Fig. 6: Influence of mechanistic deviations on the optimum K_m.

a Reverse reactions, b Competitive inhibition, c Uncompetitive inhibition, and d BEP coefficient (\(\alpha\)). The dashed line corresponds to \({K}_{m}=[{{{{{\rm{S}}}}}}]\), with \([{{{{{\rm{S}}}}}}]\,=\,10\) µM. The true optimum \({K}_{m}\) for each mechanism is shown as a solid line along with its analytical equation (refer to Supplementary Note 5 for the derivations). In a, the product concentration (\([{{{{{\rm{P}}}}}}]\)) was set to 10 µM. The top half of a was colored at an arbitrarily low activity because the reverse reaction is more favorable in this region. The large discrepancy between the dashed and solid lines at \(\Delta {G}_{T} \, > \, 0\) is physically irrelevant, because the activity of the forward reaction cannot be discussed when the net reaction proceeds in the reverse direction. In b and c, the degree of inhibition \((\gamma \equiv I/{K}_{i})\) was set to 10. In d, the BEP coefficients were set to \({\alpha }_{1}={\alpha }_{2}=0.2\). No analytical solution was obtained for d.