Stochastic lumping analysis for linear kinetics and its application to the fluctuation relations between hierarchical kinetic networks

TL;DR

This paper introduces a stochastic lumping analysis for linear kinetic networks, extending traditional methods to include fluctuations and noise, and explores how hierarchical schemes can reliably reflect experimental behaviors and physical properties.

Contribution

It generalizes lumping analysis to stochastic differential equations and master equations, establishing fluctuation relations between equivalent kinetic networks under noise.

Findings

Provides a theoretical basis for using low-dimensional models in fluctuation studies

Establishes fluctuation relations between hierarchical kinetic networks

Supports the validity of simplified models in biological kinetics

Abstract

Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.