Unintuitive effects of substrate competition on steady state concentration of product of reversible enzymatic transformations

For a closed system, we analyze the steady state effect of alternate substrates and inhibitors, for reversible transformation catalyzed by the same enzyme. Inhibitors and alternate substrates are known to decrease the initial product formation rate. Here, without using any assumptions either of pseudo-steady state or of relative concentrations of enzyme and substrates, we analytically show that alternate substrates and competitive inhibitors will not decrease the steady state product concentration, and may lead to an unexpected increase in these concentrations. For such inhibitors, though the initial rate does decrease compared to inhibitor-free reactions, the final steady state concentration never decreases, and therefore no long-term inhibition of product levels is possible. In contrast, uncompetitive inhibitors decrease the steady state product concentrations as well as initial product formation rate. We further explore closed systems where two distinct enzymes catalyze the forward and reverse transformation, and identify conditions when an alternate substrate can increase the steady state product concentration. This study shows analytically and through simulations that steady state effects of competing substrates or inhibitors on product concentrations may be qualitatively different from their effect on initial rates. These results can contribute to the design and analysis of in vitro enzyme inhibition assays.