= Illumination-initiation interaction in dye-loss controls
\b[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 contrast
$$
I_L=L_{11}-L_{10}-L_{01}+L_{00}
$$
measures <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.<A Continuous Visible Light Spectrophotometric Approach To Accurately Determine the Reactivity of Radical-Trapping Antioxidants by Evan A. Haidasz and others>[Abstract: visible-light spectrophotometric co-autoxidation and kinetic/stoichiometric interpretation]{ref}
The crucial qualification is <response-scale dependence of dye-loss interactions>. Consider an original first-order survival model with fully additive rate constants,
$$
k_{ij}=k_0+i\alpha+j\beta,\qquad L_{ij}(t)=1-e^{-k_{ij}t}.
$$
Then
$$
I_L(t)=-e^{-k_0t}(1-e^{-\alpha t})(1-e^{-\beta t}).
$$
For 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.<Guide to the expression of uncertainty in measurement by JCGM>[§5.2.2, equation 13]{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.
\Image[/dye-loss-interaction-scale.png]
{title=An original additive-rate model gives a negative interaction contrast on the fractional-loss scale. Transforming the same ideal observations back to rates gives zero rate interaction.}
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