 Illumination-initiation interaction in dye-loss controls

Illumination-initiation interaction in dye-loss controls tests whether changing illumination has the same response in the absence and presence of chemical initiation. A crossed factorial design separates the four conditions. For mean fractional losses $L_{ij}$, with $i$ indicating initiation and $j$ illumination, the contrastmeasures statistical interaction on the fractional-loss scale. In the STY-BODIPY assay context, the optical observable is carrier loss during co-autoxidation, not a direct label of its chemical cause.^[ref]

The crucial qualification is response-scale dependence of dye-loss interactions. Consider an original first-order survival model with fully additive rate constants,ThenFor positive $\alpha$, $\beta$ and $t$, this is negative even though the rates have no interaction term. With stipulated $k_0=0$, $\alpha =\beta =0.1$ in reciprocal time units and $t=1$, the losses are $0$, $0.09516$, $0.09516$ and $0.18127$, giving $I_L\approx -0.00906$. Saturation of fractional loss produces the contrast without a new chemical coupling.

On the transformed scale $Y_{ij}=-\log (1-L_{ij})/t$, the same noiseless model gives $Y_{ij}=k_{ij}$ and zero interaction contrast. This transformation is appropriate only when the measured signal genuinely follows the stated survival model; product absorption or changing backgrounds can invalidate it. A transformed zero is therefore a conditional model check, not proof of a reaction mechanism.

For independent replicate measurements, the variance of the estimated loss contrast is ${\sum }_{ij}{\sigma }_{ij}^2/n_{ij}$. Four replicates per condition with common standard deviation 0.01 give a contrast standard uncertainty of 0.01. The modeled contrast above is smaller than that scale. Shared references instead introduce covariances that must be retained.^[ref]

Match temperature, oxygen access, timing and readout exposure across conditions. Specify the response scale before interpreting a nonzero contrast as evidence about photobleaching or initiated oxidation.