Nonequilibrium Scaling Behavior in Driven Soft Biological Assemblies

Abstract

Measuring and quantifying nonequilibrium dynamics in active biological systems is a major challenge because of their intrinsic stochastic nature and the limited number of variables accessible in any real experiment. We investigate what nonequilibrium information can be extracted from noninvasive measurements using a stochastic model of soft elastic networks with a heterogeneous distribution of activities, representing enzymatic force generation. In particular, we use this model to study how the nonequilibrium activity, detected by tracking two probes in the network, scales as a function of the distance between the probes. We quantify the nonequilibrium dynamics through the cycling frequencies, a simple measure of circulating currents in the phase space of the probes. We find that these cycling frequencies exhibit power-law scaling behavior with the distance between probes. In addition, we show that this scaling behavior governs the entropy production rate that can be recovered from the two traced probes. Our results provide insight into how internal enzymatic driving generates nonequilibrium dynamics on different scales in soft biological assemblies.

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

“…. α the ensemble average over the activities, which for a large enough system can be obtained as a spatial average over the network [27]. Our analytical expressions for the scaling laws of A 2 (r) α and ω 2 (r) α provide a direct connection between these non-equilibrium measures and the properties of the active noise, such as the densities and activity intensities of monopoles and dipoles forces.…”

“…To establish a relation between mesoscopic nonequilibrium measures and the internal activity, we consider a model for an elastic assembly driven by stochastic activity [27,[46][47][48]. Our model consists of a network of N beads connected by springs of elastic constant k. The network is immersed in a thermal bath, characterized by a friction coefficient γ and temperature T .…”

“…Furthermore, the cycling frequency is informative of the partial rate of entropy produced in the reduced subspace of the pair of observed degrees of freedom, through the expression [27]. Both these non-equilibrium measures display on average a power law behavior as function of the distance r between the tracked particles [27,28]. However, different properties of the active noise in the system may give rise to different functional forms of the scaling behavior.…”

“…Frequently used measures to quantify circulating currents in phase space are the area enclosing rate and the cycling frequency of the stochastic trajectories [25,33,34]. These measures are closely related to the entropy production rate [27,28].…”

“…The interpretation of the results of various nonequilibrium measurements can be aided by considering concrete models for active systems. Recently, we considered a simple model of driven elastic assemblies consisting of a bead-spring network [27,28] where the beads can experience both thermal and active fluctuations. Using this model, we estimated the area enclosing rate and the cycling frequency from the trajectories of two probe particles.…”