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The Kramers escape problem is a paradigmatic model for the kinetics of rare events, which are usually characterized by Arrhenius law. So far, analytical approaches have failed to capture the kinetics of rare events in the important case of non-Markovian processes with long-term memory, as occurs in the context of reactions involving proteins, long polymers, or strongly viscoelastic fluids. Here, based on a minimal model of non-Markovian Gaussian process with long-term memory, we determine quantitatively the mean FPT to a rare configuration and provide its asymptotics in the limit of a large energy barrier E. Our analysis unveils a correction to Arrhenius law, induced by long-term memory, which we determine analytically. This correction, which we show can be quantitatively significant, takes the form of a second effective energy barrier E ' < E and captures the dependence of rare event kinetics on initial conditions, which is a hallmark of long-term memory. Altogether, our results quantify the impact of long-term memory on rare event kinetics, beyond Arrhenius law., (© 2024. The Author(s).)

Contraction and flow of the actin cell cortex have emerged as a common principle by which cells reorganize their cytoplasm and take shape. However, how these cortical flows interact with adjacent cytoplasmic components, changing their form and localization, and how this affects cytoplasmic organization and cell shape remains unclear. Here we show that in ascidian oocytes, the cooperative activities of cortical actomyosin flows and deformation of the adjacent mitochondria-rich myoplasm drive oocyte cytoplasmic reorganization and shape changes following fertilization. We show that vegetal-directed cortical actomyosin flows, established upon oocyte fertilization, lead to both the accumulation of cortical actin at the vegetal pole of the zygote and compression and local buckling of the adjacent elastic solid-like myoplasm layer due to friction forces generated at their interface. Once cortical flows have ceased, the multiple myoplasm buckles resolve into one larger buckle, which again drives the formation of the contraction pole-a protuberance of the zygote's vegetal pole where maternal mRNAs accumulate. Thus, our findings reveal a mechanism where cortical actomyosin network flows determine cytoplasmic reorganization and cell shape by deforming adjacent cytoplasmic components through friction forces., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2024.)

Growing evidence suggests that the physical properties of the cellular microenvironment influence cell migration. However, it is not currently understood how active physical remodelling by cells affects migration dynamics. Here we report that cell clusters seeded on deformable collagen-I networks display persistent collective migration despite not showing any apparent intrinsic polarity. Clusters generate transient gradients in collagen density and alignment due to viscoelastic relaxation of the collagen networks. Combining theory and experiments, we show that crosslinking collagen networks or reducing cell cluster size results in reduced network deformation, shorter viscoelastic relaxation time and smaller gradients, leading to lower migration persistence. Traction force and Brillouin microscopy reveal asymmetries in force distributions and collagen stiffness during migration, providing evidence of mechanical cross-talk between cells and their substrate during migration. This physical model provides a mechanism for self-generated directional migration on viscoelastic substrates in the absence of internal biochemical polarity cues., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Persistence, defined as the probability that a signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. Often, persistence decays algebraically with time with non trivial exponents. However, general analytical methods to calculate persistence exponents cannot be applied to the ubiquitous case of non-Markovian systems relaxing transiently after an imposed initial perturbation. Here, we introduce a theoretical framework that enables the non-perturbative determination of persistence exponents of Gaussian non-Markovian processes with non stationary dynamics relaxing to a steady state after an initial perturbation. Two situations are analyzed: either the system is subjected to a temperature quench at initial time, or its past trajectory is assumed to have been observed and thus known. Our theory covers the case of spatial dimension higher than one, opening the way to characterize non-trivial reaction kinetics for complex systems with non-equilibrium initial conditions., (© 2022. The Author(s).)

Cells remodel their cytoplasm with force-generating cytoskeletal motors. Their activity generates random forces that stir the cytoplasm, agitating and displacing membrane-bound organelles like the nucleus in somatic and germ cells. These forces are transmitted inside the nucleus, yet their consequences on liquid-like biomolecular condensates residing in the nucleus remain unexplored. Here, we probe experimentally and computationally diverse nuclear condensates, that include nuclear speckles, Cajal bodies, and nucleoli, during cytoplasmic remodeling of female germ cells named oocytes. We discover that growing mammalian oocytes deploy cytoplasmic forces to timely impose multiscale reorganization of nuclear condensates for the success of meiotic divisions. These cytoplasmic forces accelerate nuclear condensate collision-coalescence and molecular kinetics within condensates. Disrupting the forces decelerates nuclear condensate reorganization on both scales, which correlates with compromised condensate-associated mRNA processing and hindered oocyte divisions that drive female fertility. We establish that cytoplasmic forces can reorganize nuclear condensates in an evolutionary conserved fashion in insects. Our work implies that cells evolved a mechanism, based on cytoplasmic force tuning, to functionally regulate a broad range of nuclear condensates across scales. This finding opens new perspectives when studying condensate-associated pathologies like cancer, neurodegeneration and viral infections., (© 2022. The Author(s).)

Actin filaments assemble into force-generating systems involved in diverse cellular functions, including cell motility, adhesion, contractility and division. It remains unclear how networks of actin filaments, which individually generate piconewton forces, can produce forces reaching tens of nanonewtons. Here we use in situ cryo-electron tomography to unveil how the nanoscale architecture of macrophage podosomes enables basal membrane protrusion. We show that the sum of the actin polymerization forces at the membrane is not sufficient to explain podosome protrusive forces. Quantitative analysis of podosome organization demonstrates that the core is composed of a dense network of bent actin filaments storing elastic energy. Theoretical modelling of the network as a spring-loaded elastic material reveals that it exerts forces of a few tens of nanonewtons, in a range similar to that evaluated experimentally. Thus, taking into account not only the interface with the membrane but also the bulk of the network, is crucial to understand force generation by actin machineries. Our integrative approach sheds light on the elastic behavior of dense actin networks and opens new avenues to understand force production inside cells., (© 2022. The Author(s).)

Living cells actively migrate in their environment to perform key biological functions-from unicellular organisms looking for food to single cells such as fibroblasts, leukocytes or cancer cells that can shape, patrol or invade tissues. Cell migration results from complex intracellular processes that enable cell self-propulsion, and has been shown to also integrate various chemical or physical extracellular signals. While it is established that cells can modify their environment by depositing biochemical signals or mechanically remodelling the extracellular matrix, the impact of such self-induced environmental perturbations on cell trajectories at various scales remains unexplored. Here, we show that cells can retrieve their path: by confining motile cells on 1D and 2D micropatterned surfaces, we demonstrate that they leave long-lived physicochemical footprints along their way, which determine their future path. On this basis, we argue that cell trajectories belong to the general class of self-interacting random walks, and show that self-interactions can rule large scale exploration by inducing long-lived ageing, subdiffusion and anomalous first-passage statistics. Altogether, our joint experimental and theoretical approach points to a generic coupling between motile cells and their environment, which endows cells with a spatial memory of their path and can dramatically change their space exploration.

Unraveling the mechanisms that govern the formation and function of invadopodia is essential towards the prevention of cancer spread. Here, we characterize the ultrastructural organization, dynamics and mechanical properties of collagenotytic invadopodia forming at the interface between breast cancer cells and a physiologic fibrillary type I collagen matrix. Our study highlights an uncovered role for MT1-MMP in directing invadopodia assembly independent of its proteolytic activity. Electron microscopy analysis reveals a polymerized Arp2/3 actin network at the concave side of the curved invadopodia in association with the collagen fibers. Actin polymerization is shown to produce pushing forces that repel the confining matrix fibers, and requires MT1-MMP matrix-degradative activity to widen the matrix pores and generate the invasive pathway. A theoretical model is proposed whereby pushing forces result from actin assembly and frictional forces in the actin meshwork due to the curved geometry of the matrix fibers that counterbalance resisting forces by the collagen fibers.

For many stochastic processes, the probability [Formula: see text] of not-having reached a target in unbounded space up to time [Formula: see text] follows a slow algebraic decay at long times, [Formula: see text]. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent [Formula: see text] has been studied at length, the prefactor [Formula: see text], which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for [Formula: see text] for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for [Formula: see text] are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.

An important channel of cell-to-cell communication is direct contact. The immune synapse is a paradigmatic example of such type of interaction: it forms upon engagement of antigen receptors in lymphocytes by antigen-presenting cells and allows the local exchange of molecules and information. Although mechanics has been shown to play an important role in this process, how forces organize and impact on synapse function is unknown. We find that mechanical forces are spatio-temporally patterned at the immune synapse: global pulsatile myosin II-driven tangential forces are observed at the synapse periphery while localised forces generated by invadosome-like F-actin protrusions are detected at its centre. Noticeably, we observe that these force-producing actin protrusions constitute the main site of antigen extraction and endocytosis and require myosin II contractility to form. The interplay between global and local forces dictated by the organization of the actomyosin cytoskeleton therefore controls endocytosis at the immune synapse.

Cell migration over heterogeneous substrates during wound healing or morphogenetic processes leads to shape changes driven by different organizations of the actin cytoskeleton and by functional changes including lamellipodial protrusions and contractile actin cables. Cells distinguish between cell-sized positive and negative curvatures in their physical environment by forming protrusions at positive ones and actin cables at negative ones; however, the cellular mechanisms remain unclear. Here, we report that concave edges promote polarized actin structures with actin flow directed towards the cell edge, in contrast to well-documented retrograde flow at convex edges. Anterograde flow and contractility induce a tension anisotropy gradient. A polarized actin network is formed, accompanied by a local polymerization-depolymerization gradient, together with leading-edge contractile actin cables in the front. These cables extend onto non-adherent regions while still maintaining contact with the substrate through focal adhesions. The contraction and dynamic reorganization of this actin structure allows forward movements enabling cell migration over non-adherent regions on the substrate. These versatile functional structures may help cells sense and navigate their environment by adapting to external geometric and mechanical cues.

Multiciliated ependymal cells line all brain cavities. The beating of their motile cilia contributes to the flow of cerebrospinal fluid, which is required for brain homoeostasis and functions. Motile cilia, nucleated from centrioles, persist once formed and withstand the forces produced by the external fluid flow and by their own cilia beating. Here, we show that a dense actin network around the centrioles is induced by cilia beating, as shown by the disorganisation of the actin network upon impairment of cilia motility. Moreover, disruption of the actin network, or specifically of the apical actin network, causes motile cilia and their centrioles to detach from the apical surface of ependymal cell. In conclusion, cilia beating controls the apical actin network around centrioles; the mechanical resistance of this actin network contributes, in turn, to centriole stability.

Mitotic spindle position relies on interactions between astral microtubules nucleated by centrosomes and a rigid cortex. Some cells, such as mouse oocytes, do not possess centrosomes and astral microtubules. These cells rely only on actin and on a soft cortex to position their spindle off-centre and undergo asymmetric divisions. While the first mouse embryonic division also occurs in the absence of centrosomes, it is symmetric and not much is known on how the spindle is positioned at the exact cell centre. Using interdisciplinary approaches, we demonstrate that zygotic spindle positioning follows a three-step process: (1) coarse centring of pronuclei relying on the dynamics of an F-actin/Myosin-Vb meshwork; (2) fine centring of the metaphase plate depending on a high cortical tension; (3) passive maintenance at the cell centre. Altogether, we show that F-actin-dependent mechanics operate the switch between asymmetric to symmetric division required at the oocyte to embryo transition.

Many cellular functions rely on DNA-binding proteins finding and associating to specific sites in the genome. Yet the mechanisms underlying the target search remain poorly understood, especially in the case of the highly organized mammalian cell nucleus. Using as a model Tet repressors (TetRs) searching for a multi-array locus, we quantitatively analyse the search process in human cells with single-molecule tracking and single-cell protein-DNA association measurements. We find that TetRs explore the nucleus and reach their target by 3D diffusion interspersed with transient interactions with non-cognate sites, consistent with the facilitated diffusion model. Remarkably, nonspecific binding times are broadly distributed, underlining a lack of clear delimitation between specific and nonspecific interactions. However, the search kinetics is not determined by diffusive transport but by the low association rate to nonspecific sites. Altogether, our results provide a comprehensive view of the recruitment dynamics of proteins at specific loci in mammalian cells.

Matrix rigidity sensing regulates a large variety of cellular processes and has important implications for tissue development and disease. However, how cells probe matrix rigidity, and hence respond to it, remains unclear. Here, we show that rigidity sensing and adaptation emerge naturally from actin cytoskeleton remodelling. Our in vitro experiments and theoretical modelling demonstrate a biphasic rheology of the actin cytoskeleton, which transitions from fluid on soft substrates to solid on stiffer ones. Furthermore, we find that increasing substrate stiffness correlates with the emergence of an orientational order in actin stress fibres, which exhibit an isotropic to nematic transition that we characterize quantitatively in the framework of active matter theory. These findings imply mechanisms mediated by a large-scale reinforcement of actin structures under stress, which could be the mechanical drivers of substrate stiffness-dependent cell shape changes and cell polarity.

The immune response relies on the migration of leukocytes and on their ability to stop in precise anatomical locations to fulfil their task. How leukocyte migration and function are coordinated is unknown. Here we show that in immature dendritic cells, which patrol their environment by engulfing extracellular material, cell migration and antigen capture are antagonistic. This antagonism results from transient enrichment of myosin IIA at the cell front, which disrupts the back-to-front gradient of the motor protein, slowing down locomotion but promoting antigen capture. We further highlight that myosin IIA enrichment at the cell front requires the MHC class II-associated invariant chain (Ii). Thus, by controlling myosin IIA localization, Ii imposes on dendritic cells an intermittent antigen capture behaviour that might facilitate environment patrolling. We propose that the requirement for myosin II in both cell migration and specific cell functions may provide a general mechanism for their coordination in time and space.

Cell mechanics control the outcome of cell division. In mitosis, external forces applied on a stiff cortex direct spindle orientation and morphogenesis. During oocyte meiosis on the contrary, spindle positioning depends on cortex softening. How changes in cortical organization induce cortex softening has not yet been addressed. Furthermore, the range of tension that allows spindle migration remains unknown. Here, using artificial manipulation of mouse oocyte cortex as well as theoretical modelling, we show that cortical tension has to be tightly regulated to allow off-center spindle positioning: a too low or too high cortical tension both lead to unsuccessful spindle migration. We demonstrate that the decrease in cortical tension required for spindle positioning is fine-tuned by a branched F-actin network that triggers the delocalization of myosin-II from the cortex, which sheds new light on the interplay between actin network architecture and cortex tension.

Podosomes are adhesion structures formed in monocyte-derived cells. They are F-actin-rich columns perpendicular to the substrate surrounded by a ring of integrins. Here, to measure podosome protrusive forces, we designed an innovative experimental setup named protrusion force microscopy (PFM), which consists in measuring by atomic force microscopy the deformation induced by living cells onto a compliant Formvar sheet. By quantifying the heights of protrusions made by podosomes onto Formvar sheets, we estimate that a single podosome generates a protrusion force that increases with the stiffness of the substratum, which is a hallmark of mechanosensing activity. We show that the protrusive force generated at podosomes oscillates with a constant period and requires combined actomyosin contraction and actin polymerization. Finally, we elaborate a model to explain the mechanical and oscillatory activities of podosomes. Thus, PFM shows that podosomes are mechanosensing cell structures exerting a protrusive force.

Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.

It has long been appreciated that the transport properties of molecules can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target-the first-passage time (FPT). Determining the FPT distribution in realistic confined geometries has until now, however, seemed intractable. Here, we calculate this FPT distribution analytically and show that transport processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes. Beyond the theoretical aspect, this result changes our views on standard reaction kinetics and we introduce the concept of 'geometry-controlled kinetics'. More precisely, we argue that geometry-and in particular the initial distance between reactants in 'compact' systems-can become a key parameter. These findings could help explain the crucial role that the spatial organization of genes has in transcription kinetics, and more generally the impact of geometry on diffusion-limited reactions.