Mesoscopic non-equilibrium measures can reveal intrinsic features of the active driving

Abstract

Biological assemblies such as chromosomes, membranes, and the cytoskeleton are driven out of equilibrium at the nanoscale by enzymatic activity and molecular motors. Similar non-equilibrium dynamics can be realized in synthetic systems, such as chemically fueled colloidal particles. Characterizing the stochastic non-equilibrium dynamics of such active soft assemblies still remains a challenge. Recently, new non-invasive approaches have been proposed to determine non-equilibrium behavior, which are based on detecting broken detailed balance in the stochastic trajectories of several coordinates of the system. Inspired by the method of two-point microrheology, in which the equilibrium fluctuations of a pair of probe particles reveal the viscoelastic response of an equilibrium system, here we investigate whether we can extend such an approach to non-equilibrium assemblies: can one extract information on the nature of the active driving in a system from the analysis of a two-point non-equilibrium measure? We address this question theoretically in the context of a class of elastic systems, driven out of equilibrium by a spatially heterogeneous stochastic internal driving. We consider several scenarios for the spatial features of the internal driving that may be relevant in biological and synthetic systems, and investigate how such features of the active noise may be reflected in the long-range scaling behavior of two-point non-equilibrium measures.

Irreversibility in linear systems with colored noise

“…To reduce the complexity one commonly considers small fluctuations around a fixed point of the deterministic dynamics, for which the restoring force is approximately a linear function of the displacements. In relation to nonequilibrium dynamics and measures of irreversibility, such linear analysis has been applied in diverse contexts: driven biological assemblies [37][38][39], population dynamics [40], climate oscillations [4,41,42], or electronic circuits [36,43].…”

“…This entity can be traced back to the works of Mori and Kubo [6,7], where it was used in the derivation of the generalized Langevin equation. Recently, A has received renewed attention as a measure of irreversibility [36,37,42,43,54], it has been connected to the entropy production rate, and applied in an irreversibility-oriented dimensionality reduction scheme [55]. Measuring A is in fact equivalent to finding a linear expansion of the mean velocity field v(x) [56].…”

“…We first introduce a class of linear systems for which analytical solutions can be obtained. Then we demonstrate how the formulas for the irreversibility measures known for white-noise-driven systems [35][36][37] naturally generalize to the colored-noise case and discuss the physical mechanism behind this generalization. Finally, we present an example application of the new formulas to a model system of a driven soft biological network [37] that in the context of irreversibility has up to now only been studied within the white-noise approximation.…”

Learning the non-equilibrium dynamics of Brownian movies

“…Traditional approaches to measure microscopic forces and analyze time-lapse microscopy data typically rely on tracking the position or shape of well-defined probes, such as tracer beads, fluorescent proteins and filaments, or simply on exploiting the natural contrast of the intracellular medium to obtain such tracks 14 – 17 , 29 , 31 , 34 , 41 – 44 . The tracer trajectories can be studied through stochastic analysis techniques to extract an effective model for their dynamics and infer quantities like the entropy production rate 19 , 20 , 22 , 24 , 45 – 48 . There are, however, many cases in which tracking is impractical 49 , 50 , due to limited resolution or simply because there are no recognizable objects to use as tracers.…”

Learning the Non-Equilibrium Dynamics of Brownian Movies

“…Traditional approaches to measure microscopic forces and analyze time-lapse microscopy data typically rely on tracking the position or shape of well-defined probes such as tracer beads, fluorescent proteins and filaments, or simply on exploiting the natural contrast of the intracellular medium to obtain such tracks [13-16, 28, 30, 33, 38-41]. The tracer trajectories can be studied through stochastic analysis techniques to extract an effective model for their dynamics and infer quantities like the entropy production [18,19,21,23,[42][43][44][45]. There are, however, many cases in which tracking is impractical [46,47], due to limited resolution or simply because there are no recognizable objects to use as tracers.…”