Synergy Theory in Radiobiology.

Customized open-source software is used to characterize, exemplify, compare and critically evaluate mathematical/computational synergy analysis methods currently used in biology, and used or potentially applicable in radiobiology. As examples, we reanalyze some published results on murine Harderian gland tumors and on in vitro chromosome aberrations induced by exposure to single-ion radiations that simulate components of the galactic cosmic ray field. Baseline no-synergy/no-antagonism-mixture dose-effect relationships are calculated for corresponding mixed fields. No new experimental results are presented. Synergy analysis of effects due to a mixed radiation field whose components' individual dose-effect relationships are highly curvilinear should not consist of simply comparing to the sum of the components' effects. Such curvilinearity must often be allowed for in current radiobiology, especially when studying possible non-targeted ("bystander") effects. Consequently, many different synergy analysis theories are currently used in biology to replace simple effect additivity. We give evidence that for most synergy experiments and observations, incremental effect additivity is the most appropriate replacement. It has a large domain of applicability, being useful even when pronounced individual dose-effect relationship curvilinearity is a confounding factor. It allows calculation of 95% confidence intervals for baseline mixture dose-effect relationships taking into account parameter correlations; if non-targeted effects are important this gives much tighter intervals than neglecting the correlations. It always obeys two consistency conditions that simple effect additivity usually fails to obey: a "mixture of mixtures principle" and the standard "sham mixture principle". The mixture of mixtures principle is important in radiobiology because even nominally single-ion radiations are usually mixtures when they strike the biological target, due to intervening material. It is not yet clear whether mixing galactic cosmic ray components sometimes leads to statistically significant synergy for animal tumorigenesis. The substantial limitations of synergy theories are sometimes overlooked, and they warrant further study.