Mathematical analysis on the dynamics of COVID-19 in India using SIR Epidemic Model

The Coronavirus Disease (COVID-19), the outbreak of which emerged from the Wuhan city of China, is a matter of huge concern for the entire human race. The disease as on August 4, 2020 has invaded around 18.6 million population causing over half a million deaths worldwide and counting.  To understand the dynamics of this communicable disease and its transmission among the people in India, a mathematical model governed by ordinary differential equations with appropriate conditions has been established. The model is based on SIR (Susceptible-Infected-Removed) scheme to understand the behavior of susceptible, infective and removed (both recovered and deceased) population in India. The resulting model has been simulated using MATLAB software. The results obtained in this model are interpreted graphically and least squares method is used to predict the transmission rate, recovery rate and mortality rate in the absence of any vaccine/immunization

Variational finite element method to study the absorption rate of drug at various compartments through transdermal drug delivery system

Background: The delivery of drugs through dermal layers known as transdermal drug delivery is one of the important contributions in medical practice. It represents an alternative to oral drug delivery and is poised to provide a substitute to hypodermic injections too. The diffusion of drug from the source to the target site is therefore an important issue to address.Aim: This paper is an attempt to establish a mathematical model for the diffusion of drugs through the transdermal drug delivery system. The model identifies the pattern of drug diffusion in human body and its effective absorption rates at various compartments of skin and sub-cutaneous tissues.Methods: The finite element method has been used to obtain the solution of the mass diffusion equation with appropriate boundary conditions. The tissue absorption rate of drug has been taken as the decreasing function of drug concentration from the skin surface towards the target site. The concentration at nodal points has been calculated which in turn determines the drug absorption at various layers.Conclusion: The drug concentration at the nodal points of different dermal layers has been computed and the graphs were plotted between drug concentration and thickness of dermal layers using MATLAB software. It has been observed that due to dense network of connective tissues in dermal and sub-dermal parts, the drug absorption is maximum as compared to cutaneous tissues.Keywords: Transdermal drug delivery; Diffusion equation; Finite element metho

Targeted reprogramming of H3K27me3 resets epigenetic memory in plant paternal chromatin

Epigenetic marks are reprogrammed in the gametes to reset genomic potential in the next generation. In mammals, paternal chromatin is extensively reprogrammed through the global erasure of DNA methylation and the exchange of histones with protamines(1,2). Precisely how the paternal epigenome is reprogrammed in flowering plants has remained unclear since DNA is not demethylated and histones are retained in sperm(3,4). Here, we describe a multi-layered mechanism by which H3K27me3 is globally lost from histone-based sperm chromatin in Arabidopsis. This mechanism involves the silencing of H3K27me3 writers, activity of H3K27me3 erasers and deposition of a sperm-specific histone, H3.10 (ref. (5)), which we show is immune to lysine 27 methylation. The loss of H3K27me3 facilitates the transcription of genes essential for spermatogenesis and pre-configures sperm with a chromatin state that forecasts gene expression in the next generation. Thus, plants have evolved a specific mechanism to simultaneously differentiate male gametes and reprogram the paternal epigenome

Multiple copies of MRG19 suppress transcription of the GAL1 promoter in a GAL80-dependent manner in Saccharomyces cerevisiae

A plasmid clone that suppresses galactose toxicity in a gal7 yeast strain has been isolated from a multicopy genomic DNA library. Molecular analysis revealed that the region responsible for the suppression of galactose toxicity corresponds to the ORF YPR030w, which was named MRG19. A CEN-based plasmid carrying the above ORF was unable to suppress the toxicity. Galactokinase activity was substantially reduced in cell extracts obtained from transformants bearing multiple copies of MRG19. Multiple copies of MRG19 were also able to suppress galactokinase expression driven by the CYC1 promoter but not the TEF1 promoter. Multiple copies of MRG19 could not suppress GAL1-driven galactokinase expression in a gal80 strain. However, MRG19-mediated suppression of CYC1-driven galactokinase expression was independent of GAL80 function. These results imply that multiple copies of MRG19 suppress galactokinase expression probably at the level of transcription. In agreement with this idea, multiple copies of MRG19 also suppress B-galactosidase expression driven by the GAL1 promoter in a GAL80-dependent manner. Disruption of MRG19 leads to an increase in the cell density at stationary phase in synthetic complete medium. MRG19 encodes a previously uncharacterised 124-kDa protein that shows no sequence homology to any known proteins