Let E be an elliptic curve defined over Q. Let E(Fp) denote the elliptic curve modulo p. It is known that there exist integers i p and f p such that E(Fp) ∼= Z/ i pZ × Z/ i p f pZ. We study questions related to i p and f p . In particular, for any α > 0 and k ∈ N, we prove there exist positive constants cα and ck such that for any A > 0 ∑ p≤x (log i p) α = cα li(x) + O ( x (log x)A ) and ∑ p≤x ...

Intramolecular hydrogen bonds (IHBs) play a central role in the molecular structure, chemical reactivity and interactions of biologically active molecules. Here, we study the IHBs of seven related o-carbonyl hydroquinones and one structurally-related aromatic lactone, some of which have shown anticancer and antioxidant activity. Experimental NMR data were correlated with theoretical calculation...

The valorization of aromatic heteropolymer lignin is an important unsolved problem in the development of a biomass-based biorefinery, for which novel high-activity biocatalysts are needed. Sequencing of the genomic DNA of lignin-degrading bacterial strain Sphingobacterium sp. T2 revealed no matches to known lignin-degrading genes. Proteomic matches for two manganese superoxide dismutase protein...

The Phox homology domain (PX domain) is a phosphoinositide-binding structural domain that is critical in mediating protein and cell membrane association and has been found in more than 100 eukaryotic proteins. The abundance of PX domains in nature offers an opportunity to redesign the protein using EvoDesign, a computational approach to design new sequences based on structure profiles of multip...

Interferon-tau (IFNt) contributes towards maternal recognition of pregnancy in ruminants (like, cattle, buffalo, goat, giraffe). IFNt has been extensively studied in most of the ruminants except for buffalo Bubalus bubalis). The present study has been undertaken to predict the secondary structure of Interferon-tau in buffalo. The available amino acid sequence of bubaline IFNt (sequence database...

We consider the higher order Schrödinger operator H=(−Δ)m+V(x) in n dimensions with real-valued potential V when n>4m−1, m∈N. show that for any 2nn−4m+13 2nn−3<p≤∞ insufficiently differentiable...

Abstract N‐ or C‐methylation in natural and synthetic cyclic peptides can increase membrane permeability, but it remains unclear why this happens some cases not others. Here we compare three‐dimensional structures for from six families, including isomers differing only the location of an Cα‐methyl substituent. We show that a single methyl group increases permeability when connects expands hydro...

Three-dimensional structure and amino acid sequence of proteins are related by an unknown set of rules that is often referred to as the folding code. This code is believed to be significantly influenced by nonlocal interactions between the residues. A quantitative description of nonlocal contacts requires the identification of neighboring residues. We applied statistical geometry approach to an...

BACKGROUND Oxygen-base (O-base) oxidation in protein backbone is important in the protein backbone fragmentation due to the attack from reactive oxygen species (ROS). In this study, an alanine peptide was used model system to investigate this O-base oxidation by employing density functional theory (DFT) calculations combining with continuum solvent model. Detailed reaction steps were analyzed a...

Tertiary structure prediction of a protein from its amino acid sequence is one of the major challenges in the field of bioinformatics. Hierarchical approach is one of the persuasive techniques used for predicting protein tertiary structure, especially in the absence of homologous protein structures. In hierarchical approach, intermediate states are predicted like secondary structure, dihedral a...