Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)

In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a brief overview of charged black holes in supergravity and string theory, we give an extensive introduction to special and very special geometry, attractor flows and topological string theory, including holomorphic anomalies. We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates microscopic degeneracies to the topological string amplitude, and review precision tests of this formula on ``small'' black holes. Finally, motivated by a holographic interpretation of the OSV conjecture, we give a systematic approach to the radial quantization of BPS black holes (i.e. quantum attractors). This suggests the existence of a one-parameter generalization of the topological string amplitude, and provides a general framework for constructing automorphic partition functions for black hole degeneracies in theories with sufficient degree of symmetry.Comment: 103 pages, 8 figures, 21 exercises, uses JHEP3.cls; v5: important upgrade, prepared for the proceedings of Frascati School on Attractor Mechanism; Sec 7 was largely rewritten to incorporate recent progress; more figures, more refs, and minor changes in abstract and introductio

Metabolic conditions determining the composition and catalytic activity of cytochrome P-450 monooxygenases in Candida tropicalis

In the microsomal fraction of Candida tropicalis cells, two distinct monooxygenases were detected, depending on the growth conditions. The distinction of the two monooxygenases was evident from: (i) the absorption maxima in the reduced CO difference spectra of the terminal oxidases (cytochromes P-450 and P-448); (ii) the contents of the monooxygenase components (cytochromes P-450/P-448, NADPH-cytochrome c (P-450) reductase, and cytochrome b5) and (iii) the catalytic activity of the complete system (aliphatic hydroxylation and N-demethylation activity). The occurrence of the respective monooxygenases could be related to the carbon source (n-alkanes or glucose). Oxygen limitation led to a significant increase of cytochrome P-450/P-448 content, independent of the carbon source utilized by the cells. An improved method for the isolation of microsomes enabled us to demonstrate the presence of cytochrome P-448 in glucose-grown cells

The distinction of different types of cytochromes P-450 from the yeasts Candida tropicalis and Saccharomyces uvarum

The distinction between two types of cytochromes P-450 originating from microsomes of Candida tropicalis grown on glucose and on alkane was achieved. Criteria of differentiation between these two cytochrome P-450 forms were based on the characteristics of reduced carbon monoxide difference spectra, on substrate specificity, and on binding and inhibition kinetics of the fungistatic compound propiconazole. One cytochrome P-450 form catalyzed the 14 alpha-demethylation of lanosterol and bound propiconazole with an equimolar ratio. This form was present in microsomes from glucose-grown cells and shared similar characteristics with the cytochrome P-450 originating from Saccharomyces uvarum grown on the same carbon source. The other cytochrome P-450 form catalyzed the terminal hydroxylation of aliphatic hydrocarbons and showed a less specific binding ratio with propiconazole (10(3) mol propiconazole for 1 mol cytochrome P-450). This type of cytochrome P-450 was only present in the microsomes of C. tropicalis grown on alkane

Optimization of Candida tropicalis cytochrome P450alk gene expression in Saccharomyces cerevisiae with continuous cultures

The cytochrome P450alk gene (P45alk) from Candida tropicalis ATCC 750 was expressed in Saccharomyces cerevisiae GRF18 under control of the alcohol dehydrogenase I (ADHI) promoter. To achieve stable expression over long time periods, a 2-microns derived replicative and an integrative expression system were tested in continuous culture. The 2-microns derived replicative system could not be maintained in cells over high generation numbers. In continuous culture, the instability was more pronounced at high dilution rates (D) and high histidine concentration, for which the yeast is auxotrophic. The nature of the instability was probably due to a gene conversion event between the plasmid and the yeast chromosome. In contrast, the integrative expression system was stably maintained in cells over prolonged cultivation times. Since this work focused on the production of large quantities of P450 by heterologous expression in yeast over prolonged time periods, the integrant was used to optimize P450alk expression by varying continuous culture parameters. The P450alk expression was shown to be dependent on the D applied to the culture. The highest P450alk expression levels were obtained at high D, when cell metabolism was shifted to partial glucose oxidation, yielding ethanol as a major metabolite in the culture supernatant. In contrast, when glucose was completely oxidized at low D, the ADHI-dependent P450alk expression was reduced and followed by a corresponding decrease in heterologous protein