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Purpose: Corneal sensory nerves protect the cornea from injury. They are also thought to stimulate limbal stem cells (LSCs) to produce transparent epithelial cells constantly, enabling vision. In other organs, Schwann cells (SCs) associated with tissue-innervating axon terminals mediate tissue regeneration. This study defines the critical role of the corneal axon-ensheathing SCs in homeostatic and regenerative corneal epithelial cell renewal.
Methods: SC localization in the cornea was determined by in situ hybridization and immunohistochemistry with SC markers. In vivo SC visualization and/or ablation was performed in mice with inducible corneal SC-specific expression of TdTomato and/or Diphtheria toxin, respectively. The relative locations of SCs and LSCs was observed with immunohistochemical analysis of harvested genetically SC-pre-labeled mouse corneas with LSC-specific antibodies. The correlation between cornea-innervating axons and the appearance of SCs was ascertained using corneal denervation in rats. To determine the limbal niche cellular composition and gene expression changes associated with innervation-dependent epithelial renewal, single cell RNA sequencing (scRNA-Seq) of dissociated healthy, de-epithelized and enervated cornea limbi was performed.
Results: We observed limbal enrichment of corneal axon-associated myelinating and non-myelinating SCs. Induced local genetic ablation of SCs, while leaving corneal sensory innervation intact, markedly inhibited corneal epithelial renewal. scRNA-seq analysis (i) highlighted the transcriptional heterogeneity of cells populating the limbal niche and (ii) identified transcriptional changes associated with corneal innervation and during wound healing that model potential regulatory paracrine interactions between SCs and LSCs.
Conclusions: Limbal SCs are required for innervation-dependent corneal epithelial renewal.

Saare-Circadian clocks are self-sustained and cell-autonomous oscillators. They respond to various extracellular cues depending on the time-of-day and the signal intensity. Phase Transition Curves (PTCs) are instrumental in uncovering the full repertoire of responses to a given signal. However, the current methodologies for reconstructing PTCs are low-throughput, laborious, and resource- and time-consuming. Circadian Single-Cell Oscillators PTC Extraction (Circa-SCOPE) is a method developed by the Asher lab, for generating high-resolution PTCs. This methodology relies on continuous monitoring of single-cell oscillations to reconstruct a full PTC from a single culture, upon a one-time intervention. Using Circa-SCOPE, we characterize the effects of various pharmacological and blood-borne resetting cues, at high temporal resolution and a wide concentration range. Thus, Circa-SCOPE is a powerful tool for comprehensive analysis and screening for circadian clocks’ resetting cues and can be valuable for basic as well as translational research.

Understanding the role of depth is a fundamental endeavor in explaining the practical success of deep learning. In this talk, we will focus on the problem of approximating the maximum function over $d$ inputs using deep ReLU networks and with respect to the uniform distribution over a hypercube. We will show that while approximating the maximum using depth 2 networks to arbitrary accuracy requires arbitrary width, this can be done to arbitrary accuracy using a depth 3 network with a fixed width of $d^2$. Additionally, we will also show that this upper bound is tight, namely that width $Omega(d^2)$ is also necessary when approximating using depth 3. Moreover, using this efficient depth 3 construction, we will show that greater depths result in a lesser width requirement, where width $mathcal{O}(d)$ suffices when we allow depth $mathcal{O}(log(log(d)))$. Lastly, we will show a size lower bound of $d$ neurons for approximating the maximum using any depth. These results establish a partial depth hierarchy for approximating a naturally occuring function which helps explain the benefits of depth over width.