In this study we derive and apply a mass-based hygroscopicity parameter interaction model for efficient description of concentration-dependent water uptake by atmospheric aerosol particles with complex chemical composition. The model approach builds on the single hygroscopicity parameter model of Petters and Kreidenweis (2007). We introduce an observable mass-based hygroscopicity parameter m which can be deconvoluted into a dilute hygroscopicity parameter (0m) and additional self- and cross-interaction parameters describing non-ideal solution behavior and concentration dependencies of single- and multi-component systems.