Asymmetric response emerges between creation and disintegration of force-bearing subcellular structures as revealed by percolation analysis.

Cells dynamically remodel their internal structures by modulating the arrangement of actin filaments (AFs). In this process, individual AFs exhibit stochastic behavior without knowing the macroscopic higher-order structures they are meant to create or disintegrate, but the mechanism allowing for such stochastic process-driven remodeling of subcellular structures remains incompletely understood. Here we employ percolation theory to explore how AFs interacting only with neighboring ones without recognizing the overall configuration can nonetheless create a substantial structure referred to as stress fibers (SFs) at particular locations. We determined the interaction probabilities of AFs undergoing cellular tensional homeostasis, a fundamental property maintaining intracellular tension. We showed that the duration required for the creation of SFs is shortened by the increased amount of preexisting actin meshwork, while the disintegration occurs independently of the presence of actin meshwork, suggesting that the coexistence of tension-bearing and non-bearing elements allows cells to promptly transition to new states in accordance with transient environmental changes. The origin of this asymmetry between creation and disintegration, consistently observed in actual cells, is elucidated through a minimal model analysis by examining the intrinsic nature of mechano-signal transmission. Specifically, unlike the symmetric case involving biochemical communication, physical communication to sense environmental changes is facilitated via AFs under tension, while other free AFs dissociated from tension-bearing structures exhibit stochastic behavior. Thus, both the numerical and minimal models demonstrate the essence of intracellular percolation, in which macroscopic asymmetry observed at the cellular level emerges not from microscopic asymmetry in the interaction probabilities of individual molecules, but rather only as a consequence of the manner of the mechano-signal transmission. These results provide novel insights into the role of the mutual interplay between distinct subcellular structures with and without tension-bearing capability. Insight: Cells continuously remodel their internal elements or structural proteins in response to environmental changes. Despite the stochastic behavior of individual structural proteins, which lack awareness of the larger subcellular structures they are meant to create or disintegrate, this self-assembly process somehow occurs to enable adaptation to the environment. Here we demonstrated through percolation simulations and minimal model analyses that there is an asymmetry in the response between the creation and disintegration of subcellular structures, which can aid environmental adaptation. This asymmetry inherently arises from the nature of mechano-signal transmission through structural proteins, namely tension-mediated information exchange within cells, despite the stochastic behavior of individual proteins lacking asymmetric characters in themselves.

Asymmetric bistability of chiral particle orientation in viscous shear flows.

The migration of helical particles in viscous shear flows plays a crucial role in chiral particle sorting. Attaching a nonchiral head to a helical particle leads to a rheotactic torque inducing particle reorientation. This phenomenon is responsible for bacterial rheotaxis observed for flagellated bacteria as Escherichia coli in shear flows. Here, we use a high-resolution microprinting technique to fabricate microparticles with controlled and tunable chiral shape consisting of a spherical head and helical tails of various pitch and handedness. By observing the fully time-resolved dynamics of these microparticles in microfluidic channel flow, we gain valuable insights into chirality-induced orientation dynamics. Our experimental model system allows us to examine the effects of particle elongation, chirality, and head heaviness for different flow rates on the orientation dynamics, while minimizing the influence of Brownian noise. Through our model experiments, we demonstrate the existence of asymmetric bistability of the particle orientation perpendicular to the flow direction. We quantitatively explain the particle equilibrium orientations as a function of particle properties, initial conditions and flow rates, as well as the time-dependence of the reorientation dynamics through a theoretical model. The model parameters are determined using boundary element simulations, and excellent agreement with experiments is obtained without any adjustable parameters. Our findings lead to a better understanding of chiral particle transport and bacterial rheotaxis and might allow the development of targeted delivery applications.

Long-Term Fluorescence Recovery After Photobleaching (FRAP).

Numerous models have been developed for the analysis of fluorescence recovery after photobleaching (FRAP), by which intracellular diffusion and turnover rate are quantitatively evaluated. FRAP analyses typically focus on such events that occur within several minutes, but to precisely evaluate a slow turnover rate of particularly actin stress fibers, achieving long-term FRAP observations of more than 10 min is necessary. In such long-term observations, the effect of intracellular advection is no longer ignored, which motivated us to develop a novel method to decouple the multiple factors associated with the long FRAP response. This method allows us to distinguish the origin of mechanobiological responses of stress fibers that come from either the level of individual actin filaments or that of actin monomers.

Long-term molecular turnover of actin stress fibers revealed by advection-reaction analysis in fluorescence recovery after photobleaching.

Fluorescence recovery after photobleaching (FRAP) is a versatile technique to evaluate the intracellular molecular exchange called turnover. Mechanochemical models of FRAP typically consider the molecular diffusion and chemical reaction that simultaneously occur on a time scale of seconds to minutes. Particularly for long-term measurements, however, a mechanical advection effect can no longer be ignored, which transports the proteins in specific directions within the cells and accordingly shifts the spatial distribution of the local chemical equilibrium. Nevertheless, existing FRAP models have not considered the spatial shift, and as such, the turnover rate is often analyzed without considering the spatiotemporally updated chemical equilibrium. Here we develop a new FRAP model aimed at long-term measurements to quantitatively determine the two distinct effects of the advection and chemical reaction, i.e., the different major sources of the change in fluorescence intensity. To validate this approach, we carried out FRAP experiments on actin in stress fibers over a time period of more than 900 s, and the advection rate was shown to be comparable in magnitude to the chemical dissociation rate. We further found that the actin-myosin interaction and actin polymerization differently affect the advection and chemical dissociation. Our results suggest that the distinction between the two effects is indispensable to extract the intrinsic chemical properties of the actin cytoskeleton from the observations of complicated turnover in cells.

A statistical mechanics model for determining the length distribution of actin filaments under cellular tensional homeostasis.

Tensional homeostasis is a cellular process whereby nonmuscle cells such as fibroblasts keep a constant level of intracellular tension and signaling activities. Cells are allowed thanks to tensional homeostasis to adapt to mechanical stress, but the detailed mechanism remains unclear. Here we address from a theoretical point of view what is required for maintaining cellular tensional homeostasis. A constrained optimization problem is formulated to analytically determine the probability function of the length of individual actin filaments (AFs) responsible for sustaining cellular tension. An objective function composed of two entropic quantities measuring the extent of formation and dispersion of AFs within cells is optimized under two constraint functions dictating a constant amount of actin molecules and tension that are arguably the two most salient features of tensional homeostasis. We then derive a specific probability function of AFs that is qualitatively consistent with previous experimental observations, in which short AF populations preferably appear. Regarding the underlying mechanism, our analyses suggest that the constraint for keeping the constant tension level makes long AF populations smaller in number because long AFs have a higher chance to be involved in bearing larger forces. The specific length distribution of AFs is thus required for achieving the constrained objectives, by which individual cells are endowed with the ability to stably maintain a homeostatic tension throughout the cell, thereby potentially allowing cells to locally detect deviation in the tension, keep resulting biological functions, and hence enable subsequent adaptation to mechanical stress. Although minimal essential factors are included given the actual complexity of cells, our approach would provide a theoretical basis for understanding complicated homeostatic and adaptive behavior of the cell.

Analysis of chemomechanical behavior of stress fibers by continuum mechanics-based FRAP.

Fluorescence recovery after photobleaching (FRAP) is a common technique to analyze the turnover of molecules in living cells. Numerous physicochemical models have been developed to quantitatively evaluate the rate of turnover driven by chemical reaction and diffusion that occurs in a few seconds to minutes. On the other hand, they have limitations in interpreting long-term FRAP responses where intracellular active movement inevitably provides target molecular architectures with additional effects other than chemical reaction and diffusion, namely directed transport and structural deformation. To overcome the limitations, we develop a continuum mechanics-based model that allows for decoupling FRAP response into the intrinsic turnover rate and subcellular mechanical characteristics such as displacement vector and strain tensor. Our approach was validated using fluorescently labeled ß-actin in an actomyosin-mediated contractile apparatus called stress fibers, revealing spatially distinct patterns of the multi-physicochemical events, in which the turnover rate, which represents effective off-rate of ß-actin, was significantly higher at the center of the cell. We also found that the turnover rate is negatively correlated with the rate of displacement or velocity along stress fibers but, interestingly, not with the absolute magnitude of strain. Moreover, stress fibers are subjected to centripetal flow that is facilitated by the circulation of actin molecules. Taken together, this novel framework for long-term FRAP analysis allows for unveiling the contribution of overlooked microscopic mechanics to molecular turnover in living cells.

Wrinkle force microscopy: a machine learning based approach to predict cell mechanics from images.

Combining experiments with artificial intelligence algorithms, we propose a machine learning based approach called wrinkle force microscopy (WFM) to extract the cellular force distributions from the microscope images. The full process can be divided into three steps. First, we culture the cells on a special substrate allowing to measure both the cellular traction force on the substrate and the corresponding substrate wrinkles simultaneously. The cellular forces are obtained using the traction force microscopy (TFM), at the same time that cell-generated contractile forces wrinkle their underlying substrate. Second, the wrinkle positions are extracted from the microscope images. Third, we train the machine learning system with GAN (generative adversarial network) by using sets of corresponding two images, the traction field and the input images (raw microscope images or extracted wrinkle images), as the training data. The network understands the way to convert the input images of the substrate wrinkles to the traction distribution from the training. After sufficient training, the network is utilized to predict the cellular forces just from the input images. Our system provides a powerful tool to evaluate the cellular forces efficiently because the forces can be predicted just by observing the cells under the microscope, which is much simpler method compared to the TFM experiment. Additionally, the machine learning based approach presented here has the profound potential for being applied to diverse cellular assays for studying mechanobiology of cells.

Determining the domain-level reaction-diffusion properties of an actin-binding protein transgelin-2 within cells.

Proteins in cells undergo repeated binding to other molecules, thereby reducing the apparent extent of their intracellular diffusion. While much effort has been made to analytically decouple these combined effects of pure diffusion and chemical binding, it is difficult with conventional approaches to attribute the measured quantities to the nature of specific domains of the proteins. Motivated by the common goal in cell signaling research aimed at identifying the domains responsible for particular intermolecular interactions, here we describe a framework for determining the local physicochemical properties of cellular proteins associated with immobile scaffolds. To validate this new approach, we apply it to transgelin-2, an actin-binding protein whose intracellular dynamics remains elusive. We develop a fluorescence recovery after photobleaching (FRAP)-based framework, in which comprehensive combinations of domain-deletion mutants are created, and the difference among them in FRAP response is analyzed. We demonstrate that transgelin-2 in actin stress fibers (SFs) interacts with F-actin via two separate domains, and the chemical properties are determined for the individual domains. Its pure diffusion properties independent of the association to F-actin is also obtained. Our approach will thus be useful, as presented here for transgelin-2, in addressing the signaling mechanism of cellular proteins associated with SFs.

Magnetic Microswimmers Exhibit Bose-Einstein-like Condensation.

We study an active matter system comprised of magnetic microswimmers confined in a microfluidic channel and show that it exhibits a new type of self-organized behavior. Combining analytical techniques and Brownian dynamics simulations, we demonstrate how the interplay of nonequilibrium activity, external driving, and magnetic interactions leads to the condensation of swimmers at the center of the channel via a nonequilibrium phase transition that is formally akin to Bose-Einstein condensation. We find that the effective dynamics of the microswimmers can be mapped onto a diffusivity-edge problem, and use the mapping to build a generalized thermodynamic framework, which is verified by a parameter-free comparison with our simulations. Our work reveals how driven active matter has the potential to generate exotic classical nonequilibrium phases of matter with traits that are analogous to those observed in quantum systems.

Image based cellular contractile force evaluation with small-world network inspired CNN: SW-UNet.

We propose an image based cellular contractile force evaluation method using a machine learning technique. We use a special substrate that exhibits wrinkles when cells grab the substrate and contract, and the wrinkles can be used to visualize the force magnitude and direction. In order to extract wrinkles from the microscope images, we develop a new CNN (convolutional neural network) architecture SW-UNet (small-world U-Net), which is a CNN that reflects the concept of the small-world network. The SW-UNet shows better performance in wrinkle segmentation task compared to other methods: the error (Euclidean distance) of SW-UNet is 4.9 times smaller than the 2D-FFT (fast Fourier transform) based segmentation approach, and is 2.9 times smaller than U-Net. As a demonstration, here we compare the contractile force of U2OS (human osteosarcoma) cells and show that cells with a mutation in the KRAS oncogene show larger force compared to wild-type cells. Our new machine learning based algorithm provides us an efficient, automated and accurate method to evaluate the cell contractile force.

Degenerate states, emergent dynamics and fluid mixing by magnetic rotors.

We investigate the collective motion of magnetic rotors suspended in a viscous fluid under a uniform rotating magnetic field. The rotors are positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For a 3 × 3 array of magnets, we observe three characteristic dynamical patterns as the external field strength is varied: a synchronized pattern, an oscillating pattern, and a chessboard pattern. The relative stability of these depends on the competition between the energy due to the external magnetic field and the energy of the magnetic dipole-dipole interactions among the rotors. We argue that the chessboard pattern can be understood as an alternation in the stability of two degenerate states, characterized by striped and spin-ice configurations, as the applied magnetic field rotates. For larger arrays, we observe propagation of slip waves that are similar to metachronal waves. The rotor arrays have potential as microfluidic devices that can mix fluids and create vortices of different sizes.

Multi-well plate cell contraction assay detects negatively correlated cellular responses to pharmacological inhibitors in contractility and migration.

To enable large-scale screening of signaling molecules and drugs that regulate cellular contractility-associated mechanotransduction, we previously modified, particularly in terms of the capability of efficiently collecting big data, conventional methodologies using wrinkled substrates to determine the cellular contractility. Here, we present a new system to perform the wrinkle-based cell force assay in a multi-well plate format conformed to standardized geometric configurations and compatible with available technologies such as automated plate readers. With this highly improved throughput in terms of hardware as well as software using a deep learning-based technology, we evaluated the effect of treating cells with various types of pharmacological inhibitors on the cellular contractility. We found opposite responses of cells to the inhibitors between the contractility and collective migration activities. While similar inverse relationships between the contractility and migration have been reported in separate studies, our results here with the high-throughput screening system more broadly generalized these observations.

Controlling collective rotational patterns of magnetic rotors.

Magnetic actuation is widely used in engineering specific forms of controlled motion in microfluidic applications. A challenge, however, is how to extract different desired responses from different components in the system using the same external magnetic drive. Using experiments, simulations, and theoretical arguments, we present emergent rotational patterns in an array of identical magnetic rotors under an uniform, oscillating magnetic field. By changing the relative strength of the external field strength versus the dipolar interactions between the rotors, different collective modes are selected by the rotors. When the dipole interaction is dominant the rotors swing upwards or downwards in alternating stripes, reflecting the spin-ice symmetry of the static configuration. For larger spacings, when the external field dominates over the dipolar interactions, the rotors undergo full rotations, with different quarters of the array turning in different directions. Our work sheds light on how collective behaviour can be engineered in magnetic systems.

Tunable self-healing of magnetically propelling colloidal carpets.

The process of crystallization is difficult to observe for transported, out-of-equilibrium systems, as the continuous energy injection increases activity and competes with ordering. In emerging fields such as microfluidics and active matter, the formation of long-range order is often frustrated by the presence of hydrodynamics. Here we show that a population of colloidal rollers assembled by magnetic fields into large-scale propelling carpets can form perfect crystalline materials upon suitable balance between magnetism and hydrodynamics. We demonstrate a field-tunable annealing protocol based on a controlled colloidal flow above the carpet that enables complete crystallization after a few seconds of propulsion. The structural transition from a disordered to a crystalline carpet phase is captured via spatial and temporal correlation functions. Our findings unveil a novel pathway to magnetically anneal clusters of propelling particles, bridging driven systems with crystallization and freezing in material science.

Magnetically-actuated artificial cilium: a simple theoretical model.

We propose a theoretical model for a magnetically-actuated artificial cilium in a fluid environment and investigate its dynamical behaviour, using both analytical calculations and numerical simulations. The cilium consists of a spherical soft magnet, a spherical hard magnet, and an elastic spring that connects the two magnetic components. Under a rotating magnetic field, the cilium exhibits a transition from phase-locking at low frequencies to phase-slipping at higher frequencies. We study the dynamics of the magnetic cilium in the vicinity of a wall by incorporating its hydrodynamic influence, and examine the efficiency of the actuated cilium in pumping viscous fluids. This cilium model can be helpful in a variety of applications such as transport and mixing of viscous solutions at small scales and fabricating microswimmers.

Clustering of Magnetic Swimmers in a Poiseuille Flow.

We investigate the collective behavior of magnetic swimmers, which are suspended in a Poiseuille flow and placed under an external magnetic field, using analytical techniques and Brownian dynamics simulations. We find that the interplay between intrinsic activity, external alignment, and magnetic dipole-dipole interactions leads to longitudinal structure formation. Our work sheds light on a recent experimental observation of a clustering instability in this system.

Focusing and Sorting of Ellipsoidal Magnetic Particles in Microchannels.

We present a simple method to control the position of ellipsoidal magnetic particles in microchannel Poiseuille flow at low Reynolds number using a static uniform magnetic field. The magnetic field is utilized to pin the particle orientation, and the hydrodynamic interactions between ellipsoids and channel walls allow control of the transverse position of the particles. We employ a far-field hydrodynamic theory and simulations using the boundary element method and Brownian dynamics to show how magnetic particles can be focused and segregated by size and shape. This is of importance for particle manipulation in lab-on-a-chip devices.

Deformation of a micro-torque swimmer.

The membrane tension of some kinds of ciliates has been suggested to regulate upward and downward swimming velocities under gravity. Despite its biological importance, deformation and membrane tension of a ciliate have not been clarified fully. In this study, we numerically investigated the deformation of a ciliate swimming freely in a fluid otherwise at rest. The cell body was modelled as a capsule with a hyperelastic membrane enclosing a Newtonian fluid. Thrust forces due to the ciliary beat were modelled as torques distributed above the cell body. The effects of membrane elasticity, the aspect ratio of the cell's reference shape, and the density difference between the cell and the surrounding fluid were investigated. The results showed that the cell deformed like a heart shape, when the capillary number was sufficiently large. Under the influence of gravity, the membrane tension at the anterior end decreased in the upward swimming while it increased in the downward swimming. Moreover, gravity-induced deformation caused the cells to move gravitationally downwards or upwards, which resulted in a positive or negative geotaxis-like behaviour with a physical origin. These results are important in understanding the physiology of a ciliate's biological responses to mechanical stimuli.