On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

Cyclization of pyrrhocoricin retains structural elements crucial for the antimircobial activity of the native peptide

Pyrrhacoricin is a naturally occurring antimicrobial peptide from the European fire bug Pyrrhocoris apterus. It has submicromolar activity against a range of Gram-negative bacterial strains and has created recent interest as a lead for the development of novel antibiotic compounds. In this study, we have used NMR spectroscopy to determine the solution structures of pyrrhocoricin and a synthetic macrocyclic derivative that has improved in vivo pharmaceutical properties. Native pyrrhocoricin is largely disordered in solution, but there is evidence of a subpopulation with ordered turn regions over residues 2-5, 4-7, and 16-19. The macrocyclic derivative incorporates a nine amino acid linker joining the N- and C-termini, which does not adversely affect the antimicrobial potency but leads to a broader spectrum of activity. The NMR data suggest that the turn conformations in the cyclic derivative are similar to those in the native form, thus implicating them in the biological function. (C) 2004 Wiley Periodicals, Inc.

Structure of circulin B and implications for antimicrobial activity of the cyclotides

The solution structure of one of the first members of the cyclotide family of macrocyclic peptides to be discovered, circulin B has been determined and compared with that of circulin A and related cyclotides. Cyclotides are mini-proteins derived from plants that have the characteristic features of a head-to-tail cyclised peptide backbone and a knotted arrangement of their three disulfide bonds. First discovered because of their uterotonic or anti-HIV activity, they have also been reported to have activity against a range of Gram positive and Gram negative bacteria as well as fungi. The aim of the current study was to develop structure-activity relationships to rationalise this antimicrobial activity. Comparison of cyclotide structures and activities suggests that the presence and location of cationic residues may be a requirement for activity against Gram negative bacteria. Understanding the topological differences associated with the antimicrobial activity of the cyclotides is of significant interest and potentially may be harnessed for pharmaceutical applications.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.