Graph algorithms for DNA sequencing – origins,current models and the future

With the ubiquitous presence of next-generation sequencing in modern biological, genetic, pharmaceutical and medical research, not everyone pays attention to the underlying computational methods. Even fewer researchers know what were the origins of the current models for DNA assembly. We present original graph models used in DNA sequencing by hybridization, discuss their properties and connections between them. We also explain how these graph models evolved to adapt to the characteristics of next-generation sequencing. Moreover, we present a practical comparison of state-of-the-art DNA de novo assembly tools representing these transformed models, i.e. overlap and decomposition-based graphs. Even though the competition is tough, some assemblers perform better and certainly large differences may be observed in hardware resources utilization. Finally, we outline the most important trends in the sequencing field, and try to predict their impact on the computational models in the future.     

On the Generalized Strongly Nil-Clean Property of Matrix Rings

Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n × n matrix A over R is expressible as a sum A =E1 +…+ Es + N of (commuting) idempotent matrices Ei and a nilpotent matrix N.     

Multi-dimensional scalar balance laws with discontinuous flux

We consider scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect to both the space variable x and the unknown quantity u. We formulate the definition of entropy weak solutions and provide existence and uniqueness to the considered problem. The problem is formulated in the framework of multi-valued mappings. The notion of entropy measure-valued solutions is used to prove the so-called contraction principle and comparison principle.     

Convergence of a finite difference method for the time-fractional diffusion equation with concentrated capacity

We investigate the convergence of difference scheme for the time-fractional differential equation with fractional derivative of an order with the coefficient at the time derivative containing Dirac delta distribution. Convergence order of is proved. A numerical example demonstrates the theoretical results. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unified encoding for hyper-heuristics with application to bioinformatics

This paper introduces a new approach to applying hyper-heuristic algorithms to solve combinatorial problems with less effort, taking into account the modelling and algorithm construction process. We propose a unified encoding of a solution and a set of low level heuristics which are domain-independent and which change the solution itself. This approach enables us to address NP-hard problems and generate good approximate solutions in a reasonable time without a large amount of additional work required to tailor search methodologies for the problem in hand. In particular, we focused on solving DNA sequencing by hybrydization with errors, which is known to be strongly NP-hard. The approach was extensively tested by solving multiple instances of well-known combinatorial problems and compared with results generated by meta heuristics that have been tailored for specific problem domains.     

Temperature-sensitive behaviour of poly(glycidol)-b-poly(N-isopropylacrylamide) block copolymers

Temperature-sensitive poly(glycidol)-b-poly(N-isopropylacrylamide) block copolymers (PGl₅₅PNIPAAm_y) were synthesised and their aqueous solutions investigated by different methods including differential scanning calorimetry (DSC), UV-VIS spectroscopy as well as dynamic and static light scattering. The cloud point temperature (T _c) depended on the composition of the investigated block copolymers and increased with decreasing length of the PNIPAAm block in PGl₅₅PNIPAAm_y copolymers. In contrast, the enthalpy of phase separation of PNIPAAm segments measured by DSC decreased with decreasing length of the PNIPAAm block in the polymer. These findings can be correlated with the behaviour of homo-PNIPAAm with similar molecular weights indicating that the influence of PGl on the local environment and phase separation of PNIPAAm chains is similar to the influence observed for PNIPAAm chains bearing different low molecular weight end group. Using DLS measurement, it was shown that the aggregation process depended on the PGl/PNIPAAm block ratio. If the PGl/PNIPAAm ratio was low, stable core-shell aggregates were formed. In contrast, the tendency to formation of large unstable, loose aggregates was observed for copolymers with high PGl/PNIPAAm ratio.     

Synthesis,Characterization and Biological Investigations of Half-Sandwich Ruthenium(II) Complexes Containing Benzimidazole Moiety

Half-sandwich Ru(II) complexes belong to group of biologically active metallo-compounds with promising antimicrobial and anticancer activity. Herein, we report the synthesis and characterization of arene ruthenium complexes containing benzimidazole moiety, namely, [(η⁶-p-cymene)RuCl(bimCOO)] (1) and [(η⁶-p-cymene)RuCl₂(bim)] (2) (where bimCOO = benzimidazole-2-carboxylate and bim = 1-H-benzimidazole). The compounds were characterized by ¹H NMR, ¹³C NMR, IR, UV–vis and CV. Molecular structures of the complexes were determined by SC-XRD analysis, and the results indicated the presence of a pseudo-tetrahedral (piano stool) geometry. Interactions in the crystals of the Ru complexes using the Hirshfeld surface analysis were also examined. In addition, the biological studies of the complexes, such as antimicrobial assays (against planktonic and adherent microbes), cytotoxicity and lipophilicity, were performed. Antibacterial activity of the complexes was evaluated against S. aureus, E. coli, P. aeruginosa PAO1 and LES B58. Cytotoxic activity was tested against primary human fibroblasts and adenocarcinoma human alveolar basal epithelial cells. Obtained biological results show that the ruthenium compounds have bacteriostatic activity toward Pseudomonas aeruginosa PAO1 strain and are not toxic to normal cells. A molecular docking study was applied as a predictive source of information about the plausibility of examined structures binding with HSA as a transporting system.