Response Surface Analysis of Synergism Between Morphine and Clonidine1
- 1Temple University School of Medicine (R.J.T., J.D.M.) and 2School of Pharmacy (D.J.S., R.B.R.), Philadelphia, Pennsylvania
Abstract
Graded doses of morphine sulfate and clonidine hydrochloride were administered intrathecally to mice that were then tested for antinociception in the 55°C tail immersion test. The dose-effect relations of each compound were used in calculations that permitted the construction of a three-dimensional plot of the expected additive effect (vertical scale) against the planar domain of dose pairs representing combinations administered simultaneously. This additive response surface became the reference surface for viewing the actual effects produced by three different fixed-ratio combinations of the drugs that were used in our tests. Each combination produced effects significantly greater than indicated by the additive surface, thereby illustrating marked synergism and a method for quantifying the synergism. This quantification, measured by the value of the interaction index (α), was found to be dependent on the fixed-ratio combination; accordingly, the actual response surface could not be described by a single value of the index α. Furthermore, we found that application of the common method of isoboles gave estimates of the index that agreed well with those obtained from the more extensive surface analysis. These results confirm earlier studies, which found synergism for these drugs while also providing surface views of additivity and synergism that form the basis of isobolographic analysis.
Footnotes
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Send reprint requests to: Ronald J. Tallarida, Ph.D. Temple University School of Medicine, 3420 N. Broad St., Philadelphia, PA 19140.
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↵1 This study was supported by Grant DA 09793 from the National Institute on Drug Abuse.
- Abbreviations:
- A
- denotes drug A
- A
- dose of drug A
- α
- interaction index
- Aeq
- additive equivalent dose of drug A
- Acorr
- dose of drug A corresponding to an observed effect
- B
- denotes drug B
- B
- dose of drug B
- C
- mathematical constant
- D
- dose
- D50
- dose that gives half-maximal effect
- E
- magnitude of effect
- f
- mathematical function
- g
- mathematical function
- (a, b)
- dose combination of two drugs A and B
- p
- proportion that is drug A in a combination
- MPE
- maximum possible effect
- R
- relative potency
- Zadd
- calculated additive total dose
- Zmix
- total dose that gives specified effect
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- Received May 8, 1998.
- Accepted October 19, 1998.
- The American Society for Pharmacology and Experimental Therapeutics
