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

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

Stepwise Translocation of Dpo4 Polymerase during Error-Free Bypass of an oxoG Lesion

7,8-dihydro-8-oxoguanine (oxoG), the predominant lesion formed following oxidative damage of DNA by reactive oxygen species, is processed differently by replicative and bypass polymerases. Our kinetic primer extension studies demonstrate that the bypass polymerase Dpo4 preferentially inserts C opposite oxoG, and also preferentially extends from the oxoG•C base pair, thus achieving error-free bypass of this lesion. We have determined the crystal structures of preinsertion binary, insertion ternary, and postinsertion binary complexes of oxoG-modified template-primer DNA and Dpo4. These structures provide insights into the translocation mechanics of the bypass polymerase during a complete cycle of nucleotide incorporation. Specifically, during noncovalent dCTP insertion opposite oxoG (or G), the little-finger domain–DNA phosphate contacts translocate by one nucleotide step, while the thumb domain–DNA phosphate contacts remain fixed. By contrast, during the nucleotidyl transfer reaction that covalently incorporates C opposite oxoG, the thumb-domain–phosphate contacts are translocated by one nucleotide step, while the little-finger contacts with phosphate groups remain fixed. These stepwise conformational transitions accompanying nucleoside triphosphate binding and covalent nucleobase incorporation during a full replication cycle of Dpo4-catalyzed bypass of the oxoG lesion are distinct from the translocation events in replicative polymerases

Consecutive non-natural PZ nucleobase pairs in DNA impact helical structure as seen in 50 μs molecular dynamics simulations

Little is known about the influence of multiple consecutive ‘non-standard’ (Z, 6-amino-5-nitro-2(1H)-pyridone, and P, 2-amino-imidazo[1,2-a]-1,3,5-triazin-4(8H)-one) nucleobase pairs on the structural parameters of duplex DNA. P:Z nucleobase pairs follow standard rules for Watson–Crick base pairing but have rearranged hydrogen bonding donor and acceptor groups. Using the X-ray crystal structure as a starting point, we have modeled the motions of a DNA duplex built from a self-complementary oligonucleotide (5΄-CTTATPPPZZZATAAG-3΄) in water over a period of 50 μs and calculated DNA local parameters, step parameters, helix parameters, and major/minor groove widths to examine how the presence of multiple, consecutive P:Z nucleobase pairs might impact helical structure. In these simulations, the PZ-containing DNA duplex exhibits a significantly wider major groove and greater average values of stagger, slide, rise, twist and h-rise than observed for a ‘control’ oligonucleotide in which P:Z nucleobase pairs are replaced by G:C. The molecular origins of these structural changes are likely associated with at least two differences between P:Z and G:C. First, the electrostatic properties of P:Z differ from G:C in terms of density distribution and dipole moment. Second, differences are seen in the base stacking of P:Z pairs in dinucleotide steps, arising from energetically favorable stacking of the nitro group in Z with π–electrons of the adjacent base

Proton tunneling in hydrogen bonds and its implications in an induced-fit model of enzyme catalysis

The role of proton tunneling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyzes the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.Comment: 15 pages, 4 figures. Authors postprint versio

Coarse-grained simulations of RNA and DNA duplexes

Although RNAs play many cellular functions little is known about the dynamics and thermodynamics of these molecules. In principle, all-atom molecular dynamics simulations can investigate these issues, but with current computer facilities, these simulations have been limited to small RNAs and to short times. HiRe-RNA, a recently proposed high-resolution coarse-grained for RNA that captures many geometric details such as base pairing and stacking, is able to fold RNA molecules to near-native structures in a short computational time. So far it had been applied to simple hairpins, and here we present its application to duplexes of a couple dozen nucleotides and show how with our model and with Replica Exchange Molecular Dynamics (REMD) we can easily predict the correct double helix from a completely random configuration and study the dissociation curve. To show the versatility of our model, we present an application to a double stranded DNA molecule as well. A reconstruction algorithm allows us to obtain full atom structures from the coarse-grained model. Through atomistic Molecular Dynamics (MD) we can compare the dynamics starting from a representative structure of a low temperature replica or from the experimental structure, and show how the two are statistically identical, highlighting the validity of a coarse-grained approach for structured RNAs and DNAs.Comment: 28 pages, 11 figure