Extracellular ATP controls various signaling systems including propagation of intercellular Ca ²⁺ signals (ICS). Connexin hemichannels, P2x7 receptors (P2x7Rs), pannexin channels, anion channels, vesicles, and transporters are putative conduits for ATP release, but their involvement in ICS remains controversial. We investigated ICS in cochlear organotypic cultures, in which ATP acts as an IP ₃ -generating agonist and evokes Ca ²⁺ responses that have been linked to noise-induced hearing loss and development of hair cell-afferent synapses. Focal delivery of ATP or photostimulation with caged IP ₃ elicited Ca ²⁺ responses that spread radially to several orders of unstimulated cells. Furthermore, we recorded robust Ca ²⁺ signals from an ATP biosensor apposed to supporting cells outside the photostimulated area in WT cultures. ICS propagated normally in cultures lacking either P2x7R or pannexin-1 (Px1), as well as in WT cultures exposed to blockers of anion channels. By contrast, Ca ²⁺ responses failed to propagate in cultures with defective expression of connexin 26 (Cx26) or Cx30. A companion paper demonstrates that, if expression of either Cx26 or Cx30 is blocked, expression of the other is markedly down-regulated in the outer sulcus. Lanthanum, a connexin hemichannel blocker that does not affect gap junction (GJ) channels when applied extracellularly, limited the propagation of Ca ²⁺ responses to cells adjacent to the photostimulated area. Our results demonstrate that these connexins play a dual crucial role in inner ear Ca ²⁺ signaling: as hemichannels, they promote ATP release, sustaining long-range ICS propagation; as GJ channels, they allow diffusion of Ca ²⁺ -mobilizing second messengers across coupled cells.

Superselection rules (SSRs) limit the mechanical and quantum processing resources represented by quantum states. However, SSRs can be violated using reference systems to break the underlying symmetry. We show that there is a duality between the ability of a system to do mechanical work and to act as a reference system. Further, for a bipartite system in a globally symmetric pure state, we find a triality between the system’s ability to do local mechanical work, its ability to do “logical work” due to its accessible entanglement, and its ability to act as a shared reference system.

Connexin 26 (Cx26) and connexin 30 (Cx30) are encoded by two genes ( GJB2 and GJB6 , respectively) that are found within 50 kb in the same complex deafness locus, DFNB1. Immunocytochemistry and quantitative PCR analysis of Cx30 KO mouse cultures revealed that Cx26 is downregulated at the protein level and at the mRNA level in nonsensory cells located between outer hair cells and the stria vascularis. To explore connexin coregulation, we manipulated gene expression using the bovine adeno-associated virus. Overexpression of Cx30 in the Cx30 KO mouse by transduction with bovine adeno-associated virus restored Cx26 expression, permitted the formation of functional gap junction channels, and rescued propagating Ca ²⁺ signals. Ablation of Cx26 by transduction of Cx26 ^loxP/loxP cultures with a Cre recombinase vector caused concurrent downregulation of Cx30 and impaired intercellular communication. The coordinated regulation of Cx26 and Cx30 expression appears to occur as a result of signaling through PLC and the NF-κB pathway, because activation of IP ₃ -mediated Ca ²⁺ responses by stimulation of P2Y receptors for 20 min with 20 nM ATP increased the levels of Cx26 transcripts in Cx30 KO cultures. This effect was inhibited by expressing a stable form of the IκB repressor protein that prevents activation/translocation of NF-κB. Thus, our data reveal a Ca ²⁺ -dependent control in the expression of inner ear connexins implicated in hereditary deafness as well as insight into the hitherto unexplained observation that some deafness-associated DFNB1 alleles are characterized by hereditable reduction of both GJB2 and GJB6 expression.

We study the problem of learning from data representations that are invariant to transformations, and at the same time selective, in the sense that two points have the same representation if one is the transformation of the other. The mathematical results here sharpen some of the key claims of i-theory—a recent theory of feedforward processing in sensory cortex (Anselmi et al., 2013, Theor. Comput. Sci. and arXiv:1311.4158; Anselmi et al., 2013, Magic materials: a theory of deep hierarchical architectures for learning sensory representations. CBCL Paper; Anselmi & Poggio, 2010, Representation learning in sensory cortex: a theory. CBMM Memo No. 26).