Slow relaxation and aging in the model of randomly connected cycles network

TL;DR

This paper models cellular stress response using a large random network of feedback cycles, capturing aging and relaxation dynamics consistent with experimental observations.

Contribution

It introduces a novel statistical model of interconnected feedback cycles to describe cellular aging and stress response dynamics.

Findings

Model reproduces aging dynamics observed in experiments

Analytical and numerical solutions match empirical data

First passage time relates to cell division after stress

Abstract

We propose a statistical model of a large random network with high connectivity in order to describe the behavior of {\it E.\,coli} cells after exposure to acute stress. The building blocks of this network are feedback cycles typical of the genetic and metabolic networks of a cell. Each node on the cycles is a spin degree of freedom representing a component in the cell's network that can be in one of two states - active or inactive. The cycles are interconnected by regulation or by the exchange of metabolites. Stress is realized by an external magnetic field that drives the nodes into an inactive state, and the time the magnetization passes zero value for the first time represents the first division event of the cell after the stress period. The numerical and analytical solutions for this first passage problem reproduce the aging dynamics observed in the experimental data.