Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the pp-Adics-Quantum Group Connection

We establish a previously conjectured connection between $p$-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which ``interpolate'' between the zonal spherical functions of related real and $p$\--adic symmetric spaces. The elliptic quantum algebras underlie the $Z_n$\--Baxter models. We show that in the n \air \infty limit, the Jost function for the scattering of {\em first} level excitations in the $Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function constructed from the Macdonald polynomials associated to the root system $A_1$. The partition function of the $Z_2$\--Baxter model itself is also expressed in terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less simple way. We relate the two parameters $q$ and $t$ of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of ``$q$\--deforming'' Euler products.Comment: 25 page

LRRK2 regulates autophagic activity and localizes to specific membrane microdomains in a novel human genomic reporter cellular model

Leucine rich repeat kinase 2 (LRRK2) mutations are the most common genetic cause of Parkinson's disease (PD) although LRRK2 function remains unclear. We report a new role for LRRK2 in regulating autophagy and describe the recruitment of LRRK2 to the endosomal–autophagic pathway and specific membrane subdomains. Using a novel human genomic reporter cellular model, we found LRRK2 to locate to membrane microdomains such as the neck of caveolae, microvilli/filopodia and intraluminal vesicles of multivesicular bodies (MVBs). In human brain and in cultured human cells LRRK2 was present in cytoplasmic puncta corresponding to MVBs and autophagic vacuoles (AVs). Expression of the common R1441C mutation from a genomic DNA construct caused impaired autophagic balance evident by the accumulation of MVBs and large AVs containing incompletely degraded material and increased levels of p62. Furthermore, the R1441C mutation induced the formation of skein-like abnormal MVBs. Conversely, LRRK2 siRNA knockdown increased autophagic activity and prevented cell death caused by inhibition of autophagy in starvation conditions. The work necessitated developing a new, more efficient recombineering strategy, which we termed Sequential insertion of Target with ovErlapping Primers (STEP) to seamlessly fuse the green fluorescent protein-derivative YPet to the human LRRK2 protein in the LRRK2 genomic locus carried by a bacterial artificial chromosome. Taken together our data demonstrate the functional involvement of LRRK2 in the endosomal–autophagic pathway and the recruitment to specific membrane microdomains in a physiological human gene expression model suggesting a novel function for this important PD-related protein

Brazilian Flora 2020: Leveraging the power of a collaborative scientific network

International audienceThe shortage of reliable primary taxonomic data limits the description of biological taxa and the understanding of biodiversity patterns and processes, complicating biogeographical, ecological, and evolutionary studies. This deficit creates a significant taxonomic impediment to biodiversity research and conservation planning. The taxonomic impediment and the biodiversity crisis are widely recognized, highlighting the urgent need for reliable taxonomic data. Over the past decade, numerous countries worldwide have devoted considerable effort to Target 1 of the Global Strategy for Plant Conservation (GSPC), which called for the preparation of a working list of all known plant species by 2010 and an online world Flora by 2020. Brazil is a megadiverse country, home to more of the world's known plant species than any other country. Despite that, Flora Brasiliensis, concluded in 1906, was the last comprehensive treatment of the Brazilian flora. The lack of accurate estimates of the number of species of algae, fungi, and plants occurring in Brazil contributes to the prevailing taxonomic impediment and delays progress towards the GSPC targets. Over the past 12 years, a legion of taxonomists motivated to meet Target 1 of the GSPC, worked together to gather and integrate knowledge on the algal, plant, and fungal diversity of Brazil. Overall, a team of about 980 taxonomists joined efforts in a highly collaborative project that used cybertaxonomy to prepare an updated Flora of Brazil, showing the power of scientific collaboration to reach ambitious goals. This paper presents an overview of the Brazilian Flora 2020 and provides taxonomic and spatial updates on the algae, fungi, and plants found in one of the world's most biodiverse countries. We further identify collection gaps and summarize future goals that extend beyond 2020. Our results show that Brazil is home to 46,975 native species of algae, fungi, and plants, of which 19,669 are endemic to the country. The data compiled to date suggests that the Atlantic Rainforest might be the most diverse Brazilian domain for all plant groups except gymnosperms, which are most diverse in the Amazon. However, scientific knowledge of Brazilian diversity is still unequally distributed, with the Atlantic Rainforest and the Cerrado being the most intensively sampled and studied biomes in the country. In times of “scientific reductionism”, with botanical and mycological sciences suffering pervasive depreciation in recent decades, the first online Flora of Brazil 2020 significantly enhanced the quality and quantity of taxonomic data available for algae, fungi, and plants from Brazil. This project also made all the information freely available online, providing a firm foundation for future research and for the management, conservation, and sustainable use of the Brazilian funga and flora