Optical rheology of biological cells

i-Rheo-optical assay: Measuring the viscoelastic properties of multicellular spheroids

This study introduces a novel mechanobiology assay, named "i-Rheo-optical assay", that integrates rheology with optical microscopy for analysing the viscoelastic properties of multicellular spheroids. These spheroids serve as three-dimensional models resembling tissue structures. The innovative technique enables real-time observation and quantification of morphological responses to applied stress using a cost-effective microscope coverslip for constant compression force application. By bridging a knowledge gap in biophysical research, which has predominantly focused on the elastic properties while only minimally exploring the viscoelastic nature in multicellular systems, the i-Rheo-optical assay emerges as an effective tool. It facilitates the measurement of broadband viscoelastic compressional moduli in spheroids, here derived from cancer (PANC-1) and non-tumoral (NIH/3T3) cell lines during compression tests. This approach plays a crucial role in elucidating the mechanical properties of spheroids and holds potential for identifying biomarkers to discriminate between healthy tissues and their pathological counterparts. Offering comprehensive insights into the biomechanical behaviour of biological systems, i-Rheo-optical assay marks a significant advancement in tissue engineering, cancer research, and therapeutic development.

"Patchiness" in mechanical stiffness across a tumor as an early-stage marker for malignancy

Mechanical phenotyping of tumors, either at an individual cell level or tumor cell population level is gaining traction as a diagnostic tool. However, the extent of diagnostic and prognostic information that can be gained through these measurements is still unclear. In this work, we focus on the heterogeneity in mechanical properties of cells obtained from a single source such as a tissue or tumor as a potential novel biomarker. We believe that this heterogeneity is a conventionally overlooked source of information in mechanical phenotyping data. We use mechanics-based in-silico models of cell-cell interactions and cell population dynamics within 3D environments to probe how heterogeneity in cell mechanics drives tissue and tumor dynamics. Our simulations show that the initial heterogeneity in the mechanical properties of individual cells and the arrangement of these heterogenous sub-populations within the environment can dictate overall cell population dynamics and cause a shift towards the growth of malignant cell phenotypes within healthy tissue environments. The overall heterogeneity in the cellular mechanotype and their spatial distributions is quantified by a "patchiness" index, which is the ratio of the global to local heterogeneity in cell populations. We observe that there exists a threshold value of the patchiness index beyond which an overall healthy population of cells will show a steady shift towards a more malignant phenotype. Based on these results, we propose that the "patchiness" of a tumor or tissue sample, can be an early indicator for malignant transformation and cancer occurrence in benign tumors or healthy tissues. Additionally, we suggest that tissue patchiness, measured either by biochemical or biophysical markers, can become an important metric in predicting tissue health and disease likelihood just as landscape patchiness is an important metric in ecology.

Segregation of co-cultured multicellular systems: review and modeling consideration

Cell segregation caused by collective cell migration (CCM) is crucial for morphogenesis, functional development of tissue parts, and is an important aspect in other diseases such as cancer and its metastasis process. Efficiency of the cell segregation depends on the interplay between: (1) biochemical processes such as cell signaling and gene expression and (2) physical interactions between cells. Despite extensive research devoted to study the segregation of various co-cultured systems, we still do not understand the role of physical interactions in cell segregation. Cumulative effects of these physical interactions appear in the form of physical parameters such as: (1) tissue surface tension, (2) viscoelasticity caused by CCM, and (3) solid stress accumulated in multicellular systems. These parameters primarily depend on the interplay between the state of cell-cell adhesion contacts and cell contractility. The role of these physical parameters on the segregation efficiency is discussed on model systems such as co-cultured breast cell spheroids consisting of two subpopulations that are in contact. This review study aims to: (1) summarize biological aspects related to cell segregation, mechanical properties of cell collectives, effects along the biointerface between cell subpopulations and (2) describe from a biophysical/mathematical perspective the same biological aspects summarized before. So that overall it can illustrate the complexity of the biological systems that translate into very complex biophysical/mathematical equations. Moreover, by presenting in parallel these two seemingly different parts (biology vs. equations), this review aims to emphasize the need for experiments to estimate the variety of parameters entering the resulting complex biophysical/mathematical models.

Cell deformability heterogeneity recognition by unsupervised machine learning from in-flow motion parameters

Cell deformability is a well-established marker of cell states for diagnostic purposes. However, the measurement of a wide range of different deformability levels is still challenging, especially in cancer, where a large heterogeneity of rheological/mechanical properties is present. Therefore, a simple, versatile and cost-effective recognition method for variable rheological/mechanical properties of cells is needed. Here, we introduce a new set of in-flow motion parameters capable of identifying heterogeneity among cell deformability, properly modified by the administration of drugs for cytoskeleton destabilization. Firstly, we measured cell deformability by identification of in-flow motions, rolling (R), tumbling (T), swinging (S) and tank-treading (TT), distinctively associated with cell rheological/mechanical properties. Secondly, from a pool of motion and structural cell parameters, an unsupervised machine learning approach based on principal component analysis (PCA) revealed dominant features: the local cell velocity (V_Cell/V_Avg), the equilibrium position (Y_Eq) and the orientation angle variation (Δφ). These motion parameters clearly defined cell clusters in terms of motion regimes corresponding to specific deformability. Such correlation is verified in a wide range of rheological/mechanical properties from the elastic cells moving like R until the almost viscous cells moving as TT. Thus, our approach shows how simple motion parameters allow cell deformability heterogeneity recognition, directly measuring rheological/mechanical properties.

Dynamics and Stability of the Contractile Actomyosin Ring in the Cell

Contraction of the cytokinetic ring during cell division leads to physical partitioning of a eukaryotic cell into two daughter cells. This involves flows of actin filaments and myosin motors in the growing membrane interface at the midplane of the dividing cell. Assuming boundary driven alignment of the actomyosin filaments at the inner edge of the interface, we explore how the resulting active stresses influence the flow. Using the continuum gel theory framework, we obtain exact axisymmetric solutions of the dynamical equations. These solutions are consistent with experimental observations on closure rate. Using these solutions, we perform linear stability analysis for the contracting ring under nonaxisymmetric deformations. Our analysis shows that few low wave number modes, which are unstable during onset of the constriction, later on become stable when the ring shrinks to smaller radii, which is a generic feature of actomyosin ring closure. Our theory also captures how the effective tension in the ring decreases with its radius, causing significant slowdown in the contraction process at later times.

Cavitation controls droplet sizes in elastic media

Biological cells use droplets to separate components and spatially control their interior. Experiments demonstrate that the complex, crowded cellular environment affects the droplet arrangement and their sizes. To understand this behavior, we here construct a theoretical description of droplets growing in an elastic matrix, which is motivated by experiments in synthetic systems where monodisperse emulsions form during a temperature decrease. We show that large droplets only form when they break the surrounding matrix in a cavitation event. The energy barrier associated with cavitation stabilizes small droplets on the order of the mesh size and diminishes the stochastic effects of nucleation. Consequently, the cavitated droplets have similar sizes and highly correlated positions. In particular, we predict the density of cavitated droplets, which increases with faster cooling, as in the experiments. Our model also suggests how adjusting the cooling protocol and the density of nucleation sites affects the droplet size distribution. In summary, our theory explains how elastic matrices affect droplets in the synthetic system, and it provides a framework for understanding the biological case.

Optical manipulation of a dielectric particle along polygonal closed-loop geometries within a single water droplet

We report a new method to optically manipulate a single dielectric particle along closed-loop polygonal trajectories by crossing a suite of all-fiber Bessel-like beams within a single water droplet. Exploiting optical radiation pressure, this method demonstrates the circulation of a single polystyrene bead in both a triangular and a rectangle geometry enabling the trapped particle to undergo multiple circulations successfully. The crossing of the Bessel-like beams creates polygonal corners where the trapped particles successfully make abrupt turns with acute angles, which is a novel capability in microfluidics. This offers an optofluidic paradigm for particle transport overcoming turbulences in conventional microfluidic chips.

Single-cell mechanical analysis and tension quantification via electrodeformation relaxation

The mechanical behavior and cortical tension of single cells are analyzed using electrodeformation relaxation. Four types of cells, namely, MCF-10A, MCF-7, MDA-MB-231, and GBM, are studied, with pulse durations ranging from 0.01 to 10 s. Mechanical response in the long-pulse regime is characterized by a power-law behavior, consistent with soft glassy rheology resulting from unbinding events within the cortex network. In the subsecond short-pulse regime, a single timescale well describes the process and indicates the naive tensioned (prestressed) state of the cortex with minimal force-induced alteration. A mathematical model is employed and the simple ellipsoidal geometry allows for use of an analytical solution to extract the cortical tension. At the shortest pulse of 0.01 s, tensions for all four cell types are on the order of 10^{-2} N/m.

Elastic wrinkling of keratocyte lamellipodia driven by myosin-induced contractile stress

During actin-based cell migration, the actin cytoskeleton in the lamellipodium both generates and responds to force, which has functional consequences for the ability of the cell to extend protrusions. However, the material properties of the lamellipodial actin network and its response to stress on the timescale of motility are incompletely understood. Here, we describe a dynamic wrinkling phenotype in the lamellipodium of fish keratocytes, in which the actin sheet buckles upward away from the ventral membrane of the cell, forming a periodic pattern of wrinkles perpendicular to the cell's leading edge. Cells maintain an approximately constant wrinkle wavelength over time despite new wrinkle formation and the lateral movement of wrinkles in the cell frame of reference, suggesting that cells have a preferred or characteristic wrinkle wavelength. Generation of wrinkles is dependent upon myosin contractility, and their wavelength scales directly with the density of the actin network and inversely with cell adhesion. These results are consistent with a simple physical model for wrinkling in an elastic sheet under compression and suggest that the lamellipodial cytoskeleton behaves as an elastic material on the timescale of cell migration despite rapid actin turnover.

Mechanical Adaptability of Tumor Cells in Metastasis

The most dangerous aspect of cancer lies in metastatic progression. Tumor cells will successfully form life-threatening metastases when they undergo sequential steps along a journey from the primary tumor to distant organs. From a biomechanics standpoint, growth, invasion, intravasation, circulation, arrest/adhesion, and extravasation of tumor cells demand particular cell-mechanical properties in order to survive and complete the metastatic cascade. With metastatic cells usually being softer than their non-malignant counterparts, high deformability for both the cell and its nucleus is thought to offer a significant advantage for metastatic potential. However, it is still unclear whether there is a finely tuned but fixed mechanical state that accommodates all mechanical features required for survival throughout the cascade or whether tumor cells need to dynamically refine their properties and intracellular components at each new step encountered. Here, we review the various mechanical requirements successful cancer cells might need to fulfill along their journey and speculate on the possibility that they dynamically adapt their properties accordingly. The mechanical signature of a successful cancer cell might actually be its ability to adapt to the successive microenvironmental constraints along the different steps of the journey.

Fluctuations of a membrane nanotube covered with an actin sleeve

Many biological functions rely on the reshaping of cell membranes, in particular into nanotubes, which are covered in vivo by dynamic actin networks. Nanotubes are subject to thermal fluctuations, but the effect of these on cell functions is unknown. Here, we form nanotubes from liposomes using an optically trapped bead adhering to the liposome membrane. From the power spectral density of this bead, we study the nanotube fluctuations in the range of membrane tensions measured in vivo. We show that an actin sleeve covering the nanotube damps its high-frequency fluctuations because of the network viscoelasticity. Our work paves the way for further studies of the effect of nanotube fluctuations on cellular functions.

Contactless thin-film rheology unveiled by laser-induced nanoscale interface dynamics

One of the classical limitations for the investigation of the local rheology of small scale soft objects and/or confined fluids is related to the difficulty to control mechanical contact and its consequences. In order to overcome these issues, we implement a new local, active, fast and contactless optical strategy, called optorheology, which is based on both the optical radiation pressure of a laser wave to dynamically deform a fluid interface and interferometry to probe this deformation with nanometric resolution. This optical approach is first validated by measuring the surface tension and the viscosity of transparent Newtonian liquids. We also show how non-equilibrium situations, such as continuous evaporation, can be used to deduce the thickness dependence of the rheology of thin films and the concentration dependence of the viscosity of binary liquid mixtures and suspensions. We further extend the investigation to elasticity and viscoelasticity measurements of polymer solutions. Finally, since liquids may absorb light, we discuss the influence of a weak laser heating and the triggering of interface deformations by thermocapillary tangential stresses that could represent a complementary approach to probe the rheology at small scale.

Actomyosin Contraction Induces In-Bulk Motility of Cells and Droplets

Cell crawling on two-dimensional surfaces is a relatively well-understood phenomenon that is based on actin polymerization at a cell's front edge and anchoring on a substrate, allowing the cell to pull itself forward. However, some cells, such as cancer cells invading a three-dimensional matrigel, can also swim in the bulk, where surface adhesion is impossible. Although there is strong evidence that the self-organized engine that drives cells forward in the bulk involves myosin, the specific propulsion mechanism remains largely unclear. Here, we propose a minimal model for in-bulk self-motility of a droplet containing an isotropic and compressible contractile gel, representing a cell extract containing a disordered actomyosin network. In our model, contraction mediates a feedback loop between myosin-induced flow and advection-induced myosin accumulation, which leads to clustering and locally enhanced flow. The symmetry of such flow is then spontaneously broken through actomyosin-membrane interactions, leading to self-organized droplet motility relative to the underlying solvent. Depending on the balance between contraction, diffusion, detachment rate of myosin, and effective surface tension, this motion can be either straight or circular. Our simulations and analytical results shed new light on in-bulk myosin-driven cell motility in living cells and provide a framework to design a novel type of synthetic active matter droplet potentially resembling the motility mechanism of biological cells.

A mathematical finance approach to the stochastic and intermittent viscosity fluctuations in living cells

Here we report on the viscosity of eukaryotic living cells, as a function of time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblast cells are investigated using an active microrheological technique, where the magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in mathematical finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1-10 s and 100-200 s, not previously disclosed. The shorter time is found to be related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and the statistical results from a mathematical finance approach. The current approach could be exploited to reveal hidden features from biological complex systems or to determine new biomarkers of cellular metabolism.

Influence of hyaluronic acid binding on the actin cortex measured by optical forces

Melanoma cells are often surrounded by hyaluronic acid (HA) rich environments, which are considered to promote tumor progression and metastasis. Induced effects in compound materials consisting of cells embedded in an extracellular matrix have been studied, however, alterations of the single cells have never been addressed. Here, we explicitly addressed single cell properties and measured HA-induced biomechanical changes via deformations induced solely by optical forces. With the optical stretcher setup, cells were deformed after culturing them in either the presence or absence of HA revealing the crucial interplay of HA with the CD44 receptor. To assess the role of CD44 in transducing effects of HA, we compared a CD44 expressing variant of the melanoma cell line RPM-MC to its natural CD44-negative counterpart. Our measurements revealed a significant stiffness change, which we attribute to changes of the actin cytoskeleton.

The transmembrane protein fibrocystin/polyductin regulates cell mechanics and cell motility

Polycystic kidney disease is a disorder that leads to fluid filled cysts that replace normal renal tubes. During the process of cellular development and in the progression of the diseases, fibrocystin can lead to impaired organ formation and even cause organ defects. Besides cellular polarity, mechanical properties play major roles in providing the optimal apical-basal or anterior-posterior symmetry within epithelial cells. A breakdown of the cell symmetry that is usually associated with mechanical property changes and it is known to be essential in many biological processes such as cell migration, polarity and pattern formation especially during development and diseases such as the autosomal recessive cystic kidney disease. Since the breakdown of the cell symmetry can be evoked by several proteins including fibrocystin, we hypothesized that cell mechanics are altered by fibrocystin. However, the effect of fibrocystin on cell migration and cellular mechanical properties is still unclear. In order to explore the function of fibrocystin on cell migration and mechanics, we analyzed fibrocystin knockdown epithelial cells in comparison to fibrocystin control cells. We found that invasiveness of fibrocystin knockdown cells into dense 3D matrices was increased and more efficient compared to control cells. Using optical cell stretching and atomic force microscopy, fibrocystin knockdown cells were more deformable and exhibited weaker cell-matrix as well as cell-cell adhesion forces, respectively. In summary, these findings show that fibrocystin knockdown cells displayed increased 3D matrix invasion through providing increased cellular deformability, decreased cell-matrix and reduced cell-cell adhesion forces.

Regulation of Cell Behavior by Hydrostatic Pressure

Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.

Functional Epithelium Remodeling in Response to Applied Stress under In Vitro Conditions

Mathematical modeling is often used in tissue engineering in order to overcome one of its major challenges: transformation of complex biological and rheological behaviors of cells and tissue in a mathematically predictive and physically manipulative engineering process. The successive accomplishment of this task will greatly help in quantifying and optimizing clinical application of the tissue engineering products. One of the problems emerging in this area is the relation between resting and migrating cell groups, as well as between different configurations of migrating cells and viscoelasticity. A deeper comprehension of the relation between various configurations of migrating cells and viscoelasticity at the supracellular level represents the prerequisite for optimization of the performance of the artificial epithelium. Since resting and migrating cell groups have a considerable difference in stiffness, a change in their mutual volume ratio and distribution may affect the viscoelasticity of multicellular surfaces. If those cell groups are treated as different phases, then an analogous model may be applied to represent such systems. In this work, a two-step Eyring model is developed in order to demonstrate the main mechanical and biochemical factors that influence configurations of migrating cells. This model could be also used for considering the long-time cell rearrangement under various types of applied stress. The results of this theoretical analysis point out the cause-consequence relationship between the configuration of migrating cells and rheological behavior of multicellular surfaces. Configuration of migrating cells is influenced by mechanical and biochemical perturbations, difficult to measure experimentally, which lead to uncorrelated motility. Uncorrelated motility results in (1) decrease of the volume fraction of migrating cells, (2) change of their configuration, and (3) softening of multicellular surfaces.

High-Throughput, Time-Resolved Mechanical Phenotyping of Prostate Cancer Cells

Worldwide, prostate cancer sits only behind lung cancer as the most commonly diagnosed form of the disease in men. Even the best diagnostic standards lack precision, presenting issues with false positives and unneeded surgical intervention for patients. This lack of clear cut early diagnostic tools is a significant problem. We present a microfluidic platform, the Time-Resolved Hydrodynamic Stretcher (TR-HS), which allows the investigation of the dynamic mechanical response of thousands of cells per second to a non-destructive stress. The TR-HS integrates high-speed imaging and computer vision to automatically detect and track single cells suspended in a fluid and enables cell classification based on their mechanical properties. We demonstrate the discrimination of healthy and cancerous prostate cell lines based on the whole-cell, time-resolved mechanical response to a hydrodynamic load. Additionally, we implement a finite element method (FEM) model to characterise the forces responsible for the cell deformation in our device. Finally, we report the classification of the two different cell groups based on their time-resolved roundness using a decision tree classifier. This approach introduces a modality for high-throughput assessments of cellular suspensions and may represent a viable application for the development of innovative diagnostic devices.

Large-scale curvature sensing by directional actin flow drives cellular migration mode switching

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.

Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids over various growth conditions and cell lines

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function.

The role of heterogeneous environment and docetaxel gradient in the emergence of polyploid, mesenchymal and resistant prostate cancer cells

The ability of a population of PC3 prostate epithelial cancer cells to become resistant to docetaxel therapy and progress to a mesenchymal state remains a fundamental problem. The progression towards resistance is difficult to directly study in heterogeneous ecological environments such as tumors. In this work, we use a micro-fabricated "evolution accelerator" environment to create a complex heterogeneous yet controllable in-vitro environment with a spatially-varying drug concentration. With such a structure we observe the rapid emergence of a surprisingly large number of polyploid giant cancer cells (PGCCs) in regions of very high drug concentration, which does not occur in conventional cell culture of uniform concentration. This emergence of PGCCs in a high drug environment is due to migration of diploid epithelial cells from regions of low drug concentration, where they proliferate, to regions of high drug concentration, where they rapidly convert to PGCCs. Such a mechanism can only occur in spatially-varying rather than homogeneous environments. Further, PGCCs exhibit increased expression of the mesenchymal marker ZEB1 in the same high-drug regions where they are formed, suggesting the possible induction of an epithelial to mesenchymal transition (EMT) in these cells. This is consistent with prior work suggesting the PGCC cells are mediators of resistance in response to chemotherapeutic stress. Taken together, this work shows the key role of spatial heterogeneity and the migration of proliferative diploid cells to form PGCCs as a survival strategy for the cancer population, with implications for new therapies.

Stress-dependent amplification of active forces in nonlinear elastic media

The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that buckling in the matrix dramatically amplifies the resulting active stresses. Here we extend this result to a continuum elastic medium prone to buckling subjected to an arbitrary external stress, and derive analytical expressions for the active, nonlinear constitutive relations characterizing the full active medium. Inserting these relations into popular "active gel" descriptions of living tissues and the cytoskeleton will enable investigations into nonlinear regimes previously inaccessible due to the phenomenological nature of these theories.

Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana

One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division. How exactly cell wall mechanical properties influence cell behavior is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella, and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer-dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.

Dissecting cellular mechanics: Implications for aging, cancer, and immunity

Cells are dynamic structures that must respond to complex physical and chemical signals from their surrounding environment. The cytoskeleton is a key mediator of a cell's response to the signals of both the extracellular matrix and other cells present in the local microenvironment and allows it to tune its own mechanical properties in response to these cues. A growing body of evidence suggests that altered cellular viscoelasticity is a strong indicator of disease state; including cancer, laminopathy (genetic disorders of the nuclear lamina), infection, and aging. Here, we review recent work on the characterization of cell mechanics in disease and discuss the implications of altered viscoelasticity in regulation of immune responses. Finally, we provide an overview of techniques for measuring the mechanical properties of cells deeply embedded within tissues.

A comparison of methods to assess cell mechanical properties

The mechanical properties of cells influence their cellular and subcellular functions, including cell adhesion, migration, polarization, and differentiation, as well as organelle organization and trafficking inside the cytoplasm. Yet reported values of cell stiffness and viscosity vary substantially, which suggests differences in how the results of different methods are obtained or analyzed by different groups. To address this issue and illustrate the complementarity of certain approaches, here we present, analyze, and critically compare measurements obtained by means of some of the most widely used methods for cell mechanics: atomic force microscopy, magnetic twisting cytometry, particle-tracking microrheology, parallel-plate rheometry, cell monolayer rheology, and optical stretching. These measurements highlight how elastic and viscous moduli of MCF-7 breast cancer cells can vary 1,000-fold and 100-fold, respectively. We discuss the sources of these variations, including the level of applied mechanical stress, the rate of deformation, the geometry of the probe, the location probed in the cell, and the extracellular microenvironment.

Laser-induced surface deformation microscope for the study of the dynamic viscoelasticity of plasma membrane in a living cell

A laser-induced surface deformation (LISD) microscope is developed and applied to measurement of the dynamic relaxation responses of the plasma membrane in a living cell. A laser beam is tightly focused on an optional area of cell surface and the focused light induces microscopic deformation on the surface via radiation pressure. The LISD microscope not only allows non-contact and destruction-free measurement but provides power spectra of the surface responses depending on the frequency of the intensity of the laser beam. An optical system for the LISD is equipped via a microscope, allowing us to measure the relaxation responses in sub-cellular-sized regions of the plasma membrane. In addition, the forced oscillation caused by the radiation pressure for surface deformation extends the upper limit of the frequency range in the obtained power spectra to 106 Hz, which enables us to measure relaxation responses in local regions within the plasma membrane. From differences in power-law exponents at higher frequencies, it is realized that a cancerous cell obeys a weaker single power-law than a normal fibroblast cell. Furthermore, the power spectrum of a keratinocyte cell obeys a power-law with two exponents, indicating that alternative mechanical models to a conventional soft glassy rheology model (where single power-laws explain cells' responses below about 103 Hz) are needed for the understanding over a wider frequency range. The LISD microscope would contribute to investigation of microscopic cell rheology, which is important for clarifying the mechanisms of cell migration and tissue construction.

Maximal Fluctuations of Confined Actomyosin Gels: Dynamics of the Cell Nucleus

We investigate the effect of stress fluctuations on the stochastic dynamics of an inclusion embedded in a viscous gel. We show that, in nonequilibrium systems, stress fluctuations give rise to an effective attraction towards the boundaries of the confining domain, which is reminiscent of an active Casimir effect. We apply this generic result to the dynamics of deformations of the cell nucleus, and we demonstrate the appearance of a fluctuation maximum at a critical level of activity, in agreement with recent experiments [E. Makhija, D. S. Jokhun, and G. V. Shivashankar, Proc. Natl. Acad. Sci. U.S.A. 113, E32 (2016)PNASA60027-842410.1073/pnas.1513189113].

Mechanocellular models of epithelial morphogenesis

Embryonic epithelia achieve complex morphogenetic movements, including in-plane reshaping, bending and folding, through the coordinated action and rearrangement of individual cells. Technical advances in molecular and live-imaging studies of epithelial dynamics provide a very real opportunity to understand how cell-level processes facilitate these large-scale tissue rearrangements. However, the large datasets that we are now able to generate require careful interpretation. In combination with experimental approaches, computational modelling allows us to challenge and refine our current understanding of epithelial morphogenesis and to explore experimentally intractable questions. To this end, a variety of cell-based modelling approaches have been developed to describe cell-cell mechanical interactions, ranging from vertex and 'finite-element' models that approximate each cell geometrically by a polygon representing the cell's membrane, to immersed boundary and subcellular element models that allow for more arbitrary cell shapes. Here, we review how these models have been used to provide insights into epithelial morphogenesis and describe how such models could help future efforts to decipher the forces and mechanical and biochemical feedbacks that guide cell and tissue-level behaviour. In addition, we discuss current challenges associated with using computational models of morphogenetic processes in a quantitative and predictive way.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Cytokinesis in vertebrate cells initiates by contraction of an equatorial actomyosin network composed of randomly oriented filaments

The actomyosin ring generates force to ingress the cytokinetic cleavage furrow in animal cells, yet its filament organization and the mechanism of contractility is not well understood. We quantified actin filament order in human cells using fluorescence polarization microscopy and found that cleavage furrow ingression initiates by contraction of an equatorial actin network with randomly oriented filaments. The network subsequently gradually reoriented actin filaments along the cell equator. This strictly depended on myosin II activity, suggesting local network reorganization by mechanical forces. Cortical laser microsurgery revealed that during cytokinesis progression, mechanical tension increased substantially along the direction of the cell equator, while the network contracted laterally along the pole-to-pole axis without a detectable increase in tension. Our data suggest that an asymmetric increase in cortical tension promotes filament reorientation along the cytokinetic cleavage furrow, which might have implications for diverse other biological processes involving actomyosin rings.

Physical Model for Stabilization and Repair of Trans-endothelial Apertures

Bacterial toxins that disrupt the stability of contractile structures in endothelial cells promote the opening of large-scale apertures, thereby breaching the endothelium barrier. These apertures are formed by fusion of the basal and apical membranes into a tunnel that spans the height of the cell. Subsequent to the aperture formation, an active repair process, driven by a stimulated polymerization of actin, results in asymmetrical membrane protrusions and, ultimately, the closure of the aperture. Here, we propose a physics-based model for the generation, stabilization and repair of trans-endothelial apertures. Our model is based on the mechanical interplay between tension in the plasma membrane and stresses that develop within different actin structures at the aperture's periphery. We suggest that accumulation of cytoskeletal fragments around the aperture's rim during the expansion phase results in parallel bundles of actin filaments and myosin motors, generating progressively greater contraction forces that resist further expansion of the aperture. Our results indicate that closure of the tunnel is driven by mechanical stresses that develop within a cross-linked actin gel that forms at localized regions of the aperture periphery. We show that stresses within the gel are due to continuous polymerization of actin filaments against the membrane surfaces of the aperture's edges. Based on our mechanical model, we construct a dynamic simulation of the aperture repair process. Our model fully accounts for the phenomenology of the trans-endothelial aperture formation and stabilization, and recaptures the experimentally observed asymmetry of the intermediate aperture shapes during closure. We make experimentally testable predictions for localization of myosin motors to the tunnel periphery and of adhesion complexes to the edges of apertures undergoing closure, and we estimate the minimal nucleation size of cross-linked actin gel that can lead to a successful repair of the aperture.

Mechanical deformation induces depolarization of neutrophils

The transition of neutrophils from a resting state to a primed state is an essential requirement for their function as competent immune cells. This transition can be caused not only by chemical signals but also by mechanical perturbation. After cessation of either, these cells gradually revert to a quiescent state over 40 to 120 min. We use two biophysical tools, an optical stretcher and a novel microcirculation mimetic, to effect physiologically relevant mechanical deformations of single nonadherent human neutrophils. We establish quantitative morphological analysis and mechanical phenotyping as label-free markers of neutrophil priming. We show that continued mechanical deformation of primed cells can cause active depolarization, which occurs two orders of magnitude faster than by spontaneous depriming. This work provides a cellular-level mechanism that potentially explains recent clinical studies demonstrating the potential importance, and physiological role, of neutrophil depriming in vivo and the pathophysiological implications when this deactivation is impaired, especially in disorders such as acute lung injury.

Cell mechanics: a dialogue

Under the microscope, eukaryotic animal cells can adopt a variety of different shapes and sizes. These cells also move and deform, and the physical mechanisms driving these movements and shape changes are important in fundamental cell biology, tissue mechanics, as well as disease biology. This article reviews some of the basic mechanical concepts in cells, emphasizing continuum mechanics description of cytoskeletal networks and hydrodynamic flows across the cell membrane. We discuss how cells can generate movement and shape changes by controlling mass fluxes at the cell boundary. These mass fluxes can come from polymerization/depolymerization of actin cytoskeleton, as well as osmotic and hydraulic pressure-driven flow of water across the cell membrane. By combining hydraulic pressure control with force balance conditions at the cell surface, we discuss a quantitative mechanism of cell shape and volume control. The broad consequences of this model on cell mechanosensation and tissue mechanics are outlined.

Fluidization and Active Thinning by Molecular Kinetics in Active Gels

We derive the constitutive equations of an active polar gel from a model for the dynamics of elastic molecules that link polar elements. Molecular binding kinetics induces the fluidization of the material, giving rise to Maxwell viscoelasticity and, provided that detailed balance is broken, to the generation of active stresses. We give explicit expressions for the transport coefficients of active gels in terms of molecular properties, including nonlinear contributions on the departure from equilibrium. In particular, when activity favors linker unbinding, we predict a decrease of viscosity with activity-active thinning-of kinetic origin, which could explain some experimental results on the cell cortex. By bridging the molecular and hydrodynamic scales, our results could help understand the interplay between molecular perturbations and the mechanics of cells and tissues.

In vivo quantification of spatially varying mechanical properties in developing tissues

The mechanical properties of the cellular microenvironment and their spatiotemporal variations are thought to play a central role in sculpting embryonic tissues, maintaining organ architecture and controlling cell behavior, including cell differentiation. However, no direct in vivo and in situ measurement of mechanical properties within developing 3D tissues and organs has yet been performed. Here we introduce a technique that employs biocompatible, magnetically responsive ferrofluid microdroplets as local mechanical actuators and allows quantitative spatiotemporal measurements of mechanical properties in vivo. Using this technique, we show that vertebrate body elongation entails spatially varying tissue mechanics along the anteroposterior axis. Specifically, we find that the zebrafish tailbud is viscoelastic (elastic below a few seconds and fluid after just 1 min) and displays decreasing stiffness and increasing fluidity toward its posterior elongating region. This method opens new avenues to study mechanobiology in vivo, both in embryogenesis and in disease processes, including cancer.

Measuring Cell Viscoelastic Properties Using a Microfluidic Extensional Flow Device

The quantification of cellular mechanical properties is of tremendous interest in biology and medicine. Recent microfluidic technologies that infer cellular mechanical properties based on analysis of cellular deformations during microchannel traversal have dramatically improved throughput over traditional single-cell rheological tools, yet the extraction of material parameters from these measurements remains quite complex due to challenges such as confinement by channel walls and the domination of complex inertial forces. Here, we describe a simple microfluidic platform that uses hydrodynamic forces at low Reynolds number and low confinement to elongate single cells near the stagnation point of a planar extensional flow. In tandem, we present, to our knowledge, a novel analytical framework that enables determination of cellular viscoelastic properties (stiffness and fluidity) from these measurements. We validated our system and analysis by measuring the stiffness of cross-linked dextran microparticles, which yielded reasonable agreement with previously reported values and our micropipette aspiration measurements. We then measured viscoelastic properties of 3T3 fibroblasts and glioblastoma tumor initiating cells. Our system captures the expected changes in elastic modulus induced in 3T3 fibroblasts and tumor initiating cells in response to agents that soften (cytochalasin D) or stiffen (paraformaldehyde) the cytoskeleton. The simplicity of the device coupled with our analytical model allows straightforward measurement of the viscoelastic properties of cells and soft, spherical objects.

Immersed Boundary Simulations of Active Fluid Droplets

We present numerical simulations of active fluid droplets immersed in an external fluid in 2-dimensions using an Immersed Boundary method to simulate the fluid droplet interface as a Lagrangian mesh. We present results from two example systems, firstly an active isotropic fluid boundary consisting of particles that can bind and unbind from the interface and generate surface tension gradients through active contractility. Secondly, a droplet filled with an active polar fluid with homeotropic anchoring at the droplet interface. These two systems demonstrate spontaneous symmetry breaking and steady state dynamics resembling cell motility and division and show complex feedback mechanisms with minimal degrees of freedom. The simulations outlined here will be useful for quantifying the wide range of dynamics observable in these active systems and modelling the effects of confinement in a consistent and adaptable way.

A Comprehensive Review of Optical Stretcher for Cell Mechanical Characterization at Single-Cell Level

This paper presents a comprehensive review of the development of the optical stretcher, a powerful optofluidic device for single cell mechanical study by using optical force induced cell stretching. The different techniques and the different materials for the fabrication of the optical stretcher are first summarized. A short description of the optical-stretching mechanism is then given, highlighting the optical force calculation and the cell optical deformability characterization. Subsequently, the implementations of the optical stretcher in various cell-mechanics studies are shown on different types of cells. Afterwards, two new advancements on optical stretcher applications are also introduced: the active cell sorting based on cell mechanical characterization and the temperature effect on cell stretching measurement from laser-induced heating. Two examples of new functionalities developed with the optical stretcher are also included. Finally, the current major limitation and the future development possibilities are discussed.

Optically trapping tumor cells to assess differentiation and prognosis of cancers

We report an optical trapping method that may enable assessment of the differentiation status of cancerous cells by determining the minimum time required for cell-cell adhesion to occur. A single, live cell is trapped and brought into close proximity of another; the minimum contact time required for cell-cell adhesion to occur is measured using transformed cells from neural tumor cell lines: the human neuroblastoma SK-N-SH and rat C6 glioma cells. Earlier work on live adult rat hippocampal neural progenitors/stem cells had shown that a contact minimum of ~5 s was required for cells to adhere to each other. We now find the average minimum time for adhesion of cells from both tumor cell lines to substantially increase to ~20-25 s, in some cases up to 45 s. Upon in vitro differentiation of these cells with all-trans retinoic acid the average minimum time reverts to ~5-7 s. This proof-of-concept study indicates that optical trapping may be a quick, sensitive, and specific method for determining differentiation status and, thereby, the prognosis of cancer cells.

Probing Cell Deformability via Acoustically Actuated Bubbles

An acoustically actuated, bubble-based technique is developed to investigate the deformability of cells suspended in microfluidic devices. A microsized bubble is generated by an optothermal effect near the targeted cells, which are suspended in a microfluidic chamber. Subsequently, acoustic actuation is employed to create localized acoustic streaming. In turn, the streaming flow results in hydrodynamic forces that deform the cells in situ. The deformability of the cells is indicative of their mechanical properties. The method in this study measures mechanical biomarkers from multiple cells in a single experiment, and it can be conveniently integrated with other bioanalysis and drug-screening platforms. Using this technique, the mean deformability of tens of HeLa, HEK, and HUVEC cells is measured to distinguish their mechanical properties. HeLa cells are deformed upon treatment with Cytochalasin. The technique also reveals the deformability of each subpopulation in a mixed, heterogeneous cell sample by the use of both fluorescent markers and mechanical biomarkers. The technique in this study, apart from being relevant to cell biology, will also enable biophysical cellular diagnosis.

An inverted dielectrophoretic device for analysis of attached single cell mechanics

Dielectrophoresis (DEP), the force induced on a polarizable body by a non-uniform electric field, has been widely used to manipulate single cells in suspension and analyze their stiffness. However, most cell types do not naturally exist in suspension but instead require attachment to the tissue extracellular matrix in vivo. Cells alter their cytoskeletal structure when they attach to a substrate, which impacts cell stiffness. It is therefore critical to be able to measure mechanical properties of cells attached to a substrate. We present a novel inverted quadrupole dielectrophoretic device capable of measuring changes in the mechanics of single cells attached to a micropatterned polyacrylamide gel. The device is positioned over a cell of defined size, a directed DEP pushing force is applied, and cell centroid displacement is dynamically measured by optical microscopy. Using this device, single endothelial cells showed greater centroid displacement in response to applied DEP pushing force following actin cytoskeleton disruption by cytochalasin D. In addition, transformed mammary epithelial cell (MCF10A-NeuT) showed greater centroid displacement in response to applied DEP pushing force compared to untransformed cells (MCF10A). DEP device measurements were confirmed by showing that the cells with greater centroid displacement also had a lower elastic modulus by atomic force microscopy. The current study demonstrates that an inverted DEP device can determine changes in single attached cell mechanics on varied substrates.

FACS-style detection for real-time cell viscoelastic cytometry

Cell mechanical properties have been established as a label-free biophysical marker of cell viability and health; however, real-time methods with significant throughput for accurately and non-destructively measuring these properties remain widely unavailable. Without appropriate labels for use with fluorescence activated cell sorters (FACS), easily implemented real-time technology for tracking cell-level mechanical properties remains a current need. Employing modulated optical forces and enabled by a low-dimensional FACS-style detection method introduced here, we present a viscoelasticity cytometer (VC) capable of real-time and continuous measurements. We demonstrate the utility of this approach by tracking the high-frequency cell physical properties of populations of chemically-modified cells at rates of ~ 1 s-1 and explain observations within the context of a simple theoretical model.

Emergent material properties of developing epithelial tissues

BACKGROUND

Force generation and the material properties of cells and tissues are central to morphogenesis but remain difficult to measure in vivo. Insight is often limited to the ratios of mechanical properties obtained through disruptive manipulation, and the appropriate models relating stress and strain are unknown. The Drosophila amnioserosa epithelium progressively contracts over 3 hours of dorsal closure, during which cell apices exhibit area fluctuations driven by medial myosin pulses with periods of 1.5-6 min. Linking these two timescales and understanding how pulsatile contractions drive morphogenetic movements is an urgent challenge.

RESULTS

We present a novel framework to measure in a continuous manner the mechanical properties of epithelial cells in the natural context of a tissue undergoing morphogenesis. We show that the relationship between apicomedial myosin fluorescence intensity and strain during fluctuations is consistent with a linear behaviour, although with a lag. We thus used myosin fluorescence intensity as a proxy for active force generation and treated cells as natural experiments of mechanical response under cyclic loading, revealing unambiguous mechanical properties from the hysteresis loop relating stress to strain. Amnioserosa cells can be described as a contractile viscoelastic fluid. We show that their emergent mechanical behaviour can be described by a linear viscoelastic rheology at timescales relevant for tissue morphogenesis. For the first time, we establish relative changes in separate effective mechanical properties in vivo. Over the course of dorsal closure, the tissue solidifies and effective stiffness doubles as net contraction of the tissue commences. Combining our findings with those from previous laser ablation experiments, we show that both apicomedial and junctional stress also increase over time, with the relative increase in apicomedial stress approximately twice that of other obtained measures.

CONCLUSIONS

Our results show that in an epithelial tissue undergoing net contraction, stiffness and stress are coupled. Dorsal closure cell apical contraction is driven by the medial region where the relative increase in stress is greater than that of stiffness. At junctions, by contrast, the relative increase in the mechanical properties is the same, so the junctional contribution to tissue deformation is constant over time. An increase in myosin activity is likely to underlie, at least in part, the change in medioapical properties and we suggest that its greater effect on stress relative to stiffness is fundamental to actomyosin systems and confers on tissues the ability to regulate contraction rates in response to changes in external mechanics.

Nano-rheology of hydrogels using direct drive force modulation atomic force microscopy

We present a magnetic force-based direct drive modulation method to measure local nano-rheological properties of soft materials across a broad frequency range (10 Hz to 2 kHz) using colloid-attached atomic force microscope (AFM) probes in liquid. The direct drive method enables artefact-free measurements over several decades of excitation frequency, and avoids the need to evaluate medium-induced hydrodynamic drag effects. The method was applied to measure the local mechanical properties of polyacrylamide hydrogels. The frequency-dependent storage stiffness, loss stiffness, and loss tangent (tan δ) were quantified for hydrogels having high and low crosslinking densities by measuring the amplitude and the phase response of the cantilever while the colloid was in contact with the hydrogel. The frequency bandwidth was further expanded to lower effective frequencies (0.1 Hz to 10 Hz) by obtaining force-displacement (FD) curves. Slow FD measurements showed a recoverable but highly hysteretic response, with the contact mechanical behaviour dependent on the loading direction: approach curves showed Hertzian behaviour while retraction curves fit the JKR contact mechanics model well into the adhesive regime, after which multiple detachment instabilities occurred. Using small amplitude dynamic modulation to explore faster rates, the load dependence of the storage stiffness transitioned from Hertzian to a dynamic punch-type (constant contact area) model, indicating significant influence of material dissipation coupled with adhesion. Using the appropriate contact model across the full frequency range measured, the storage moduli were found to remain nearly constant until an increase began near ∼100 Hz. The softer gels' storage modulus increased from 7.9 ± 0.4 to 14.5 ± 2.1 kPa (∼85%), and the stiffer gels' storage modulus increased from 16.3 ± 1.1 to 31.7 ± 5.0 kPa (∼95%). This increase at high frequencies may be attributed to a contribution from solvent confinement in the hydrogel (poroelasticity). The storage moduli measured by both macro-rheometry and AFM FD curves were comparable to those measured using the modulation method at their overlapping frequencies (10-25 Hz). In all cases, care was taken to ensure the contact mechanics models were applied within the important limit of small relative deformations. This study thus highlights possible transitions in the probe-material contact mechanical behaviour for soft matter, especially when the applied strain rates and the material relaxation rates become comparable. In particular, at low frequencies, the modulus follows Hertzian contact mechanics, while at high frequencies adhesive contact is well represented by punch-like behaviour. More generally, use of the Hertz model on hydrogels at high loading rates, at high strains, or during the retraction portion of FD curves, leads to significant errors in the calculated moduli.