Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the associated extended expressions called hairpin expressions. More precisely, we extend partial derivation of regular expressions to two-sided partial derivation of hairpin expressions and we show how to deduce a recognizer for a hairpin expression from its two-sided derived term automaton, providing an alternative proof of the fact that hairpin completions of regular languages are linear context-free.Comment: 28 page

It Is NL-complete to Decide Whether a Hairpin Completion of Regular Languages Is Regular

The hairpin completion is an operation on formal languages which is inspired by the hairpin formation in biochemistry. Hairpin formations occur naturally within DNA-computing. It has been known that the hairpin completion of a regular language is linear context-free, but not regular, in general. However, for some time it is was open whether the regularity of the hairpin completion of a regular language is is decidable. In 2009 this decidability problem has been solved positively by providing a polynomial time algorithm. In this paper we improve the complexity bound by showing that the decision problem is actually NL-complete. This complexity bound holds for both, the one-sided and the two-sided hairpin completions

Hairpin lengthening: algorithmic results.

We consider here a new variant of the hairpin completion, called hairpin lengthening, which seems more appropriate for practical implementation. The variant considered here concerns the lengthening of the word that forms a hairpin structure, such that this structure is preserved, without necessarily completing the hairpin. Although our motivation is based on biological phenomena, the present paper is more about some algorithmic properties of this operation. Finally, we propose an algorithm for computing the hairpin lengthening distance between two words in quadratic time

Formal models of the extension activity of DNA polymerase enzymes

The study of formal language operations inspired by enzymatic actions on DNA is part of ongoing efforts to provide a formal framework and rigorous treatment of DNA-based information and DNA-based computation. Other studies along these lines include theoretical explorations of splicing systems, insertion-deletion systems, substitution, hairpin extension, hairpin reduction, superposition, overlapping concatenation, conditional concatenation, contextual intra- and intermolecular recombinations, as well as template-guided recombination. First, a formal language operation is proposed and investigated, inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called the primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called the template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. This language operation is called L1-directed extension of L2 and the closure properties of various language classes, including the classes in the Chomsky hierarchy, are studied under directed extension. Furthermore, the question of finding necessary and sufficient conditions for a given language of target strings to be generated from a given template language when the primer language is unknown is answered. The canonic inverse of directed extension is used in order to obtain the optimal solution (the minimal primer language) to this question. The second research project investigates properties of the binary string and language operation overlap assembly as defined by Csuhaj-Varju, Petre and Vaszil as a formal model of the linear self-assembly of DNA strands: The overlap assembly of two strings, xy and yz, which share an overlap y, results in the string xyz. In this context, we investigate overlap assembly and its properties: closure properties of various language families under this operation, and related decision problems. A theoretical analysis of the possible use of iterated overlap assembly to generate combinatorial DNA libraries is also given. The third research project continues the exploration of the properties of the overlap assembly operation by investigating closure properties of various language classes under iterated overlap assembly, and the decidability of the completeness of a language. The problem of deciding whether a given string is terminal with respect to a language, and the problem of deciding if a given language can be generated by an overlap assembly operation of two other given languages are also investigated

Synthetic RNA modules for fine-tuning gene expression levels in yeast by modulating RNase III activity

The design of synthetic gene networks requires an extensive genetic toolbox to control the activities and levels of protein components to achieve desired cellular functions. Recently, a novel class of RNA-based control modules, which act through post-transcriptional processing of transcripts by directed RNase III (Rnt1p) cleavage, were shown to provide predictable control over gene expression and unique properties for manipulating biological networks. Here, we increase the regulatory range of the Rnt1p control elements, by modifying a critical region for enzyme binding to its hairpin substrates, the binding stability box (BSB). We used a high throughput, cell-based selection strategy to screen a BSB library for sequences that exhibit low fluorescence and thus high Rnt1p processing efficiencies. Sixteen unique BSBs were identified that cover a range of protein expression levels, due to the ability of the sequences to affect the hairpin cleavage rate and to form active cleavable complexes with Rnt1p. We further demonstrated that the activity of synthetic Rnt1p hairpins can be rationally programmed by combining the synthetic BSBs with a set of sequences located within a different region of the hairpin that directly modulate cleavage rates, providing a modular assembly strategy for this class of RNA-based control elements

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Insights into DNA platination within unusual structural settings

2D [1H, 15N] HSQC NMR spectroscopy has been used to monitor reaction and product formation between [Pt(15NH3)2I2] and nucleic acids possessing irregular topologies and containing site specific phosphorothioate substitution in the phosphodiester backbone. Comparison of the reaction profiles of dimer nucleic acids with and without phosphorothioate substitution is made with their short nucleic acid counterparts containing the key dimer components. Whereas d(GpA) is relatively unreactive towards [Pt(15NH3)2I2], NMR evidence suggests that the tandem sheared mismatch duplex d(GCG3pAGC)2 reacts to form the head-to-tail inter-strand G3-N7-Pt-G3-N7 cross-link. The equivalent phosphorothioate R,S-d(GsA) reacts to form a mono-iodo, mono-sulphur adduct, whereas the tandem sheared mismatch phosphorothioate duplex d(GCGsAG5C)2 (VIs) reacts to form the unusual intra-strand macrochelate [Pt(15NH3)2{d(VIs-G5-N7)},S]2+ in which platinum is attached at both sulphur and G5-N7. Experimental evidence supports the formation of a stabilized mismatch duplex in which platinum is attached to two nitrogen centres in the sequence d(CGCGpTGCG) in contrast to R,S-d(CGCGsT5GCG) for which NMR evidence supports macrochelate-stabilized hairpin loop formation cross-linked at both phosphorothioate sulphur and T5-N

Conformational Dynamics of metallo-β-lactamase CcrA during Catalysis Investigated by Using DEER Spectroscopy

Previous crystallographic and mutagenesis studies have implicated the role of a position-conserved hairpin loop in the metallo-β-lactamases in substrate binding and catalysis. In an effort to probe the motion of that loop during catalysis, rapid-freeze-quench double electron–electron resonance (RFQ-DEER) spectroscopy was used to interrogate metallo-β-lactamase CcrA, which had a spin label at position 49 on the loop and spin labels (at positions 82, 126, or 233) 20–35 Å away from residue 49, during catalysis. At 10 ms after mixing, the DEER spectra show distance increases of 7, 10, and 13 Å between the spin label at position 49 and the spin labels at positions 82, 126, and 233, respectively. In contrast to previous hypotheses, these data suggest that the loop moves nearly 10 Å away from the metal center during catalysis and that the loop does not clamp down on the substrate during catalysis. This study demonstrates that loop motion during catalysis can be interrogated on the millisecond time scale