Decay times in turnover statistics of single enzymes

TL;DR

This paper investigates the statistical properties of enzymatic turnover times in non-equilibrium steady states, revealing unique decay time behaviors that simplify modeling and data analysis of enzyme kinetics.

Contribution

It uncovers that the number of decay constants in turnover distributions can be fewer than the number of enzyme states, due to eigenvalue cancellations in the kinetic mechanism.

Findings

Half of the decay times vanish from the distribution.

Decay times relate to eigenvalues of a sub-matrix of the master equation.

Results facilitate easier modeling and measurement of enzyme turnovers.

Abstract

The first passage times for enzymatic turnovers in non-equilibrium steady state display a statistical symmetry property related to non-equilibrium fluctuation theorems, that makes it possible to extract the chemical driving force from single molecule trajectories in non-equilibrium steady state. Below, we show that this system violates the general expectation that the number of decay constants needed to fit a first passage time distribution reflects the number of states in the escape problem. In fact, the structure of the kinetic mechanism makes half of the decay times vanish identically from the turnover time distribution. The terms that cancel out correspond to the eigenvalues of a certain sub-matrix of the master equation matrix for the first exit time problem. We discuss how these results make modeling and data analysis easier for such systems, and how the turnovers can be measured.