A formal model for analyzing drug combination effects and its application in TNF-α-induced NFκB pathway

In this paper, we deduced a mathematical model which can simplify the serial structure and parallel structure of biological pathway for synergy evaluation of drug combinations. We demonstrated in steady state the sign of the synergism assessment factor derivative of the original system can be predicted by the sign of its simplified system. In addition, we analyzed the influence of feedback structure on survival ratio of the serial structure. We provided a sufficient condition under which the combination effect could be maintained. Furthermore, we applied our method to find three synergistic drug combinations on tumor necrosis factor α-induced NFκB pathway and subsequently verified by the cell experiment.We identified several structural properties underlying the Bliss independence criterion, and developed a systematic simplification framework for drug combiation desgin by combining simulation and system reaction network topology analysis. We hope that this work can provide insights to tackle the challenging problem of assessment of combinational drug therapy effect in a large scale signaling pathway. And hopefully in the future our method could be expanded to more general criteria.Drug combination therapy is commonly used in clinical practice [1-3]. For example, herbal remedies in traditional Chinese medicine are believed to have synergism effect [4,5]. How to define the drug synergism has been a long-standing controversy amongst pharmacologists, toxicologists and biologists [6,7]. Among existing methods, under the assumption that two drugs acting by independent mechanisms, Bliss independence model is used to define combined effect of two drugs [8]; given that two similar drugs competitively acting on a target, Loewe additivity model is used to predict the combined effect of two drugs [9]. Chou-Talalay further proposed the Combination Index (CI) theorem, serving as a general expression and quantification of drug interaction based on the mass-action law in biophysics