Characterization of almost LpL^p-eigenfunctions of the Laplace-Beltrami operator

In \cite{Roe} Roe proved that if a doubly-infinite sequence $\{f_k\}$ of functions on $\R$ satisfies $f_{k+1}=(df_{k}/dx)$ and $|f_{k}(x)|\leq M$ for all $k=0,\pm 1,\pm 2,...$ and $x\in \R$, then $f_0(x)=a\sin(x+\varphi)$ where $a$ and $\varphi$ are real constants. This result was extended to $\R^n$ by Strichartz \cite{Str} where $d/dx$ is substituted by the Laplacian on $\R^n$. While it is plausible to extend this theorem for other Riemannian manifolds or Lie groups, Strichartz showed that the result holds true for Heisenberg groups, but fails for hyperbolic 3-space. This negative result can be indeed extended to any Riemannian symmetric space of noncompact type. We observe that this failure is rooted in the $p$-dependance of the $L^p$-spectrum of the Laplacian on the hyperbolic spaces. Taking this into account we shall prove that for all rank one Riemannian symmetric spaces of noncompact type, or more generally for the harmonic $NA$ groups, the theorem actually holds true when uniform boundedness is replaced by uniform "almost $L^p$ boundedness". In addition we shall see that for the symmetric spaces this theorem is capable of characterizing the Poisson transforms of $L^p$ functions on the boundary, which some what resembles the original theorem of Roe on $\R$.Comment: 30 page

Gene Editing and Systems Biology Tools for Pesticide Bioremediation: A Review

Bioremediation is the degradation potential of microorganisms to dissimilate the complex chemical compounds from the surrounding environment. The genetics and biochemistry of biodegradation processes in datasets opened the way of systems biology. Systemic biology aid the study of interacting parts involved in the system. The significant keys of system biology are biodegradation network, computational biology, and omics approaches. Biodegradation network consists of all the databases and datasets which aid in assisting the degradation and deterioration potential of microorganisms for bioremediation processes. This review deciphers the bio-degradation network, i.e., the databases and datasets (UM-BBD, PAN, PTID, etc.) aiding in assisting the degradation and deterioration potential of microorganisms for bioremediation processes, computational biology and multi omics approaches like metagenomics, genomics, transcriptomics, proteomics, and metabolomics for the efficient functional gene mining and their validation for bioremediation experiments. Besides, the present review also describes the gene editing tools like CRISPR Cas, TALEN, and ZFNs which can possibly make design microbe with functional gene of interest for degradation of particular recalcitrant for improved bioremediation

Bio-Based Formulations for Sustainable Applications in Agri-Food-Pharma

Currently, there is a strong enduring interest towards obtaining high-value, sustainable bio-based bioactive compounds from natural resources, as there is great demand for these compounds in various market sectors such as agriculture, food, pharma, cosmeceuticals, and others. This demand has encouraged researchers to isolate, identify and characterize novel natural bioactive compounds with potential therapeutic and commercial values with industrial importance [1]. These bioactive compounds are generally secondary metabolites (synthesized via plant biosynthetic pathways) and include polyphenols, carotenoids, flavonoids, sterols, dietary fiber, essential vitamins, coenzyme Q, phytosterols, glucosinolates and others with potential beneficial roles as nutraceuticals, surfactants and bio-stimulants. Understanding the molecular characteristics, physicochemical properties, biological activity, and stability of these bioactives under different conditions is vital for their commercial exploitation. The efficacy of these bioactives can often be improved by encapsulating them in nanobased-formulations designed for application in the agriculture, food, pharmaceutical industries. These delivery systems can be designed to increase the dispersibility, stability, bioavailability, and bioactivity imparted by the bioactives. Moreover, they may be useful for minimizing undesirable side-effects, facilitating targeted delivery to certain cells, and enhancing the shelf life of food products

Vaccine and antibody production in plants : developments and computational tools

K.K.D. and P.S. sincerely acknowledge the support and facility provided by the M.D. University, Rohtak, Haryana. P.S. acknowledges the infrastructural support from Department of Science and Technology, Govt. of India through FIST grant (Grant No. 1196 SR/FST/LS-I/2017/4).Plants as bioreactors have been widely used to express efficient vaccine antigens against viral, bacterial and protozoan infections. To date, many different plant-based expression systems have been analyzed, with a growing preference for transient expression systems. Antibody expression in diverse plant species for therapeutic applications is well known, and this review provides an overview of various aspects of plant-based biopharmaceutical production. Here, we highlight conventional and gene expression technologies in plants along with some illustrative examples. In addition, the portfolio of products that are being produced and how they relate to the success of this field are discussed. Stable and transient gene expression in plants, agrofiltration and virus infection vectors are also reviewed. Further, the present report draws attention to antibody epitope prediction using computational tools, one of the crucial steps of vaccine design. Finally, regulatory issues, biosafety and public perception of this technology are also discussed.PostprintPeer reviewe

Plant microbe interactions in post genomic era: perspectives and applications

Deciphering plant-microbe interactions is a promising aspect to understand the benefits and the pathogenic effect of microbes and crop improvement. The advancement in sequencing technologies and various ‘omics’ tool has impressively accelerated the research in biological sciences in this area. The recent and ongoing developments provide a unique approach to describing these intricate interactions and test hypotheses. In the present review, we discuss the role of plant-pathogen interaction in crop improvement. The plant innate immunity has always been an important aspect of research and leads to some interesting information like the adaptation of unique immune mechanisms of plants against pathogens. The development of new techniques in the post - genomic era has greatly enhanced our understanding of the regulation of plant defense mechanisms against pathogens. The present review also provides an overview of beneficial plant-microbe interactions with special reference to Agrobacterium tumefaciens-plant interactions where plant derived signal molecules and plant immune responses are important in pathogenicity and transformation efficiency. The construction of various Genome-scale metabolic models of microorganisms and plants presented a better understanding of all metabolic interactions activated during the interactions. This review also lists the emerging repertoire of phytopathogens and its impact on plant disease resistance. Outline of different aspects of plant-pathogen interactions is presented in this review to bridge the gap between plant microbial ecology and their immune responses