The additive damage model: a mathematical model for cellular responses to drug combinations

Abstract

Mathematical models to describe dose-dependent cellular responses to drug combinations are an essential component of computational simulations for predicting therapeutic responses. Here, a new model, the additive damage model, is introduced and tested in cases where varying concentrations of two drugs are applied with a fixed exposure schedule. In the model, cell survival is determined by whether cellular damage, which depends on the concentrations of the drugs, exceeds a lethal threshold, which varies randomly in the cell population with a prescribed statistical distribution. Cellular damage is assumed to be additive, and is expressed as a sum of separate terms for each drug. Each term has a saturable dependence on drug concentration. The model has appropriate behavior over the entire range of drug concentrations, and is predictive, given single-agent dose-response data for each drug. The proposed model is compared with several other models, by testing their ability to fit 24 data sets for platinum-taxane combinations and 21 data sets for various other combinations. The Akaike Information Criterion is used to assess goodness of fit, taking into account the number of unknown parameters in each model. Overall, the additive damage model provides a better fit to the data sets than any previous model. The proposed model provides a basis for computational simulations of therapeutic responses. It predicts responses to drug combinations based on data for each drug acting as a single agent, and can be used as an improved null reference model for assessing synergy in the action of drug combinations.

Keywords: Cellular pharmacodynamics; Chemotherapy; Cytotoxicity; Dose–response; Drug synergy.