ABSTRACT
Given the complexity of diseases and etiology of multiple targets and links,therapies with multi-drug combination towards multiple targets are better options for treating serious diseases,such as cancer,than a single-target medicine. Multi-drug combination may cause interactions at different levels,but the efficacy of these drugs manifests itself as synergism,addition or antagonism. Because there is no reliable quantitative method for synergism,addition and antagonism that can simultaneously withstand double test of mathematics and pharmacology,the development of novel drug combinations has come to a standstill. By exchanging the equivalent doses and introducing two basic principles that have been long neglected in the pharmacological field(the sequential principle for multi-drug use and the collective property of efficacy)into the geometrical analysis of the dose- effect relationships,the author has found the mathematical laws for the expected additive effect in multi-target drug combina?tion,and worked out a universal formula. The dose-effect relationship of the expected addition is a number set function of multi-drug combination doses with a closed interval,which performs as a belt in a two- dimensional coordinate,while the actual observed one presents as a curve. The number of curves that constitute the belt increases exponentially whith the incnease of combined drugs. By solv? ing the equation groups composed of the belt and the curve,related parameters in multi-drug combina?tion can be precisely calculated,such as dose ranges of synergism,addition and antagonism,as well as combination indexes based on dose and one based on efficacy,which will also provide a quantita?tive analysis method for interactions between various factors in biological systems.