# Soft inclusion in a confined fluctuating active gel

## TL;DR

This paper models the stochastic dynamics of inclusions in a confined active gel, revealing how active noise influences their positioning and shape, with implications for biological cell components.

## Contribution

It introduces a detailed Langevin-based framework for inclusions in active gels, analyzing shape and position dynamics with exact steady-state distributions.

## Key findings

- Active noise causes attraction to domain edges.
- A sharp transition in shape distribution occurs with noise amplitude.
- The model applies to biological inclusions like organelles and nuclei.

## Abstract

We study stochastic dynamics of a point and extended inclusion within a one dimensional confined active viscoelastic gel. We show that the dynamics of a point inclusion can be described by a Langevin equation with a confining potential and multiplicative noise. Using a systematic adiabatic elimination over the fast variables, we arrive at an overdamped equation with a proper definition of the multiplicative noise. To highlight various features and to appeal to different biological contexts, we treat the inclusion in turn as a rigid extended element, an elastic element and a viscoelastic (Kelvin-Voigt) element. The dynamics for the shape and position of the extended inclusion can be described by coupled Langevin equations. Deriving exact expressions for the corresponding steady state probability distributions, we find that the active noise induces an attraction to the edges of the confining domain. In the presence of a competing centering force, we find that the shape of the probability distribution exhibits a sharp transition upon varying the amplitude of the active noise. Our results could help understanding the positioning and deformability of biological inclusions, eg. organelles in cells, or nucleus and cells within tissues.