Inertia and Prediction in the Response to External Perturbation of Noisy Variables

TL;DR

This paper explores how noisy variables in stochastic systems respond slowly to external perturbations, emphasizing the relationship between variability, stability, and lability, and illustrating these concepts through models like the cell cycle, harmonic oscillator, and active oscillator.

Contribution

It introduces a phenomenological model linking variability and response efficiency, extending the understanding of response dynamics beyond linear regimes.

Findings

Variability inversely relates to stability and directly to lability.

The model explains response behaviors in cell cycle and oscillatory systems.

Comparisons with harmonic oscillator highlight universal response principles.

Abstract

For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation Dissipation Theorem (FDT). In a previous paper, we proposed a phenomenological model for the response of the cell cycle duration distribution to environmental changes which correlated the width of this distribution to response efficiency when FDT was not applicable. Here we emphasize how that model may be used to illustrate this general principle, that the stochasticity of a variable while inversely proportional to stability is often directly proportional to lability. Comparisons are made between this discrete-time model and the simple harmonic oscillator. We then consider a simple continuous dynamical system, the 'Active Oscillator', which illustrates this principle in another fashion.