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 each containing a consensus nucleotide-binding site (NBS), where ATP hydrolysis takes place. Each of these sites can be either in an open or closed conformation. Despite this near symmetry, 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 two, as one might expect, the corresponding substitution in NBSII (E485Q) shows a so far unexplained tenfold increase. To address this issue, we used Markov models to study how such drastic asymmetry can arise. Specifically, we asked if previously proposed direct allosteric interaction between the two nucleotide-binding sites, such as electrostatic interactions, are required to explain this observation. 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 without such direct allosteric interaction. In particular, our results show that the structure-induced property that opening and closing always involves both nucleotide-binding sites suffices to explain the observed remarkable asymmetry. 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 down wild-type kinetics. Our Baysian Markov approach may help to quantitatively explain similar non-intuitive Braess-type kinetics also in other enzymes where chemical/conformation coupling is essential.