Interrelation between precisions on integrated currents and on recurrence times in Markov jump processes

Area of Science:

• * Stochastic processes
• * Biophysics
• * Chemical kinetics

Background:

• * Markov jump processes model systems with discrete states and transitions.
• * Understanding transition dynamics is crucial in biochemical systems (e.g., enzyme catalysis, molecular motors).
• * The randomness parameter quantifies timing precision in these systems.

Purpose of the Study:

• * To derive a general expression for the squared coefficient of variation of integrated current in Markov jump processes.
• * To establish the interrelation between this measure and the precision of transition timing.
• * To extend existing analyses to finite observation times and reversible transitions.

Main Methods:

• * Derivation of an explicit expression for the squared coefficient of variation for net transitions.
• * Mathematical elaboration to connect this expression with timing precision.
• * Analysis in the long-time limit and extension to finite time and reversibility.

Main Results:

• * A general formula for the squared coefficient of variation of integrated current was obtained.
• * The relationship between integrated current variation and transition timing precision was clarified.
• * New insights were provided for finite time and reversible transitions, expanding upon previous long-time, irreversible models.

Conclusions:

• * The derived expression facilitates numerical calculations for Markov jump processes.
• * The study enhances understanding of timing precision in biochemical dynamics.
• * The findings offer a more comprehensive framework for analyzing complex biological processes.