Understanding P450‐mediated Bio‐transformations into Epoxide and Phenolic Metabolites

Adverse drug reactions are commonly the result of cytochrome P450 enzymes (CYPs) converting the drugs into reactive metabolites. Thus, information about the CYP bioactivation of drugs would not only provide insight into metabolic stability, but also into the potential toxicity. For example, oxidation of phenyl rings may lead to either toxic epoxides or safer phenols. Herein, we demonstrate that the potential to form reactive metabolites is encoded primarily in the properties of the molecule to be oxidized. While the enzyme positions the molecule inside the binding pocket (selects the site of metabolism), the subsequent reaction is only dependent on the substrate itself. To test this hypothesis, we used this observation as a predictor of drug inherent toxicity. This approach was used to successfully identify the formation of reactive metabolites in over 100 drug molecules. These results provide a new perspective on the impact of functional groups on aromatic oxidation of drugs and their effects on toxicity.     

Twistor spaces of hypercomplex manifolds are balanced

A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the three structures, and such that the corresponding Hermitian forms are closed, the manifold is said to be hyperkähler. In the paper “Non-Hermitian Yang–Mills connections” [13], Kaledin and Verbitsky proved that the twistor space of a hyperkähler manifold admits a balanced metric; these were first studied in the article “On the existence of special metrics in complex geometry” [17] by Michelsohn. In the present article, we review the proof of this result and then generalize it and show that twistor spaces of general compact hypercomplex manifolds are balanced.     

Atmosph?rische Luft

Ohne Zusammenfassung     

On reconstruction of a matrix by its minors

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.     

Example of a Stable but Fiberwise Nonstable Bundle on the Twistor Space of a Hyper-Kähler Manifold

Mathematical Notes -     

Conditions for auto-oscillations in nonlinear systems

Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 180–194, July–August, 1989.