Dear

Authors as Andrew C. Storer and Athel Cornish-Bowden have worked on coupled enzyme and their manuscript could help for understanding.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1168067/

https://www.ncbi.nlm.nih.gov/pubmed/9025915

The assay should be set up in such a way that the coupling enzyme should never be rate limiting, even when the primary enzyme is at Vmax. You can test for this problem by seeing whether the rate of the reaction increases when the coupling enzyme concentration increases. If that happens, then the coupling enzyme concentration was too low.

Imagine that the activity of the coupling enzyme is sufficient to keep up with the primary enzyme when the primary enzyme's substrate concentration is low, but insufficient to keep up when the concentration is high. As the substrate concentration is increased, the rate of the reaction will reach an apparent Vmax that is lower than the actual Vmax. As a result, the Km will appear to be lower than the actual Km, not higher.

On the other hand, if the product of the primary reaction acts as a competitive inhibitor of that reaction, as sometimes happens, and if the coupling enzyme activity is insufficient to consume it, the product concentration could increase to the point where the competitive inhibition becomes significant. In that case, the apparent Km of the substrate for the primary reaction will increase due to the competitive inhibition.

Other possible reasons for the 2-fold difference between your new Km measurement and the previous one include: changes in the buffer conditions, a temperature difference, differences in the purity of the substrate (including water content), and error in the substrate stock solution concentration.