 Cell-free tetrazolium interaction contrast

A 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 defineThe final term restores a baseline that would otherwise be subtracted twice. In the additive modelthe 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 givesFour 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.^[ref]

Direct cell-free MTT reduction by selected compounds motivated this kind of control.^[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.