Effective temperature of red-blood-cell membrane fluctuations

Fluctuation Theorems for Heat Exchanges between Passive and Active Baths

In addition to providing general constraints on probability distributions, fluctuation theorems allow us to infer essential information on the role played by temperature in heat exchange phenomena. In this numerical study, we measure the temperature of an out-of-equilibrium active bath using a fluctuation theorem that relates the fluctuations in the heat exchanged between two baths to their temperatures. Our setup consists of a single particle moving between two wells of a quartic potential accommodating two different baths. The heat exchanged between the two baths is monitored according to two definitions: as the kinetic energy carried by the particle whenever it jumps from one well to the other and as the work performed by the particle on one of the two baths when immersed in it. First, we consider two equilibrium baths at two different temperatures and verify that a fluctuation theorem featuring the baths temperatures holds for both heat definitions. Then, we introduce an additional Gaussian coloured noise in one of the baths, so as to make it effectively an active (out-of-equilibrium) bath. We find that a fluctuation theorem is still satisfied with both heat definitions. Interestingly, in this case the temperature obtained through the fluctuation theorem for the active bath corresponds to the kinetic temperature when considering the first heat definition, while it is larger with the second one. We interpret these results by looking at the particle jump phenomenology.

Viscoelastic phenotyping of red blood cells

Red blood cells (RBCs) are the simplest cell types with complex dynamical and viscoelastic phenomenology. While the mechanical rigidity and the flickering noise of RBCs have been extensively investigated, an accurate determination of the constitutive equations of the relaxational kinetics is lacking. Here we measure the force relaxation of RBCs under different types of tensional and compressive extension-jump protocols by attaching an optically trapped bead to the RBC membrane. Relaxational kinetics follows linear response from 60 pN (tensional) to -20 pN (compressive) applied forces, exhibiting a triple exponential function with three well-separated timescales over four decades (0.01-100 s). While the fast timescale (τF∼0.02(1)s) corresponds to the relaxation of the membrane, the intermediate and slow timescales (τI=4(1)s; τS=70(8)s) likely arise from the cortex dynamics and the cytosol viscosity. Relaxation is highly heterogeneous across the RBC population, yet the three relaxation times are correlated, showing dynamical scaling. Finally, we find that glucose depletion and laser illumination of RBCs lead to faster triple exponential kinetics and RBC rigidification. Viscoelastic phenotyping is a promising dynamical biomarker applicable to other cell types and active systems.

Coherent light scattering from cellular dynamics in living tissues

This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.

Variance sum rule for entropy production

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

Non-Markovian Modeling of Nonequilibrium Fluctuations and Dissipation in Active Viscoelastic Biomatter

Based on a Hamiltonian that incorporates the elastic coupling between a tracer particle and the embedding active viscoelastic biomatter, we derive a generalized non-Markovian Langevin model for the nonequilibrium mechanical tracer response. Our analytical expressions for the frequency-dependent tracer response function and the tracer positional autocorrelation function agree quantitatively with experimental data for red blood cells and actomyosin networks with and without adenosine triphosphate over the entire frequency range and in particular reproduce the low-frequency violation of the fluctuation-dissipation theorem. The viscoelastic power laws, the elastic constants and effective friction coefficients extracted from the experimental data allow straightforward physical interpretation.

Anisotropic short-range attractions precisely model branched erythrocyte aggregates

Homogeneous suspensions of red blood cells (RBCs or erythrocytes) in blood plasma are unstable in the absence of driving forces and form elongated stacks, called rouleaux. These erythrocyte aggregates are often branched porous networks - a feature that existing red blood cell aggregation models and simulations fail to predict exactly. Here we establish that alignment-dependent attractive forces in a system of dimers can precisely generate branched structures similar to RBC aggregates observed under a microscope. Our simulations consistently predict that the growth rate of typical mean rouleau size remains sub-linear - a hallmark from past studies - which we also confirm by deriving a reaction kernel taking into account appropriate collision cross-section, approach velocities, and an area-dependent sticking probability. The system exhibits unique features such as the existence of percolated and/or single giant cluster states, multiple coexisting mass-size scalings, and transition to a branched phase upon fine-tuning of model parameters. Upon decreasing the depletion thickness we find that the percolation threshold increases but the morphology of the structures opens up towards an increased degree of branching. Remarkably the system self-organizes to produce a universal power-law size distribution scaling irrespective of the model parameters.

Trapped tracer in a non-equilibrium bath: dynamics and energetics

We study the dynamics of a tracer that is elastically coupled to active particles being kept at two different temperatures, as a prototype of tracer dynamics in a non-equilibrium bath. Employing analytical techniques, we find the exact solution of the probability density function for the effective motion of the tracer. The analytical results are supported by numerical simulations. By combining the experimentally accessible quantities such as the response function and the power spectrum, we measure the non-equilibrium fluctuations in terms of the effective temperature. In addition, we compute the energy dissipation rate to find the precise effects of activity. Our study is relevant in understanding athermal fluctuations arising in cytoskeletal networks or inside a chromosome.

Topologically constrained fluctuations and thermodynamics regulate nonequilibrium response

The limits on a system's response to external perturbations inform our understanding of how physical properties can be shaped by microscopic characteristics. Here, we derive constraints on the steady-state nonequilibrium response of physical observables in terms of the topology of the microscopic state space and the strength of thermodynamic driving. Notably, evaluation of these limits requires no kinetic information beyond the state-space structure. When applied to models of receptor binding, we find that sensitivity is bounded by the steepness of a Hill function with a Hill coefficient enhanced by the chemical driving beyond the structural equilibrium limit.

Centripetal nuclear shape fluctuations associate with chromatin condensation in early prophase

The nucleus plays a central role in several key cellular processes, including chromosome organisation, DNA replication and gene transcription. Recent work suggests an association between nuclear mechanics and cell-cycle progression, but many aspects of this connection remain unexplored. Here, by monitoring nuclear shape fluctuations at different cell cycle stages, we uncover increasing inward fluctuations in late G2 and in early prophase, which are initially transient, but develop into instabilities when approaching the nuclear-envelope breakdown. We demonstrate that such deformations correlate with chromatin condensation by perturbing both the chromatin and the cytoskeletal structures. We propose that the contrasting forces between an extensile stress and centripetal pulling from chromatin condensation could mechanically link chromosome condensation with nuclear-envelope breakdown, two main nuclear processes occurring during mitosis.

Phase behavior of active and passive dumbbells

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

Measurement of the low-frequency charge noise of bacteria

Bacteria meticulously regulate their intracellular ion concentrations and create ionic concentration gradients across the bacterial membrane. These ionic concentration gradients provide free energy for many cellular processes and are maintained by transmembrane transport. Given the physical dimensions of a bacterium and the stochasticity in transmembrane transport, intracellular ion concentrations and hence the charge state of a bacterium are bound to fluctuate. Here we investigate the charge noise of hundreds of nonmotile bacteria by combining electrical measurement techniques from condensed matter physics with microfluidics. In our experiments, bacteria in a microchannel generate charge density fluctuations in the embedding electrolyte due to random influx and efflux of ions. Detected as electrical resistance noise, these charge density fluctuations display a power spectral density proportional to 1/f^{2} for frequencies 0.05Hz≤f≤1Hz. Fits to a simple noise model suggest that the steady-state charge of a bacterium fluctuates by ±1.30×10^{6}e(e≈1.60×10^{-19}C), indicating that bacterial ion homeostasis is highly dynamic and dominated by strong charge noise. The rms charge noise can then be used to estimate the fluctuations in the membrane potential; however, the estimates are unreliable due to our limited understanding of the intracellular concentration gradients.

Arrested coalescence of multicellular aggregates

Multicellular aggregates are known to exhibit liquid-like properties. The fusion process of two cell aggregates is commonly studied as the coalescence of two viscous drops. However, tissues are complex materials and can exhibit viscoelastic behaviour. It is known that elastic effects can prevent the complete fusion of two drops, a phenomenon known as arrested coalescence. Here we study this phenomenon in stem cell aggregates and provide a theoretical framework which agrees with the experiments. In addition, agent-based simulations show that active cell fluctuations can control a solid-to-fluid phase transition, revealing that arrested coalescence can be found in the vicinity of an unjamming transition. By analysing the dynamics of the fusion process and combining it with nanoindentation measurements, we obtain the effective viscosity, shear modulus and surface tension of the aggregates. More generally, our work provides a simple, fast and inexpensive method to characterize the mechanical properties of viscoelastic materials.

Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions

We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.

Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise

We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a nonthermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in the case of a purely thermal bath, the distribution is double exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate, is investigated carefully. In addition, we study the first-arrival properties of the system in the presence of a delta-function sink with strength κ, where κ=0 and κ=∞ correspond to fully nonreactive and fully reactive sinks, respectively. We explore the effect of two competitive mechanisms: the diffusive spread in the presence of two noises and the increase in probability density around the initial position due to stochastic resetting. We show that there exists an optimal resetting rate, which minimizes the mean first-arrival time (MFAT) to the sink for a given value of the sink strength. We also explore the effect of the strength of the Poissonian noise on MFAT, in addition to sink strength. Our formalism generalizes the diffusion-limited reaction under resetting in a nonequilibrium bath and provides an efficient search strategy for a reactant to find a target site, relevant in a range of biophysical processes.

Inertial effects on the Brownian gyrator

The recent interest into the Brownian gyrator has been confined chiefly to the analysis of Brownian dynamics both in theory and experiment despite the applicability of general cases with definite mass. Considering mass explicitly in the solution of the Fokker-Planck equation and Langevin dynamics simulations, we investigate how inertia can change the dynamics and energetics of the Brownian gyrator. In the Langevin model, the inertia reduces the nonequilibrium effects by diminishing the declination of the probability density function and the mean of a specific angular momentum, j_{θ}, as a measure of rotation. Another unique feature of the Langevin description is that rotation is maximized at a particular anisotropy while the stability of the rotation is minimized at a particular anisotropy or mass. Our results suggest that the Langevin dynamics description of the Brownian gyrator is intrinsically different from that with Brownian dynamics. In addition, j_{θ} is proven to be essential and convenient for estimating stochastic energetics such as heat currents and entropy production even in the underdamped regime.

Extensions of the worm-like-chain model to tethered active filaments under tension

Intracellular elastic filaments such as microtubules are subject to thermal Brownian noise and active noise generated by molecular motors that convert chemical energy into mechanical work. Similarly, polymers in living fluids such as bacterial suspensions and swarms suffer bending deformations as they interact with single bacteria or with cell clusters. Often, these filaments perform mechanical functions and interact with their networked environment through cross-links or have other similar constraints placed on them. Here, we examine the mechanical properties-under tension-of such constrained active filaments under canonical boundary conditions motivated by experiments. Fluctuations in the filament shape are a consequence of two types of random forces-thermal Brownian forces and activity derived forces with specified time and space correlation functions. We derive force-extension relationships and expressions for the mean square deflections for tethered filaments under various boundary conditions including hinged and clamped constraints. The expressions for hinged-hinged boundary conditions are reminiscent of the worm-like-chain model and feature effective bending moduli and mode-dependent non-thermodynamic effective temperatures controlled by the imposed force and by the activity. Our results provide methods to estimate the activity by measurements of the force-extension relation of the filaments or their mean square deflections, which can be routinely performed using optical traps, tethered particle experiments, or other single molecule techniques.

Fluctuating Motion in an Active Environment

We derive the fluctuation dynamics of a probe in weak coupling with a living medium, modeled as particles undergoing an active Ornstein-Uhlenbeck dynamics. Nondissipative corrections to the fluctuation-dissipation relation are written out explicitly in terms of time correlations in the active medium. A first term changes the inertial mass of the probe as a consequence of the persistence of the active medium. A second correction modifies the friction kernel. The resulting generalized Langevin equation benchmarks the motion induced on probes immersed in active versus passive media. The derivation uses nonequilibrium response theory.

Learning the non-equilibrium dynamics of Brownian movies

Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.

Learning Entropy Production via Neural Networks

This Letter presents a neural estimator for entropy production (NEEP), that estimates entropy production (EP) from trajectories of relevant variables without detailed information on the system dynamics. For steady state, we rigorously prove that the estimator, which can be built up from different choices of deep neural networks, provides stochastic EP by optimizing the objective function proposed here. We verify the NEEP with the stochastic processes of the bead spring and discrete flashing ratchet models and also demonstrate that our method is applicable to high-dimensional data and can provide coarse-grained EP for Markov systems with unobservable states.

Translational and rotational dynamics of a self-propelled Janus probe in crowded environments

We computationally investigate the dynamics of a self-propelled Janus probe in crowded environments. The crowding is caused by the presence of viscoelastic polymers or non-viscoelastic disconnected monomers. Our simulations show that the translational as well as rotational mean square displacements have a distinctive three-step growth for fixed values of self-propulsion force, and steadily increase with self-propulsion, irrespective of the nature of the crowder. On the other hand, in the absence of crowders, the rotational dynamics of the Janus probe is independent of self-propulsion force. On replacing the repulsive polymers with sticky ones, translational and rotational mean square displacements of the Janus probe show a sharp drop. Since different faces of a Janus particle interact differently with the environment, we show that the direction of self-propulsion also affects its dynamics. The ratio of long-time translational and rotational diffusivities of the self-propelled probe with a fixed self-propulsion, when plotted against the area fraction of the crowders, passes through a minimum and at higher area fraction merges to its value in the absence of the crowder. This points towards the decoupling of the translational and rotational dynamics of the self-propelled probe at an intermediate area fraction of the crowders. However, such translational-rotational decoupling is absent for passive probes.

Escape of a passive particle from an activity-induced energy landscape: emergence of slow and fast effective diffusion

Spontaneous persistent motions driven by active processes play a central role in maintaining living cells far from equilibrium. In the majority of research studies, the steady state dynamics of an active system has been described in terms of an effective temperature. By contrast, we have examined a prototype model for diffusion in an activity-induced rugged energy landscape to describe the slow dynamics of a tagged particle in a dense active environment. The expression for the mean escape time from the activity-induced rugged energy landscape holds only in the limit of low activity and the mean escape time from the rugged energy landscape increases with activity. The precise form of the active correlation will determine whether the mean escape time will depend on the persistence time or not. The activity-induced rugged energy landscape approach also allows an estimate of the non-equilibrium effective diffusivity characterizing the slow diffusive motion of the tagged particle due to activity. On the other hand, in a dilute environment, high activity augments the diffusion of the tagged particle. The enhanced diffusion can be attributed to an effective temperature higher than the ambient temperature and this is used to calculate the Kramers' mean escape time, which decreases with activity. Our results have direct relevance to recent experiments on tagged particle diffusion in condensed phases.

Quantifying the non-equilibrium activity of an active colloid

Active matter systems exhibit rich emergent behavior due to constant injection and dissipation of energy at the level of individual agents. Since these systems are far from equilibrium, their dynamics and energetics cannot be understood using the framework of equilibrium statistical mechanics. Recent developments in stochastic thermodynamics extend classical concepts of work, heat, and energy dissipation to fluctuating non-equilibrium systems. We use recent advances in experiment and theory to study the non-thermal dissipation of individual light-activated self-propelled colloidal particles. We focus on characterizing the transition from thermal to non-thermal fluctuations and show that energy dissipation rates on the order of ∼kBT s-1 are measurable from finite time series data.

Mechanics of Multicentrosomal Clustering in Bipolar Mitotic Spindles

To segregate chromosomes in mitosis, cells assemble a mitotic spindle, a molecular machine with centrosomes at two opposing cell poles and chromosomes at the equator. Microtubules and molecular motors connect the poles to kinetochores, specialized protein assemblies on the centromere regions of the chromosomes. Bipolarity of the spindle is crucial for the proper cell division, and two centrosomes in animal cells naturally become two spindle poles. Cancer cells are often multicentrosomal, yet they are able to assemble bipolar spindles by clustering centrosomes into two spindle poles. Mechanisms of this clustering are debated. In this study, we computationally screen effective forces between 1) centrosomes, 2) centrosomes and kinetochores, 3) centrosomes and chromosome arms, and 4) centrosomes and cell cortex to understand mechanics that determines three-dimensional spindle architecture. To do this, we use the stochastic Monte Carlo search for stable mechanical equilibria in the effective energy landscape of the spindle. We find that the following conditions have to be met to robustly assemble the bipolar spindle in a multicentrosomal cell: 1) the strengths of centrosomes' attraction to each other and to the cell cortex have to be proportional to each other and 2) the strengths of centrosomes' attraction to kinetochores and repulsion from the chromosome arms have to be proportional to each other. We also find that three other spindle configurations emerge if these conditions are not met: 1) collapsed, 2) monopolar, and 3) multipolar spindles, and the computational screen reveals mechanical conditions for these abnormal spindles.

Active Contact Forces Drive Nonequilibrium Fluctuations in Membrane Vesicles

We analyze the nonequilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria-membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria-membrane contact forces. Taking advantage of the lengthscale and timescale separation of these contact forces and thermal noise, we further corroborate our results with an approximate theoretical solution to the dynamical membrane equations. Our theory and simulations demonstrate excellent agreement with nonequilibrium fluctuations observed in experiments. Moreover, our theory reveals that the fluctuation-dissipation theorem is not broken by the bacteria; rather, membrane fluctuations can be decomposed into thermal and active components.

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

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 the 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.

Three-Dimensional Shapes and Cell Deformability of Rat Red Blood Cells during and after Asphyxial Cardiac Arrest

Changes in microcirculation are believed to perform an important role after cardiac arrest. In particular, rheological changes in red blood cells (RBCs) have been observed during and after ischemic-reperfusion injury. Employing three-dimensional laser interferometric microscopy, we investigated three-dimensional shapes and deformability of RBCs during and after asphyxial cardiac arrest in rats at the individual cell level. Rat cardiac arrest was induced by asphyxia. Five rats were maintained for 7 min of no-flow time, and then, cardiopulmonary resuscitation (CPR) was started. Blood samples were obtained before cardiac arrest, during CPR, and 60 min after return of spontaneous circulation (ROSC). Quantitative phase imaging (QPI) techniques based on laser interferometry were used to measure the three-dimensional refractive index (RI) tomograms of the RBC, from which structural and biochemical properties were retrieved. Dynamic membrane fluctuations in the cell membrane were also quantitatively and sensitively measured in order to investigate cell deformability. Mean corpuscular hemoglobin, mean cell volume, mean corpuscular hemoglobin concentration, and red blood cell distribution width remained unchanged during CPR and after ROSC compared with those before cardiac arrest. QPI results revealed that RBC membrane fluctuations, sphericity, and surface area did not change significantly during CPR or after ROSC compared with initial values. In conclusion, no three-dimensional shapes and cell deformability changes in RBCs were detected.

Irreversibility and emergent structure in active matter

Active matter is rapidly becoming a key paradigm of out-of-equilibrium soft matter exhibiting complex collective phenomena, yet the thermodynamics of such systems remain poorly understood. In this article we study the dynamical irreversibility of large-scale active systems capable of motility-induced phase separation and polar alignment. We use a model with momenta in both translational and rotational degrees of freedom, revealing a hidden component not previously reported in the literature. Steady-state irreversibility is quantified at each point in the phase diagram which exhibits sharp discontinuities at phase transitions. Identification of the irreversibility in individual particles lays the groundwork for discussion of the thermodynamics of microfeatures, such as defects in the emergent structure. The interpretation of the time reversal symmetry in the dynamics of the particles is found to be crucial.

Quantitative analysis of three-dimensional morphology and membrane dynamics of red blood cells during temperature elevation

The optimal functionality of red blood cells is closely associated with the surrounding environment. This study was undertaken to analyze the changes in membrane profile, mean corpuscular hemoglobin (MCH), and cell membrane fluctuations (CMF) of healthy red blood cells (RBC) at varying temperatures. The temperature was elevated from 17 °C to 41 °C within a duration of less than one hour, and the holograms were recorded by an off-axis configuration. After hologram reconstruction, we extracted single RBCs and evaluated their morphologically related features (projected surface area and sphericity coefficient), MCH, and CMF. We observed that elevating the temperature results in changes in the three-dimensional (3D) profile. Since CMF amplitude is highly correlated to the bending curvature of RBC membrane, temperature-induced shape changes can alter CMF’s map and amplitude; mainly larger fluctuations appear on dimple area at a higher temperature. Regardless of the shape changes, no alterations in MCH were seen with temperature variation.

Generalized Ornstein-Uhlenbeck model for active motion

We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E 90, 012111 (2014)10.1103/PhysRevE.90.012111]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.

Scaling behavior of nonequilibrium measures in internally driven elastic assemblies

Detecting and quantifying nonequilibrium activity is essential for studying internally driven assemblies, including synthetic active matter and complex living systems such as cells or tissue. We discuss a noninvasive approach of measuring nonequilibrium behavior based on the breaking of detailed balance. We focus on "cycling frequencies"-the average frequency with which the trajectories of pairs of degrees of freedom revolve in phase space-and explain their connection with other nonequilibrium measures, including the area enclosing rate and the entropy production rate. We test our approach on simple toy models composed of elastic networks immersed in a viscous fluid with site-dependent internal driving. We prove both numerically and analytically that the cycling frequencies obey a power law as a function of distance between the tracked degrees of freedom. Importantly, the behavior of the cycling frequencies contains information about the dimensionality of the system and the amplitude of active noise. The mapping we use in our analytical approach thus offers a convenient framework for predicting the behavior of two-point nonequilibrium measures for a given activity distribution in the network.

Statistical mechanics of a single active slider on a fluctuating interface

We study the statistical mechanics of a single active slider on a fluctuating interface, by means of numerical simulations and theoretical arguments. The slider, which moves by definition towards the interface minima, is active as it also stimulates growth of the interface. Even though such a particle has no counterpart in thermodynamic systems, active sliders may provide a simple model for ATP-dependent membrane proteins that activate cytoskeletal growth. We find a wide range of dynamical regimes according to the ratio between the timescales associated with the slider motion and the interface relaxation. If the interface dynamics is slow, the slider behaves like a random walker in a random environment, which, furthermore, is able to escape environmental troughs by making them grow. This results in different dynamic exponents to the interface and the particle: the former behaves as an Edward-Wilkinson surface with dynamic exponent 2, whereas the latter has dynamic exponent 3/2. When the interface is fast, we get sustained ballistic motion with the particle surfing a membrane wave created by itself. However, if the interface relaxes immediately (i.e., it is infinitely fast), particle motion becomes symmetric and goes back to diffusive. Due to such a rich phenomenology, we propose the active slider as a toy model of fundamental interest in the field of active membranes and, generally, whenever the system constituent can alter the environment by spending energy.

Active Mechanics Reveal Molecular-Scale Force Kinetics in Living Oocytes

Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in vitro by single molecule approaches, but their in vivo behavior remains elusive. Here, we study the active diffusion of vesicles in mouse oocytes, where this process plays a key role in nuclear positioning during development, and combine an experimental and theoretical framework to extract molecular-scale force kinetics (force, power stroke, and velocity) of the in vivo active process. Assuming a single dominant process, we find that the nonequilibrium activity induces rapid kicks of duration τ ∼ 300 μs resulting in an average force of F ∼ 0.4 pN on vesicles in in vivo oocytes, remarkably similar to the kinetics of in vitro myosin-V. Our results reveal that measuring in vivo active fluctuations allows extraction of the molecular-scale activity in agreement with single-molecule studies and demonstrates a mesoscopic framework to access force kinetics.

Spatial Fluctuations at Vertices of Epithelial Layers: Quantification of Regulation by Rho Pathway

In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin, and cross-linkers. Such an approach deliberately avoids consideration of the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho signaling pathway, which is composed of multiple layers of coupled activators and inhibitors. Here, we investigate how such a pathway controls the dynamics of confluent epithelial tissues by tracking the displacements of the junction points between cells. Using a phenomenological model to analyze the vertex fluctuations, we rationalize the effects of different Rho signaling targets on the emergent tissue activity by quantifying the effective diffusion coefficient, and the persistence time and length of the fluctuations. Our results reveal an unanticipated correlation between layers of activation/inhibition and spatial fluctuations within tissues. Overall, this work connects regulation via biochemical signaling with mesoscopic spatial fluctuations, with potential application to the study of structural rearrangements in epithelial tissues.

Signatures of motor susceptibility to forces in the dynamics of a tracer particle in an active gel

We study a model for the motion of a tracer particle inside an active gel, exposing the properties of the van Hove distribution of the particle displacements. Active events of a typical force magnitude can give rise to non-Gaussian distributions having exponential tails or side peaks. The side peaks are predicted to appear when the local bulk elasticity of the gel is large enough and few active sources are dominant. We explain the regimes of the different distributions and study the structure of the side peaks for active sources that are susceptible to the elastic stress that they cause inside the gel. We show how the van Hove distribution is altered by both the duty cycle of the active sources and their susceptibility, and suggest it as a sensitive probe to analyze microrheology data in active systems with restoring elastic forces.

Stationary superstatistics distributions of trapped run-and-tumble particles

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.

A gradient-based, GPU-accelerated, high-precision contour-segmentation algorithm with application to cell membrane fluctuation spectroscopy

We present a novel intensity-gradient based algorithm specifically designed for nanometer-segmentation of cell membrane contours obtained with high-resolution optical microscopy combined with high-velocity digital imaging. The algorithm relies on the image oversampling performance and computational power of graphical processing units (GPUs). Both, synthetic and experimental data are used to quantify the sub-pixel precision of the algorithm, whose analytic performance results comparatively higher than in previous methods. Results from the synthetic data indicate that the spatial precision of the presented algorithm is only limited by the signal-to-noise ratio (SNR) of the contour image. We emphasize on the application of the new algorithm to membrane fluctuations (flickering) in eukaryotic cells, bacteria and giant vesicle models. The method shows promising applicability in several fields of cellular biology and medical imaging for nanometer-precise boundary-determination and mechanical fingerprinting of cellular membranes in optical microscopy images. Our implementation of this high-precision flicker spectroscopy contour tracking algorithm (HiPFSTA) is provided as open-source at www.github.com/michaelmell/hipfsta.

Active dumbbells: Dynamics and morphology in the coexisting region

With the help of molecular dynamics simulations we study an ensemble of active dumbbells in purely repulsive interaction. We derive the phase diagram in the density-activity plane and we characterise the various phases with liquid, hexatic and solid character. The analysis of the structural and dynamical properties, such as enstrophy, mean-square displacement, polarisation, and correlation functions, shows the continuous character of liquid and hexatic phases in the coexisting region when the activity is increased starting from the passive limit.

Effective temperature of active fluids and sheared soft glassy materials

The dynamics within active fluids, driven by internal activity of the self-propelled particles, is a subject of intense study in non-equilibrium physics. These systems have been explored using simulations, where the motion of a passive tracer particle is followed. Similar studies have been carried out for a soft glassy material that is driven by shearing its boundaries. In both types of systems the non-equilibrium motion have been quantified by defining a set of "effective temperatures", using both the tracer particle kinetic energy and the fluctuation-dissipation relation. We demonstrate that these effective temperatures extracted from the many-body simulations fit analytical expressions that are obtained for a single active particle inside a visco-elastic fluid. This result provides testable predictions and suggests a unified description for the dynamics inside active systems.

Living Matter: Mesoscopic Active Materials

An introduction to the physical properties of living active matter at the mesoscopic scale (tens of nanometers to micrometers) and their unique features compared with "dead," nonactive matter is presented. This field of research is increasingly denoted as "biological physics" where physics includes chemical physics, soft matter physics, hydrodynamics, mechanics, and the related engineering sciences. The focus is on the emergent properties of these systems and their collective behavior, which results in active self-organization and how they relate to cellular-level biological function. These include locomotion (cell motility and migration) forces that give rise to cell division, the growth and form of cellular assemblies in development, the beating of heart cells, and the effects of mechanical perturbations such as shear flow (in the bloodstream) or adhesion to other cells or tissues. An introduction to the fundamental concepts and theory with selected experimental examples related to the authors' own research is presented, including red-blood-cell membrane fluctuations, motion of the nucleus within an egg cell, self-contracting acto-myosin gels, and structure and beating of heart cells (cardiomyocytes), including how they can be driven by an oscillating, mechanical probe.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Dynamics of networks in a viscoelastic and active environment

We investigate the dynamics of fractals and other networks in a viscoelastic and active environment. The viscoelastic dynamics is modeled based on the generalized Langevin equation, where the activity is introduced to it by means of the exponentially correlated noise. The intramolecular interactions are taken into account by the bead-spring picture. The microscopic connectivity (studied in the form of Vicsek fractals, of dual Sierpiński gaskets, of NT_D trees, and of a family of deterministic small-world networks) reveals itself in the multiscale monomeric dynamics, which shows vastly different behaviors in the active and passive baths. In particular, the dynamics under active forces leads to a swelling that is characterized through power laws which are not present in the passive case. In all cases, the dynamics reflects the broad scaling behavior of the density of states and not necessarily the maximal relaxation time of the structures in a passive bath, as it is exemplified on the NT_D trees.

Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles

The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion force f₀ and a persistence time τ_p. Using the extended MCT and a generalized fluctuation-dissipation theorem, we calculate the effective temperature T_eff of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent T_eff that approaches a constant in the long-time limit, which depends on the activity parameters f₀ and τ_p. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that τ_α, the α-relaxation time, behaves as τ_α ∼ f₀^-2γ, where γ = 1.74 is the MCT exponent for the passive system. τ_α may increase or decrease as a function of τ_p depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent γ. Comparison with the numerical solution of the nonequilibrium MCT and simulation results give excellent agreement with scaling analysis.

Macroscopic violation of the law of heat conduction

We analyze a model describing an anharmonic macroscopic chain in contact with general reservoirs that follow the Lévy-Itô theorem on the Gaussian-Poissonian decomposition of the measure. We do so by considering a perturbative approach to compute the heat flux and the (canonical) temperature profile when the system reaches the steady state. This approach allows observing a macroscopic violation of the law of the heat conduction equivalent to that found for small (N=2) systems in contact with general reservoirs, which conveys the ascendency of the nature of the reservoirs over the size of the system.

Dynamic fatigue measurement of human erythrocytes using dielectrophoresis

Erythrocytes must undergo severe deformation to pass through narrow capillaries and submicronic splenic slits for several hundred thousand times in their normal lifespan. Studies of erythrocyte biomechanics have been mainly focused on cell deformability and rheology measured from a single application of stress and mostly under a static or quasi-static state using classical biomechanical techniques, such as optical tweezers and micropipette aspiration. Dynamic behavior of erythrocytes in response to cyclic stresses that contributes to the membrane failure in blood circulation is not fully understood. This paper presents a new experimental method for dynamic fatigue analysis of erythrocytes, using amplitude modulated electrokinetic force field in a microfluidic platform. We demonstrate the capability of this new technique using a low cycle fatigue analysis of normal human erythrocytes and ATP-depleted erythrocytes. Cyclic tensile stresses are generated to induce repeated uniaxial stretching and extensional recovery of single erythrocytes. Results of morphological and biomechanical parameters of individually tracked erythrocytes show strong correlations with the number of the loading cycles. Under a same strength of electric field, after 180 stress cycles, for normal erythrocytes, maximum stretch ratio decreases from 3.80 to 2.86, characteristic time of cellular extensional recovery increases from 0.16s to 0.37s, membrane shear viscosity increases from 1.0(µN/m)s to 1.6(µN/m)s. Membrane deformation in a small number of erythrocytes becomes irreversible after large deformation for about 200 cyclic loads. ATP-depleted cells show similar trends in decreased deformation and increased characteristic time with the loading cycles. These results show proof of concept of the new microfluidics technique for dynamic fatigue analysis of human erythrocytes.

STATEMENT OF SIGNIFICANCE

Red blood cells (RBCs) experience a tremendous number of deformation in blood circulation before losing their mechanical deformability and eventually being degraded in the reticuloendothelial system. Prior efforts in RBC biomechanics have mostly focused on a single-application of stress, or quasi-static loading through physical contact to deform cell membranes, thus with limited capabilities in probing cellular dynamic responses to cyclic stresses. We present a unique electrokinetic microfluidic system for the study of dynamic fatigue behavior of RBCs subjected to cyclic loads. Our work shows quantitatively how the cyclic stretching loads cause membrane mechanical degradation and irreversibly deformed cells. This new technique can be useful to identify biomechanical markers for prediction of the mechanical stability and residual lifespan of circulating RBCs.

Colloidal heat engines: a review

Stochastic heat engines can be built using colloidal particles trapped using optical tweezers. Here we review recent experimental realizations of microscopic heat engines. We first revisit the theoretical framework of stochastic thermodynamics that allows to describe the fluctuating behavior of the energy fluxes that occur at mesoscopic scales, and then discuss recent implementations of the colloidal equivalents to the macroscopic Stirling, Carnot and steam engines. These small-scale motors exhibit unique features in terms of power and efficiency fluctuations that have no equivalent in the macroscopic world. We also consider a second pathway for work extraction from colloidal engines operating between active bacterial reservoirs at different temperatures, which could significantly boost the performance of passive heat engines at the mesoscale. Finally, we provide some guidance on how the work extracted from colloidal heat engines can be used to generate net particle or energy currents, proposing a new generation of experiments with colloidal systems.

Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging

The functionality and viability of stored human red blood cells (RBCs) is an important clinical issue in transfusions. To systematically investigate changes in stored whole blood, the hematological properties of individual RBCs were quantified in blood samples stored for various periods with and without a preservation solution called citrate phosphate dextrose adenine-1 (CPDA-1). With 3-D quantitative phase imaging techniques, the optical measurements for 3-D refractive index (RI) distributions and membrane fluctuations were done at the individual cell level. From the optical measurements, the morphological (volume, surface area and sphericity), biochemical (hemoglobin content and concentration), and mechanical parameters (dynamic membrane fluctuation) were simultaneously quantified to investigate the functionalities and progressive alterations of stored RBCs. Our results show that stored RBCs without CPDA-1 had a dramatic morphological transformation from discocytes to spherocytes within two weeks which was accompanied by significant decreases in cell deformability and cell surface area, and increases in sphericity. However, the stored RBCs with CPDA-1 maintained their morphology and deformability for up to 6 weeks.

How Far from Equilibrium Is Active Matter?

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective fluctuation-dissipation theorem akin to that of thermal equilibrium systems. Last, we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a viscoelastic bath but driven out of equilibrium by nonconservative forces, hence providing energetic insight into the departure of active systems from equilibrium.