the repolarizing phase of the action potential (AP). They have been implicated as a cause of lethal cardiac arrhythmias [7][8][9] and have been widely investigated in experiments [8,[10][11][12] and also in simulations [13][14][15][16]. It is commonly agreed that EADs occur when inward (depolarizing) currents are increased and/or outward (repolarizing) currents are decreased. But many such changes do not produce EADs, and the general underlying dynamical mechanism still remains unknown. In single myocytes, EADs typically occur irregularly [10][11][12], which is generally attributed to random fluctuations of the underlying ion channels [13]. In a recent study [16], we presented evidence from isolated myocyte experiments and computational simulations that irregular EAD behavior is not random, but rather dynamical chaos, and gives rise to novel tissue scale dynamics.EADs have typically been studied in computational simulations using highly detailed AP models making dynamical analysis difficult [13][14][15][16] Dynamical origin of EADsThere are typically three time scales in a normal cardiac AP. The sodium (Na) current activates very rapidly, causing the fast upstroke of the AP, and then rapidly inactivates. The L-type calcium (Ca) current activates and inactivates more slowly than the Na current, playing a key role in maintaining the long AP plateau. Time-dependent potassium (K) currents activate even more slowly and eventually overcome the inward currents, repolarizing the cell back to the resting potential. EADs have typically been studied using highly detailed AP models [13][14][15][16] where C m = 1 µF/cm 2 ; I Na is the Na current; We set E si = 80 mV and E K = −77 mV. To study the effects of the time constants for the gating variables d, f, and x on the AP dynamics, we change these time constants by multiplying them by a scalar factor, i.e.,, and τ x (V) → γτ x (V). We refer to this modified LR1 model ...

The synchronization of coupled oscillators plays an important role in many biological systems, including the heart. In heart diseases, cardiac myocytes can exhibit abnormal electrical oscillations, such as early afterdepolarizations (EADs), which are associated with lethal arrhythmias. A key unanswered question is how cellular EADs partially synchronize in tissue, as is required for them to propagate. Here, we present evidence, from computational simulations and experiments in isolated myocytes, that irregular EAD behavior is dynamical chaos. We then show in electrically homogeneous tissue models that chaotic EADs synchronize globally when the tissue is smaller than a critical size. However, when the tissue exceeds the critical size, electrotonic coupling can no longer globally synchronize EADs, resulting in regions of partial synchronization that shift in time and space. These regional partially synchronized EADs then form premature ventricular complexes that propagate into recovered tissue without EADs. This process creates multiple hat propagate “shifting” foci resembling polymorphic ventricular tachycardia. Shifting foci encountering shifting repolarization gradients can also develop localized wave breaks leading to reentry and fibrillation. As predicted by the theory, rabbit hearts exposed to oxidative stress (H 2 O 2 ) exhibited multiple shifting foci causing polymorphic tachycardia and fibrillation. This mechanism explains how collective cellular behavior integrates at the tissue scale to generate lethal cardiac arrhythmias over a wide range of heart rates.

Summary Rbfox proteins control alternative splicing and posttranscriptional regulation in mammalian brain, and are implicated in neurological disease. These proteins recognize the RNA sequence (U)GCAUG, but their structures and diverse roles imply a variety of protein-protein interactions. We find that nuclear Rbfox proteins are bound within a large assembly of splicing regulators (LASR), a multimeric complex containing the proteins hnRNP M, hnRNP H, hnRNP C, Matrin3, NF110/NFAR-2, NF45, and DDX5, all approximately equimolar to Rbfox. We show that splicing repression mediated by hnRNP M is stimulated by Rbfox. Virtually all the intron-bound Rbfox is associated with LASR, and hnRNP M motifs are enriched adjacent to Rbfox crosslinking sites in vivo. These findings demonstrate that Rbfox proteins bind RNA with a defined set of cofactors, and affect a broader set of exons than previously recognized. The function of this multimeric LASR complex has implications for deciphering the regulatory codes controlling splicing networks.

Summary LDL receptor-related proteins 5 and 6 (LRP5/6) are co-receptors for Wnt growth factors, and also bind Dkk proteins, secreted inhibitors of Wnt signaling. The LRP5/6 ectodomain contains four β-propeller/EGF-like domain repeats. The first two repeats (LRP6(1-2)) bind to several Wnt variants, whereas LRP6(3-4) binds other Wnts. We present the crystal structure of the Dkk1 C-terminal domain bound to LRP6(3-4), and show that the Dkk1 N-terminal domain binds to LRP6(1-2), demonstrating that a single Dkk1 molecule can bind to both portions of the LRP6 ectodomain and thereby inhibit different Wnts. Small-angle x-ray scattering analysis of LRP6(1-4) bound to a non-inhibitory antibody fragment or to full-length Dkk1 shows that in both cases the ectodomain adopts a curved conformation that places the first three repeats at a similar height relative to the membrane. Thus, Wnts bound to either portion of the LRP6 ectodomain likely bear a similar spatial relationship to Frizzled co-receptors.