= Cell-free tetrazolium interaction contrast
A \b[cell-free tetrazolium interaction contrast] isolates the part of an optical change that depends jointly on adding the test compound and adding the <tetrazolium salt>, in a specified <tetrazolium cell-free control>. All four mixtures lack cells; the comparison tests chemical or optical interference rather than cellular survival.
Write $R$ for reagent present, $0$ for reagent absent, $T$ for test compound and $V$ for its matched vehicle. From the four <absorbance> readings define
$$
I=A_{R,T}-A_{0,T}-A_{R,V}+A_{0,V}.
$$
The final term restores a baseline that would otherwise be subtracted twice. In the additive model
$$
A_{R,T}=\mu+r+t+i,\quad A_{0,T}=\mu+t,\quad
A_{R,V}=\mu+r,\quad A_{0,V}=\mu,
$$
the contrast equals the interaction $i$. The terms $r$ and $t$ describe the reagent-only and compound-only contributions relative to the vehicle baseline. This is an algebraic separation under stated conditions, not an assumption that the underlying chemical reactions are always additive.
An original example with readings $0.32,0.12,0.08,0.05$ in that order gives $I=0.17$. Subtracting only $A_{R,V}$ gives $0.24$ and retains the compound-only increment $0.07$. Adding the same constant optical offset to every reading leaves $I$ unchanged, whereas multiplying every reading by an unknown gain also multiplies $I$.
For <tetrazolium contrast uncertainty>, let the four readings have <covariance matrix> $\Sigma$ in the order above and put $w=(1,-1,-1,1)^{\mathsf T}$. Linear <uncertainty propagation> gives
$$
u_I^2=w^{\mathsf T}\Sigma w.
$$
Four independent readings with equal <standard uncertainty> $u$ give $u_I=2u$. A single shared additive offset contributes zero because the coefficients sum to zero; treating it as four independent offsets would overstate that contribution. Correlations require the appropriate input model.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[Sections 5.1–5.2, uncorrelated and correlated input quantities]{ref}
Direct cell-free <MTT> reduction by selected compounds motivated this kind of control.<Interference of plant extracts, phytoestrogens and antioxidants with the MTT tetrazolium assay by Regina Bruggisser and others>[Abstract, cell-free formazan formation]{ref} A nonzero contrast establishes a reagent-dependent cell-free optical effect under the matched conditions. Identifying that effect as a particular <formazan> requires suitable chemical or spectral evidence; transferring its magnitude to a cell-containing sample additionally requires a validated response model.
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