Hydrolytic stability of 2',3'-O-methyleneadenos-5'-yl 2',5'-di-O-methylurid-3'-yl 5'-O-methylurid-3'(2')-yl phosphate: implications to feasibility of existence of phosphate-branched RNA under physiological conditions

Hydrolytic reactions of 2',3'-O-methyleneadenos-5'-yl 2',5'-di-O-methylurid-3'-yl 5'-O-methylurid-3'(2')-yl phosphate (1a,b) have been followed by RP-HPLC over a wide pH range to evaluate the feasibility of occurrence of phosphate-branched RNA under physiological conditions. At pH <2, where the decomposition of is first order in [H3O+], the P-O5' bond is cleaved 1.5 times as rapidly as the P-O3' bond. Under these conditions, the reaction probably proceeds by an attack of the 2'-OH on the phosphotriester monocation. Over a relatively wide range from pH 2 to 5, the hydrolysis is pH-independent, referring to rapid initial deprotonation of the attacking 2'-OH followed by general acid catalyzed departure of the leaving nucleoside. The P-O5' bond is cleaved 3 times as rapidly as the P-O3' bond. At pH 6, the reaction becomes first order in [HO-], consistent with an attack of the 2'-oxyanion on neutral phosphate. The product distribution is gradually inversed: in 10 mmol L(-1) aqueous sodium hydroxide, cleavage of the P-O3' bond is favored over P-O5' by a factor of 7.3. The results of the present study suggest that the half-life for the cleavage of under physiological conditions is only 100 s. Even at pH 2, where is most stable, the half-life for its cleavage is less than one hour and the isomerization between and is even more rapid than cleavage. The mechanisms of the partial reactions are discussed.     

Nucleated polymerization with secondary pathways. III. Equilibrium behavior and oligomer populations

We explore the long-time behavior and equilibrium properties of a system of linear filaments growing through nucleated polymerisation. We show that the length distribution for breakable filaments evolves through two well defined limiting cases: first, a steady state distribution determined by the balance of breakage and elongation is reached; upon monomer depletion at the end of the growth phase, an equilibrium length distribution biased towards smaller filament fragments emerges. We furthermore compute the time evolution of the concentration of small oligomeric filament fragments. For frangible filaments, oligomers are present both at early times and at equilibrium, whereas in the absence of fragmentation, oligomers are only present in significant quantities at the beginning of the polymerisation reaction. Finally, we discuss the significance of these results for the biological consequences of filamentous protein aggregation.     

Slicing Sets and Measures, and the Dimension of Exceptional Parameters

We consider the problem of slicing a compact metric space Ω with sets of the form $\pi_{\lambda}^{-1}\{t\}$ , where the mappings π _λ :Ω→?, λ∈?, are generalized projections, introduced by Yuval Peres and Wilhelm Schlag in 2000. The basic question is: Assuming that Ω has Hausdorff dimension strictly greater than one, what is the dimension of the “typical” slice $\pi_{\lambda}^{-1}\{t\}$ , as the parameters λ and t vary. In the special case of the mappings π _λ being orthogonal projections restricted to a compact set Ω??², the problem dates back to a 1954 paper by Marstrand; he proved that for almost every λ there exist positively many t∈? such that $\dim\pi_{\lambda }^{-1}\{t\} = \dim\varOmega- 1$ . For generalized projections, the same result was obtained 50 years later by Järvenpää, Järvenpää and Niemelä. In this paper, we improve the previously existing estimates by replacing the phrase “almost all λ” with a sharp bound for the dimension of the exceptional parameters.     

Positive sesquilinear form measures and generalized eigenvalue expansions

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized eigenvalue type expansions. Though there are formal similarities with earlier approaches to special cases of the problem, the paper differs e.g. from standard rigged Hilbert space constructions and avoids the introduction of nuclear spaces. The techniques are predominantly measure theoretic and hence the Hilbert spaces involved are separable. The results range from a Naimark type dilation result to direct integral representations and a fairly concrete generalized eigenvalue expansion for unbounded normal operators.     

Non-homogeneous T1 theorem for bi-parameter singular integrals

We prove a non-homogeneous T1 theorem for certain bi-parameter singular integral operators. Moreover, we discuss the related non-homogeneous Journé's lemma and product BMO theory.     

Affine coordinates for Teichmüller spaces

Partially supported by the National Science Foundation     

Simple test cases for validating a finite element unstructured grid fecal bacteria transport model

This paper presents analytical test cases for tracer advection–diffusion-decay problems. The test cases are used to validate a finite element, unstructured grid fecal bacteria transport model. The test cases include the following domains: one-dimensional infinitely long river, two-dimensional half plane and two-dimensional infinitely long channel. In this work the bacteria are considered to enter the domain only through point sources. Analytical solutions are derived using either a Dirac delta function or a variable-width Gaussian function as a point source. Both analytical derivations and numerical simulations suggest that the error is maximised at the source. We present formulae for estimating the error caused by replacing a Dirac source with a Gaussian function in the numerical model. Furthermore, numerical simulations suggest that the best approximation for a Dirac source is a Gaussian whose width parameter is one third of the local mesh size.     

Autocorrelation in meter induction: the role of accent structure

The performance of autocorrelation-based meter induction was tested with two large collections of folk melodies, consisting of approximately 13 000 melodies for which the correct meters were available. The performance was measured by the proportion of melodies whose meter was correctly classified by a discriminant function. Furthermore, it was examined whether including different melodic accent types would improve the classification performance. By determining the components of the autocorrelation functions that were significant in the classification it was found that periodicity in note onset locations was the most important cue for the determination of meter. Of the melodic accents included, Thomassen's melodic accent was found to provide the most reliable cues for the determination of meter. The discriminant function analyses suggested that periodicities longer than one measure may provide cues for meter determination that are more reliable than shorter periodicities. Overall, the method predicted notated meter with an accuracy reaching 96% for binary classification and 75% for classification into nine categories of meter.