Nonequilibrium mechanics of active cytoskeletal networks

Shp2 contributes to the regulation of nuclear shape and cellular viscoelasticity in response to substrate spatial cues

Cell polarization can be guided by substrate topology through space constraints and adhesion induction, which are part of cellular mechanosensing pathways. Here, we demonstrated that protein tyrosine phosphatase Shp2 plays a crucial role in mediating the response of cells to substrate spatial cues. When compared to cells spreading on surfaces coated uniformly with fibronectin (FN), cells attached to 10 μm-width FN-strip micropattern (MP), which provides spatial cues for uniaxial spreading, exhibited elongated focal adhesions (FAs) and aligned stress fibers in the direction of the MP. As a result of uniaxial cell spreading, nuclei became elongated, dependent on ROCK-mediated actomyosin contractility. Additionally, intracellular viscoelasticity also increased. Shp2-deficient cells did not display elongated FAs mediated by MP, well-aligned stress fibers, or changes in nuclear shape and intracellular viscoelasticity. Overall, our data suggest that Shp2 is involved in regulating FAs and the actin cytoskeleton to modulate nuclear shape and intracellular physical properties in response to substrate spatial cues.

Tension directs cancer cell migration over fiber alignment through energy minimization

Cell migration during many fundamental biological processes including metastasis requires cells to traverse tissue with heterogeneous mechanical cues that direct migration as well as determine force and energy requirements for motility. However, the influence of discrete structural and mechanical cues on migration remains challenging to determine as they are often coupled. Here, we decouple the pro-invasive cues of collagen fiber alignment and tension to study their individual impact on migration. When presented with both cues, cells preferentially travel in the axis of tension against fiber alignment. Computational and experimental data show applying tension perpendicular to alignment increases potential energy stored within collagen fibers, lowering requirements for cell-induced matrix deformation and energy usage during migration compared to motility in the direction of fiber alignment. Energy minimization directs migration trajectory, and tension can facilitate migration against fiber alignment. These findings provide a conceptual understanding of bioenergetics during migration through a fibrous matrix.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses

The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing.

Data-driven classification of individual cells by their non-Markovian motion

We present a method to differentiate organisms solely by their motion based on the generalized Langevin equation (GLE) and use it to distinguish two different swimming modes of strongly confined unicellular microalgae Chlamydomonas reinhardtii. The GLE is a general model for active or passive motion of organisms and particles that can be derived from a time-dependent general many-body Hamiltonian and in particular includes non-Markovian effects (i.e., the trajectory memory of its past). We extract all GLE parameters from individual cell trajectories and perform an unbiased cluster analysis to group them into different classes. For the specific cell population employed in the experiments, the GLE-based assignment into the two different swimming modes works perfectly, as checked by control experiments. The classification and sorting of single cells and organisms is important in different areas; our method, which is based on motion trajectories, offers wide-ranging applications in biology and medicine.

Directional change during active diffusion of viral ribonucleoprotein particles through cytoplasm

A mesh of cytoskeletal fibers, consisting of microtubules, intermediate filaments, and fibrous actin, prevents the Brownian diffusion of particles with a diameter larger than 0.10 μm, such as vesicular stomatitis virus ribonucleoprotein (RNP) particles, in mammalian cells. Nevertheless, RNP particles do move in random directions but at a lower rate than Brownian diffusion, which is thermally driven. This nonthermal biological transport process is called "active diffusion" because it is driven by ATP. The ATP powers motor proteins such as myosin II. The motor proteins bend and cross-link actin fibers, causing the mesh to jiggle. Until recently, little was known about how RNP particles get through the mesh. It has been customary to analyze the tracks of particles like RNPs by computing the slope of the ensemble-averaged mean-squared displacement of the particles as a signature of mechanism. Although widely used, this approach "loses information" about the timing of the switches between physical mechanisms. It has been recently shown that machine learning composed of variational Bayesian analysis, Gaussian mixture models, and hidden Markov models can use "all the information" in a single track to reveal that that the positions of RNP particles are spatially clustered. Machine learning assigns a number, called a state, to each cluster. RNP particles remain in one state for 0.2-1.0 s before switching (hopping) to a different state. This earlier work is here extended to analyze the movements of a particle within a state and to determine particle directionality within and between states.

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.

Confined run-and-tumble particles with non-Markovian tumbling statistics

Confined active particles constitute simple, yet realistic, examples of systems that converge into a nonequilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution g(t) of waiting times between tumbling events whose mean value is equal to τ. Unless g(t) is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviation and/or small-τ regime, where the SSD can be related to the the large-deviation function, s(x), via the scaling relation P_{st}(x)∼e^{-s(x)/τ}.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses

The Hill functions, ℋ h ( x ) = x h / 1 + x h , have been widely used in biology for over a century but, with the exception of ℋ 1 , they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, co-regulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalises most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ω m ⊂ ℝ + 2 , for any equilibrium model with m input binding sites. Ω m exhibits a cusp which approaches, but never exceeds, the sharpness of ℋ m but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ω m , whose structure may be of mathematical interest, and suggest the importance of characterising Hopfield barriers for other forms of cellular information processing.

A surge in cytoplasmic viscosity triggers nuclear remodeling required for Dux silencing and pre-implantation embryo development

Embryonic genome activation (EGA) marks the transition from dependence on maternal transcripts to an embryonic transcriptional program. The precise temporal regulation of gene expression, specifically the silencing of the Dux/murine endogenous retrovirus type L (MERVL) program during late 2-cell interphase, is crucial for developmental progression in mouse embryos. How this finely tuned regulation is achieved within this specific window is poorly understood. Here, using particle-tracking microrheology throughout the mouse oocyte-to-embryo transition, we identify a surge in cytoplasmic viscosity specific to late 2-cell interphase brought about by high microtubule and endomembrane density. Importantly, preventing the rise in 2-cell viscosity severely impairs nuclear reorganization, resulting in a persistently open chromatin configuration and failure to silence Dux/MERVL. This, in turn, derails embryo development beyond the 2- and 4-cell stages. Our findings reveal a mechanical role of the cytoplasm in regulating Dux/MERVL repression via nuclear remodeling during a temporally confined period in late 2-cell interphase.

Mechanisms of active diffusion of vesicular stomatitis virus inclusion bodies and cellular early endosomes in the cytoplasm of mammalian cells

Viral and cellular particles too large to freely diffuse have two different types of mobility in the eukaryotic cell cytoplasm: directed motion mediated by motor proteins moving along cytoskeletal elements with the particle as its load, and motion in random directions mediated by motor proteins interconnecting cytoskeletal elements. The latter motion is referred to as "active diffusion." Mechanisms of directed motion have been extensively studied compared to mechanisms of active diffusion, despite the observation that active diffusion is more common for many viral and cellular particles. Our previous research showed that active diffusion of vesicular stomatitis virus (VSV) ribonucleoproteins (RNPs) in the cytoplasm consists of hopping between traps and that actin filaments and myosin II motors are components of the hop-trap mechanism. This raises the question whether similar mechanisms mediate random motion of larger particles with different physical and biological properties. Live-cell fluorescence imaging and a variational Bayesian analysis used in pattern recognition and machine learning were used to determine the molecular mechanisms of random motion of VSV inclusion bodies and cellular early endosomes. VSV inclusion bodies are membraneless cellular compartments that are the major sites of viral RNA synthesis, and early endosomes are representative of cellular membrane-bound organelles. Like VSV RNPs, inclusion bodies and early endosomes moved from one trapped state to another, but the distance between states was inconsistent with hopping between traps, indicating that the apparent state-to-state movement is mediated by trap movement. Like VSV RNPs, treatment with the actin filament depolymerizing inhibitor latrunculin A increased VSV inclusion body mobility by increasing the size of the traps. In contrast neither treatment with latrunculin A nor depolymerization of microtubules by nocodazole treatment affected the size of traps that confine early endosome mobility, indicating that intermediate filaments are likely major trap components for these cellular organelles.

The effects of asymmetry in active noises on the efficiency of single colloidal Stirling engines with active noises

Molecular machines, which operate in highly fluctuating environments far from equilibrium, may benefit from their non-equilibrium environments. It is, however, a topic of controversy how the efficiency of the microscopic engines can be enhanced. Recent experiments showed that microscopic Stirling engines in bacterial reservoirs could show high performance beyond the equilibrium thermodynamics. In this work, we perform overdamped Langevin dynamics simulations for microscopic Stirling heat engines in bacterial reservoirs and show that the temperature dependence of the magnitude of active noises should be responsible for such high efficiency. Only when we introduce temperature-dependent active noises, the efficiency of the microscopic Stirling engines is enhanced significantly as in experiments.

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.

Defective Biomechanics and Pharmacological Rescue of Human Cardiomyocytes with Filamin C Truncations

Actin-binding filamin C (FLNC) is expressed in cardiomyocytes, where it localizes to Z-discs, sarcolemma, and intercalated discs. Although FLNC truncation variants (FLNCtv) are an established cause of arrhythmias and heart failure, changes in biomechanical properties of cardiomyocytes are mostly unknown. Thus, we investigated the mechanical properties of human-induced pluripotent stem cells-derived cardiomyocytes (hiPSC-CMs) carrying FLNCtv. CRISPR/Cas9 genome-edited homozygous FLNCKO-/- hiPSC-CMs and heterozygous knock-out FLNCKO+/- hiPSC-CMs were analyzed and compared to wild-type FLNC (FLNCWT) hiPSC-CMs. Atomic force microscopy (AFM) was used to perform micro-indentation to evaluate passive and dynamic mechanical properties. A qualitative analysis of the beating traces showed gene dosage-dependent-manner "irregular" peak profiles in FLNCKO+/- and FLNCKO-/- hiPSC-CMs. Two Young's moduli were calculated: E1, reflecting the compression of the plasma membrane and actin cortex, and E2, including the whole cell with a cytoskeleton and nucleus. Both E1 and E2 showed decreased stiffness in mutant FLNCKO+/- and FLNCKO-/- iPSC-CMs compared to that in FLNCWT. The cell adhesion force and work of adhesion were assessed using the retraction curve of the SCFS. Mutant FLNC iPSC-CMs showed gene dosage-dependent decreases in the work of adhesion and adhesion forces from the heterozygous FLNCKO+/- to the FLNCKO-/- model compared to FLNCWT, suggesting damaged cytoskeleton and membrane structures. Finally, we investigated the effect of crenolanib on the mechanical properties of hiPSC-CMs. Crenolanib is an inhibitor of the Platelet-Derived Growth Factor Receptor α (PDGFRA) pathway which is upregulated in FLNCtv hiPSC-CMs. Crenolanib was able to partially rescue the stiffness of FLNCKO-/- hiPSC-CMs compared to control, supporting its potential therapeutic role.

Unlocking the potential of information flow: Maximizing free-energy transduction in a model of an autonomous rotary molecular motor

Molecular motors fulfill critical functions within all living beings. Understanding their underlying working principles is therefore of great interest. Here we develop a simple model inspired by the two-component biomolecular motor F_{o}-F_{1} ATP synthase. We analyze its energetics and characterize information flows between the machine's components. At maximum output power we find that information transduction plays a minor role for free-energy transduction. However, when the two components are coupled to different environments (e.g., when in contact with heat baths at different temperatures), we show that information flow becomes a resource worth exploiting to maximize free-energy transduction. Our findings suggest that real-world powerful and efficient information engines could be found in machines whose components are subjected to fluctuations of different strength, since in this situation the benefit gained from using information for work extraction can outweigh the costs of information generation.

Chromatin Remodeling Due to Transient-Link-and-Pass Activity Enhances Subnuclear Dynamics

Spatiotemporal coordination of chromatin and subnuclear compartments is crucial for cells. Numerous enzymes act inside nucleus-some of those transiently link and pass two chromatin segments. Here, we study how such an active perturbation affects fluctuating dynamics of an inclusion in the chromatic medium. Using numerical simulations and a versatile effective model, we categorize inclusion dynamics into three distinct modes. The transient-link-and-pass activity speeds up inclusion dynamics by affecting a slow mode related to chromatin remodeling, viz., size and shape of the chromatin meshes.

α-divergence improves the entropy production estimation via machine learning

Recent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose minimization guarantees the accurate EP estimation. In this study we show that there exists a host of loss functions, namely, those implementing a variational representation of the α-divergence, which can be used for the EP estimation. By fixing α to a value between -1 and 0, the α-NEEP (Neural Estimator for Entropy Production) exhibits a much more robust performance against strong nonequilibrium driving or slow dynamics, which adversely affects the existing method based on the Kullback-Leibler divergence (α=0). In particular, the choice of α=-0.5 tends to yield the optimal results. To corroborate our findings, we present an exactly solvable simplification of the EP estimation problem, whose loss function landscape and stochastic properties give deeper intuition into the robustness of the α-NEEP.

Jensen bound for the entropy production rate in stochastic thermodynamics

Bounding and estimating entropy production has long been an important goal of nonequilibrium thermodynamics. We recently derived a lower bound on the total and subsystem entropy production rates of continuous stochastic systems. This "Jensen bound" has led to fundamental limits on the performance of collective transport systems and permitted thermodynamic inference of free-energy transduction between components of bipartite molecular machines. Our original derivation relied on a number of assumptions, which restricted the bound's regime of applicability. Here we derive the Jensen bound far more generally for multipartite overdamped Langevin dynamics. We then consider several extensions, allowing for position-dependent diffusion coefficients, underdamped dynamics, and non-multipartite overdamped dynamics. Our results extend the Jensen bound to a far broader class of systems.

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.

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.

Activity-dependent glassy cell mechanics II: Nonthermal fluctuations under metabolic activity

The glassy cytoplasm, crowded with bio-macromolecules, is fluidized in living cells by mechanical energy derived from metabolism. Characterizing the living cytoplasm as a nonequilibrium system is crucial in elucidating the intricate mechanism that relates cell mechanics to metabolic activities. In this study, we conducted active and passive microrheology in eukaryotic cells, and quantified nonthermal fluctuations by examining the violation of the fluctuation-dissipation theorem. The power spectral density of active force generation was estimated following the Langevin theory extended to nonequilibrium systems. However, experiments performed while regulating cellular metabolic activity showed that the nonthermal displacement fluctuation, rather than the active nonthermal force, is linked to metabolism. We discuss that mechano-enzymes in living cells do not act as microscopic objects. Instead, they generate meso-scale collective fluctuations with displacements controlled by enzymatic activity. The activity induces structural relaxations in glassy cytoplasm. Even though the autocorrelation of nonthermal fluctuations is lost at long timescales due to the structural relaxations, the nonthermal displacement fluctuation remains regulated by metabolic reactions. Our results therefore demonstrate that nonthermal fluctuations serve as a valuable indicator of a cell's metabolic activities, regardless of the presence or absence of structural relaxations.

Mechanical criticality of fiber networks at a finite temperature

At zero temperature, spring networks with connectivity below Maxwell's isostatic threshold undergo a mechanical phase transition from a floppy state at small strains to a rigid state for applied shear strain above a critical strain threshold. Disordered networks in the floppy mechanical regime can be stabilized by entropic effects at finite temperature. We develop a scaling theory for this mechanical phase transition at finite temperature, yielding relationships between various scaling exponents. Using Monte Carlo simulations, we verify these scaling relations and identify anomalous entropic elasticity with sublinear T dependence in the linear elastic regime. While our results are consistent with prior studies of phase behavior near the isostatic point, the present work also makes predictions relevant to the broad class of disordered thermal semiflexible polymer networks for which the connectivity generally lies far below the isostatic threshold.

Simultaneous Nanorheometry and Nanothermometry Using Intracellular Diamond Quantum Sensors

The viscoelasticity of the cytoplasm plays a critical role in cell morphology, cell division, and intracellular transport. Viscoelasticity is also interconnected with other biophysical properties, such as temperature, which is known to influence cellular bioenergetics. Probing the connections between intracellular temperature and cytoplasmic viscoelasticity provides an exciting opportunity for the study of biological phenomena, such as metabolism and disease progression. The small length scales and transient nature of changes in these parameters combined with their complex interdependencies pose a challenge for biosensing tools, which are often limited to a single readout modality. Here, we present a dual-mode quantum sensor capable of performing simultaneous nanoscale thermometry and rheometry in dynamic cellular environments. We use nitrogen-vacancy centers in diamond nanocrystals as biocompatible sensors for in vitro measurements. We combine subdiffraction resolution single-particle tracking in a fluidic environment with optically detected magnetic resonance spectroscopy to perform simultaneous sensing of viscoelasticity and temperature. We use our sensor to demonstrate probing of the temperature-dependent viscoelasticity in complex media at the nanoscale. We then investigate the interplay between intracellular forces and the cytoplasmic rheology in live cells. Finally, we identify different rheological regimes and reveal evidence of active trafficking and details of the nanoscale viscoelasticity of the cytoplasm.

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.

Non-Gaussian fluctuations of a probe coupled to a Gaussian field

The motion of a colloidal probe in a complex fluid, such as a micellar solution, is usually described by the generalized Langevin equation, which is linear. However, recent numerical simulations and experiments have shown that this linear model fails when the probe is confined and that the intrinsic dynamics of the probe is actually nonlinear. Noting that the kurtosis of the displacement of the probe may reveal the nonlinearity of its dynamics also in the absence confinement, we compute it for a probe coupled to a Gaussian field and possibly trapped by a harmonic potential. We show that the excess kurtosis increases from zero at short times, reaches a maximum, and then decays algebraically at long times, with an exponent which depends on the spatial dimensionality and on the features and correlations of the dynamics of the field. Our analytical predictions are confirmed by numerical simulations of the stochastic dynamics of the probe and the field where the latter is represented by a finite number of modes.

Motor-free contractility of active biopolymer networks

Contractility in animal cells is often generated by molecular motors such as myosin, which require polar substrates for their function. Motivated by recent experimental evidence of motor-independent contractility, we propose a robust motor-free mechanism that can generate contraction in biopolymer networks without the need for substrate polarity. We show that contractility is a natural consequence of active binding-unbinding of crosslinkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We have extended our earlier work to discuss the motor-free contraction of viscoelastic biopolymer networks. We calculate the resulting contractile velocity using a microscopic model and show that it can be reduced to a simple coarse-grained model under certain limits. Our model may provide an explanation of recent reports of motor-independent contractility in cells. Our results also suggest a mechanism for generating contractile forces in synthetic active materials.

Studying fluctuating trajectories of optically confined passive tracers inside cells provides familiar active forces

In recent years, there has been a growing interest in studying the trajectories of microparticles inside living cells. Among other things, such studies are useful in understanding the spatio-temporal properties of a cell. In this work, we study the stochastic trajectories of a passive microparticle inside a cell using experiments and theory. Our theory is based on modeling the microparticle inside a cell as an active particle in a viscoelastic medium. The activity is included in our model from an additional stochastic term with non-zero persistence in the Langevin equation describing the dynamics of the microparticle. Using this model, we are able to predict the power spectral density (PSD) measured in the experiment and compute active forces. This caters to the situation where a tracer particle is optically confined and then yields a PSD for positional fluctuations. The low frequency part of the PSD yields information about the active forces that the particle feels. The fit to the model extracts such active force. Thus, we can conclude that trapping the particle does not affect the values of the forces extracted from the active fits if accounted for appropriately by proper theoretical models. In addition, the fit also provides system properties and optical tweezers trap stiffness.

Mechanical microscopy of cancer cells: TGF-β induced epithelial to mesenchymal transition corresponds to low intracellular viscosity in cancer cells

Viscosity is an essential parameter that regulates bio-molecular reaction rates of diffusion-driven cellular processes. Hence, abnormal viscosity levels are often associated with various diseases and malfunctions like cancer. For this reason, monitoring intracellular viscosity becomes vital. While several approaches have been developed for in vitro and in vivo measurement of viscosity, analysis of intracellular viscosity in live cells has not yet been well realized. Our research introduces a novel, natural frequency-based, non-invasive method to determine the intracellular viscosity in cells. This method can not only efficiently analyze the differences in intracellular viscosity post modulation with molecules like PEG or glucose but is sensitive enough to distinguish the difference in intra-cellular viscosity among various cancer cell lines such as Huh-7, MCF-7, and MDAMB-231. Interestingly, TGF-β a cytokine reported to induce epithelial to mesenchymal transition (EMT), a feature associated with cancer invasiveness resulted in reduced viscosity of cancer cells, as captured through our method. To corroborate our findings with existing methods of analysis, we analyzed intra-cellular viscosity with a previously described viscosity-sensitive molecular rotor-based fluorophore-TPSII. In parity with our position sensing device (PSD)-based approach, an increase in fluorescence intensity was observed with viscosity enhancers, while, TGF-β exposure resulted in its reduction in the cells studied. This is the first study of its kind that attempts to characterize differences in intracellular viscosity using a novel, non-invasive PSD-based method.

Measuring fluctuating dynamics of sparsely crosslinked actin gels with dual-feedback nonlinear microrheology

We investigate the fluctuating dynamics of colloidal particles in weakly crosslinked F-actin networks with optical-trap-based microrheology. Using the dual-feedback technology, embedded colloidal particles were stably forced beyond the linear regime in a manner that does not suppress spontaneous fluctuations of particles. Upon forcing, a particle that was stably confined in a cage made of the network's crosslinks started to intermittently jump to the next caging microenvironments. By investigating the statistics of the jump dynamics, we discuss how heterogeneous relaxations observed in equilibrium systems became homogeneous when similar jumps were activated under constant forcing beyond the linear regime.

Information Engine in a Nonequilibrium Bath

Information engines can convert thermal fluctuations of a bath at temperature T into work at rates of order k_{B}T per relaxation time of the system. We show experimentally that such engines, when in contact with a bath that is out of equilibrium, can extract much more work. We place a heavy, micron-scale bead in a harmonic potential that ratchets up to capture favorable fluctuations. Adding a fluctuating electric field increases work extraction up to ten times, limited only by the strength of the applied field. Our results connect Maxwell's demon with energy harvesting and demonstrate that information engines in nonequilibrium baths can greatly outperform conventional engines.

Nonequilibrium steady state of trapped active particles

We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle, etc.), that is confined by an external potential. Focusing on the limit in which the correlation time τ of the active noise is small, we find the nonequilibrium steady-state distribution P_{st}(X) of the particle's position X. While typical fluctuations of X follow a Boltzmann distribution with an effective temperature that is not difficult to find, the tails of P_{st}(X) deviate from a Boltzmann behavior: In the limit τ→0, they scale as P_{st}(X)∼e^{-s(X)/τ}. We calculate the large-deviation function s(X) exactly for arbitrary trapping potential and active noise in dimension d=1, by relating it to the rate function that describes large deviations of the position of the same active particle in absence of an external potential at long times. We then extend our results to d>1 assuming rotational symmetry.

From the membrane to the nucleus: mechanical signals and transcription regulation

Mechanical forces drive and modulate a wide variety of processes in eukaryotic cells including those occurring in the nucleus. Relevantly, forces are fundamental during development since they guide lineage specifications of embryonic stem cells. A sophisticated macromolecular machinery transduces mechanical stimuli received at the cell surface into a biochemical output; a key component in this mechanical communication is the cytoskeleton, a complex network of biofilaments in constant remodeling that links the cell membrane to the nuclear envelope. Recent evidence highlights that forces transmitted through the cytoskeleton directly affect the organization of chromatin and the accessibility of transcription-related molecules to their targets in the DNA. Consequently, mechanical forces can directly modulate transcription and change gene expression programs. Here, we will revise the biophysical toolbox involved in the mechanical communication with the cell nucleus and discuss how mechanical forces impact on the organization of this organelle and more specifically, on transcription. We will also discuss how live-cell fluorescence imaging is producing exquisite information to understand the mechanical response of cells and to quantify the landscape of interactions of transcription factors with chromatin in embryonic stem cells. These studies are building new biophysical insights that could be fundamental to achieve the goal of manipulating forces to guide cell differentiation in culture systems.

Inferring scale-dependent non-equilibrium activity using carbon nanotubes

In living systems, irreversible, yet stochastic, molecular interactions form multiscale structures (such as cytoskeletal networks), which mediate processes (such as cytokinesis and cellular motility) in a close relationship between the structure and function. However, owing to a lack of methods to quantify non-equilibrium activity, their dynamics remain poorly characterized. Here, by measuring the time-reversal asymmetry encoded in the conformational dynamics of filamentous single-walled carbon nanotubes embedded in the actomyosin network of Xenopus egg extract, we characterize the multiscale dynamics of non-equilibrium activity encoded in bending-mode amplitudes. Our method is sensitive to distinct perturbations to the actomyosin network and the concentration ratio of adenosine triphosphate to adenosine diphosphate. Thus, our method can dissect the functional coupling of microscopic dynamics to the emergence of larger scale non-equilibrium activity. We relate the spatiotemporal scales of non-equilibrium activity to the key physical parameters of a semiflexible filament embedded in a non-equilibrium viscoelastic environment. Our analysis provides a general tool to characterize steady-state non-equilibrium activity in high-dimensional spaces.

Reconfiguration, Interrupted Aging, and Enhanced Dynamics of a Colloidal Gel Using Photoswitchable Active Doping

We study quasi-2D gels made of a colloidal network doped with Janus particles activated by light. Following the gel formation, we monitor both the structure and dynamics before, during, and after the activation period. Before activity is switched on, the gel is slowly aging. During the activation, the mobility of the passive particles exhibits a characteristic scale-dependent response, while the colloidal network remains connected, and the gel maintains its structural integrity. Once activity is switched off, the gel stops aging and keeps the memory of the structure inherited from the active phase. Remarkably, the motility remains larger than that of the gel, before the active period. The system has turned into a genuinely softer gel, with frozen dynamics, but with more space for thermal fluctuations. The above conclusions remain valid long after the activity period.

Reliable and robust control of nucleus centering is contingent on nonequilibrium force patterns

Cell centers their division apparatus to ensure symmetric cell division, a challenging task when the governing dynamics is stochastic. Using fission yeast, we show that the patterning of nonequilibrium polymerization forces of microtubule (MT) bundles controls the precise localization of spindle pole body (SPB), and hence the division septum, at the onset of mitosis. We define two cellular objectives, reliability, the mean SPB position relative to the geometric center, and robustness, the variance of the SPB position, which are sensitive to genetic perturbations that change cell length, MT bundle number/orientation, and MT dynamics. We show that simultaneous control of reliability and robustness is required to minimize septum positioning error achieved by the wild type (WT). A stochastic model for the MT-based nucleus centering, with parameters measured directly or estimated using Bayesian inference, recapitulates the maximum fidelity of WT. Using this, we perform a sensitivity analysis of the parameters that control nuclear centering.

Activity-dependent glassy cell mechanics Ⅰ: Mechanical properties measured with active microrheology

Active microrheology was conducted in living cells by applying an optical-trapping force to vigorously fluctuating tracer beads with feedback-tracking technology. The complex shear modulus G(ω)=G'(ω)-iG″(ω) was measured in HeLa cells in an epithelial-like confluent monolayer. We found that G(ω)∝(-iω)1/2 over a wide range of frequencies (1 Hz < ω/2π < 10 kHz). Actin disruption and cell-cycle progression from G1 to S and G2 phases only had a limited effect on G(ω) in living cells. On the other hand, G(ω) was found to be dependent on cell metabolism; ATP-depleted cells showed an increased elastic modulus G'(ω) at low frequencies, giving rise to a constant plateau such that G(ω)=G0+A(-iω)1/2. Both the plateau and the additional frequency dependency ∝(-iω)1/2 of ATP-depleted cells are consistent with a rheological response typical of colloidal jamming. On the other hand, the plateau G0 disappeared in ordinary metabolically active cells, implying that living cells fluidize their internal states such that they approach the critical jamming point.

Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids

Microtubule-based active fluids exhibit turbulent-like autonomous flows, which are driven by the molecular motor powered motion of filamentous constituents. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal patterning of the active stress controls the evolution of the ubiquitous bend instability of extensile active fluids and determines its critical length dependence. Combining optically controlled clusters with conventional kinesin motors enables one-time switching from contractile to extensile active stresses. These results open a path towards real-time control of the autonomous flows generated by active fluids.

Mitochondrial cellular organization and shape fluctuations are differentially modulated by cytoskeletal networks

The interactions between mitochondria and the cytoskeleton have been found to alter mitochondrial function; however, the mechanisms underlying this phenomenon are largely unknown. Here, we explored how the integrity of the cytoskeleton affects the cellular organization, morphology and mobility of mitochondria in Xenopus laevis melanocytes. Cells were imaged in control condition and after different treatments that selectively affect specific cytoskeletal networks (microtubules, F-actin and vimentin filaments). We observed that mitochondria cellular distribution and local orientation rely mostly on microtubules, positioning these filaments as the main scaffolding of mitochondrial organization. We also found that cytoskeletal networks mold mitochondria shapes in distinct ways: while microtubules favor more elongated organelles, vimentin and actin filaments increase mitochondrial bending, suggesting the presence of mechanical interactions between these filaments and mitochondria. Finally, we identified that microtubule and F-actin networks play opposite roles in mitochondria shape fluctuations and mobility, with microtubules transmitting their jittering to the organelles and F-actin restricting the organelles motion. All our results support that cytoskeleton filaments interact mechanically with mitochondria and transmit forces to these organelles molding their movements and shapes.

Optical trapping with holographically structured light for single-cell studies

A groundbreaking work in 1970 by Arthur Ashkin paved the way for developing various optical trapping techniques. Optical tweezers have become an established method for the manipulation of biological objects, due to their noninvasiveness and precise controllability. Recent innovations are accelerating and now enable single-cell manipulation through holographic light structuring. In this review, we provide an overview of recent advances in optical tweezer techniques for studies at the individual cell level. Our review focuses on holographic optical tweezers that utilize active spatial light modulators to noninvasively manipulate live cells. The versatility of the technology has led to valuable integrations with microscopy, microfluidics, and biotechnological techniques for various single-cell studies. We aim to recapitulate the basic principles of holographic optical tweezers, highlight trends in their biophysical applications, and discuss challenges and future prospects.

Nonaffine Deformation of Semiflexible Polymer and Fiber Networks

Networks of semiflexible or stiff polymers such as most biopolymers are known to deform inhomogeneously when sheared. The effects of such nonaffine deformation have been shown to be much stronger than for flexible polymers. To date, our understanding of nonaffinity in such systems is limited to simulations or specific 2D models of athermal fibers. Here, we present an effective medium theory for nonaffine deformation of semiflexible polymer and fiber networks, which is general to both 2D and 3D and in both thermal and athermal limits. The predictions of this model are in good agreement with both prior computational and experimental results for linear elasticity. Moreover, the framework we introduce can be extended to address nonlinear elasticity and network dynamics.

Bona fide stochastic resonance under nonGaussian active fluctuations

We report on the experimental observation of stochastic resonance (SR) in a nonGaussian active bath without any periodic modulation. A Brownian particle hopping in a nanoscale double-well potential under the influence of nonGaussian correlated noise, with mean interval τ_P and correlation time τ_c, shows a series of equally-spaced peaks in the residence time distribution at integral multiples of τ_P. The strength of the first peak is found to be maximum when the mean residence time _d matches the double condition, 4τ_c ≈ τ_P ≈ _d/2, demonstrating a new type of bona fide SR. The experimental findings agree with a simple model that explains the emergence of SR without periodic modulation of the double-well potential. Additionally, we show that generic SR under periodic modulation, known to degrade in strongly correlated continuous noise, is recovered by the discrete nonGaussian kicks.

Dynamics of self-propelled tracer particles inside a polymer network

The transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers can be passive, such as colloids, or active (self-propelled), for example, synthetic nanomotors or bacteria. Computer simulations in principle could be extremely useful in exploring the mechanism of the active transport of tracer particles through mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside the network. Our main objective is to elucidate the effect of the self-propulsion on the tracer particle dynamics as a function of the tracer size and the stiffness of the polymer network. We compute the time-averaged mean-squared displacement (MSD) and the van-Hove correlations of the tracer. On the one hand, in the case of a bigger sticky particle, the caging caused by the network particles wins over the escape assisted by the self-propulsion. This results an intermediate-time subdiffusion. On the other hand, smaller tracers or tracers with high self-propulsion velocities can easily escape from the cages and show intermediate-time superdiffusion. The stiffer the network, the slower the dynamics of the tracer, and bigger tracers exhibit longer lived intermediate time superdiffusion, since the persistence time scales as ∼σ³, where σ is the diameter of the tracer. At the intermediate time, non-Gaussianity is more pronounced for active tracers. At the long time, the dynamics of the tracer, if passive or weakly active, becomes Gaussian and diffusive, but remains flat for tracers with high self-propulsion, accounting for their seemingly unrestricted motion inside the network.

Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

We discuss some of the practical challenges that one faces in using stochastic thermodynamics to infer directionality of molecular machines from experimental single-molecule trajectories. Because of the limited spatiotemporal resolution of single-molecule experiments and because both forward and backward transitions between the same pairs of states cannot always be detected, differentiating between the forward and backward directions of, e.g., an ATP-consuming molecular machine that operates periodically, turns out to be a nontrivial task. Using a simple extension of a Markov-state model that is commonly employed to analyze single-molecule transition-path measurements, we illustrate how irreversibility can be hidden from such measurements but in some cases can be uncovered when non-Markov effects in low-dimensional single-molecule trajectories are considered.

Mitochondrial fission and bioenergetics mediate human lung fibroblast durotaxis

Pulmonary fibrosis is characterized by stiffening of the extracellular matrix. Fibroblasts migrate in the direction of greater stiffness, a phenomenon termed durotaxis. The mechanically guided fibroblast migration could be a crucial step in the progression of lung fibrosis. In this study, we found primary human lung fibroblasts sense increasing matrix stiffness with a change of mitochondrial dynamics in favor of mitochondrial fission and increased production of ATP. Mitochondria polarize in the direction of a physiologically relevant stiffness gradient, with conspicuous localization to the leading edge, primarily lamellipodia and filopodia, of migrating lung fibroblasts. Matrix stiffness-regulated mitochondrial fission and durotactic lung fibroblast migration are mediated by a dynamin-related protein 1/mitochondrial fission factor-dependent (DRP1/MFF-dependent) pathway. Importantly, we found that the DRP1/MFF pathway is activated in fibrotic lung myofibroblasts in both human IPF and bleomycin-induced mouse lung fibrosis. These findings suggest that energy-producing mitochondria need to be sectioned via fission and repositioned in durotactic lung fibroblasts to meet the higher energy demand. This represents a potentially new mechanism through which mitochondria may contribute to the progression of fibrotic lung diseases. Inhibition of durotactic migration of lung fibroblasts may play an important role in preventing the progression of human idiopathic pulmonary fibrosis.

PI(4,5)P2 and Cholesterol: Synthesis, Regulation, and Functions

Phosphatidylinositol 4,5-bisphosphate (PI(4,5)P₂) is the most abundant membrane phosphoinositide and cholesterol is an essential component of the plasma membrane (PM). Both lipids play key roles in a variety of cellular functions including as signaling molecules and major regulators of protein function. This chapter provides an overview of these two important lipids. Starting from a brief description of their structure, synthesis, and regulation, the chapter continues to describe the primary functions and signaling processes in which PI(4,5)P₂ and cholesterol are involved. While PI(4,5)P₂ and cholesterol can act independently, they often act in concert or affect each other's impact. The chapters in this volume on "Cholesterol and PI(4,5)P₂ in Vital Biological Functions: From Coexistence to Crosstalk" focus on the emerging relationship between cholesterol and PI(4,5)P₂ in a variety of biological systems and processes. In this chapter, the next section provides examples from the ion channel field demonstrating that PI(4,5)P₂ and cholesterol can act via common mechanisms. The chapter ends with a discussion of future directions.

Engineered hydrogels for mechanobiology

Cells' local mechanical environment can be as important in guiding cellular responses as many well-characterized biochemical cues. Hydrogels that mimic the native extracellular matrix can provide these mechanical cues to encapsulated cells, allowing for the study of their impact on cellular behaviours. Moreover, by harnessing cellular responses to mechanical cues, hydrogels can be used to create tissues in vitro for regenerative medicine applications and for disease modelling. This Primer outlines the importance and challenges of creating hydrogels that mimic the mechanical and biological properties of the native extracellular matrix. The design of hydrogels for mechanobiology studies is discussed, including appropriate choice of cross-linking chemistry and strategies to tailor hydrogel mechanical cues. Techniques for characterizing hydrogels are explained, highlighting methods used to analyze cell behaviour. Example applications for studying fundamental mechanobiological processes and regenerative therapies are provided, along with a discussion of the limitations of hydrogels as mimetics of the native extracellular matrix. The article ends with an outlook for the field, focusing on emerging technologies that will enable new insights into mechanobiology and its role in tissue homeostasis and disease.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Nonlinear Microscale Mechanics of Actin Networks Governed by Coupling of Filament Crosslinking and Stabilization

Actin plays a vital role in maintaining the stability and rigidity of biological cells while allowing for cell motility and shape change. The semiflexible nature of actin filaments-along with the myriad actin-binding proteins (ABPs) that serve to crosslink, bundle, and stabilize filaments-are central to this multifunctionality. The effect of ABPs on the structural and mechanical properties of actin networks has been the topic of fervent investigation over the past few decades. Yet, the combined impact of filament stabilization, stiffening and crosslinking via ABPs on the mechanical response of actin networks has yet to be explored. Here, we perform optical tweezers microrheology measurements to characterize the nonlinear force response and relaxation dynamics of actin networks in the presence of varying concentrations of α-actinin, which transiently crosslinks actin filaments, and phalloidin, which stabilizes filamentous actin and increases its persistence length. We show that crosslinking and stabilization can act both synergistically and antagonistically to tune the network resistance to nonlinear straining. For example, phalloidin stabilization leads to enhanced elastic response and reduced dissipation at large strains and timescales, while the initial microscale force response is reduced compared to networks without phalloidin. Moreover, we find that stabilization switches this initial response from that of stress stiffening to softening despite the increased filament stiffness that phalloidin confers. Finally, we show that both crosslinking and stabilization are necessary to elicit these emergent features, while the effect of stabilization on networks without crosslinkers is much more subdued. We suggest that these intriguing mechanical properties arise from the competition and cooperation between filament connectivity, bundling, and rigidification, shedding light on how ABPs with distinct roles can act in concert to mediate diverse mechanical properties of the cytoskeleton and bio-inspired polymeric materials.

F-actin architecture determines constraints on myosin thick filament motion

Active stresses are generated and transmitted throughout diverse F-actin architectures within the cell cytoskeleton, and drive essential behaviors of the cell, from cell division to migration. However, while the impact of F-actin architecture on the transmission of stress is well studied, the role of architecture on the ab initio generation of stresses remains less understood. Here, we assemble F-actin networks in vitro, whose architectures are varied from branched to bundled through F-actin nucleation via Arp2/3 and the formin mDia1. Within these architectures, we track the motions of embedded myosin thick filaments and connect them to the extent of F-actin network deformation. While mDia1-nucleated networks facilitate the accumulation of stress and drive contractility through enhanced actomyosin sliding, branched networks prevent stress accumulation through the inhibited processivity of thick filaments. The reduction in processivity is due to a decrease in translational and rotational motions constrained by the local density and geometry of F-actin.

Fluctuation-Dissipation Relations for Spiking Neurons

Spontaneous fluctuations and stimulus response are essential features of neural functioning, but how they are connected is poorly understood. I derive fluctuation-dissipation relations (FDR) between the spontaneous spike and voltage correlations and the firing rate susceptibility for (i) the leaky integrate-and-fire (IF) model with white noise and (ii) an IF model with arbitrary voltage dependence, an adaptation current, and correlated noise. The FDRs can be used to derive thus far unknown statistics analytically [model (i)] or the otherwise inaccessible intrinsic noise statistics [model (ii)].