Biphasic Mathematical Model of Cell–Drug Interaction That Separates Target-Specific and Off-Target Inhibition and Suggests Potent Targeted Drug Combinations for Multi-Driver Colorectal Cancer Cells

Quantifying the response of cancer cells to a drug, and understanding the mechanistic basis of the response, are the cornerstones for anti-cancer drug discovery. Classical single target-based IC(50) measurements are inadequate at describing cancer cell responses to targeted drugs. In this study, based on an analysis of targeted inhibition of colorectal cancer cell lines, we develop a new biphasic mathematical model that accurately describes the cell–drug response. The model describes the drug response using three kinetic parameters: ratio of target-specific inhibition, F(1), potency of target-specific inhibition, K(d1), and potency of off-target toxicity, K(d2). Determination of these kinetic parameters also provides a mechanistic basis for predicting effective combination targeted therapy for multi-driver cancer cells. The experiments confirmed that a combination of inhibitors, each blocking a driver pathway and having a distinct target-specific effect, resulted in a potent and synergistic blockade of cell viability, improving potency over mono-agent treatment by one to two orders of magnitude. We further demonstrate that mono-driver cancer cells represent a special scenario in which F(1) becomes nearly 100%, and the drug response becomes monophasic. Application of this model to the responses of >400 cell lines to kinase inhibitor dasatinib revealed that the ratio of biphasic versus monophasic responses is about 4:1. This study develops a new mathematical model of quantifying cancer cell response to targeted therapy, and suggests a new framework for developing rational combination targeted therapy for colorectal and other multi-driver cancers.