# Braess’ Paradox in Enzyme Kinetics: Asymmetry from Population Balance without Direct Cooperativity

## TL;DR

This paper explains how a protein's asymmetric ATP hydrolysis can arise from structural constraints rather than direct interactions between its parts.

## Contribution

A novel Bayesian Markov model explains asymmetric enzyme kinetics without requiring direct allosteric interactions.

## Key findings

- Markov models predict observed ATP hydrolysis rates without assuming direct interactions between nucleotide-binding domains.
- The asymmetry in ATPase kinetics is explained by structural constraints that couple domain opening and closing.
- A mutation in one domain leads to faster kinetics by avoiding a kinetic trap state.

## Abstract

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.