Analytical description of the lag phase in coupled-enzyme substrate assays

The finite excess of the non-limiting enzymes in a coupled-enzyme assay causes an initial delay that can lead to inaccuracies in the kinetic read-out of substrate assays. We derive a new correction term to the well-known analytical Lambert W based expression of the progress curve. The key parameter in comparing the activities of the various enzymes in the chain is their pseudo first order rate constant k' = V-max/ K-m. The order in which the limiting (L) and non-limiting (NL) enzymes appear in the chain has little to no effect on the final progress curves. On simulated data the model gives good recoveries of unknown substrate concentrations as well as of the k(L)' of the limiting enzyme, even with excess ratio of the non-limiting over the limiting enzymes k(r) =/k(NL)'/k(L)' as low as 3, and including the case of multiple non-limiting enzymes with low excess. In the presence of noise and on experimental data the new analytical expression shows superior performance in smoothing the progress curves compared to traditional non-parametric smoothing techniques. This results in reduced scatter on the dose response curves, on par or even exceeding the performance of endpoint analysis but in shorter time. The analytical expression remains very robust in the presence of low excess ratios.