One-Way Communication Complexity of Partial XOR Functions

Boolean function $F(x,y)$ for $x,y \in \{0,1\}^n$ is an XOR function if $F(x,y)=f(x\oplus y)$ for some function $f$ on $n$ input bits, where $\oplus$ is a bit-wise XOR. XOR functions are relevant in communication complexity, partially for allowing Fourier analytic technique. For total XOR functions it is known that deterministic communication complexity of $F$ is closely related to parity decision tree complexity of $f$. Montanaro and Osbourne (2009) observed that one-sided communication complexity $D_{cc}^{\rightarrow}(F)$ of $F$ is exactly equal to nonadaptive parity decision tree complexity $NADT^{\oplus}(f)$ of $f$. Hatami et al. (2018) showed that unrestricted communication complexity of $F$ is polynomially related to parity decision tree complexity of $f$. We initiate the studies of a similar connection for partial functions. We show that in case of one-sided communication complexity whether these measures are equal, depends on the number of undefined inputs of $f$. On the one hand, if $D_{cc}^{\rightarrow}(F)=t$ and $f$ is undefined on at most $O(\frac{2^{n-t}}{\sqrt{n-t}})$, then $NADT^{\oplus}(f)=t$. On the other hand, for a wide range of values of $D_{cc}^{\rightarrow}(F)$ and $NADT^{\oplus}(f)$ (from constant to $n-2$) we provide partial functions for which $D_{cc}^{\rightarrow}(F) < NADT^{\oplus}(f)$. In particular, we provide a function with an exponential gap between the two measures. Our separation results translate to the case of two-sided communication complexity as well, in particular showing that the result of Hatami et al. (2018) cannot be generalized to partial functions. Previous results for total functions heavily rely on Boolean Fourier analysis and the technique does not translate to partial functions. For the proofs of our results we build a linear algebraic framework instead. Separation results are proved through the reduction to covering codes

ADIPOR1 is essential for vision and its RPE expression is lost in the Mfrp

The knockout (KO) of the adiponectin receptor 1 (AdipoR1) gene causes retinal degeneration. Here we report that ADIPOR1 protein is primarily found in the eye and brain with little expression in other tissues. Further analysis of AdipoR1 KO mice revealed that these animals exhibit early visual system abnormalities and are depleted of RHODOPSIN prior to pronounced photoreceptor death. A KO of AdipoR1 post-development either in photoreceptors or the retinal pigment epithelium (RPE) resulted in decreased expression of retinal proteins, establishing a role for ADIPOR1 in supporting vision in adulthood. Subsequent analysis of the Mfr

Single cell RNA sequencing of stem cell-derived retinal ganglion cells

We used single cell sequencing technology to characterize the transcriptomes of 1,174 human embryonic stem cell-derived retinal ganglion cells (RGCs) at the single cell level. The human embryonic stem cell line BRN3B-mCherry (A81-H7), was differentiated to RGCs using a guided differentiation approach. Cells were harvested at day 36 and prepared for single cell RNA sequencing. Our data indicates the presence of three distinct subpopulations of cells, with various degrees of maturity. One cluster of 288 cells showed increased expression of genes involved in axon guidance together with semaphorin interactions, cell-extracellular matrix interactions and ECM proteoglycans, suggestive of a more mature RGC phenotype

IN VITRO GENERATION OF HUMAN RETINAL GANGLION CELLS VIA DIRECT CONVERSION AND STEM CELL DIFFERENTIATION

Retinal ganglion cells (RGCs) are essential for human visual perception, as they mediate the transfer of visual information from the eye to the brain. In the event of RGC death, as happens in diseases such as glaucoma, vision is permanently lost because the mammalian central nervous system (CNS) does not regenerate. In order to find novel treatments for the RGC diseases, a number of different research approaches have been undertaken. One relatively recent approach involves the use of pluripotent stem cell (PSC) technologies. As human PSCs can be differentiated to the RGC lineage, it has become possible to utilize human RGCs for drug discovery, disease modeling, or transplantation experiments to attempt visual system recovery. The field of PSC differentiation to RGCs has been steadily developing, but many hurdles remain. Initial reports involved co-culture of mouse stem cells with primary embryonic retinal cells or conditioned media, and yielded only small numbers of cells. Evolution of ocular stem cell biology over the past few years has greatly improved the technology for generation of three-dimensional optic vesicles that develop all of the retinal layers, including the RGC layer. Although such reports were very encouraging, these studies failed to demonstrate that RGCs could be isolated from culture and deeper profiles of the RGCs were missing. Here, we describe a novel, simplified protocol for RGC differentiation from human PSCs. We took advantage of recently developed CRISPR-Cas9 technologies to genetically engineer a stem cell reporter line for RGCs based on the BRN3B/POU4F2 gene. Using this line, we developed a fluorescence-activated cell sorting (FACS) protocol that yields highly purified RGCs, and we subsequently characterized the purified cells in terms of their expression pattern of RGC-associated genes and other cellular properties. Despite the power of FACS to provide purified populations of fluorescent RGCs, FACS-based purification schemes also have their limitations. A main limitation is the relatively slow speed and restricted throughput of FACS. In order to get around these limitations, we developed an alternative approach by genetically engineering a unique cell surface antigen driven by the BRN3B gene into stem cells, allowing us to isolate populations of pure differentiated RGCs by affinity purification in an efficient, large scale, and time saving manner that makes possible the use of human RGCs in a variety of studies including high throughput drug discovery screens. In addition to developing this new RGC purification strategy, which has implications for developing improved systems for the purification of a wide variety of different cell types, we have also optimized our initial differentiation protocol by manipulating known signaling pathways via small molecule supplementation to guide the cells toward a retinal cell fate. In addition to developing and characterizing improved stem cell-based approaches for generating RGCs, we have also been pursuing the generation of RGCs from non-stem cell lines through trans-differentiation and direct reprogramming. Through this work, we have identified a combination of four transcription factors that can directly reprogram the human retinal pigment epithelium (RPE) cell line ARPE19 into RGC-like cells. Expression of ATOH7, BRN2, BRN3B, and MYT1 in ARPE19 cells transformed their morphology to a neuronal phenotype and induced the expression of pan-neuronal and RGC-associated genes. Moreover, when overexpressed in stem cells undergoing retinal differentiation, these factors were able to boost the percentage of cells differentiating to the RGC lineage, an effect that could be further increased by our previously identified small molecules. Lastly, we discuss the development of a new method to enhance homology directed repair for the purpose of generating reporter lines in an easier and more routine way. Taken together, these studies provide powerful tools for the use of stem cell technology to study RGC differentiation and biology, and the mechanisms of RGC injury and cell death. Additionally, they provide the means to provide well-characterized and large supplies of RGCs for drug discovery screens and lay the groundwork for possible future cell-based therapeutic approaches for treatment of vision loss and blindness from glaucoma and other forms of optic nerve disease