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.

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

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

Hierarchical Development of Motile Polarity in Durotactic Cells Just Crossing an Elasticity Boundary.

Cellular durotaxis has been extensively studied in the field of mechanobiology. In principle, asymmetric mechanical field of a stiffness gradient generates motile polarity in a cell, which is a driving factor of durotaxis. However, the actual process by which the motile polarity in durotaxis develops is still unclear. In this study, to clarify the details of the kinetics of the development of durotactic polarity, we investigated the dynamics of both cell-shaping and the microscopic turnover of focal adhesions (FAs) for Venus-paxillin-expressing fibroblasts just crossing an elasticity boundary prepared on microelastically patterned gels. The Fourier mode analysis of cell-shaping based on a persistent random deformation model revealed that motile polarity at a cell-body scale was established within the first few hours after the leading edges of a moving cell passed through the boundary from the soft to the stiff regions. A fluorescence recovery after photobleaching (FRAP) analysis showed that the mobile fractions of paxillin at FAs in the anterior part of the cells exhibited an asymmetric increase within several tens of minutes after cells entered the stiff region. The results demonstrated that motile polarity in durotactic cells is established through the hierarchical step-wise development of different types of asymmetricity in the kinetics of FAs activity and cell-shaping with a several-hour time lag.Key words: Microelasticity patterned gel, durotaxis, cell polarity, focal adhesions, paxillin.

Self-replicating segregation patterns in horizontally vibrated binary mixture of granules.

Fluidized granular mixtures of various particle sizes exhibit intriguing patterns as different species segregate and condense. However, understanding the segregation dynamics is hindered by the inability to directly observe the time evolution of the internal structure. We discover self-replicating bands within a quasi-2D container subjected to horizontal agitation, resulting in steady surface waves. Through direct observation of surface flow and evolving internal structures, we reveal the crucial role of coupling among segregation, surface flow, and hysteresis in granular fluidity. We develop Bonhoeffer-van der Pol type equations grounded in experimental observations, reproducing complex band dynamics, such as replication, oscillation, and breathing. It suggests the similarity between pattern formation in granular segregation and that in reaction-diffusion systems.

Convection of monodisperse particles in a highly filled rotating cylinder.

We investigate the occurrence of spontaneous convection in a coaxial cylinder highly filled with monodisperse spheres. To analyze the flow field noninvasively, initial pulses consisting of colored particles are placed at equal intervals. By analyzing the spatiotemporal distribution of these pulses, we obtained axial velocity profiles for both the surface and subsurface regions. Our advection-diffusion equations with steady advection terms incorporate experimentally obtained axial velocity profiles in the surface layer, while the rest of the components are estimated using azimuthal symmetry and volume conservation. The validity of our model is confirmed by comparing experimental data with numerical solutions for both the spatiotemporal distribution and cross-sectional profile of the colored particles.

Segregation patterns in rotating cylinders determined by the size difference, density ratio, and cylinder diameter.

Granular materials often segregate under mechanical agitation, which differs from the expectation of mixing. It is well known that a bidisperse mixture of granular materials in a partially filled rotating cylinder exhibits alternating bands depending on the combination of the two species. The dynamic angle of repose, which is the angle that a steady avalanche makes with the horizontal, has been considered the dominant parameter that determines the segregated state. However, the previously known angle of repose condition was not always satisfied in different experimental cases. To clarify the experimental conditions, we conducted an exhaustive parameter search with three dimensionless parameters: the particle size difference normalized by the average particle size, the specific density ratio, and the ratio of the cylinder diameter to the average particle size. Additional experiments were conducted to explore the effect of the rotational speed of the cylinder. This systematic approach enabled us to predict the segregated state. Moreover, we discovered that the band width can be effectively scaled by combining these three parameters.

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.

Interplay among cell migration, shaping, and traction force on a matrix with cell-scale stiffness heterogeneity.

In living tissues where cells migrate, the spatial distribution of mechanical properties, especially matrix stiffness, is generally heterogeneous, with cell scales ranging from 10 to 1000 µm. Since cell migration in the body plays a critical role in morphogenesis, wound healing, and cancer metastasis, it is essential to understand the migratory dynamics on the matrix with cell-scale stiffness heterogeneity. In general, cell migration is driven by the extension and contraction of the cell body owing to the force from actin polymerization and myosin motors in the actomyosin cytoskeleton. When a cell is placed on a matrix with a simple stiffness gradient, directional migration called durotaxis emerges because of the asymmetric extension and contraction of the pseudopodia, which is accompanied by the asymmetric distribution of focal adhesions. Similarly, to determine cell migration on a matrix with cell-scale stiffness heterogeneity, the interaction between cell-scale stiffness heterogeneity and cellular responses, such as the dynamics of the cell-matrix adhesion site, intracellular prestress, and cell shape, should play a key role. In this review, we summarize systematic studies on the dynamics of cell migration, shaping, and traction force on a matrix with cell-scale stiffness heterogeneity using micro-elastically patterned hydrogels. We also outline the cell migration model based on cell-shaping dynamics that explains the general durotaxis induced by cell-scale stiffness heterogeneity. This review article is an extended version of the Japanese article, Dynamics of Cell Shaping and Migration on the Matrix with Cell-scale Stiffness-heterogeneity, published in SEIBUTSU BUTSURI Vol. 61, p. 152-156 (2021).

Avoiding tensional equilibrium in cells migrating on a matrix with cell-scale stiffness-heterogeneity.

Intracellular stresses affect various cell functions, including proliferation, differentiation and movement, which are dynamically modulated in migrating cells through continuous cell-shaping and remodeling of the cytoskeletal architecture induced by spatiotemporal interactions with extracellular matrix stiffness. When cells migrate on a matrix with cell-scale stiffness-heterogeneity, which is a common situation in living tissues, what intracellular stress dynamics (ISD) emerge? In this study, to explore this issue, finite element method-based traction force microscopy was applied to cells migrating on microelastically patterned gels. Two model systems of microelastically patterned gels (stiff/soft stripe and stiff triangular patterns) were designed to characterize the effects of a spatial constraint on cell-shaping and of the presence of different types of cues to induce competing cellular taxis (usual and reverse durotaxis) on the ISD, respectively. As the main result, the prolonged fluctuation of traction stress on a whole-cell scale was markedly enhanced on single cell-size triangular stiff patterns compared with homogeneous gels. Such ISD enhancement was found to be derived from the interplay between the nomadic migration of cells to regions with different degrees of stiffness and domain shape-dependent traction force dynamics, which should be an essential factor for keeping cells far from tensional equilibrium.

General cellular durotaxis induced with cell-scale heterogeneity of matrix-elasticity.

Stiffness-gradient-induced cellular taxis, so-called durotaxis, has been extensively studied on a substrate with a single broad or steep stiffness gradient. However, in actual living tissues, cells should sense cell-scaled heterogeneous elasticity distribution in the extracellular matrix. In this study, to clarify the effect of the cell-scale heterogeneity of matrix-elasticity on durotaxis, we examined the motility of different types of cells on microelastically-striped patterned gels with different cell-sized widths. We found that cells accumulated in stiff regions with specific width on cell-type-dependency, even when a stiffness gradient is too small to induce usual durotaxis with a monotonic stiffness gradient. Fibroblast cells accumulated in a wide stiff region of multicellular size, while mesenchymal stem cells localized in a narrow stiff region of single-cell size. It was revealed that durotactic activity is critically affected not only with the cell type but also with the cell-scale heterogeneity of matrix-elasticity. Based on the shape-fluctuation-based analysis of cell migration, the dynamics of the pseudopodia were found to play a key role in determining the behaviors of general durotaxis. Our results suggest that design of cell-scale heterogeneity of matrix-elasticity is pivotal in controlling directional cell migration, the spontaneous cell-patterning, and development of the tissue on the biomaterials surfaces.

Persistent random deformation model of cells crawling on a gel surface.

In general, cells move on a substrate through extension and contraction of the cell body. Though cell movement should be explained by taking into account the effect of such shape fluctuations, past approaches to formulate cell-crawling have not sufficiently quantified the relationship between cell movement (velocity and trajectory) and shape fluctuations based on experimental data regarding actual shaping dynamics. To clarify this relationship, we experimentally characterized cell-crawling in terms of shape fluctuations, especially extension and contraction, by using an elasticity-tunable gel substrate to modulate cell shape. As a result, an amoeboid swimmer-like relation was found to arise between the cell velocity and cell-shape dynamics. To formulate this experimentally-obtained relationship between cell movement and shaping dynamics, we established a persistent random deformation (PRD) model based on equations of a deformable self-propelled particle adopting an amoeboid swimmer-like velocity-shape relationship. The PRD model successfully explains the statistical properties of velocity, trajectory and shaping dynamics of the cells including back-and-forth motion, because the velocity equation exhibits time-reverse symmetry, which is essentially different from previous models. We discuss the possible application of this model to classify the phenotype of cell migration based on the characteristic relation between movement and shaping dynamics.

Model of heap formation in vibrated gravitational suspensions.

In vertically vibrated dense suspensions, several localized structures have been discovered, such as heaps, stable holes, expanding holes, and replicating holes. Because an inclined free fluid surface is difficult to maintain because of gravitational pressure, the mechanism of those structures is not understood intuitively. In this paper, as a candidate for the driving mechanism, we focus on the boundary condition on a solid wall: the slip-nonslip switching boundary condition in synchronization with vertical vibration. By applying the lubrication approximation, we derived the time evolution equation of the fluid thickness from the Oldroyd-B fluid model. In our model we show that the initially flat fluid layer becomes unstable in a subcritical manner, and heaps and convectional flow appear. The obtained results are consistent with those observed experimentally. We also find that heaps climb a slope when the bottom is slightly inclined. We show that viscoelasticity enhances heap formation and climbing of a heap on the slope.

Swimming droplets driven by a surface wave.

Self-propelling motion is ubiquitous for soft active objects such as crawling cells, active filaments, and liquid droplets moving on surfaces. Deformation and energy dissipation are required for self-propulsion of both living and non-living matter. From the perspective of physics, searching for universal laws of self-propelled motions in a dissipative environment is worthwhile, regardless of the objects' details. In this article, we propose a simple experimental system that demonstrates spontaneous migration of a droplet under uniform mechanical agitation. As we vary control parameters, spontaneous symmetry breaking occurs sequentially, and cascades of bifurcations of the motion arise. Equations describing deformable particles and hydrodynamic simulations successfully describe all of the observed motions. This system should enable us to improve our understanding of spontaneous motions of self-propelled objects.

Steadily oscillating axial bands of binary granules in a nearly filled coaxial cylinder.

Granular materials often segregate under mechanical agitation such as flowing, shaking, or rotating, in contrast to an expectation of mixing. It is well known that bidisperse mixtures of granular materials in a partially filled rotating cylinder exhibit monotonic coarsening dynamics of segregation. Here we report the steady oscillation of segregated axial bands under the stationary rotation of a nearly filled coaxial cylinder for O(10(3)) revolutions. The axial bands demonstrate steady back-and-forth motion along the axis of rotation. Experimental findings indicated that these axial band dynamics are driven by global convection throughout the system. The essential features of the spatiotemporal dynamics are reproduced with a simple phenomenological equation that incorporates the effect of global convection.