Mathematical rules for synergistic, additive, and antagonistic effects of multi-drug combinations and their application in research and development of combinatorial drugs and special medical food combinations

ABSTRACT Multi-drug (or multi-element) combinations are often prescribed in the practice of clinical medicine and as foods for special medical purposes. The main motivations for these combinations are that most diseases contain multiple related targets and an appropriate combination can maximize benefits while minimizing adverse reactions. As such, it is especially important to derive mathematical models for their quantitative calculation. In this paper, we introduce mathematical rules for the synergistic, additive, and antagonistic effects of multi-drug combinations developed in our laboratory. We have established a "one-belt, one-line" model and provide examples of the quantitative calculation of the synergistic, additive, and antagonistic effects of a combination of multiple components. We also explain how to scientifically and precisely determine the intensity of these synergies, additions and antagonisms, as well as their corresponding dose ranges, thereby laying a solid theoretical foundation for market listing combinatorial drugs and foods for special medical purposes.