High-frequency affine mechanics and nonaffine relaxation in a model cytoskeleton

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.

Activity-dependent glassy cell mechanics Ⅰ: 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.

Microrheology of semiflexible filament solutions based on relaxation simulations

We present an efficient computational methodology to obtain the viscoelastic response of dilute solutions of semiflexible filaments. By considering an approach based on the fluctuation-dissipation theorem, we were able to evaluate the dynamical properties of probe particles immersed in solutions of semiflexible filaments from relaxation simulations with a relatively low computational cost and higher precision in comparison to those based on stochastic dynamics. We used a microrheological approach to obtain the complex shear modulus and the complex viscosity of the solution through its compliance which was obtained directly from the dynamical properties of a probe particle attached to an effective medium described by a mesoscopic model, i.e., an effective filament model (EFM). The relaxation simulations were applied to assess the effects of the bending energy on the viscoelasticity of the semiflexible filament solutions, and our methodology was validated by comparing the numerical results to the experimental data on DNA and collagen solutions.

Inverse integral transformation method to derive local viscosity distribution measured by optical tweezers

Complex fluids have a non-uniform local inner structure; this is enhanced under deformation, inducing a characteristic flow, such as an abrupt increase in extensional viscosity and drag reduction. However, it is challenging to derive and quantify the non-uniform local structure of a low-concentration solution. In this study, we attempted to characterize the non-uniformity of dilute and semi-dilute polymer and worm-like micellar solutions using the local viscosity at the micro scale. The power spectrum density (PSD) of the particle displacement, measured using optical tweezers, was analyzed to calculate the local viscosity, and two methods were compared. One is based on the PSD roll-off method, which yields a single representative viscosity of the solution. The other is based on our proposed method, called the inverse integral transformation method (IITM), for deriving the local viscosity distribution. The distribution obtained through the IITM reflects the non-uniformity of the solutions at the micro scale, i.e., the distribution widens above the entanglement concentrations of the polymer or viscoelastic worm-like micellar solutions.

The Structural Function of Nestin in Cell Body Softening is Correlated with Cancer Cell Metastasis

Intermediate filaments play significant roles in governing cell stiffness and invasive ability. Nestin is a type VI intermediate filament protein that is highly expressed in several high-metastatic cancer cells. Although inhibition of nestin expression was shown to reduce the metastatic capacity of tumor cells, the relationship between this protein and the mechanism of cancer cell metastasis remains unclear. Here, we show that nestin softens the cell body of the highly metastatic mouse breast cancer cell line FP10SC2, thereby enhancing the metastasis capacity. Proximity ligation assay demonstrated increased binding between actin and vimentin in nestin knockout cells. Because nestin copolymerizes with vimentin and nestin has an extremely long tail domain in its C-terminal region, we hypothesized that the tail domain functions as a steric inhibitor of the vimentin-actin interaction and suppresses association of vimentin filaments with the cortical actin cytoskeleton, leading to reduced cell stiffness. To demonstrate this function, we mechanically pulled vimentin filaments in living cells using a nanoneedle modified with vimentin-specific antibodies under manipulation by atomic force microscopy (AFM). The tensile test revealed that mobility of vimentin filaments was increased by nestin expression in FP10SC2 cells.

Universal glass-forming behavior of in vitro and living cytoplasm

Physiological processes in cells are performed efficiently without getting jammed although cytoplasm is highly crowded with various macromolecules. Elucidating the physical machinery is challenging because the interior of a cell is so complex and driven far from equilibrium by metabolic activities. Here, we studied the mechanics of in vitro and living cytoplasm using the particle-tracking and manipulation technique. The molecular crowding effect on cytoplasmic mechanics was selectively studied by preparing simple in vitro models of cytoplasm from which both the metabolism and cytoskeletons were removed. We obtained direct evidence of the cytoplasmic glass transition; a dramatic increase in viscosity upon crowding quantitatively conformed to the super-Arrhenius formula, which is typical for fragile colloidal suspensions close to jamming. Furthermore, the glass-forming behaviors were found to be universally conserved in all the cytoplasm samples that originated from different species and developmental stages; they showed the same tendency for diverging at the macromolecule concentrations relevant for living cells. Notably, such fragile behavior disappeared in metabolically active living cells whose viscosity showed a genuine Arrhenius increase as in typical strong glass formers. Being actively driven by metabolism, the living cytoplasm forms glass that is fundamentally different from that of its non-living counterpart.

Feedback-tracking microrheology in living cells

Living cells are composed of active materials, in which forces are generated by the energy derived from metabolism. Forces and structures self-organize to shape the cell and drive its dynamic functions. Understanding the out-of-equilibrium mechanics is challenging because constituent materials, the cytoskeleton and the cytosol, are extraordinarily heterogeneous, and their physical properties are strongly affected by the internally generated forces. We have analyzed dynamics inside two types of eukaryotic cells, fibroblasts and epithelial-like HeLa cells, with simultaneous active and passive microrheology using laser interferometry and optical trapping technology. We developed a method to track microscopic probes stably in cells in the presence of vigorous cytoplasmic fluctuations, by using smooth three-dimensional (3D) feedback of a piezo-actuated sample stage. To interpret the data, we present a theory that adapts the fluctuation-dissipation theorem (FDT) to out-of-equilibrium systems that are subjected to positional feedback, which introduces an additional nonequilibrium effect. We discuss the interplay between material properties and nonthermal force fluctuations in the living cells that we quantify through the violations of the FDT. In adherent fibroblasts, we observed a well-known polymer network viscoelastic response where the complex shear modulus scales as G* ∝ (-iω)3/4. In the more 3D confluent epithelial cells, we found glassy mechanics with G* ∝ (-iω)1/2 that we attribute to glassy dynamics in the cytosol. The glassy state in living cells shows characteristics that appear distinct from classical glasses and unique to nonequilibrium materials that are activated by molecular motors.

Importance of non-affine viscoelastic response in disordered fibre networks

Disordered fibre networks are ubiquitous in nature and have a wide range of industrial applications as novel biomaterials. Predicting their viscoelastic response is straightforward for affine deformations that are uniform over all length scales, but when affinity fails, as has been observed experimentally, modelling becomes challenging. Here we present a numerical methodology, related to an existing framework for amorphous packings, to predict the steady-state viscoelastic spectra and degree of affinity for disordered fibre networks driven at arbitrary frequencies. Applying this method to a peptide gel model reveals a monotonic increase of the shear modulus as the soft, non-affine normal modes are successively suppressed as the driving frequency increases. In addition to being dominated by fibril bending, these low frequency network modes are also shown to be delocalised. The presented methodology provides insights into the importance of non-affinity in the viscoelastic response of peptide gels, and is easily extendible to all types of fibre networks.

Viscoelastic properties of marginal networks in a solvent

Polymer networks at the margins of mechanical stability are known to be highly sensitive to applied forces and fields and to exhibit an anomalously large resistance to deformation. In this paper, we study the effects of hydrodynamic interactions on the behavior of marginal networks using a hybrid molecular dynamics and multiparticle collision dynamics simulation technique. We examine how the filament and solvent properties affect the response of marginal networks to shear. We find that the stiffening of the network shows a stronger dependence on the shear frequency when hydrodynamic interactions are present than when they are not. The network shear modulus scales as G'∼ω(α(c)), with a critical stiffening exponent α(c) that can be controlled by varying the relative concentrations of the network and the solvent. Our results show that this arises due to the solvent aiding the relaxation of the network and suppressing the network nonaffinity, with the system deforming more affinely when hydrodynamic interactions are maximized.