Evidence of hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium

TL;DR

This paper presents a theoretical model based on the generalized Langevin equation to describe the complex motion of tracers in viscoelastic media, capturing inertial, hydrodynamic, subdiffusive, and trapping effects, validated by experimental data.

Contribution

The paper introduces a minimal phenomenological model that simultaneously accounts for hydrodynamic and subdiffusive behaviors in viscoelastic media, supported by experimental validation.

Findings

Both subdiffusive scaling and hydrodynamic effects observed in experiments.

Analytical formulas accurately describe tracer dynamics.

Model successfully fits experimental trajectories of tracers in actin gels.

Abstract

We propose a theoretical model which relies on the generalized Langevin equation and may account for various dynamical features of the thermal motion of organelles, vesicles or macromolecules in viscoelastic media such as polymer networks. In particular, we consider inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventually optical trapping at long times. Simple analytical formulas for the mean square displacement and velocity auto-correlation function are derived. The developed theory is applied to the analysis of fifty-second long trajectories of micron-sized spherical tracers in actin gels that were acquired at one microsecond temporal resolution by using optical tweezers single-particle tracking. For the first time, both the subdiffusive scaling and hydrodynamic effects are observed within a single experiment and accurately described by a minimal phenomenological model.