Braess' Paradox in Enzyme Kinetics: Asymmetry from Population Balance without Direct Cooperativity.

The ATPase ABCE1, a member of the ubiquitous ATP-Binding Cassette protein superfamily, is essential in eukaryotic and archaeal ribosome recycling. It comprises a pair of homologous nucleotide-binding domains (NBDs), each containing a consensus nucleotide-binding site (NBS), where ATP hydrolysis takes place. Each of these sites can be in either an open or closed conformation. Despite the near symmetry of the two NBDs, and quite unexpectedly, their hydrolysis kinetics are highly asymmetric. While substitution of the catalytic glutamate (E238Q) in NBSI reduced the overall turnover rate of the ATPase by a factor of 2, as one might expect, the corresponding substitution in NBSII (E485Q) shows a so far unexplained 10-fold increase. To address this issue, we used Markov models to study how such a drastic asymmetry can arise. Specifically, we asked whether this observation can be explained without previously proposed direct allosteric interactions, such as electrostatic interactions, between the two NBSs. Indeed, using a Bayesian approach, we found Markov models that quantitatively predict the experimentally observed kinetics, as well as additional steady-state ATP occupancy data, both without such direct allosteric interaction. In particular, our results show that the observed remarkable asymmetry is fully explained by the structure-induced property that opening and closing always involves both NBSs. These models can explain the unexpected fast kinetics of the mutant of NBSII in terms of a drastic population shift due to the mutation, which circumvents a kinetic trap state that slows wild-type kinetics. Our Bayesian Markov approach may help to quantitatively explain similar nonintuitive Braess-type kinetics also in other enzymes where chemical/conformation coupling is essential.