In radiobiology, and throughout translational biology, synergy theories for multi-component agent mixtures use 1-agent dose-effect relations (DERs) to calculate baseline neither synergy nor antagonism mixture DERs. The most used synergy theory, simple effect additivity, is not self-consistent when curvilinear 1-agent DERs are involved, and many alternatives have been suggested. In this paper we present the mathematical aspects of a new alternative, generalized Loewe additivity (GLA). To the best of our knowledge, generalized Loewe additivity is the only synergy theory that can systematically handle mixtures of agents that are malstressors (tend to produce disease) with countermeasures – agents that oppose malstressors and ameliorate malstressor damage. In practice countermeasures are often very important, so generalized Loewe additivity is potentially far-reaching. Our paper is a proof-of-principle preliminary study. Unfortunately, generalized Loewe additivity's scope is restricted, in various unwelcome but perhaps unavoidable ways. Our results illustrate its strengths and its weaknesses. One area where our methodology has potentially important applications is analyzing counter-measure mitigation of galactic cosmic ray damage to astronauts during interplanetary travel.

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