Polymerase recognition of synthetic oligodeoxyribonucleotides incorporating degenerate pyrimidine and purine bases

A universal base that is capable of substituting for any of the four natural bases in DNA would be of great utility in both mutagenesis and recombinant DNA experiments. This paper describes the properties of oligonucleotides incorporating two degenerate bases, the pyrimidine base 6H,8H-3,4-dihydropyrimido[4,5-c][1,2]oxazin-7-one and the purine base N6-methoxy-2,6-diaminopurine, designated P and K, respectively. An equimolar mixture of the analogues P and K (called M) acts, in primers, as a universal base. The thermal stability of oligonucleotide duplexes were only slightly reduced when natural bases were replaced by P or K. Templates containing the modified bases were copied by Taq polymerase; P behaved as thymine in 60% of copying events and as cytosine in 40%, whereas K behaved as if it were guanine (13%) or adenine (87%). The dUTPase gene of Caenorhabditis elegans, which we have found to contain three nonidentical homologous repeats, was used as a model system to test the use of these bases in primers for DNA synthesis. A pair of oligodeoxyribonucleotides, each 20 residues long and containing an equimolar mixture of P and K at six positions, primed with high specificity both T7 DNA polymerase in sequencing reactions and Taq polymerase in PCRs; no nonspecific amplification was obtained on genomic DNA of C. elegans. Use of P and K can significantly reduce the complexity of degenerate oligonucleotide mixtures, and when used together, P and K can act as a universal base.

Tumor necrosis factor (TNF)-mediated kinase cascades: Bifurcation of Nuclear Factor-κB and c-jun N-terminal kinase (JNK/SAPK) pathways at TNF receptor-associated factor 2

TNF-induced activation of the transcription factor NF-κB and the c-jun N-terminal kinase (JNK/SAPK) requires TNF receptor-associated factor 2 (TRAF2). The NF-κB-inducing kinase (NIK) associates with TRAF2 and mediates TNF activation of NF-κB. Herein we show that NIK interacts with additional members of the TRAF family and that this interaction requires the conserved “WKI” motif within the TRAF domain. We also investigated the role of NIK in JNK activation by TNF. Whereas overexpression of NIK potently induced NF-κB activation, it failed to stimulate JNK activation. A kinase-inactive mutant of NIK was a dominant negative inhibitor of NF-κB activation but did not suppress TNF- or TRAF2-induced JNK activation. Thus, TRAF2 is the bifurcation point of two kinase cascades leading to activation of NF-κB and JNK, respectively.

Whole genome amplification using a degenerate oligonucleotide primer allows hundreds of genotypes to be performed on less than one nanogram of genomic DNA

Genetic analysis of limiting quantities of genomic DNA play an important role in DNA forensics, paleoarcheology, genetic disease diagnosis, genetic linkage analysis, and genetic diversity studies. We have tested the ability of degenerate oligonucleotide primed polymerase chain reaction (DOP-PCR) to amplify picogram quantities of human genomic DNA for the purpose of increasing the amount of template for genotyping with microsatellite repeat markers. DNA was uniformly amplified at a large number of typable loci throughout the human genome with starting template DNAs from as little as 15 pg to as much as 400 ng. A much greater-fold enrichment was seen for the smaller genomic DOP-PCRs. All markers tested were amplified from starting genomic DNAs in the range of 0.6–40 ng with amplifications of 200- to 600-fold. The DOP-PCR-amplified genomic DNA was an excellent and reliable template for genotyping with microsatellites, which give distinct bands with no increase in stutter artifact on di-, tri-, and tetranucleotide repeats. There appears to be equal amplification of genomic DNA from 55 of 55 tested discrete microsatellites implying near complete coverage of the human genome. Thus, DOP-PCR appears to allow unbiased, hundreds-fold whole genome amplification of human genomic DNA for genotypic analysis.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

The equation ∂tu = u∂xx2u − (c − 1)(∂xu)2 is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. An open problem caused by the nonuniqueness of the solution of the Cauchy problem is discussed.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

RNA: a method to specifically inhibit PCR amplification of known members of a multigene family by degenerate primers

The polymerase chain reaction (PCR) is a versatile method to amplify specific DNA with oligonucleotide primers. By designing degenerate PCR primers based on amino acid sequences that are highly conserved among all known gene family members, new members of a multigene family can be identified. The inherent weakness of this approach is that the degenerate primers will amplify previously identified, in addition to new, family members. To specifically address this problem, we synthesized a specific RNA for each known family member so that it hybridized to one strand of the template, adjacent to the 3′-end of the primer, allowing the degenerate primer to bind yet preventing extension by DNA polymerase. To test our strategy, we used known members of the soluble, nitric oxide-sensitive guanylyl cyclase family as our templates and degenerate primers that discriminate this family from other guanylyl cyclases. We demonstrate that amplification of known members of this family is effectively and specifically inhibited by the corresponding RNAs, alone or in combination. This robust method can be adapted to any application where multiple PCR products are amplified, as long as the sequence of the desired and the undesired PCR product(s) is sufficiently distinct between the primers.

A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

On the solution of a class of Wiener-Hopf integral equations in finite and infinite ranges /

"Sponsored by: Wright Air Development Center"

The finite range Wiener-Hopf integral equation and a boundary value problem in a waveguide /

"Contract No. AF33(616)-6079 Project No. 9-(13-6278) Task 40572. Sponsored by: Wright Air Development Center"

On the structure of Hopf algebras

Caption title.

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The Exbeta system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the Exepsilon models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the Exbeta system, the ground states of the Exepsilon model always exhibit entanglement. For the Exbeta case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the Exepsilon case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.