Rescue of an abasic hairpin ribozyme by cationic nucleobases: evidence for a novel mechanism of RNA catalysis

The hairpin ribozyme catalyzes a reversible phosphodiester cleavage reaction. We examined the roles of conserved nucleobases in catalysis using an abasic ribozyme rescue strategy. Loss of the active site G8 nucleobase reduced the cleavage rate constant by 350-fold while loss of A9 and A10 nucleobases reduced activity less than 10-fold. Certain heterocyclic amines restored partial activity when provided in solution to the variant lacking G8. Heterocyclic amines that were capable of rescue shared the exocyclic amine and cyclic amide in common with the Watson-Crick hydrogen bonding face of guanine. In contrast to the shallow pH dependence of unmodified ribozyme activity, rescue activity increased sharply with decreasing pH. These results support a novel model for RNA catalysis in which a cationic nucleobase contributes electrostatic stabilization to negative charge developing in the transition state.     

Convolutions of cantor measures without resonance

Denote by µ _a the distribution of the random sum \((1 - a)\sum\nolimits_{j = 0}^\infty {{w_j}{a^j}} \), where P(ω _j = 0) = P(ω _j = 1) = 1/2 and all the choices are independent. For 0 < a < 1/2, the measure µ _a is supported on C _a , the central Cantor set obtained by starting with the closed united interval, removing an open central interval of length (1 ? 2a), and iterating this process inductively on each of the remaining intervals. We investigate the convolutions µ _a * (µ _b ° S _λ ^?1 ), where S _λ (x) = λx is a rescaling map. We prove that if the ratio log b/ log a is irrational and λ ≠ 0, then

$D({\mu _a} * ({\mu _b} \circ S_\lambda ^{ - 1})) = \min ({\dim _H}({C_a}) + {\dim _H}({C_b}),1)$

, where D denotes any of correlation, Hausdorff or packing dimension of a measure.

We also show that, perhaps surprisingly, for uncountably many values of λ the convolution µ_1/4* (µ_1/3 ° S _λ ^?1 ) is a singular measure, although dim _H (C _1/4) + dim _H (C _1/3) > 1 and log(1/3)/ log(1/4) is irrational.     

On a question of A. E. Nussbaum on measurability of families of closed linear operators in a Hilbert space

The purpose of this note is to answer a question A. E. Nussbaum formulated in 1964 about the possible equivalence between weak measurability of a family of densely defined, closed operators {T(t)} _t∈ℝ in a separable complex Hilbert space H\mathcal{H} on one hand, and the notion of measurability of the 2 × 2 operator-valued matrix of projections {(P(Γ(T(t))) _j,k )_1⩽j,k⩽2} _t∈ℝ onto the graph Γ(T(t)) of T(t) on the other, in the negative.     

Lead Finder docking and virtual screening evaluation with Astex and DUD test sets

Lead Finder is a molecular docking software. Sampling uses an original implementation of the genetic algorithm that involves a number of additional optimization procedures. Lead Finder's scoring functions employ a set of semi-empiric molecular mechanics functionals that have been parameterized independently for docking, binding energy predictions and rank-ordering for virtual screening. Sampling and scoring both utilize a staged approach, moving from fast but less accurate algorithm versions to computationally more intensive but more accurate versions. Lead Finder includes tools for the preparation of full atom protein and ligand models. In this exercise, Lead Finder achieved 72.9% docking success rate on the Astex test set when the original author-prepared full atom models were used, and 74.1% success rate when the structures were prepared by Lead Finder. The major cause of docking failures were scoring errors resulting from the use of imperfect solvation models. In many cases, docking errors could be corrected by the proper protonation and the use of correct cyclic conformations of ligands. In virtual screening experiments on the DUD test set the early enrichment factor of several tens was achieved on average. However, the area under the ROC curve ("AUC ROC") ranged from 0.70 to 0.74 depending on the screening protocol used, and the separation from the null model was not perfect-0.12-0.15 units of AUC ROC. We assume that effective virtual screening in the whole range of enrichment curve and not just at the early enrichment stages requires more accurate solvation modeling and accounting for the protein backbone flexibility.     

Carbometallic derivatives of hydroborons C2h and D5d: A list of substitution isomers

The problem of determining the number and type of X-substituted (where X represents certain substituents) carbometallic derivatives of hydroborons [Co(C₂B₉H₁₁)₂]⁻ C _2h and [Co(C₅B₆H₁₁)₂]⁻ D _5d (from apexes) was solved on the basis of G. Pólya’s theorem by means of combinatory analysis. The formulae of symmetry Z and generating functions of the number of achiral substitution isomers were determined. The family distributions of isomers (depending on the type and number of substituents) and the sites of possible substitution depending on the number m were determined. Mono and di-X-substituted isomers of [Co(C₅B₆H₁₁)₂]⁻ C _2h , as well as mono and di-X-substituted isomers of [Co(C₅B₆H₁₁)₂]⁻ D _5d , were identified. The procedure for plotting an additive model of calculating the properties of isomers of apical substitution of [Co(C₅B₆H₁₁)₂]⁻ D _5d was described on the basis of splitting of polygonal numbers (K ₃, K _TE, K ₅, and so on) of Pascal triangle, upon use of which there is no randomization in the choice of parameters of calculation model. The additive schemes containing 7 and 25 parameters for the calculation of properties of X-substituted carbometallic derivative of hydroboron [Co(C₅B₆H₁₁)₂]⁻ D _5d to various approximations were obtained.     

Induced Super‐Halogen Behavior of Metal Moieties in Halogen‐Doped Clusters: LinI(‐) and AlnI(‐), n = 13, 1, 2, 3.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.     

On a possible empirical meaning of meets and joins for quantum propositions

Following up an idea of Jauch, an empirical basis is worked out for the meets (and joins) of quantum propositions through approximate measurement to an arbitrary degree of accuracy of special yes-no effects constructed from chains of yes-no measurements. This is done with a view to interpreting the meets (and joins) as Dedekind's cuts in analogy with irrationals.     

Mott's cloud-chamber theory made explicit and the relative-collapse interpretation of quantum mechanics thus obtained

It is pointed out that the concept of a shiftable split between object and subject with a well-defined subject, introduced and utilized in two preceding articles of the author, is present in Mott's historical cloud-chamber measurement theory. The crucial question of the occurrence of the subject events (the main constituents of the subject) is also given a tacit answer in Mott's text. When Mott's theory is made sufficiently explicit, the object-subject complementarity principle (an elaborated form of Bohr's macroscopic complementarity principle) emerges. The (individual-system) relative-collapse postulate, which appears as a natural completion of Born's (ensemble) postulate, takes form in it. The proposed interpretation is compared with the many-worlds and the modal approaches, which share with the former the idea of nondestruction of coherence (in contrast to interpretations that contain the idea of an absolute, i.e., observer-independent collapse, which destroys coherence irrevocably).