Skewness and Kurtosis in Statistical Kinetics

TL;DR

This paper derives bounds on skewness and kurtosis for cycle completion times in enzymatic reactions, showing how higher moments reveal details about the reaction scheme beyond traditional measures.

Contribution

It introduces bounds on higher order moments (skewness and kurtosis) related to enzyme reaction states, providing new insights from single molecule data.

Findings

Bounds on skewness and kurtosis depend on the number of enzyme states.

Higher moments can reveal additional information about enzymatic schemes.

Results extend understanding of enzyme kinetics beyond the randomness parameter.

Abstract

We obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to a well known lower bound on the randomness parameter, the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network. Our results demonstrate that evaluating these higher order moments with single molecule data can lead to information about the enzymatic scheme that is not contained in the randomness parameter.