JOURNAL ARTICLE

Isometric Embeddings of Riemannian Manifolds

Matthias Günther

Year: 2010 Journal:   Chemico-Biological Interactions Vol: 28 (2-3)Pages: 211-24   Publisher: Elsevier BV

Abstract

The antitumour agent chlorambucil (4[4-bis(2-chloroethyl)aminophenyl]-butyric acid) is converted by beta-oxidation in vivo into phenylacetic mustard (2[4-bis(2-chloroethyl)aminophenyl]acetic acid). This process may be disadvantageous from a therapeutic viewpoint since the metabolite has half the therapeutic index of the parent drug against the Walker 256 carcinoma in rats. In seeking to retard beta-oxidation, selectively deuterated analogues have been synthesised and administered to rats. Plasma levels of phenylacetic mustard after giving chlorambucil-beta-d2 were lower than those given by unlabelled drug, but the therapeutic activity was not significantly altered by deuteration. A dehydro derivative of chlorambucil was detected as an intermediate in the beta-oxidation pathway. The isotopic compositions of this metabolite, and of recovered chlorambucil, were measured in plasma samples taken after giving labelled chlorambucil (alpha-d2 and beta-d2 variants) to rats. Deuterium was almost totally lost from the alpha-d2 form and from its metabolite after 30 min and partially lost in 10 min. The beta-d2 variant and its dehydro-derivative retained the label. Possible mechanisms for deuteration loss are discussed. The design of novel analogues, based on these metabolic studies, is proposed.

Keywords:
Embedding Mathematics Pure mathematics Manifold (fluid mechanics) Riemannian manifold Dimension (graph theory) Immersion (mathematics) Combinatorics Computer science

Metrics

47
Cited By
2.14
FWCI (Field Weighted Citation Impact)
14
Refs
0.87
Citation Normalized Percentile
Is in top 1%
Is in top 10%

Citation History

Topics

Quantum chaos and dynamical systems
Physical Sciences →  Physics and Astronomy →  Statistical and Nonlinear Physics
Geometric Analysis and Curvature Flows
Physical Sciences →  Mathematics →  Applied Mathematics
Mathematical Dynamics and Fractals
Physical Sciences →  Mathematics →  Mathematical Physics

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