A comprehensive analysis of non-sequential alignments between all protein structures

<p>Abstract</p> <p>Background</p> <p>The majority of relations between proteins can be represented as a conventional sequential alignment. Nevertheless, unusual non-sequential alignments with different connectivity of the aligned fragments in compared proteins have been reported by many researchers. It is interesting to understand those non-sequential alignments; are they unique, sporadic cases or they occur frequently; do they belong to a few specific folds or spread among many different folds, as a common feature of protein structure. We present here a comprehensive large-scale study of non-sequential alignments between available protein structures in Protein Data Bank.</p> <p>Results</p> <p>The study has been conducted on a non-redundant set of 8,865 protein structures aligned with the aid of the TOPOFIT method. It has been estimated that between 17.4% and 35.2% of all alignments are non-sequential depending on variations in the parameters. Analysis of the data revealed that non-sequential relations between proteins do occur systematically and in large quantities. Various sizes and numbers of non-sequential fragments have been observed with all possible complexities of fragment rearrangements found for alignments consisting of up to 12 fragments. It has been found that non-sequential alignments are not limited to proteins of any particular fold and are present in more than two hundred of them. Moreover, many of them are found between proteins with different fold assignments. It has been shown that protein structure symmetry does not explain non-sequential alignments. Therefore, compelling evidences have been provided that non-sequential alignments between proteins are systematic and widespread across the protein universe.</p> <p>Conclusion</p> <p>The phenomenon of the widespread occurrence of non-sequential alignments between proteins might represent a missing rule of protein structure organization. More detailed study of this phenomenon will enhance our understanding of protein stability, folding, and evolution.</p

Rings of formal matrices close to regular

© 2015, Allerton Press, Inc. We give a description of rings of formalmatrices belonging to one of the following classes of rings: semiartinian rings, max-rings, V -rings, SV -rings. We study semiartinian SSP-rings and SSP-rings of formal matrices

Regular semiartinian rings

We study the structure of rings over which every right module is an essential extension of a semisimple module by an injective one. A ring R is called a right max-ring if every nonzero right R-module has a maximal submodule. We describe normal regular semiartinian rings whose endomorphism ring of the minimal injective cogenerator is a max-ring. © 2012. Allerton Press, Inc

Generalized SV -rings of bounded index of nilpotency

We obtain a criterion under which all right modules over a ring of bounded index are weakly regular. © 2011 Allerton Press, Inc

Generalized SV-modules

Given an arbitrary quasiprojective right R-module P, we prove that every module in the category σ(P) is weakly regular if and only if every module in σ(M/I(M)) is lifting, where M is a generating object in σ(P). In particular, we describe the rings over which every right module is weakly regular. © 2009 Pleiades Publishing, Ltd

RIBFIND: a web server for identifying rigid bodies in protein structures and to aid flexible fitting into cryo EM maps

Motivation: To better analyze low-resolution cryo electron microscopy maps of macromolecular assemblies, component atomic structures frequently have to be flexibly fitted into them. Reaching an optimal fit and preventing the fitting process from getting trapped in local minima can be significantly improved by identifying appropriate rigid bodies in the fitted component. Results: Here we present the RIBFIND server, a tool for identifying rigid bodies in protein structures. The server identifies rigid bodies in proteins by calculating spatial proximity between their secondary structural elements. Availability: The RIBFIND web server and its standalone program are available at http://ribfind.ismb.lon.ac.uk

Fully idempotent homomorphisms

For arbitrary modules A and B we introduce and study the notion of a fully idempotent Hom (A, B). As a corollary we obtain some well-known properties of fully idempotent rings and modules. © 2011 Allerton Press, Inc

Weakly regular modules over normal rings

Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right R-module M, we prove that every module in the category σ(M) is weakly regular if and only if each module in σ(M) is either semisimple or contains a nonzero M-injective submodule. We describe the normal rings over which all modules are weakly regular. © 2008 Pleiades Publishing, Ltd

On some classes of semiartinian rings

The weakly regularity of all right R-modules with R an arbitrary ring does not imply the same property of all left R-modules. We describe the rings over which every right and left module is weakly regular and also obtain some description of semiartinian CSL-rings. © 2012 Pleiades Publishing, Ltd