Abstract
A possible experimental design for combination experiments is to compare the doseresponse curve of a single agent with the corresponding curve of the same agent using either a fixed amount of a second one or a fixed dose ratio. No interaction is then often defined by a parallel shift of these curves. We have performed a systematic study for various types of doseresponse relations both for the dose-additivity (Loewe additivity) and for the independence (Bliss independence) criteria for defining zero interaction. Parallelism between doseresponse curves of a single agent and those of the same agent in the presence of a fixed amount of another one is found for the Loewe-additivity criterion for linear doseresponse relations. For nonlinear relations, one has to differentiate between effect parallelism (parallel shift on the effect scale) and dose parallelism (parallel shift on the dose scale). In the case of Loewe additivity, zero-interaction dose parallelism is found for power, Weibull, median-effect and logistic doseresponse relations, given that special parameter relationships are fulfilled. The mechanistic model of competitive interaction exhibits dose parallelism but not effect parallelism for Loewe additivity. Bliss independence and Loewe additivity lead to identical results for exponential doseresponse curves. This is the only case for which dose parallelism was found for Bliss independence. Parallelism between single-agent doseresponse relations and Loewe additivity mixture relations is found for examples with a fixed doseratio design. However, this is again not a general property of the design adopted but holds only if special conditions are fulfilled. The comparison of combination doseresponse curves with single-agent relations has to be performed taking into account both potency and shape parameters. The results of this analysis lead to the conclusion that parallelism between zero interaction combination and single-agent doseresponse relations is found only for special cases and cannot be used as a general criterion for defining zero-interaction in combined-action assessment even if the correct potency shift is taken into account.
Similar content being viewed by others
References
Ariens, E. J., J. M. Van Rossum and A. M. Simonis (1956). A theoretical basis of molecular pharmacology. Arzneimittelforschung 6, 282–293, 611–621, 737–746.
Berenbaum, M. C. 1989. What is synergy? Pharmacol. Rev. 41, 93–141.
Berger, M. R., D. Schmahl and H. Zerban (1987). Combination experiments with very low doses of three genotoxic N-nitrosamines with similar organotropic carcinogenicity in rats. Carcinogenesis 8, 1635–1643.
Brennan, J. F. and P. J. Jastreboff (1989). Interaction of salicylate and noise results in mortality of rats. Experientia 45, 731–734.
Caplan, R. A. and J. Y. Su (1986). Interaction of halothane and verapamil in isolated papillary muscle. Anesth. Analg. 65, 463–468.
Caudle, R. M. and G. M. Williams (1993). The misuse of analysis of variance to detect synergy in combination drug studies. Pain 55, 313–317.
Chou, T.-C. and P. Talalay (1984). Quantative analysis of dose-effect relationships: the combined effects of multiple drugs or enzyme inhibitors. Adv. Enzyme Regul. 22, 27–55.
Fraser, T. R. (1870–1871). An experimental research on the antagonism between the actions of physostigma and atropia. Proc. R. Soc. Edinburgh 7, 506–511.
Gebhart, G. F. (1992). Comments on the isobole method for analysis of drug interactions. Pain 51, 381.
Greco, W., H.-D. Unkelbach, G. Pöch, J. Sühnel, M. Kundi and W. Bödeker, (1992). Consensus on concepts and terminology for combined-action assessment: the Saariselkä agreement. Arch. Complex Environ. Stud. 4, 65–69.
Greco, W. R., O. Bravo and J. C. Parsons (1995). The search for synergy: a critical review from a response surface perspective. Pharmacol. Rev. 47, 331–385.
Harvey, M. J. and C. D. Klaassen (1983). Interaction of metals and carbon tetrachloride on lipid peroxidation and hepatoxicity. Toxicol. Appl. Pharmacol. 71, 316–322.
Hill, A. V. (1913). The combinations of hemoglobin with oxygen and with carbon monoxide. Biochem. J. 7, 471–480.
Katahira, K., H. Mikami, T. Ogihara, K. Kohara, A. Otsuka, Y. Kumahar and M. C. Khosla (1989). Synergism of intraventricular NaCl infusion and subpressor angiotensins in rats. Am. J. Physiol. 256, H1–H8.
Kopia, G. A., L. J. Kopaciewicz, E. H. Ohlstein, S. Horohonich, B. L. Storer and R. J. Shebuski (1989). Combination of the thromboxane receptor antagonist, sulotraban (BM 13.177; SK & F 95587) with streptokinase: demonstration of thrombolytic synergy. J. Pharmacol. Exp. Ther. 250, 887–895.
Loewe, S. (1953). The problem of synergism and antagonism of combined drugs. Arzneimittelforschung 3, 285–290.
Loomis, C. W., B. Milne and F. W. Cervenko (1988). A study of the interaction between clonidine and morphine on analgesia and blood pressure during continuous intrathecal infusion in the rat. Neuropharmacology 27, 191–199.
Mao, J., D. D. Price, D. J. Mayer, J. Lu and R. L. Hayes (1992). Intrathecal MK-801 and local nerve anesthesia synergistically reduce nociceptive behaviors in rats with experimental peripheral mononeuropathy. Brain Res. 576, 254–262.
Miaskoski, C., Y. O. Taiwo and J. D. Levine (1990). Kappa-and delta-opioid agonists synergize to produce potent analgesia. Brain Res. 509, 165–168.
Miaskowski, C., K. A. Sutters, Y. O. Taiwo and J. D. Levine (1992a). Antinoceptive and motor effects of delta/mu and kappa/mu combinations of intrathecal opioid agonists. Pain 49, 137–144.
Miaskowski, C. and J. D. Levine (1992b). Comments on the evaluation of drug interactions using isobolographic analysis and analysis of variance. Pain 49, 383–387.
Oksenberg, D., B. S. Dieckmann and P. L. Greenberg (1990). Functional interactions between colony-stimulating factors and the insulin family hormones for myeloid leukemic cells. Cancer Res. 50, 6471–6477.
Pöch, G. (1993). Combined Effects of Drugs and Toxic Agents. Wien: Springer-Verlag.
Pöch, G., P. Dittrich, R. J. Reiffenstein, W. Lenk and A. Schuster (1990). Evaluation of experimental combined toxicity by use of dose-frequency curves: comparison with theoretical additivity as well as independence. Can. J Physiol. Pharmacol. 68, 1338–1345.
Sato, K., Y. Fujii, K. Kasano, M. Ozawa, H. Imamura, Y. Kanaji, H. Kurosawa, H. T. Tsushima and K. Shizume (1989). Parathyroid hormone-related protein and interleukin-1α synergistically stimulate bone resorption in vitro and increase the serum calcium concentration in mice in vivo. Endocrinology 124, 2172–2178.
Shaikh, N. A., A. M. Owen, M. W. Ghilchik and H. Braunsberg (1989). Actions of medroxyprogesterone acetate on the efficiacy of cytotoxic drugs: studies with human breast cancer cells in culture. Int. J. Cancer 43, 458–463.
Sühnel, J. (1990). Evaluation of synergism or antagonism for the combined action of antiviral agents. Antiviral Res. 13, 23–39.
Sühnel, J. (1992a). Zero interaction response surfaces, interaction functions and difference response surfaces for combinations of biologically active agents. Arzneimittelforschung 42, 1251–1258.
Sühnel, J. (1992b). Assessment of interaction of biologically active agents by means of the isobole approach: Fundamental assumptions and recent developments. Arch. Complex Environ. Stud. 4, 35–44.
Sühnel, J. (1993). Evaluation of interaction in olfactory and taste mixtures. Chem. Senses 18, 131–149.
Sühnel, J. (1996). Zero interaction response surfaces for combined-action assessment. Food Chem. Toxicol. 34, 1151–1153.
Sutters, K. A., C. Miaskowski, Y. O. Taiwo and J. D. Levine (1990). Analgesic synergy and improved motor function produced by combinations of mu-delta-and mu-kappa-opioids. Brain Res. 530, 290–294.
Suzuki, S. (1994). The synergistic action of mixed irradiation with high-LET and low-LET radiation. Radiat. Res. 138, 297–301.
Tallarida, R. J., F. Porreca and A. Cowan (1989). Statistical analysis of drug-drug and site-site interactions with isobolograms. Life Sci. 45, 947–961.
Thompson, C.I. and A.N. Epstein (1991). Salt appetite in rat pups: ontogeny of angiotensin II.-aldosterone synergy. Am. J. Physiol. 260, R421–R429.
Woodward, D. F., A. L. Nieves, L. S. Williams, R. K. Gary, M. A. Wasserman and J. G. Gleason (1989). Interactive effects of peptidoleukotrienes and histamine on microvascular permeability and their involvement in experimental cutaneous and conjunctival immediate hypersensitivity. Eur. J. Pharmacol. 164, 323–333.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sühnel, J. Parallel dose-response curves in combination experiments. Bull. Math. Biol. 60, 197–213 (1998). https://doi.org/10.1006/bulm.1997.0009
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1006/bulm.1997.0009