A novel approach to combinatorial library design

We address the problem of designing a general-purpose combinatorial library to screen for pharmaceutical leads. Conventional approaches focus on diversity as the primary factor in designing such libraries. We suggest making screening libraries out of a set of pharmaceutically relevant scaffolds, with multiple analogs per scaffold. The rationale for this rests on the fact that even though the hit-rate in active series is much higher than in the database as a whole, often a large fraction of the compounds in active series are inactive. This is especially true when the series has not been optimized for the target under study. We introduce the concept of hit-rate within a series and use historic screening data to arrive at a crude estimate for it. We then use simple probability arguments to show that 50-100 compounds are required in each series in order to be nearly certain of finding at least one active compound in each true active series for any given target.     

Long-term neprilysin gene transfer is associated with reduced levels of intracellular Abeta and behavioral improvement in APP transgenic mice

Background  

Proteolytic degradation has emerged as a key pathway involved in controlling levels of the Alzheimer's disease (AD)-associated amyloid-β (Aβ) peptide in the brain. The endopeptidase, neprilysin, has been implicated as a major Aβ degrading enzyme in mice and humans. Previous short and intermediate term studies have shown the potential therapeutic application of neprilysin by delivering this enzyme into the brain of APP transgenic mice using gene transfer with viral vectors. However the effects of long-term neprilysin gene transfer on other aspects of Aβ associated pathology have not been explored yet in APP transgenic mice.     

Possible effects of a cosmological constant on black hole evolution

We explore possible effects of vacuum energy on the evolution of black holes. If the universe contains a cosmological constant, and if black holes can absorb energy from the vacuum, then black hole evaporation could be greatly suppressed. For the magnitude of the cosmological constant suggested by current observations, black holes larger than 4×10²⁴ g would accrete energy rather than evaporate. In this scenario, all stellar and supermassive black holes would grow with time until they reach a maximum mass scale of 6×10⁵⁵ g, comparable to the mass contained within the present day cosmological horizon.     

Studies on the rate of isotopic oxygen exchange between [Re(py)4O2]+ and solvent water

The rate of oxygen exchange between trans-[Re(py)₄O₂]⁺ and solvent water in pypyH⁺ buffer solution follows simple first-order kinetics and both oxygens are equivalent. The half-life for isotopic oxygen exchange is about 12 h at a pH of 5.0, 25°C, and [py] = 0.10 M. The observed rate constant for exchange increases with acidity, in the pH range 4 to 6, decreases with [py], and is nearly independent of ionic strength. A small but significant increase of k_obs occurs with increasing complex concentration. The rate of exchange follows the rate equation k_obs/2 = k₀ + k₁/[py] with k₀ = 1.4 × 10^?5(2) s^?1 and k₁ = 4.7 × 10^?7(1) M, s^?1 at 25°C. The activation parameters for the reaction at pH = 7.15 (predominately the k₀ term) are: ΔH* = +137.(1) kJ/M and ΔS* = +126.(1) J/MK. The pH effect and complex concentration effect are discussed in mechanistic terms. These results are compared to those found for [Re(en)₂O₂]⁺ and [Re(CN)₄O₂]^3?.     

Necessary conditions for normed convergence of critical multitype Bienaymé-Galton-Watson processes without variance

The condition on the offspring distribution in the critical multitype Bienaymé-Galton-Watson process without variance, which was previously shown to be sufficient for the existence of the analogue of the exponential limit law, is now shown also to be necessary. This completely extends previous one-type work of R. S. Slack.     

Convergence of double Fourier series

Summary Let a2π-periodic function f(x, y) be continuous in some neighbourhood of the point (x, y) except possibly along finitely many lines l ₁ , l ₂ , ..., l_k terminating at (x, y). The problem of convergence of the Fourier series of f(x, y) at the point (x, y) is examined in some detail. It is established that under certain restrictions on the variation of f(x, y), and also on the lines l ₁ , l ₂ , ..., l_k, the fourier series converges to a value bounded above by the limit superior, and below by the limit inferior of f(x+u, y+v), u, v →0, this value depending on the manner in which the series is summed. The preparation of this paper was financed, in part, by a Canadian Mathematical Congress Summer Research Grant (1968). Entrata in Redazione il 3 febbraio 1969.