End invasion of peptide nucleic acids (PNAs) with mixed-base composition into linear DNA duplexes

Peptide nucleic acid (PNA) is a synthetic DNA mimic with valuable properties and a rapidly growing scope of applications. With the exception of recently introduced pseudocomplementary PNAs, binding of common PNA oligomers to target sites located inside linear double-stranded DNAs (dsDNAs) is essentially restricted to homopurine–homopyrimidine sequence motifs, which significantly hampers some of the PNA applications. Here, we suggest an approach to bypass this limitation of common PNAs. We demonstrate that PNA with mixed composition of ordinary nucleobases is capable of sequence-specific targeting of complementary dsDNA sites if they are located at the very termini of DNA duplex. We then show that such targeting makes it possible to perform capturing of designated dsDNA fragments via the DNA-bound biotinylated PNA as well as to signal the presence of a specific dsDNA sequence, in the case a PNA beacon is employed. We also examine the PNA–DNA conjugate and prove that it can initiate the primer-extension reaction starting from the duplex DNA termini when a DNA polymerase with the strand-displacement ability is used. We thus conclude that recognition of duplex DNA by mixed-base PNAs via the end invasion has a promising potential for site-specific and sequence-unrestricted DNA manipulation and detection.National Institutes of Health (CA74175, GM059173); Boston University (PIF and SPRING awards

End invasion of peptide nucleic acids (PNAs) with mixed-base composition into linear DNA duplexes

Peptide nucleic acid (PNA) is a synthetic DNA mimic with valuable properties and a rapidly growing scope of applications. With the exception of recently introduced pseudocomplementary PNAs, binding of common PNA oligomers to target sites located inside linear double-stranded DNAs (dsDNAs) is essentially restricted to homopurine–homopyrimidine sequence motifs, which significantly hampers some of the PNA applications. Here, we suggest an approach to bypass this limitation of common PNAs. We demonstrate that PNA with mixed composition of ordinary nucleobases is capable of sequence-specific targeting of complementary dsDNA sites if they are located at the very termini of DNA duplex. We then show that such targeting makes it possible to perform capturing of designated dsDNA fragments via the DNA-bound biotinylated PNA as well as to signal the presence of a specific dsDNA sequence, in the case a PNA beacon is employed. We also examine the PNA–DNA conjugate and prove that it can initiate the primer-extension reaction starting from the duplex DNA termini when a DNA polymerase with the strand-displacement ability is used. We thus conclude that recognition of duplex DNA by mixed-base PNAs via the end invasion has a promising potential for site-specific and sequence-unrestricted DNA manipulation and detection.National Institutes of Health (CA74175, GM059173); Boston University (PIF and SPRING awards

Master equation approach to DNA-breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.Comment: 12 pages, 8 figure

Ribbon polymers in poor solvents: layering transitions in annular and tubular condensates

We study the structures of a ribbon or ladder polymer immersed in poor solvents. The anisotropic bending rigidity coupled with the surface tension leads ribbon polymers to spontaneous formation of highly anisotropic condensates in poor solvents. Unlike ordinary flexible polymers these condensates undergo a number of distinct layering transitions as a function of chain length or solvent quality, and the size of condensates becomes non-monotonic function of chain length. We show that the fluctuations of the condensates are in general small and these condensates are stable.Comment: 5 pages, 5 figures, visulaize missing figure number

Gauge vortex dynamics at finite mass of bosonic fields

The simple derivation of the string equation of motion adopted in the nonrelativistic case is presented, paying the special attention to the effects of finite masses of bosonic fields of an Abelian Higgs model. The role of the finite mass effects in the evaluation of various topological characteristics of the closed strings is discussed. The rate of the dissipationless helicity change is calculated. It is demonstrated how the conservation of the sum of the twisting and writhing numbers of the string is recovered despite the changing helicity.Comment: considerably revised to include errata to journal versio

On topological interpretation of quantum numbers

It is shown how one can define vector topological charges for topological exitations of non-linear sigma-models on compact homogeneous spaces T_G and G/T_G (where G is a simple compact Lie group and T_G is its maximal commutative subgroup). Explicit solutions for some cases, their energies and interaction of different topological charges are found. A possibility of the topological interpretation of the quantum numbers of groups and particles is discussed.Comment: 20 pages, Latex 2e, modified versio

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For the semilinear heat equation $u_t= \Delta u+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure

Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references added