Certain Mathieu-type Series Pertaining to Incomplete H-Functions

In the present article, we derive closed integral form expressions for a family of convergent Mathieu type a-series along with its alternating variants, whose terms contain incomplete H-functions, which are a notable generalization of familiar H-function. The results established herewith are very general in nature and provide an exquisite generalization of closed integral form expressions of aforementioned series whose terms contain H-function and Fox-Wright function, respectively. Next, we present some new and interesting special cases of our main results

Characterization of symbiotic bacteria found in a female reproductive organ of multiple cephalopod species

Cephalopod International Advisory Council Conference, Cephalopods in the Anthropocene: Multiple Challenges in a Changing Ocean, April 2-8, 2022, Sesimbra, PortugalAnimals often recruit symbiotic bacteria that are used for digestion, defense, and/or development. Many female decapod cephalopods possess a reproductive organ called the accessory nidamental gland (ANG), which hosts a consortium of bacteria that is acquired from the environment. Bacteria from the ANG are transferred to egg jelly coats where they are hypothesized to provide protection against fouling and pathogenic microorganisms. Bacteria from the ANG of some cephalopod species also have demonstrated antimicrobial activity against bacteria and fungi. To understand the geographic and taxonomic distribution of ANG symbionts among cephalopods, we characterized the ANG microbiome from eleven species of squid and cuttlefish from four families that include Sepiolidae, Loliginidae, Idiospiidae, and Sepiidae and span seven different geographic locations. Sequencing and analysis of the V4 region of the 16S ribosomal gene revealed that the ANG microbiomes of the four different cephalopod families were significantly different (p < 0.001). However, members of the Sepiolidae and Idiosepiidae that were collected from five distinct geographic regions had similar ANG microbiomes consisting of bacteria from the Class Verrucomicrobiae, Alphaproteobacteria and Gammaproteobacteria. Similar ANG communities shared among these cephalopod groups may indicate a conserved antimicrobial function involved with egg defense. Understanding ANG bacterial diversity will also assist with the development of tractable cephalopod species that can be used as model organisms to study host-microbe interactionsN

Evolutionary history influences the microbiomes of a female symbiotic reproductive organ in cephalopods.

Many female squids and cuttlefishes have a symbiotic reproductive organ called the accessory nidamental gland (ANG) that hosts a bacterial consortium involved with egg defense against pathogens and fouling organisms. While the ANG is found in multiple cephalopod families, little is known about the global microbial diversity of these ANG bacterial symbionts. We used 16S rRNA gene community analysis to characterize the ANG microbiome from different cephalopod species and assess the relationship between host and symbiont phylogenies. The ANG microbiome of 11 species of cephalopods from four families (superorder: Decapodiformes) that span seven geographic locations was characterized. Bacteria of class Alphaproteobacteria, Gammaproteobacteria, and Flavobacteriia were found in all species, yet analysis of amplicon sequence variants by multiple distance metrics revealed a significant difference between ANG microbiomes of cephalopod families (weighted/unweighted UniFrac, Bray-Curtis, P = 0.001). Despite being collected from widely disparate geographic locations, members of the family Sepiolidae (bobtail squid) shared many bacterial taxa including (~50%) Opitutae (Verrucomicrobia) and Ruegeria (Alphaproteobacteria) species. Furthermore, we tested for phylosymbiosis and found a positive correlation between host phylogenetic distance and bacterial community dissimilarity (Mantel test r = 0.7). These data suggest that closely related sepiolids select for distinct symbionts from similar bacterial taxa. Overall, the ANGs of different cephalopod species harbor distinct microbiomes and thus offer a diverse symbiont community to explore antimicrobial activity and other functional roles in host fitness.IMPORTANCEMany aquatic organisms recruit microbial symbionts from the environment that provide a variety of functions, including defense from pathogens. Some female cephalopods (squids, bobtail squids, and cuttlefish) have a reproductive organ called the accessory nidamental gland (ANG) that contains a bacterial consortium that protects eggs from pathogens. Despite the wide distribution of these cephalopods, whether they share similar microbiomes is unknown. Here, we studied the microbial diversity of the ANG in 11 species of cephalopods distributed over a broad geographic range and representing 15-120 million years of host divergence. The ANG microbiomes shared some bacterial taxa, but each cephalopod species had unique symbiotic members. Additionally, analysis of host-symbiont phylogenies suggests that the evolutionary histories of the partners have been important in shaping the ANG microbiome. This study advances our knowledge of cephalopod-bacteria relationships and provides a foundation to explore defensive symbionts in other systems