Dissecting fat-tailed fluctuations in the cytoskeleton with active micropost arrays

Universal to nonuniversal transition of the statistics of rare events during the spread of random walks

Through numerous experiments that analyzed rare event statistics in heterogeneous media, it was discovered that in many cases the probability density function for particle position, P(X,t), exhibits a slower decay rate than the Gaussian function. Typically, the decay behavior is exponential, referred to as Laplace tails. However, many systems exhibit an even slower decay rate, such as power-law, log-normal, or stretched exponential. In this study, we utilize the continuous-time random walk method to investigate the rare events in particle hopping dynamics and find that the properties of the hop size distribution induce a critical transition between the Laplace universality of rare events and a more specific, slower decay of P(X,t). Specifically, when the hop size distribution decays slower than exponential, such as e^{-|x|^{β}} (β>1), the Laplace universality no longer applies, and the decay is specific, influenced by a few large events, rather than by the accumulation of many smaller events that give rise to Laplace tails.

Experimental observations of fractal landscape dynamics in a dense emulsion

Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening foam, suggested that the random motions of its bubbles are due to the system configuration moving over a fractal energy landscape in high-dimensional space. Here we show that the salient geometrical features of such high-dimensional fractal landscapes can be explored and reliably quantified, using empirical trajectory data from many degrees of freedom, in a model-free manner. For a mayonnaise-like dense emulsion, analysis of the observed trajectories of oil droplets quantitatively reproduces the high-dimensional fractal geometry of the configuration path and its associated local energy minima generated using a computational model. That geometry in turn drives the droplets' complex random motion observed in real space. Our results indicate that experimental studies can elucidate whether the similar dynamics in different soft and biological materials may also be due to fractal landscape dynamics.

Nucleation causes an actin network to fragment into multiple high-density domains

Actin networks rely on nucleation mechanisms to generate new filaments because spontaneous nucleation is kinetically disfavored. Branching nucleation of actin filaments by actin-related protein (Arp2/3), in particular, is critical for actin self-organization. In this study, we use the simulation platform for active matter MEDYAN to generate 2000 s long stochastic trajectories of actin networks, under varying Arp2/3 concentrations, in reaction volumes of biologically meaningful size (>20 μm3). We find that the dynamics of Arp2/3 increase the abundance of short filaments and increases network treadmilling rate. By analyzing the density fields of F-actin, we find that at low Arp2/3 concentrations, F-actin is organized into a single connected and contractile domain, while at elevated Arp2/3 levels (10 nM and above), such high-density actin domains fragment into smaller domains spanning a wide range of volumes. These fragmented domains are extremely dynamic, continuously merging and splitting, owing to the high treadmilling rate of the underlying actin network. Treating the domain dynamics as a drift-diffusion process, we find that the fragmented state is stochastically favored, and the network state slowly drifts toward the fragmented state with considerable diffusion (variability) in the number of domains. We suggest that tuning the Arp2/3 concentration enables cells to transition from a globally coherent cytoskeleton, whose response involves the entire cytoplasmic network, to a fragmented cytoskeleton, where domains can respond independently to locally varying signals.

Measuring Cytoskeletal Mechanical Fluctuations and Rheology with Active Micropost Arrays

The dynamics of the cellular actomyosin cytoskeleton are crucial to many aspects of cellular function. Here, we describe techniques that employ active micropost array detectors (AMPADs) to measure cytoskeletal rheology and mechanical force fluctuations. The AMPADS are arrays of flexible poly(dimethylsiloxane) (PDMS) microposts with magnetic nanowires embedded in a subset of microposts to enable actuation of those posts via an externally applied magnetic field. Techniques are described to track the magnetic microposts' motion with nanometer precision at up to 100 video frames per second to measure the local cellular rheology at well-defined positions. Application of these high-precision tracking techniques to the full array of microposts in contact with a cell also enables mapping of the cytoskeletal mechanical fluctuation dynamics with high spatial and temporal resolution. This article describes (1) the fabrication of magnetic micropost arrays, (2) measurement protocols for both local rheology and cytoskeletal force fluctuation mapping, and (3) special-purpose software routines to reduce and analyze these data. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Fabrication of magnetic micropost arrays Basic Protocol 2: Data acquisition for cellular force fluctuations on non-magnetic micropost arrays Basic Protocol 3: Data acquisition for local cellular rheology measurements with magnetic microposts Basic Protocol 4: Data reduction: determining microposts' motion Basic Protocol 5: Data analysis: determining local rheology from magnetic microposts Basic Protocol 6: Data analysis for force fluctuation measurements Support Protocol 1: Fabrication of magnetic Ni nanowires by electrodeposition Support Protocol 2: Configuring Streampix for magnetic rheology measurements.

Pervasive cytoquakes in the actomyosin cortex across cell types and substrate stiffness

The actomyosin cytoskeleton enables cells to resist deformation, crawl, change their shape and sense their surroundings. Despite decades of study, how its molecular constituents can assemble together to form a network with the observed mechanics of cells remains poorly understood. Recently, it has been shown that the actomyosin cortex of quiescent cells can undergo frequent, abrupt reconfigurations and displacements, called cytoquakes. Notably, such fluctuations are not predicted by current physical models of actomyosin networks, and their prevalence across cell types and mechanical environments has not previously been studied. Using micropost array detectors, we have performed high-resolution measurements of the dynamic mechanical fluctuations of cells' actomyosin cortex and stress fiber networks. This reveals cortical dynamics dominated by cytoquakes-intermittent events with a fat-tailed distribution of displacements, sometimes spanning microposts separated by 4 μm, in all cell types studied. These included 3T3 fibroblasts, where cytoquakes persisted over substrate stiffnesses spanning the tissue-relevant range of 4.3 kPa-17 kPa, and primary neonatal rat cardiac fibroblasts and myofibroblasts, human embryonic kidney cells and human bone osteosarcoma epithelial (U2OS) cells, where cytoquakes were observed on substrates in the same stiffness range. Overall, these findings suggest that the cortex self-organizes into a marginally stable mechanical state whose physics may contribute to cell mechanical properties, active behavior and mechanosensing.

Active gels, heavy tails, and the cytoskeleton

The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to "cytoquakes" or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles naturally creates heavy power-law tails in cytoskeletal displacements. We predict that this power law exponent should depend on the geometry and dimensionality of where force dipoles are distributed through the cell; we find qualitatively different results for force dipoles in a 3D cytoskeleton and a quasi-two-dimensional cortex. We then discuss potential applications of this model both in cells and in synthetic active gels.

Understanding cytoskeletal avalanches using mechanical stability analysis

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine-learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide a connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

AFM and Fluorescence Microscopy of Single Cells with Simultaneous Mechanical Stimulation via Electrically Stretchable Substrates

We have developed a novel experimental set-up that simultaneously, (i) applies static and dynamic deformations to adherent cells in culture, (ii) allows the visualization of cells under fluorescence microscopy, and (iii) allows atomic force microscopy nanoindentation measurements of the mechanical properties of the cells. The cell stretcher device relies on a dielectric elastomer film that can be electro-actuated and acts as the cell culture substrate. The shape and position of the electrodes actuating the film can be controlled by design in order to obtain specific deformations across the cell culture chamber. By using optical markers we characterized the strain fields under different electrode configurations and applied potentials. The combined setup, which includes the cell stretcher device, an atomic force microscope, and an inverted optical microscope, can assess in situ and with sub-micron spatial resolution single cell topography and elasticity, as well as ion fluxes, during the application of static deformations. Proof of performance on fibroblasts shows a reproducible increase in the average cell elastic modulus as a response to applied uniaxial stretch of just 4%. Additionally, high resolution topography and elasticity maps on a single fibroblast can be acquired while the cell is deformed, providing evidence of long-term instrumental stability. This study provides a proof-of-concept of a novel platform that allows in situ and real time investigation of single cell mechano-transduction phenomena with sub-cellular spatial resolution.

Motion magnification analysis of microscopy videos of biological cells

It is well recognized that isolated cardiac muscle cells beat in a periodic manner. Recently, evidence indicates that other, non-muscle cells, also perform periodic motions that are either imperceptible under conventional lab microscope lens or practically not easily amenable for analysis of oscillation amplitude, frequency, phase of movement and its direction. Here, we create a real-time video analysis tool to visually magnify and explore sub-micron rhythmic movements performed by biological cells and the induced movements in their surroundings. Using this tool, we suggest that fibroblast cells perform small fluctuating movements with a dominant frequency that is dependent on their surrounding substrate and its stiffness.

Force-dependent trans-endocytosis by breast cancer cells depletes costimulatory receptor CD80 and attenuates T cell activation

In this study, we investigated the biophysical interaction between cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) and CD80. CTLA-4 is a key molecule in immunosuppression, and CD80 is a costimulatory receptor promoting T cell activation. We observed that after cell-cell contact was established between breast cancer cells and antigen presenting cells (APCs), CTLA-4 expressed on the breast cancer cells bind to CD80 expressed on the APCs, and underwent trans-endocytosis to deplete CD80. Force measurement and live cell imaging revealed that upon binding to CD80, forces generated by breast cancer cells and transmitted via CTLA-4 were sufficiently strong to displace CD80 from the surface of APCs to be internalized by breast cancer cells. We further demonstrated that because of the force-dependent trans-endocytosis of CD80, the capacity of APCs to activate T cells was significantly attenuated. Furthermore, inhibiting force generation in cancer cells would increase the T cell activating capacity of APCs. Our results provide a possible mechanism behind the immunosuppression commonly seen in breast cancer patients, and may lead to a new strategy to restore anti-tumor immunity by inhibiting pathways of force-generation.

The role of the Arp2/3 complex in shaping the dynamics and structures of branched actomyosin networks

Actomyosin networks give cells the ability to move and divide. These networks contract and expand while being driven by active energy-consuming processes such as motor protein walking and actin polymerization. Actin dynamics is also regulated by actin-binding proteins, such as the actin-related protein 2/3 (Arp2/3) complex. This complex generates branched filaments, thereby changing the overall organization of the network. In this work, the spatiotemporal patterns of dynamical actin assembly accompanying the branching-induced reorganization caused by Arp2/3 were studied using a computational model (mechanochemical dynamics of active networks [MEDYAN]); this model simulates actomyosin network dynamics as a result of chemical reactions whose rates are modulated by rapid mechanical equilibration. We show that branched actomyosin networks relax significantly more slowly than do unbranched networks. Also, branched networks undergo rare convulsive movements, "avalanches," that release strain in the network. These avalanches are associated with the more heterogeneous distribution of mechanically linked filaments displayed by branched networks. These far-from-equilibrium events arising from the marginal stability of growing actomyosin networks provide a possible mechanism of the "cytoquakes" recently seen in experiments.