Fig. 7: Parallel reaction mechanism.

a A schematic representation of a model involving two parallel catalytic steps. The free enzyme, \(E\) can bind with a substrate molecule via two parallel processes to form the first substrate-bound conformer, \(E{S}_{1}\) or the second bound-enzymatic state, \(E{S}_{2}.\) These branched substrate-binding channels have splitting probabilities \(p\) and \(1-p\), respectively. Both bound states can form the product, \(P\) through irreversible catalytic events. From \(E{S}_{1}\) and \(E{S}_{2}\), unbinding events can occur that lead back to the free enzyme. The described kinetic processes are characterized by the rates of binding \(\left({k}_{{on}}\left[S\right]\right)\) where \(\left[S\right]\) is the substrate concentration, unbinding \(\left({k}_{{off}}\right)\), the first \(\left({k}_{{cat}}^{1}\right)\) and second \(\left({k}_{{cat}}^{2}\right)\) catalytic transitions, respectively. b 2D color map of the error factor \(\frac{\left\langle {W}_{{ES}}\right\rangle }{\left\langle {W}_{{ES}}^{{cat}}\right\rangle }\) in the space of the normalized catalytic rates \(\frac{{k}_{{cat}}^{1}}{{k}_{{off}}}\) and \(\frac{{k}_{{cat}}^{2}}{{k}_{{off}}}\), for the splitting probability \(p=0.5\). Here \(\left\langle {W}_{{ES}}\right\rangle\) and \(\left\langle {W}_{{ES}}^{{cat}}\right\rangle\) are the mean waiting times of the bound-enzymatic state and the conditional catalysis times, respectively. Note that for \(\frac{{k}_{{cat}}^{1}}{{k}_{{off}}}\) and \(\frac{{k}_{{cat}}^{2}}{{k}_{{off}}}\) that span four orders of magnitude, the error factor is always <30, and in most cases significantly smaller than this upper bound.