Optimizing enzyme assays with one or two coupling enzymes

The cost of assays using one or two coupling enzymes is optimized by using equations to calculate the minimum amount(s) of enzyme(s) which should be used to obtain a given time (t₉₉) in which 99% of the rate V₀ of the first reaction is obtained. Using two coupling enzymes and given a value of t₉₉, the induction period L = L₁ + L₂ fulfills the requirement $\text{t}{}_{99}\text{2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{4.6}\text{≥ L ≥}\text{t}{}_{99}\text{4.6}$, allowing one to choose a cost lower than that derived from the until-now generally applied assumption of t₉₉ = 4.6L. Being $\text{α =}\text{L}{}_1\text{L}{}_2$, in optimized assays the values α, t₉₉, and L are related by $\text{T}{}_{99}\text{=4.6}\text{(1+α)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{1+α}\text{L}$, thus allowing (graphical) calculation of the amounts of coupling enzymes which will minimize the cost for every chosen t₉₉ or L. Maximum practical rates, allowed in some supposed interesting cases, have been calculated.