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We present three linear algorithms for as many formulations of the problem of finding motifs with gaps. The three versions of the problem are distinct in that they assume different constraints on the size of the gaps. The outline of the algorithm is always the same, although this is adapted each time to the specific problem, while maintaining a linear time complexity with respect to the input size. The approach we suggest is based on a re-writing of the text that uses a new alphabet made of labels representing words of the original input text. The computational complexity of the algorithm allows the use of it also to find long motifs. The algorithm is in fact general enough that it could be applied to several variants of the problem other than those suggested in this paper.

The purpose of this paper is to present various algebraic views of multisets, and certain connections between the theory of multisets (with multiplicities in the semiring of positive integers) and natural computing, in particular membrane and DNA computing. We introduce a Gödel encoding of multisets, and find some results regarding this encoding together with new connections and interpretations. We also introduce the norm of a multiset and we find some relationships between multiset theory and number theory.

A nonempty circular string C(x) of length n is said to be covered by a set U_k of strings each of fixed length k≤n iff every position in C(x) lies within an occurrence of some string u∈U_k. In this paper we consider the problem of determining the minimum cardinality of a set U_k which guarantees that every circular string C(x) of length n≥k can be covered. In particular, we show how, for any positive integer m, to choose the elements of U_k so that, for sufficiently large k, u_k≈σ^k–m, where u_k=|U_k| and σ is the size of the alphabet on which the strings are defined. The problem has application to DNA sequencing by hybridization using oligonucleotide probes.

A brief summary is provided of selected current activities in the field of nanoelectronics, which is taken here to mean the fabrication and integration of active microelectronic components with feature dimensions of tens of nanometers or less. Particular emphasis is placed upon the classes of nanoelectronic devices that were discussed at the 2002 WOFE Conference.

Terahertz signal transmission in DNA is simulated and analyzed using molecular dynamics and digital signal processing techniques to demonstrate that signals encoded in vibrational movements of hydrogen bonds can travel along the backbone of DNA and eventually be recovered and analyzed using digital signal processing techniques.

Biomolecules such as DNA and proteins exhibit a wealth of modes in the Terahertz (THz) range from the rotational, vibrational and stretching modes of biomolecules. Many materials such as drywall that are opaque to human eyes are transparent to THz. Therefore, it can be used as a powerful tool for biomolecular sensing, biomedical analysis and through-the-wall imaging. Experiments were carried out to study the absorption of various materials including DNA and see-through imaging of drywall using FTIR spectrometer and Time Domain Spectroscopy (TDS) system.

The convergence of terahertz spectroscopy and single molecule experimentation offers significant promise of enhancement in sensitivity and selectivity in molecular recognition, identification and quantitation germane to military and security applications. This paper provides a brief overview of the constraints set by single molecule recognition systems and reports the results of experiments which address fundamental barriers to the integration of large, patterned bio-compatible molecular opto-electronic systems with silicon based microelectronic systems. Central to this thrust is an approach involving sequential epitaxy on surface bound single stranded DNA one-dimensional substrates. The challenge of producing highly structured macromolecular substrates, which are necessary in order to implement molecular nanolithography, has been addressed experimentally by combining “designer” synthetic DNA with biosynthetically derived plasmid components. By design, these one dimensional templates are composed of domains which contain sites which are recognized, and therefore addressable by either complementary DNA sequences and/or selected enzymes. Such design is necessary in order to access the nominal 2 nm linewidth potential resolution of nanolithography on these one-dimensional substrates. The recognition and binding properties of DNA ensure that the lithographic process is intrinsically self-organizing, and therefore self-aligning, a necessity for assembly processes at the requisite resolution. Another requirement of this molecular epitaxy approach is that the substrate must be immobilized. The challenge of robust surface immobilization is being addressed via the production of the equivalent of molecular tube sockets. In this application, multi-valent core-shell fluorescent quantum dots provide a mechanism to prepare surface attachment sites with a pre-determined 1:1 attachment site : substrate (DNA) molecule ratio.

A novel nanoscale-engineering methodology is presented that has potential for the first-time development of a microscope-system capable of collecting terahertz (THz) frequency spectroscopic signatures from microscopic biological (bio) structures. This unique THz transmission microscopy approach is motivated by prior studies on bio-materials and bio-agents (e.g., DNA, RNA and bacterial spores) that have produced spectral features within the THz frequency regime (i.e., ~ 300 GHz to 1000 GHz) that appear to be representative of the internal structure and characteristics of the constituent bio-molecules. The suggested THz transmission microscopy is a fundamentally new technological approach that seeks to avoid the limitations that exist in traditional experiments (i.e., that must average over large numbers of microscopic molecules) by prescribing a viable technique whereby the THz frequency signatures may be collected from individual bio-molecules and/or microscopic biological constructs. Specifically, it is possible to envision the development of a “nanoscale imaging array” that possesses the characteristics necessary (e.g., sub-wavelength resolution) for successfully performing “THz-frequency microscopy.”

Pathogen diseases cause considerable loses in production of food which impact human health from diverse bacterial/viral infections. Precise spotting and diagnosis of such infectious disease is significant to prevent it from further outbreak issues. Moreover, to detect this kind of diseases at an early stage with highly sensitive and selective basis is necessary to avoid the spread of invasive pathogens. The conventional methods such as ELISA, PCR techniques are currently in use to diagnose bacterial/viral disease with high throughput. Though these diagnostic techniques assist in detect and identify the diseases, there are few modern challenges to be meet in order to make this diagnostic more effective in recent days. In this paper, our designed device consists of Bionanosensor works on nucleic acid-based testing provides result with high specificity and selectivity which is vital for early stage identification in a rapid real-time effective manner

The Duke–Rubinstein model of gel electrophoresis is applied to calculate the velocity of DNA molecules. We have found that the velocity distribution becomes flat at high electric fields. Simultaneously, the percentage of immobile molecules increases. Effectively, the mean velocity starts to decrease at high fields. The field value, where the mean velocity is maximal, decreases with the molecule length. The results are compared with those from similar calculations obtained by Heukelum and Beljaars within the cage model.

We study the interplay of the tautomeric transitions amino/keto → imino/enol of DNA base pairs and the elastic properties of the DNA, by employing the numerical simulation of the nonlinear and nonlocal Schrödinger equation that describes the concerted tunneling of protons in the hydrogen bonds of base pairs. We show that the dynamics of tunneling is characterized by solitary waves for the tunneling amplitudes. The velocity of solitons is generally small, of the order 10^-3–10^-2cm/sec. We also found a phenomenon similar to the freak wave of nonlinear theory; in the context of DNA, it means that the conformation of the base pairs and the proton states, for which a tautomeric transition is only of low probability, could move along the DNA molecule and focus on a smaller set of base pairs so that the rate of transition increases. This result may have a bearing on the phenomenon of spontaneous mutations. We suggest that the irradiation of DNA with electromagnetic waves at frequencies in the infrared region, corresponding to the proton tunneling, could cause mutations.

A multiscale approach is used to simulate the translocation of DNA through a nanopore. Within this scheme, the interactions of the molecule with the surrounding fluid (solvent) are explicitly taken into account. By generating polymers of various initial configurations and lengths we map the probability distibutions of the passage times of the DNA through the nanopore. A scaling law behavior for the most probable of these times with respect to length is derived, and shown to exhibit an exponent that is in a good agreement with the experimental findings. The essential features of the DNA dynamics as it passes through the pore are explored.

In this paper, we show the reaction of a hydroxyl, phenyl and phenoxy radicals with DNA base pairs by the density functional theory (DFT) calculations. The influence of solvation on the mechanism is also presented by the same DFT calculations under the continuum solvation model. The results showed that hydroxyl, phenyl and phenoxy radicals increase the length of the nearest hydrogen bond of adjacent DNA base pair which is accompanied by decrease in the length of furthest hydrogen bond of DNA base pair. Also, hydroxyl, phenyl and phenoxy radicals influenced the dihedral angle between DNA base pairs. According to the results, hydrogen bond lengths between AT and GC base pairs in water solvent are longer than vacuum. All of presented radicals influenced the structure and geometry of AT and GC base pairs, but phenoxy radical showed more influence on geometry and electronic properties of DNA base pairs compared with the phenyl and hydroxyl radicals.

Mathematical and numerical models for studying the electrophoresis of topologically nontrivial molecules in two and three dimensions are presented. The molecules are modeled as polygons residing on a square lattice and a cubic lattice whereas the electrophoretic media of obstacle network are simulated by removing vertices from the lattices at random. The dynamics of the polymeric molecules are modeled by configurational readjustments of segments of the polygons. Configurational readjustments arise from thermal fluctuations and they correspond to piecewise reptation in the simulations. A Metropolis algorithm is introduced to simulate these dynamics, and the algorithms are proven to be reversible and ergodic. Monte Carlo simulations of steady field random obstacle electrophoresis are performed and the results are presented.

Localization property in the disordered few-chain DNA systems with a long-range correlation is numerically investigated. We apply the chain system with the correlated disorder in the interchain and/or intrachain hoppings to the simple model of a double strand of DNA. Numerical results for the density of states and the Lyapunov exponent of the wave function in the two- or three-chain models are given. It is found that the correlation effect enhances the localization length (the inverse least non-negative Lyapunov exponent) around the band center.

We revisit the problem of the electronic properties of a single strand of DNA, formulating the Hückel approximation for π-electrons in both the sugar-phosphate backbone chain and the π-stacking of nitrogenous bases in a single strand of DNA where the nitrogenous bases are adenine (A), guanine (G), cytosine (C) and thymine (T), respectively. We calculate the electronic band structure of π-electrons: (i) in the single nitrogenous base molecules such as A, G, C and T, (ii) in the single sugar-phosphate molecule, (iii) in the single nucleotide systems such as A, G, C, T with the single sugar-phosphate group, and (iv) in the system of a single strand of DNA with an infinite repetition of a nucleotide such as A, G, C and T, respectively. We find the following: In the case of (i), there is an energy gap between the energy levels for the HOMO and LUMO in the nitrogenous base. This guarantees the semiconducting character of the bases as a mother material. In the case of (ii), there are the HOMO localized at the oxygen site with a double bond and the LUMO localized around the phosphorus atom, which have a quite large energy gap. In the case of (iii), the energy levels for the HOMO and LUMO of the nitrogenous base remain almost the same as those of the nucleotide, while those of the sugar-phosphate group remain the same as well. The HOMO of the sugar-phosphate group exists right below the HOMO of the nitrogenous base. Therefore, comparing the energy levels for the HOMOs of the nitrogenous base group with those of the sugar-phosphate group, the nitrogenous base group behaves as a donor while the sugar-phosphate group behaves as an acceptor. In the case of (iv), there are energy bands and band gaps for the extended states in the nitrogenous base group and the sugar-phosphate group as well as the discrete levels for the localized states at the phosphate site in the spectrum. There is a transition from semiconductor to semimetal as the π-electron hopping between the nitrogenous bases of nucleotide is increased. The details of the above will be discussed in the present paper. Thus, we show the powerfulness of the Hückel theory in the study of DNA as well, although this theory is, at the first glance, oversimplified and purely phenomenological.

A statistical mechanical model was used to calculate the curvature of the 5 chemically synthesized DNAs which contain repeats sequences (CCTG)_n · (CAGG)_n and (ATTCT)_n · (AGAAT)_n associated with human diseases. 8% polyacrylamide gel analyses were also performed for these 5 DNAs. The results indicate the curvature of the sequences CCTG/bend and ATTCT/bend are larger than that of the sequences CCTG/straight and ATTCT/straight. The curvature of straight/bend is larger than that of CCTG/straight and ATTCT/straight, and smaller than that of CCTG/bend and ATTCT/bend. There exists good consistent between theoretical prediction and experimental data.

The factors that affect the structures and stability of the adducts of cisamminedichloro(2-methylpyridine)platinum(II) with a duplex DNA were probed into by the mixed quantum chemistry and molecular mechanics (QM/MM), molecular dynamics (MD) and molecular mechanics (MM) methods. It shows that the coordinate bonds between Pt and N7G, the hydrogen bond between the amine and O6G, the weak interactions between drug molecule and DNA and the positive electron charge center position of the drug molecule in the adduct affect the stability and the steric selection of the adduct greatly. And in return the structure of the adduct determine the comparatively strengths of the coordinate bonds in the adduct.

We have thoroughly analyzed the electronic structure of stacked DNA Watson–Crick (WC) base pair dimers using ab initio Hartree–Fock and semiempirical Hartree–Fock-configuration-interaction quantum chemistry. We consider all the possible base compositions and sequences at the nucleoside level in vacuo. The results show that in such systems charge carrier generation could in principle be possible via charge transfer excitons, which turn out to dominate the first excited electronic states of the WC base pairs and their stacked dimers, and this process is largely sequence- and conformation-dependent. Possible consequences of this result for polymeric DNA duplexes are discussed.

We study nonclassic solitonic structures on the modified oscillator — chain proposed by Peyrard and Bishop to model DNA. The two DNA's strands are linked together by hydrogen bonds that are modeled by the Morse potential. This Peyrard–Bishop model with inharmonic potential in the optical part of the Hamiltonian gives rise to several nonclassical solutions, i.e., compact-cusp and anti-peak or crowd like soliton solutions. These structures could represent not only local openings of base pairs, but also the inverse process that heals the formation of broken hydrogen bonds.