Monte Carlo determination of multiple extremal eigenpairs.

We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector. The algorithm, a Monte Carlo implementation of a deterministic one we recently benchmarked, is an extension of the power method. In the implementation presented, we used a basic Monte Carlo splitting and termination method called the comb, incorporated the weight cancellation method of Arnow et al, and exploited a sampling method, the sewing method, that does a large state space sampling as a succession of small state space samplings. We illustrate the effectiveness of the algorithm by its determination of the two largest eigenvalues of the transfer matrices for variously sized two-dimensional, zero-field Ising models. While very likely useful for other transfer-matrix problems, the algorithm is however quite general and should find application to a larger variety of problems requiring a few dominant eigenvalues of a matrix.

Interaction of bleomycin A2 with poly(deoxyadenylylthymidylic acid). A proton nuclear magnetic resonance study of the influence of temperature, pH, and ionic strength.

The binding of bleomycin A2 to poly(deoxyadenylylthymidylic acid) [poly(dA-dT)] has been monitored by proton nuclear magnetic resonance spectroscopy. This study includes an analysis of the effects of temperature, ionic strength, and pH. Sites of drug-nucleic acid interaction have been delineated on the basis of chemical shift perturbations of drug and nucleic acid resonances. The data indicate that the binding of the antibiotic occurs with partial intercalation of the aromatic bithiazole group and immobilization of the cationic dimethylsulfonium group. This complex dissociates as the nucleic acid is denatured to the single-stranded form. The absence of significant pH effects suggests that the N terminus of bleomycin A2, which contains the titratable groups, does not contribute to the interaction of the drug molecule with poly(dA-dT). The problems associated with assigning a specific geometry to the drug-nucleic acid complex are discussed.

Synthesis and DNA binding of [3-[2'-(2-acetamidoethyl)-2,4'-bithiazole-4-carboxamido]propyl[dimethylsulfonium chloride, a fragment of bleomycin A2.

[3-[2'-(2-Acetamidoethyl)-2,4'-bithiazole-4-carboxamido]propyl]dimethylsulfonium chloride (1), the acetyl derivative of the cationic terminal dipeptide of bleomycin A2, has been synthesized and its binding to DNA and poly(dA-dT) has been studied by proton NMR and fluorescence spectroscopy. The spectral perturbations which occur upon binding of the compound to either nucleic acid indicate that that portion of bleomycin which binds to the nucleic acid can, for the most part, be mimicked by the fragment. The data are discussed in terms of the structure of the drug and the drug-nucleic acid complex.