The long-held view that radiation-induced biological damage must be initiated in the cell nucleus, either on or near DNA itself, is being confronted by mounting evidence to suggest otherwise. While the efficacy of cell death may be determined by radiation damage to nuclear DNA, a plethora of less deterministic biological responses has been observed when DNA is not targeted. These so-called nontargeted responses cannot be understood in the framework of DNA-centric radiobiological models; what is needed are new physically motivated models that address the damage-sensing signalling pathways triggered by the production of reactive free radicals. To this end, we have conducted a series of in silico experiments aimed at elucidating the underlying physical processes responsible for nontargeted biological responses to radiation. Our simulation studies implement new results on very low-energy electromagnetic interactions in liquid water (applicable down to nanoscales) and we also consider a realistic simulation of extranuclear microbeam irradiation of a cell. Our results support the idea that organelles with important functional roles, such as mitochondria and lysosomes, as well as membranes, are viable targets for ionizations and excitations, and their chemical composition and density are critical to determining the free radical yield and ensuing biological responses.