Nonequilibrium mechanics of active cytoskeletal networks

Non-Markovian equilibrium and non-equilibrium barrier-crossing kinetics in asymmetric double-well potentials

Barrier-crossing processes in nature are often non-Markovian and typically occur over an asymmetric double-well free-energy landscape. However, most theories and numerical studies on barrier-crossing rates assume symmetric free-energy profiles. Here, we use a one-dimensional generalized Langevin equation (GLE) to investigate non-Markovian reaction kinetics in asymmetric double-well potentials. We derive a general formula, confirmed by extensive simulations, that accurately predicts mean first-passage times from well to barrier top in an asymmetric double-well potential with arbitrary memory time and reaction coordinate mass. We extend our formalism to non-equilibrium non-Markovian systems, confirming its broad applicability to equilibrium and non-equilibrium systems in biology, chemistry, and physics.

Differential Elasticity Affects Lineage Segregation of Embryonic Stem Cells

The question of what guides lineage segregation is central to development, where cellular differentiation leads to segregated cell populations destined for specialized functions. Here, using optical tweezers measurements of mouse embryonic stem cells, we reveal a mechanical mechanism based on differential elasticity in the second lineage segregation of the embryonic inner cell mass into epiblast (EPI) cells, which will develop into the fetus, and primitive endoderm (PrE), which will form extraembryonic structures such as the yolk sac. Remarkably, we find that these mechanical differences already occur during priming, not just after a cell has committed to differentiation. Specifically, we show that PrE-primed cells exhibit significantly higher elasticity than EPI-primed cells, characterized by lower power spectrum scaling exponents, higher Young's modulus, and lower loss tangent. Using a model of two cell types differing only in elasticity, we show that differential elasticity alone is sufficient to lead to segregation between cell types, suggesting that the mechanical attributes of the cells contribute to the segregation process. Importantly, we find that this process relies on cellular activity. Our findings present differential elasticity as a previously unknown mechanical contributor to lineage segregation during embryo morphogenesis.

DNA photofluids show life-like motion

As active matter, cells exhibit non-equilibrium structures and behaviours such as reconfiguration, motility and division. These capabilities arise from the collective action of biomolecular machines continuously converting photoenergy or chemical energy into mechanical energy. Constructing similar dynamic processes in vitro presents opportunities for developing life-like intelligent soft materials. Here we report an active fluid formed from the liquid-liquid phase separation of photoresponsive DNA nanomachines. The photofluids can orchestrate and amplify nanoscale mechanical movements by orders of magnitude to produce macroscopic cell-like behaviours including elongation, division and rotation. We identify two dissipative processes in the DNA droplets, photoalignment and photofibrillation, which are crucial for harnessing stochastic molecular motions cooperatively. Our results demonstrate an active liquid molecular system that consumes photoenergy to create ordered out-of-equilibrium structures and behaviours. This system may help elucidate the physical principles underlying cooperative motion in active matter and pave the way for developing programmable interactive materials.

Exact moments for a run-and-tumble particle with a finite tumble time in a harmonic trap

We study the problem of a run-and-tumble particle in a harmonic trap, with a finite run-and-tumble time, by direct integration of the equation of motion. An exact one-dimensional steady state distribution is obtained. Diagram laws and a programmable Volterra difference equation are derived to calculate any order of moments in any dimension, both for the steady state as well as the time Laplace transform for the intermediate states. We finally infer the complete distribution from the moments by considering a Gaussian quadrature for the corresponding measure and from the scaling law of higher order moments.

Flow of Energy and Information in Molecular Machines

Molecular machines transduce free energy between different forms throughout all living organisms. Unlike their macroscopic counterparts, molecular machines are characterized by stochastic fluctuations, overdamped dynamics, and soft components, and operate far from thermodynamic equilibrium. In addition, information is a relevant free energy resource for molecular machines, leading to new modes of operation for nanoscale engines. Toward the objective of engineering synthetic nanomachines, an important goal is to understand how molecular machines transduce free energy to perform their functions in biological systems. In this review, we discuss the nonequilibrium thermodynamics of free energy transduction within molecular machines, with a focus on quantifying energy and information flows between their components. We review results from theory, modeling, and inference from experiments that shed light on the internal thermodynamics of molecular machines, and ultimately explore what we can learn from considering these interactions.

A Benzodiazepine-Derived Molecule That Interferes with the Bio-Mechanical Properties of Glioblastoma-Astrocytoma Cells Altering Their Proliferation and Migration

Glioblastoma multiforme (grade IV glioma) is characterized by a high invasive potential, making surgical intervention extremely challenging and patient survival very limited. Current pharmacological approaches show, at best, slight improvements in the therapy against this type of tumor. Microtubules are often the target of antitumoral drugs, and specific drugs affecting their dynamics by acting on microtubule-associated proteins (MAPs) without producing their depolymerization could affect both glioma cell migration/invasion and cell proliferation. Here, we analyzed on a cellular model of glioblastoma multiforme, the effect of a molecule (1-(4-amino-3,5-dimethylphenyl)-3,5-dihydro-7,8-ethylenedioxy-4h2,3-benzodiazepin-4-one, hereafter named 1g) which was shown to act as a cytostatic drug in other cell types by affecting microtubule dynamics. We found that the molecule acts also as a migration suppressor by inducing a loss of cell polarity. We characterized the mechanics of U87MG cell aggregates exposed to 1g by different biophysical techniques. We considered both 3D aggregates and 2D cell cultures, testing substrates of different stiffness. We established that this molecule produces a decrease of cell spheroid contractility and it impairs 3D cell invasion. At the same time, in the case of isolated cells, 1g selectively produces an almost instantaneous loss of cell polarity blocking migration and it also produces a disorganization of the mitotic spindle when cells reach mitosis, leading to frequent mitotic slippage events followed by cell death. We can state that the studied molecule produces similar effects to other molecules that are known to affect the dynamics of microtubules, but probably indirectly via microtubule-associated proteins (MAPs) and following different biochemical pathways. Consistently, we report evidence that, regarding its effect on cell morphology, this molecule shows a specificity for some cell types such as glioma cells. Interestingly, being a molecule derived from a benzodiazepine, the 1g chemical structure could allow this molecule to easily cross the blood-brain barrier. Thanks to its chemical/physical properties, the studied molecule could be a promising new drug for the specific treatment of GBM.

Dynamical organization of vimentin intermediate filaments in living cells revealed by MoNaLISA nanoscopy

Intermediate filaments are intimately involved in the mechanical behavior of cells. Unfortunately, the resolution of optical microscopy limits our understanding of their organization. Here, we combined nanoscopy, single-filament tracking, and numerical simulations to inspect the dynamical organization of vimentin intermediate filaments in live cells. We show that a higher proportion of peripheral versus perinuclear vimentin pools are constrained in their lateral motion in the seconds time window, probably due to their cross-linking to other cytoskeletal networks. In a longer time scale, active forces become evident and affect similarly both pools of filaments. Our results provide a detailed description of the dynamical organization of the vimentin network in live cells and give some cues on its response to mechanical stimuli.

Hypoxia-Initiated Supramolecular Free Radicals Induce Intracellular Polymerization for Precision Tumor Therapy

Despite the development of various controlled release systems for antitumor therapies, off-target side effects remain a persistent challenge. In situ therapeutic synthesis from biocompatible substances offers a safer and more precise alternative. This study presents a hypoxia-initiated supramolecular free radical system capable of inducing intracellular polymerization, thereby disrupting the cytoskeleton and organelles within 4T1 cells. The system utilizes a 2:1 supramolecular host-guest complex of cucurbit[7]uril (CB[7]) and perylene diimide derivative (PDI), termed PDI+2CB[7], which is selectively reduced by the tumor's hypoxic and reducing environment to generate delocalized free radical anions. CB[7] effectively stabilizes these anions, enabling the PDI+2CB[7] complex to initiate free radical polymerization with 2-hydroxyethyl methacrylate (HEMA) inside the 4T1 cells. The resulting in situ polymerization significantly disrupts tumor metabolism, leading to a strong antitumor response without systemic toxicity. This study demonstrates that stable, endogenous stimulus-induced supramolecular free radicals can trigger intracellular polymerization reactions, achieving a selective and effective antitumor therapy without conventional chemotherapeutic agents.

Multiscale modelling of active hydrogel elasticity driven by living polymers: softening by bacterial motor protein FtsZ

We present a neo-Hookean elasticity theory for hybrid mechano-active hydrogels, integrating motor proteins into polymer meshes to create composite materials with active softening due to modulable chain overlaps. Focusing on polyacrylamide (PA) hydrogels embedded with FtsZ, a bacterial cytokinetic protein powered by GTP, we develop a multiscale model using microscopic Flory theory of rubbery meshes through mesoscopic De Gennes' scaling concepts for meshwork dynamics and phenomenological Landau's formalism for second-order phase transitions. Our theoretical multiscale model explains the active softening observed in hybrid FtsZ-PA hydrogels by incorporating modulable meshwork dynamics, such as overlapping functionality and reptation dynamics, into an active mean-field of unbinding interactions. The novel FtsZ-based metamaterial and companion multiscale theory offer insights for designing, predicting, and controlling complex active hydrogels, with potential applications in technology and biomedicine.

Characteristic frequencies of localized stress relaxation in scaling-law rheology of living cells

Living cells are known to exhibit power-law viscoelastic responses and localized stress relaxation behaviors in the frequency spectrum. However, the precise interplay between molecular-scale cytoskeletal dynamics and macroscale dynamical rheological responses remains elusive. Here, we propose a mechanism-based general theoretical model showing that cytoskeleton dissociation generates a peak in the loss modulus as a function of frequency, while the cytoplasmic viscosity promotes its recovery, producing a subsequent trough. We define two characteristic frequencies (ωc1 and ωc2) related to the dissociation rate of crosslinkers and the viscosity of the cytoplasm, where the loss modulus 1) exhibits peak and trough values for ωc1<ωc2 and 2) monotonically increases with frequency for ωc1>ωc2. Furthermore, the characteristic frequency ωc1 exhibits a biphasic stress-dependent behavior, with a local minimum at sufficiently high stress due to the stress-dependent dissociation rate. Moreover, the characteristic frequency ωc2 evolves with age, following a power-law relationship. The predictions of the dissociation-based multiscale theoretical mechanical model align well with experimental observations. Our model provides a comprehensive description of the dynamical viscoelastic behaviors of cells and cell-like materials.

Stochastic resetting in a nonequilibrium environment

This study examines the dynamics of a tracer particle diffusing in a nonequilibrium medium under stochastic resetting. The nonequilibrium state is induced by harmonic coupling between the tracer and bath particles, generating memory effects with an exponential decay in time. We explore the tracer's behavior under a Poissonian resetting protocol, where resetting does not disturb the bath environment, with a focus on key dynamical behavior and first-passage properties, both in the presence and absence of an external force. The interplay between coupling strength and diffusivity of bath particles significantly impacts both the tracer's relaxation dynamics and search time, with external forces further modulating these effects. Our analysis identifies distinct hot and cold bath particles based on their diffusivities, revealing that coupling to a hot particle facilitates the searching process, whereas coupling to a cold particle hinders it. Using a combination of numerical simulations and analytical methods, this study provides a comprehensive framework for understanding resetting mechanisms in non-Markovian systems, with potential applications to complex environments such as active and viscoelastic media, where memory-driven dynamics and nonequilibrium interactions are significant.

Effect of frequency-dependent shear and volume viscosities on molecular friction in liquids

The relation between the frequency-dependent friction of a molecule in a liquid and the hydrodynamic properties of the liquid is fundamental for molecular dynamics. We investigate this connection for a water molecule moving in liquid water using all-atomistic molecular dynamics (MD) simulations and linear hydrodynamic theory. We analytically calculate the frequency-dependent friction of a sphere with finite surface slip moving in a viscoelastic compressible fluid by solving the linear transient Stokes equation, including frequency-dependent shear and volume viscosities, both determined from MD simulations of bulk liquid water. From MD simulation trajectories, we also determine the frequency-dependent friction of a single water molecule moving in liquid water, as defined by the generalized Langevin equation. The frequency dependence of the shear viscosity of liquid water requires careful consideration of hydrodynamic finite-size effects to observe the asymptotic hydrodynamic power-law tail. By fitting the effective sphere radius and the slip length, the frequency-dependent friction and velocity autocorrelation function from the transient Stokes equation and simulations quantitatively agree. This shows that the transient Stokes equation accurately describes the important features of the frequency-dependent friction of a single water molecule in liquid water and thus applies down to molecular length and time scales, provided accurate frequency-dependent viscosities are used. In contrast, for a methane molecule moving in water, the frequency-dependent friction cannot be predicted based on a homogeneous model, which, supported by the extraction of the frequency-dependent surface slip, suggests that a methane molecule is surrounded by a finite-thickness hydration layer with viscoelastic properties that differ significantly from those of bulk water.

Second Law of Thermodynamics without Einstein Relation

Materials that are constantly driven out of thermodynamic equilibrium, such as active and living systems, typically violate the Einstein relation. This may arise from active contributions to particle fluctuations which are unrelated to the dissipative resistance of the surrounding medium. We show that in these cases the widely used relation between informatic entropy production and heat dissipation does not hold. Consequently, fluctuation relations for the mechanical work, such as the Jarzynski and Crooks theorems, are invalid. We relate the breaking of the correspondence between entropy production and heat dissipation to departure from the fluctuation-dissipation theorem. We propose a temperaturelike variable that restores this correspondence and gives rise to a generalized second law of thermodynamics, whereby the dissipated heat is necessarily non-negative and vanishes at equilibrium. The Clausius inequality, Carnot maximum efficiency theorem, and relation between the extractable work and the change of free energy are recovered as well.

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.

Rapid mechanical phenotyping of breast cancer cells based on stochastic intracellular fluctuations

Predicting the phenotypic impact of genetic variants and treatments is crucial in cancer genetics and precision oncology. Here, we have developed a noise decorrelation method that enables quantitative phase imaging (QPI) with the capability for label-free noninvasive mapping of intracellular dry mass fluctuations within the millisecond-to-second timescale regime, previously inaccessible due to temporal phase noise. Applied to breast cancer cells, this method revealed regions driven by thermal forces and regions of intense activity fueled by ATP hydrolysis. Intriguingly, as malignancy increases, the cells strategically expand these active regions to satisfy increasing energy demands. We propose parameters encapsulating key information about the spatiotemporal distribution of intracellular fluctuations, enabling precise phenotyping. This technique addresses the need for accurate, rapid functional screening methods in cancer medicine.

The fluctuation-dissipation relation holds for a macroscopic tracer in an active bath

The fluctuation-dissipation relation (FDR) links thermal fluctuations and dissipation at thermal equilibrium through temperature. Extending it beyond equilibrium conditions in pursuit of broadening thermodynamics is often feasible, albeit with system-dependent specific conditions. We demonstrate experimentally that a generalized FDR holds for a harmonically trapped tracer colliding with self-propelled walkers. The generalized FDR remains valid across a large spectrum of active fluctuation frequencies, extending from underdamped to critically damped dynamics, which we attribute to a single primary channel for energy input and dissipation in our system.

Structural dynamics and optimal transport of an active polymer

We study the spontaneous configuration transitions of an active semi-flexible polymer between spiral and non-spiral states, and show that the configuration dynamics is fully described by a subcritical pitchfork bifurcation. Exploiting the fact that an active polymer barely moves in spiral states and exhibits net displacements in non-spiral states, we theoretically prove that the motion of the active polymer is consistent with a run-and-tumble-like dynamics. Moreover, we find that there exists an optimal self-propelling force that maximizes the diffusion coefficient.

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.

Accessing activity and viscoelastic properties of artificial and living systems from passive measurement

Living systems are complex dynamic entities that operate far from thermodynamic equilibrium. Their active, non-equilibrium behaviour requires energy to drive cellular organization and dynamics. Unfortunately, most statistical mechanics approaches are not valid in non-equilibrium situations, forcing researchers to use intricate and often invasive methods to study living processes. Here we experimentally demonstrate that an observable termed mean back relaxation quantifies the active mechanics of living cells from passively observed particle trajectories. The mean back relaxation represents the average trajectory of a particle after a recent motion and is calculated from three-point probabilities. We show that this parameter allows the detection of broken detailed balance in confined systems. We experimentally observe that it provides access to the non-equilibrium generating energy and viscoelastic properties of artificial bulk materials and living cells. These findings suggest that the mean back relaxation can function as a marker of non-equilibrium dynamics and is a non-invasive avenue to determine viscoelastic material properties from passive measurements.

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.

The structure and mechanics of the cell cortex depend on the location and adhesion state

Cells exist in different phenotypes and can transition between them. A phenotype may be characterized by many different aspects. Here, we focus on the example of whether the cell is adhered or suspended and choose particular parameters related to the structure and mechanics of the actin cortex. The cortex is essential to cell mechanics, morphology, and function, such as for adhesion, migration, and division of animal cells. To predict and control cellular functions and prevent malfunctioning, it is necessary to understand the actin cortex. The structure of the cortex governs cell mechanics; however, the relationship between the architecture and mechanics of the cortex is not yet well enough understood to be able to predict one from the other. Therefore, we quantitatively measured structural and mechanical cortex parameters, including cortical thickness, cortex mesh size, actin bundling, and cortex stiffness. These measurements required developing a combination of measurement techniques in scanning electron, expansion, confocal, and atomic force microscopy. We found that the structure and mechanics of the cortex of cells in interphase are different depending on whether the cell is suspended or adhered. We deduced general correlations between structural and mechanical properties and show how these findings can be explained within the framework of semiflexible polymer network theory. We tested the model predictions by perturbing the properties of the actin within the cortex using compounds. Our work provides an important step toward predictions of cell mechanics from cortical structures and suggests how cortex remodeling between different phenotypes impacts the mechanical properties of cells.

Derivation of the nonequilibrium generalized Langevin equation from a time-dependent many-body Hamiltonian

It has become standard practice to describe systems that remain far from equilibrium even in their steady state by Langevin equations with colored noise which is chosen independently from the friction contribution. Since these Langevin equations are typically not derived from first-principle Hamiltonian dynamics, it is not clear whether they correspond to physically realizable scenarios. By exact Mori projection in phase space we derive the nonequilibrium generalized Langevin equation (GLE) for an arbitrary phase-space dependent observable A from a generic many-body Hamiltonian with a time-dependent external force h(t) acting on the same observable A. This is the same Hamiltonian from which the standard fluctuation-dissipation theorem is derived, which reflects the generality of our approach. The observable A could, for example, be the position of an atom, of a molecule or of a macroscopic object, the distance between two such entities or a more complex phase-space function such as the reaction coordinate of a chemical reaction or of the folding of a protein. The Hamiltonian could, for example, describe a fluid, a solid, a viscoelastic medium, or even a turbulent inhomogeneous environment. The GLE, which is a closed-form equation of motion for the observable A, is obtained in explicit form to all orders in h(t) and without restrictions on the type of many-body Hamiltonian or the observable A. If the dynamics of the observable A corresponds to a Gaussian process, the resultant GLE has a similar form as the equilibrium Mori GLE, and in particular the friction memory kernel is given by the two-point autocorrelation function of the sum of the complementary and the external force h(t). This is a nontrivial and useful result, as many observables that characterize nonequilibrium systems display Gaussian statistics. For non-Gaussian nonequilibrium observables correction terms appear in the GLE and in the relation between the force autocorrelation and the friction memory kernel, which are explicitly given in terms of cubic correlation functions of A. Interpreting the external force h(t) as a stochastic process, we derive nonequilibrium corrections to the fluctuation-dissipation theorem and present methods to extract all GLE parameters from experimental or simulation time-series data, thus making our nonequilibrium GLE a practical tool to study and model general nonequilibrium systems.

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.

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.