Loewe additivity

In Pharmacology, Loewe Additivity (or dose additivity) is one of several common reference models used for measuring the effects of drug combinations.

Let $d_{1}$ and $d_{2}$ be doses of compounds 1 and 2 producing in combination an effect $e$ . We denote by $D_{e1}$ and $D_{e2}$ the doses of compounds 1 and 2 required to produce effect $e$ alone (assuming this conditions uniquely define them, i.e. that the individual dose-response functions are bijective). $D_{e1}/D_{e2}$ quantifies the potency of compound 1 relatively to that of compound 2.

$d_{2}D_{e1}/D_{e2}$ can be interpreted as the dose $d_{2}$ of compound 2 converted into the corresponding dose of compound 1 after accounting for difference in potency.

Loewe additivity is defined as the situation where $d_{1}+d_{2}D_{e1}/D_{e2}=D_{e1}$ or $d_{1}/D_{e1}+d_{2}/D_{e2}=1$ .

Geometrically, Loewe additivity is the situation where isoboles are segments joining the points $(D_{e1},0)$ and $(0,D_{e2})$ in the domain $(d_{1},d_{2})$ .

If we denote by $f_{1}(d_{1})$ , $f_{2}(d_{2})$ and $f_{12}(d_{1},d_{2})$ the dose-response functions of compound 1, compound 2 and of the mixture respectively, then dose additivity holds when

{\frac {d_{1}}{f_{1}^{-1}(f_{12}(d_{1},d_{2}))}}+{\frac {d_{2}}{f_{2}^{-1}(f_{12}(d_{1},d_{2}))}}=1

References

William R Greco, Gregory Bravo, and John Parsons "The Search for Synergy: A Critical Review from a Response Surface Perspective", Pharmacological Reviews 47(2) 331-385 (1995)
Loewe and Muischnek. "Effect of combinations: mathematical basis of the problem" Arch. Exp. Pathol. Pharmakol. 114: 313-326, 1926
Pamela J. Yeh, Matthew J. Hegreness, Aviva Presser Aiden & Roy Kishony "Nature Reviews Microbiology" 7, 460-466 (June 2009)
Tang, J., K. Wennerberg, and T. Aittokallio. "What Is Synergy? The Saariselkä Agreement Revisited." Frontiers in Pharmacology 6. Frontiers: 181. (2015)

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.