Systems in thermodynamic equilibrium are not only characterized by time-independent macroscopic properties, but also satisfy the principle of detailed balance in the transitions between microscopic configurations. Living systems function out of equilibrium and are characterized by directed fluxes through chemical states, which violate detailed balance at the molecular scale. Here we introduce a method to probe for broken detailed balance and demonstrate how such nonequilibrium dynamics are manifest at the mesosopic scale. The periodic beating of an isolated flagellum from Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes. With a model, we show how the breaking of detailed balance can also be quantified in stationary, nonequilibrium stochastic systems in the absence of periodic motion. We further demonstrate such broken detailed balance in the nonperiodic fluctuations of primary cilia of epithelial cells. Our analysis provides a general tool to identify nonequilibrium dynamics in cells and tissues.

Cells are active systems with molecular force generation that drives complex dynamics at the supramolecular scale. We present a quantitative study of molecular motions in cells over times from milliseconds to hours. Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random "stirring" that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

Systems coupled to multiple thermodynamic reservoirs can exhibit nonequilibrium dynamics, breaking detailed balance to generate currents. To power these currents, the entropy of the reservoirs increases. The rate of entropy production, or dissipation, is a measure of the statistical irreversibility of the nonequilibrium process. By measuring this irreversibility in several biological systems, recent experiments have detected that particular systems are not in equilibrium. Here we discuss three strategies to replace binary classification (equilibrium versus nonequilibrium) with a quantification of the entropy production rate. To illustrate, we generate time-series data for the evolution of an analytically tractable bead-spring model. Probability currents can be inferred and utilized to indirectly quantify the entropy production rate, but this approach requires prohibitive amounts of data in high-dimensional systems. This curse of dimensionality can be partially mitigated by using the thermodynamic uncertainty relation to bound the entropy production rate using statistical fluctuations in the probability currents.

The vaporization of a superheated droplet emulsion into gas bubbles using ultrasound – termed acoustic droplet vaporization (ADV) – has potential therapeutic applications in embolotherapy and drug delivery. The optimization of ADV for therapeutic applications can be enhanced by understanding the physical mechanisms underlying ADV, which are currently not clearly elucidated. Acoustic cavitation is one possible mechanism. This paper investigates the relationship between the ADV and inertial cavitation (IC) thresholds (measured as peak rarefactional pressures) by studying parameters that are known to influence the IC threshold. These parameters include bulk fluid properties such as gas saturation, temperature, viscosity, and surface tension; droplet parameters such as degree of superheat, surfactant type, and size; and acoustic properties such as pulse repetition frequency and pulse width. In all cases the ADV threshold occurred at a lower rarefactional pressure than the IC threshold indicating that the phase-transition occurs before IC events. The viscosity and temperature of the bulk fluid are shown to influence both thresholds directly and inversely, respectively. An inverse trend is observed between threshold and diameter for droplets in the 1 to 2.5 μ range. Based on a choice of experimental parameters, it is possible to achieve ADV with or without IC.

The thermal motion of stiff filaments in a crowded environment is highly constrained and anisotropic; it underlies the behavior of such disparate systems as polymer materials, nanocomposites, and the cell cytoskeleton. Despite decades of theoretical study, the fundamental dynamics of such systems remains a mystery. Using near-infrared video microscopy, we studied the thermal diffusion of individual single-walled carbon nanotubes (SWNTs) confined in porous agarose networks. We found that even a small bending flexibility of SWNTs strongly enhances their motion: The rotational diffusion constant is proportional to the filament-bending compliance and is independent of the network pore size. The interplay between crowding and thermal bending implies that the notion of a filament's stiffness depends on its confinement. Moreover, the mobility of SWNTs and other inclusions can be controlled by tailoring their stiffness.

By relating nanotechnology to soft condensed matter, understanding the mechanics and dynamics of single-walled carbon nanotubes (SWCNTs) in fluids is crucial for both fundamental and applied science. Here, we study the Brownian bending dynamics of individual chirality-assigned SWCNTs in water by fluorescence microscopy. The bending stiffness scales as the cube of the nanotube diameter and the shape relaxation times agree with the semiflexible chain model. This suggests that SWCNTs may be the archetypal semiflexible filaments, highly suited to act as nanoprobes in complex fluids or biological systems.actin ͉ microrheology ͉ semiflexible filaments and polymers ͉ stochastic dynamics ͉ nanomechanics

Myosin motor proteins drive vigorous steady-state fluctuations in the actin cytoskeleton of cells. Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as singlewalled carbon nanotubes are used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in such biopolymer networks. Here, we analytically calculate shape fluctuations of semiflexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under nonequilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.

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