Solving the Problem of Assessing Synergy and Antagonism for Non-Traditional Dosing Curve Compounds Using the DE/ZI Method: Application to Nrf2 Activators

Abstract

Multi-drug combination therapy carries significant promise for pharmacological intervention, primarily better efficacy with less toxicity and fewer side effects. However, the field lacks methodology to assess synergistic or antagonistic interactions for drugs with non-traditional dose response curves. Specifically, our goal was to assess small-molecule modulators of antioxidant response element (ARE)-driven gene expression, which is largely regulated by the Nrf2 transcription factor. Known as Nrf2 activators, this class of compounds upregulates a battery of cytoprotective genes and shows significant promise for prevention of numerous chronic diseases. For example, sulforaphane sourced from broccoli sprouts is the subject of over 70 clinical trials. Nrf2 activators generally have non-traditional dose response curves that are hormetic, or U-shaped. We introduce a method based on the principles of Loewe Additivity to assess synergism and antagonism for two compounds in combination. This method, termed Dose-Equivalence/Zero Interaction (DE/ZI), can be used with traditional Hill-slope response curves, and it also can assess interactions for compounds with non-traditional curves, using a nearest-neighbor approach. Using a Monte-Carlo method, DE/ZI generates a measure of synergy or antagonism for each dosing pair with an associated error and p-value, resulting in a 3D response surface. For the assessed Nrf2 activators, sulforaphane and di-tert-butylhydroquinone, this approach revealed synergistic interactions at higher dosing concentrations consistently across data sets and potential antagonistic interactions at lower concentrations. DE/ZI eliminates the need to determine the best fit equation for a given data set and values experimentally-derived results over formulated fits.