Quantifying cell-to-cell variation in power-law rheology

Mechanical properties of epithelial cells in domes investigated using atomic force microscopy

As epithelial cells in vitro reach a highly confluent state, the cells often form a microscale dome-like architecture that encloses a fluid-filled lumen. The domes are stabilized by mechanical stress and luminal pressure. However, the mechanical properties of cells that form epithelial domes remain poorly characterized at the single-cell level. In this study, we used atomic force microscopy (AFM) to measure the mechanical properties of cells forming epithelial domes. AFM showed that the apparent Young's modulus of cells in domes was significantly higher when compared with that in the surrounding monolayer. AFM also showed that the stiffness and tension of cells in domes were positively correlated with the apical cell area, depending on the degree of cell stretching. This correlation disappeared when actin filaments were depolymerized or when the ATPase activity of myosin II was inhibited, which often led to a large fluctuation in dome formation. The results indicated that heterogeneous actomyosin structures organized by stretching single cells played a crucial role in stabilizing dome formation. Our findings provide new insights into the mechanical properties of three-dimensional deformable tissue explored using AFM at the single-cell level.

Average Rheological Quantities of Cells in Monolayers

The method of cell monolayer rheology enables quantifying average rheological properties of cell in a single experimental run of few millions cells together in a single layer. Here we describe step-by-step procedure as to how to employ a modified commercial rotational rheometer to run rheological measurement and detect average viscoelastic properties of cells while maintaining the necessary precision level at the same time.

Atomic force microscopy identifies the alteration of rheological properties of the cardiac fibroblasts in idiopathic restrictive cardiomyopathy

Restrictive cardiomyopathy (RCM) is a rare disease characterized by increased ventricular stiffness and preserved ventricular contraction. Various sarcomere gene variants are known to cause RCM; however, more than a half of patients do not harbor such pathogenic variants. We recently demonstrated that cardiac fibroblasts (CFs) play important roles in inhibiting the diastolic function of cardiomyocytes via humoral factors and direct cell–cell contact regardless of sarcomere gene mutations. However, the mechanical properties of CFs that are crucial for intercellular communication and the cardiomyocyte microenvironment remain less understood. In this study, we evaluated the rheological properties of CFs derived from pediatric patients with RCM and healthy control CFs via atomic force microscopy. Then, we estimated the cellular modulus scale factor related to the cell stiffness, fluidity, and Newtonian viscosity of single cells based on the single power-law rheology model and analyzed the comprehensive gene expression profiles via RNA-sequencing. RCM-derived CFs showed significantly higher stiffness and viscosity and lower fluidity compared to healthy control CFs. Furthermore, RNA-sequencing revealed that the signaling pathways associated with cytoskeleton elements were affected in RCM CFs; specifically, cytoskeletal actin-associated genes (ACTN1, ACTA2, and PALLD) were highly expressed in RCM CFs, whereas several tubulin genes (TUBB3, TUBB, TUBA1C, and TUBA1B) were down-regulated. These results implies that the signaling pathways associated with cytoskeletal elements alter the rheological properties of RCM CFs, particularly those related to CF–cardiomyocyte interactions, thereby leading to diastolic cardiac dysfunction in RCM.

Narrow-Gap Rheometry: A Novel Method for Measuring Cell Mechanics

The viscoelastic properties of a cell cytoskeleton contain abundant information about the state of a cell. Cells show a response to a specific environment or an administered drug through changes in their viscoelastic properties. Studies of single cells have shown that chemical agents that interact with the cytoskeleton can alter mechanical cell properties and suppress mitosis. This envisions using rheological measurements as a non-specific tool for drug development, the pharmacological screening of new drug agents, and to optimize dosage. Although there exists a number of sophisticated methods for studying mechanical properties of single cells, studying concentration dependencies is difficult and cumbersome with these methods: large cell-to-cell variations demand high repetition rates to obtain statistically significant data. Furthermore, method-induced changes in the cell mechanics cannot be excluded when working in a nonlinear viscoelastic range. To address these issues, we not only compared narrow-gap rheometry with commonly used single cell techniques, such as atomic force microscopy and microfluidic-based approaches, but we also compared existing cell monolayer studies used to estimate cell mechanical properties. This review provides insight for whether and how narrow-gap rheometer could be used as an efficient drug screening tool, which could further improve our current understanding of the mechanical issues present in the treatment of human diseases.

Pharmacological Alteration of Cellular Mechanical Properties in Pulmonary Arterial Smooth Muscle Cells of Idiopathic Pulmonary Arterial Hypertension

Background

Idiopathic pulmonary arterial hypertension (IPAH) is a progressive disease caused by vascular remodeling of the pulmonary arteries with elevated pulmonary vascular resistance. Recently, various pulmonary vasodilator drugs have become available in the clinical field, and have dramatically ameliorated the prognosis of IPAH. However, little is known about how the mechanical properties of pulmonary arterial smooth muscle cells (PASMCs) are altered under drug supplementation.

Methods

Atomic force microscopy (AFM) was used to investigate the mechanical properties of PASMCs derived from a patient with IPAH (PAH-PASMCs) and a healthy control (N-PASMCs) which received the supplementation of clinically used drugs for IPAH: sildenafil, macitentan, and riociguat.

Results

PASMCs derived from PAH-PASMCs were stiffer than those derived from N-PASMCs. With sildenafil treatment, the apparent Young's modulus (E ₀) of cells significantly decreased in PAH-PASMCs but remained unchanged in N-PASMCs. The decrease in E ₀ of PAH-PASMCs was also observed in macitentan and riociguat treatment. The stress relaxation AFM revealed that the decrease in E ₀ of PAH-PASMCs resulted from a decrease in the cell elastic modulus and/or increase in cell fluidity. The combination treatment of macitentan and riociguat showed an additive effect on cell mechanical properties, implying that this clinically accepted combination therapy for IPAH influences the intracellular mechanical components.

Conclusions

Pulmonary vasodilator drugs affect the mechanical properties of PAH-PASMCs, and there exists a mechanical effect of combination treatment on PAH-PASMCs.

Rheology of rounded mammalian cells over continuous high-frequencies

Understanding the viscoelastic properties of living cells and their relation to cell state and morphology remains challenging. Low-frequency mechanical perturbations have contributed considerably to the understanding, yet higher frequencies promise to elucidate the link between cellular and molecular properties, such as polymer relaxation and monomer reaction kinetics. Here, we introduce an assay, that uses an actuated microcantilever to confine a single, rounded cell on a second microcantilever, which measures the cell mechanical response across a continuous frequency range ≈ 1-40 kHz. Cell mass measurements and optical microscopy are co-implemented. The fast, high-frequency measurements are applied to rheologically monitor cellular stiffening. We find that the rheology of rounded HeLa cells obeys a cytoskeleton-dependent power-law, similar to spread cells. Cell size and viscoelasticity are uncorrelated, which contrasts an assumption based on the Laplace law. Together with the presented theory of mechanical de-embedding, our assay is generally applicable to other rheological experiments.

Spatiotemporal dynamics of single cell stiffness in the early developing ascidian chordate embryo

During the developmental processes of embryos, cells undergo massive deformation and division that are regulated by mechanical cues. However, little is known about how embryonic cells change their mechanical properties during different cleavage stages. Here, using atomic force microscopy, we investigated the stiffness of cells in ascidian embryos from the fertilised egg to the stage before gastrulation. In both animal and vegetal hemispheres, we observed a Rho kinase (ROCK)-independent cell stiffening that the cell stiffness exhibited a remarkable increase at the timing of cell division where cortical actin filaments were organized. Furthermore, in the vegetal hemisphere, we observed another mechanical behaviour, i.e., a ROCK-associated cell stiffening, which was retained even after cell division or occurred without division and propagated sequentially toward adjacent cells, displaying a characteristic cell-to-cell mechanical variation. The results indicate that the mechanical properties of embryonic cells are regulated at the single cell level in different germ layers.

Fujii et al. investigate the stiffness of cells in ascidian embryos from the fertilised egg to the stage before gastrulation. They find two types of cell stiffening, occurring during cell division and in the interphase, the latter of which is associated with the Rho kinase pathway. They conclude that the mechanical properties of early embryonic cells are regulated specifically at the single cell level.

Cell nucleus as a microrheological probe to study the rheology of the cytoskeleton

Mechanical properties of the cell are important biomarkers for probing its architectural changes caused by cellular processes and/or pathologies. The development of microfluidic technologies has enabled measuring the cell's mechanical properties at high throughput so that mechanical phenotyping can be applied to large samples in reasonable timescales. These studies typically measure the stiffness of the cell as the only mechanical biomarker and do not disentangle the rheological contributions of different structural components of the cell, including the cell cortex, the interior cytoplasm and its immersed cytoskeletal structures, and the nucleus. Recent advancements in high-speed fluorescent imaging have enabled probing the deformations of the cell cortex while also tracking different intracellular components in rates applicable to microfluidic platforms. We present a, to our knowledge, novel method to decouple the mechanics of the cell cortex and the cytoplasm by analyzing the correlation between the cortical deformations that are induced by external microfluidic flows and the nucleus displacements, induced by those cortical deformations, i.e., we use the nucleus as a high-throughput microrheological probe to study the rheology of the cytoplasm, independent of the cell cortex mechanics. To demonstrate the applicability of this method, we consider a proof-of-concept model consisting of a rigid spherical nucleus centered in a spherical cell. We obtain analytical expressions for the time-dependent nucleus velocity as a function of the cell deformations when the interior cytoplasm is modeled as a viscous, viscoelastic, porous, and poroelastic material and demonstrate how the nucleus velocity can be used to characterize the linear rheology of the cytoplasm over a wide range of forces and timescales/frequencies.

Sensorless Self-Excited Vibrational Viscometer with Two Hopf Bifurcations Based on a Piezoelectric Device

In this study, we propose a high-sensitivity sensorless viscometer based on a piezoelectric device. Viscosity is an essential parameter frequently used in many fields. The vibration type viscometer based on self-excited oscillation generally requires displacement sensor although they can measure high viscosity without deterioration of sensitivity. The proposed viscometer utilizes the sensorless self-excited oscillation without any detection of the displacement of the cantilever, which uses the interaction between the mechanical dynamics of the cantilever and the electrical dynamics of the piezoelectric device attached to the cantilever. Since the proposed viscometer has fourth-order dynamics and two coupled oscillator systems, the systems can produce different self-excited oscillations through different Hopf bifurcations. We theoretically showed that the response frequency jumps at the two Hopf bifurcation points and this distance between them depends on the viscosity. Using this distance makes measurement highly sensitive and easier because the jump in the response frequency can be easily detected. We experimentally demonstrate the efficiency of the proposed sensorless viscometer by a macro-scale measurement system. The results show the sensitivity of the proposed method is higher than that of the previous method based on self-excited oscillation with a displacement sensor.

Environmentally controlled magnetic nano-tweezer for living cells and extracellular matrices

The magnetic tweezer technique has become a versatile tool for unfolding or folding of individual molecules, mainly DNA. In addition to single molecule analysis, the magnetic tweezer can be used to analyze the mechanical properties of cells and extracellular matrices. We have established a magnetic tweezer that is capable of measuring the linear and non-linear viscoelastic behavior of a wide range of soft matter in precisely controlled environmental conditions, such as temperature, CO₂ and humidity. The magnetic tweezer presented in this study is suitable to detect specific differences in the mechanical properties of different cell lines, such as human breast cancer cells and mouse embryonic fibroblasts, as well as collagen matrices of distinct concentrations in the presence and absence of fibronectin crosslinks. The precise calibration and control mechanism employed in the presented magnetic tweezer setup provides the ability to apply physiological force up to 5 nN on 4.5 µm superparamagnetic beads coated with fibronectin and coupled to the cells or collagen matrices. These measurements reveal specific local linear and non-linear viscoelastic behavior of the investigated samples. The viscoelastic response of cells and collagen matrices to the force application is best described by a weak power law behavior. Our results demonstrate that the stress stiffening response and the fluidization of cells is cell type specific and varies largely between differently invasive and aggressive cancer cells. Finally, we showed that the viscoelastic behavior of collagen matrices with and without fibronectin crosslinks measured by the magnetic tweezer can be related to the microstructure of these matrices.

Fractional viscoelastic models for power-law materials

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response.

Mechanical adaptions of collective cells nearby free tissue boundaries

Mechanical adaptions of cells, including stiffness variation, cytoskeleton remodeling, motion coordination, and shape changing, are essential for tissue morphogenesis, wound healing, and malignant progression. In this paper, we take confluent monolayers of Madin-Darby canine kidney (MDCK) and mouse myoblast (C2C12) cells as model systems to probe how cells collectively adapt their mechanical features in response to a free tissue boundary. We show that the free boundary not only can trigger unjamming transition but also induces cell fluidization nearby the boundary. The Young's moduli of cells near the boundary are found to be much lower than those of interior cells. We demonstrate that the stiffness of cells in monolayers with a free tissue boundary exhibits negative dependence on the projected cell area, in contrast to previous studies where cells were found to stiffen as cellular area increases in a confluent MDCK monolayer without boundary. In addition, the free tissue boundary may activate cell remodeling, rendering volume enlargement and cell-specified cytoskeleton organization. Our study emphasizes the important role of geometrical boundary in regulating biomechanical properties of cell aggregates.

Double power-law viscoelastic relaxation of living cells encodes motility trends

Living cells are constantly exchanging momentum with their surroundings. So far, there is no consensus regarding how cells respond to such external stimuli, although it reveals much about their internal structures, motility as well as the emergence of disorders. Here, we report that twelve cell lines, ranging from healthy fibroblasts to cancer cells, hold a ubiquitous double power-law viscoelastic relaxation compatible with the fractional Kelvin-Voigt viscoelastic model. Atomic Force Microscopy measurements in time domain were employed to determine the mechanical parameters, namely, the fast and slow relaxation exponents, the crossover timescale between power law regimes, and the cell stiffness. These cell-dependent quantities show strong correlation with their collective migration and invasiveness properties. Beyond that, the crossover timescale sets the fastest timescale for cells to perform their biological functions.

Measuring viscoelasticity of soft biological samples using atomic force microscopy

Mechanical properties play important roles at different scales in biology. At the level of a single cell, the mechanical properties mediate mechanosensing and mechanotransduction, while at the tissue and organ levels, changes in mechanical properties are closely connected to disease and physiological processes. Over the past three decades, atomic force microscopy (AFM) has become one of the most widely used tools in the mechanical characterization of soft samples, ranging from molecules, cell organoids and cells to whole tissue. AFM methods can be used to quantify both elastic and viscoelastic properties, and significant recent developments in the latter have been enabled by the introduction of new techniques and models for data analysis. Here, we review AFM techniques developed in recent years for examining the viscoelastic properties of cells and soft gels, describe the main steps in typical data acquisition and analysis protocols, and discuss relevant viscoelastic models and how these have been used to characterize the specific features of cellular and other biological samples. We also discuss recent trends and potential directions for this field.

Increased stiffness and flow resistance of the inner wall of Schlemm's canal in glaucomatous human eyes

The cause of the elevated outflow resistance and consequent ocular hypertension characteristic of glaucoma is unknown. To investigate possible causes for this flow resistance, we used atomic force microscopy (AFM) with 10-µm spherical tips to probe the stiffness of the inner wall of Schlemm's canal as a function of distance from the tissue surface in normal and glaucomatous postmortem human eyes, and 1-µm spherical AFM tips to probe the region immediately below the tissue surface. To localize flow resistance, perfusion and imaging methods were used to characterize the pressure drop in the immediate vicinity of the inner wall using giant vacuoles that form in Schlemm's canal cells as micropressure sensors. Tissue stiffness increased with increasing AFM indentation depth. Tissues from glaucomatous eyes were stiffer compared with normal eyes, with greatly increased stiffness residing within ∼1 µm of the inner-wall surface. Giant vacuole size and density were similar in normal and glaucomatous eyes despite lower flow rate through the latter due to their higher flow resistance. This implied that the elevated flow resistance found in the glaucomatous eyes was localized to the same region as the increased tissue stiffness. Our findings implicate pathological changes to biophysical characteristics of Schlemm's canal endothelia and/or their immediate underlying extracellular matrix as cause for ocular hypertension in glaucoma.

A distribution-based approach for determining lot sizes in the filling of human-induced pluripotent stem cells

Introduction

Toward the commercial production of human-induced pluripotent stem (hiPS) cells, the process design and operation have to be standardized. Considering the change in cell quality during filling of the hiPS cells into containers, lot sizing during filling also needs to be standardized.

Methods

We present a distribution-based approach that can be used for determining the lot sizes in the filling of hiPS cells by considering change in cell quality during filling. The approach describes the “survival capability” of the cells as a continuous probability distribution, and expresses the change in quality during filling by “trimming” the distribution.

Results

A lognormal distribution was assumed as the survival capability distribution of the cells that were to be filled. The distributions after different filling times were calculated, which were compared with the distribution of the initial filling time regarding the yield of the cells and the similarity. These conditions served as strong quality constraints in determining an economically optimal lot size.

Conclusions

The presented conceptual approach would be effective in determining the lot size considering the change in cell quality during filling. For actual application, measuring the distribution information on the survival capability of hiPS cells is encouraged.

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A novel lot sizing approach was developed for filling hiPS cells.

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Survival capability of hiPS cells was assumed to follow a lognormal distribution.

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The distributions of survival capability were calculated to determine the lot size.

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Monte Carlo simulation was useful in comparing distributions.

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A case study demonstrated the effectiveness of the approach.

Mapping the creep compliance of living cells with scanning ion conductance microscopy reveals a subcellular correlation between stiffness and fluidity

Living cells exhibit complex material properties, which play a crucial role in many aspects of cell function in health and disease, including migration, proliferation, differentiation, and apoptosis. Various techniques exist to probe the viscoelastic material properties of living cells and a frequent observation is a cell-to-cell correlation between average stiffness and fluidity in populations of cells. However, the origin of this correlation is still under discussion. Here, we introduce an imaging technique based on the scanning ion conductance microscope (SICM) to measure the creep compliance of soft samples, which allowed us to generate images of viscoelastic material properties of living cells with high spatial and temporal resolution. We observe a strong subcellular correlation between the local stiffness and fluidity across the individual living cell: stiff regions exhibit lower fluidity while soft regions exhibit higher fluidity. We find that this subcellular correlation is identical to the previously observed cell-to-cell correlation. The subcellular correlation reversibly vanishes after drug-induced disruption of the cytoskeleton, indicating that the subcellular correlation is a property of the intact cytoskeleton of the living cell.

Combined atomic force microscopy (AFM) and traction force microscopy (TFM) reveals a correlation between viscoelastic material properties and contractile prestress of living cells

Living cells exhibit a complex mechanical behavior, whose underlying mechanisms are still largely unknown. Emerging from the molecular structure and dynamics of the cytoskeleton, the mechanical behavior comprises "passive" viscoelastic material properties and "active" contractile prestress. To directly investigate the connection between these quantities at the single-cell level, we here present the combination of atomic force microscopy (AFM) with traction force microscopy (TFM). With this combination, we simultaneously measure viscoelastic material parameters (stiffness, fluidity) and contractile prestress of adherent fibroblast and epithelial cells. Although stiffness, fluidity, and contractile prestress greatly vary within a cell population, they are highly correlated: stiffer cells have a lower fluidity and a larger prestress than softer cells. We show that viscoelastic material properties and contractile prestress are both governed by the activity of the actomyosin machinery. Our results underline the connection between a cell's viscoelastic material properties and its contractile prestress and their importance in cell mechanics.

Spontaneous Spatial Correlation of Elastic Modulus in Jammed Epithelial Monolayers Observed by AFM

For isolated single cells on a substrate, the intracellular stiffness, which is often measured as the Young's modulus, E, by atomic force microscopy (AFM), depends on the substrate rigidity. However, little is known about how the E of cells is influenced by the surrounding cells in a cell population system in which cells physically and tightly contact adjacent cells. In this study, we investigated the spatial heterogeneities of E in a jammed epithelial monolayer in which cell migration was highly inhibited, allowing us to precisely measure the spatial distribution of E in large-scale regions by AFM. The AFM measurements showed that E can be characterized using two spatial correlation lengths: the shorter correlation length, l_S, is within the single cell size, whereas the longer correlation length, l_L, is longer than the distance between adjacent cells and corresponds to the intercellular correlation of E. We found that l_L decreased significantly when the actin filaments were disrupted or calcium ions were chelated using chemical treatments, and the decreased l_L recovered to the value in the control condition after the treatments were washed out. Moreover, we found that l_L decreased significantly when E-cadherin was knocked down. These results indicate that the observed long-range correlation of E is not fixed within the jammed state but inherently arises from the formation of a large-scale actin filament structure via E-cadherin-dependent cell-cell junctions.

Probe Sensitivity to Cortical versus Intracellular Cytoskeletal Network Stiffness

In development, wound healing, and pathology, cell biomechanical properties are increasingly recognized as being of central importance. To measure these properties, experimental probes of various types have been developed, but how each probe reflects the properties of heterogeneous cell regions has remained obscure. To better understand differences attributable to the probe technology, as well as to define the relative sensitivity of each probe to different cellular structures, here we took a comprehensive approach. We studied two cell types-Schlemm's canal endothelial cells and mouse embryonic fibroblasts (MEFs)-using four different probe technologies: 1) atomic force microscopy (AFM) with sharp tip, 2) AFM with round tip, 3) optical magnetic twisting cytometry (OMTC), and 4) traction microscopy (TM). Perturbation of Schlemm's canal cells with dexamethasone treatment, α-actinin overexpression, or RhoA overexpression caused increases in traction reported by TM and stiffness reported by sharp-tip AFM as compared to corresponding controls. By contrast, under these same experimental conditions, stiffness reported by round-tip AFM and by OMTC indicated little change. Knockout (KO) of vimentin in MEFs caused a diminution of traction reported by TM, as well as stiffness reported by sharp-tip and round-tip AFM. However, stiffness reported by OMTC in vimentin-KO MEFs was greater than in wild type. Finite-element analysis demonstrated that this paradoxical OMTC result in vimentin-KO MEFs could be attributed to reduced cell thickness. Our results also suggest that vimentin contributes not only to intracellular network stiffness but also cortex stiffness. Taken together, this evidence suggests that AFM sharp tip and TM emphasize properties of the actin-rich shell of the cell, whereas round-tip AFM and OMTC emphasize those of the noncortical intracellular network.

Distinct relaxation timescales of neurites revealed by rate-dependent indentation, relaxation and micro-rheology tests

Although the dynamic response of neurites is believed to play crucial roles in processes like axon outgrowth and formation of the neural network, the dynamic mechanical properties of such protrusions remain poorly understood. In this study, by using AFM (atomic force microscopy) indentation, we systematically examined the dynamic behavior of well-developed neurites on primary neurons under different loading modes (step loading, oscillating loading and ramp loading). Interestingly, the response was found to be strongly rate-dependent, with an apparent initial and long-term elastic modulus around 800 and 80 Pa, respectively. To better analyze the measurement data and extract information of key interest, the finite element simulation method (FEM) was also conducted where the neurite was treated as a viscoelastic solid consisting of multiple characteristic relaxation times. It was found that a minimum of three relaxation timescales, i.e. ∼0.01, 0.1 and 1 seconds, are needed to explain the observed relaxation curve as well as fit simulation results to the indentation and rheology data under different loading rates and driving frequencies. We further demonstrated that these three characteristic relaxation times likely originate from the thermal fluctuations of the microtubule, membrane relaxation and cytosol viscosity, respectively. By identifying key parameters describing the time-dependent behavior of neurites, as well as revealing possible physical mechanisms behind, this study could greatly help us understand how neural cells perform their biological duties over a wide spectrum of timescales.

Discrimination between Normal and Cancerous Cells from Dynamic Viscoelastic Properties with a Laser-induced Surface Deformation Microscope

We have clarified the differences in the power-law between normal and corresponding cancerous cells from dynamic viscoelastic measurements in a frequency range of 10² to 10⁵ Hz with a laser-induced surface deformation (LISD) microscope. From the differences in the power spectra at higher frequencies, it has been clarified that a normal cell obeys the power-law with a single exponent, while a cancer cell with two exponents, indicating that the plasma membrane in the cancerous cell has at least two layers with different viscoelastic properties. In LISD measurements, the extension of the upper limit of the applied frequency up to 10⁵ Hz allows us to clarify the existence of the two power-law exponents in the cancerous cell. Understanding the differences between normal and cancerous cells from the power-law in addition to conventional elasticity would be useful for the identification of cancerous cells and for the construction of a mechanical model for their invasion.

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.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

Quantitative Deformability Cytometry: Rapid, Calibrated Measurements of Cell Mechanical Properties

Advances in methods that determine cell mechanical phenotype, or mechanotype, have demonstrated the utility of biophysical markers in clinical and research applications ranging from cancer diagnosis to stem cell enrichment. Here, we introduce quantitative deformability cytometry (q-DC), a method for rapid, calibrated, single-cell mechanotyping. We track changes in cell shape as cells deform into microfluidic constrictions, and we calibrate the mechanical stresses using gel beads. We observe that time-dependent strain follows power-law rheology, enabling single-cell measurements of apparent elastic modulus, E_a, and power-law exponent, β. To validate our method, we mechanotype human promyelocytic leukemia (HL-60) cells and thereby confirm q-DC measurements of E_a = 0.53 ± 0.04 kPa. We also demonstrate that q-DC is sensitive to pharmacological perturbations of the cytoskeleton as well as differences in the mechanotype of human breast cancer cell lines (E_a = 2.1 ± 0.1 and 0.80 ± 0.19 kPa for MCF-7 and MDA-MB-231 cells). To establish an operational framework for q-DC, we investigate the effects of applied stress and cell/pore-size ratio on mechanotype measurements. We show that E_a increases with applied stress, which is consistent with stress stiffening behavior of cells. We also find that E_a increases for larger cell/pore-size ratios, even when the same applied stress is maintained; these results indicate strain stiffening and/or dependence of mechanotype on deformation depth. Taken together, the calibrated measurements enabled by q-DC should advance applications of cell mechanotype in basic research and clinical settings.

Temporal Variation in Single-Cell Power-Law Rheology Spans the Ensemble Variation of Cell Population

Changes in the cytoskeletal organization within cells can be characterized by large spatial and temporal variations in rheological properties of the cell (e.g., the complex shear modulus G^∗). Although the ensemble variation in G^∗ of single cells has been elucidated, the detailed temporal variation of G^∗ remains unknown. In this study, we investigated how the rheological properties of individual fibroblast cells change under a spatially confined environment in which the cell translational motion is highly restricted and the whole cell shape remains unchanged. The temporal evolution of single-cell rheology was probed at the same measurement location within the cell, using atomic force microscopy-based oscillatory deformation. The measurements reveal that the temporal variation in the power-law rheology of cells is quantitatively consistent with the ensemble variation, indicating that the cell system satisfies an ergodic hypothesis in which the temporal statistics are identical to the ensemble statistics. The autocorrelation of G^∗ implies that the cell mechanical state evolves in the ensemble of possible states with a characteristic timescale.

Cobalt and titanium nanoparticles influence on mesenchymal stem cell elasticity and turgidity

Bone cells are damaged by wear particles originating from total joint replacement implants. We investigated Mesenchymal stem cells (MSCs) nanomechanical properties when exposed to cobalt and titanium nanoparticles (resembling wear debris) of different sizes for up to 3days using AFM nanoindentation; along with flow-cytometry and MTT assay. The results demonstrated that cells exposed to increasing concentrations of nanoparticles had a lower value of elasticity and spring constant without significant effect on cell metabolic activity and viability but some morphological alteration (bleeping). Cobalt induced greater effects than titanium and this is consistent with the general knowledge of cyto-compatibility of the later. This work demonstrates for the first time that metal nanoparticles do not only influence MSCs enzymes activity but also cell structure; however, they do not result in full membrane damage. Furthermore, the mechanical changes are concentration and particles composition dependent but little influenced by the particle size.

Unbiased High-Precision Cell Mechanical Measurements with Microconstrictions

We describe a quantitative, high-precision, high-throughput method for measuring the mechanical properties of cells in suspension with a microfluidic device, and for relating cell mechanical responses to protein expression levels. Using a high-speed (750 fps) charge-coupled device camera, we measure the driving pressure Δp, maximum cell deformation εmax, and entry time tentry of cells in an array of microconstrictions. From these measurements, we estimate population averages of elastic modulus E and fluidity β (the power-law exponent of the cell deformation in response to a step change in pressure). We find that cell elasticity increases with increasing strain εmax according to E ∼ εmax, and with increasing pressure according to E ∼ Δp. Variable cell stress due to driving pressure fluctuations and variable cell strain due to cell size fluctuations therefore cause significant variability between measurements. To reduce measurement variability, we use a histogram matching method that selects and analyzes only those cells from different measurements that have experienced the same pressure and strain. With this method, we investigate the influence of measurement parameters on the resulting cell elastic modulus and fluidity. We find a small but significant softening of cells with increasing time after cell harvesting. Cells harvested from confluent cultures are softer compared to cells harvested from subconfluent cultures. Moreover, cell elastic modulus increases with decreasing concentration of the adhesion-reducing surfactant pluronic. Lastly, we simultaneously measure cell mechanics and fluorescence signals of cells that overexpress the GFP-tagged nuclear envelope protein lamin A. We find a dose-dependent increase in cell elastic modulus and decrease in cell fluidity with increasing lamin A levels. Together, our findings demonstrate that histogram matching of pressure, strain, and protein expression levels greatly reduces the variability between measurements and enables us to reproducibly detect small differences in cell mechanics.

Manipulation and Motion of Organelles and Single Molecules in Living Cells

The biomolecule is among the most important building blocks of biological systems, and a full understanding of its function forms the scaffold for describing the mechanisms of higher order structures as organelles and cells. Force is a fundamental regulatory mechanism of biomolecular interactions driving many cellular processes. The forces on a molecular scale are exactly in the range that can be manipulated and probed with single molecule force spectroscopy. The natural environment of a biomolecule is inside a living cell, hence, this is the most relevant environment for probing their function. In vivo studies are, however, challenged by the complexity of the cell. In this review, we start with presenting relevant theoretical tools for analyzing single molecule data obtained in intracellular environments followed by a description of state-of-the art visualization techniques. The most commonly used force spectroscopy techniques, namely optical tweezers, magnetic tweezers, and atomic force microscopy, are described in detail, and their strength and limitations related to in vivo experiments are discussed. Finally, recent exciting discoveries within the field of in vivo manipulation and dynamics of single molecule and organelles are reviewed.

Average Rheological Quantities of Cells in Monolayers

Measuring rheological properties of cells in monolayers enables quantifying average cell properties in single experimental runs despite large cell-to-cell variations. Here, we describe how to modify a commercial rotational rheometer to accomplish the necessary precision for a monolayer rheometer and we delineate the steps for setting up experiments detecting average viscoelastic cell properties.

Mapping intracellular mechanics on micropatterned substrates

The mechanical properties of cells impact on their architecture, their migration, intracellular trafficking, and many other cellular functions and have been shown to be modified during cancer progression. We have developed an approach to map the intracellular mechanical properties of living cells by combining micropatterning and optical tweezers-based active microrheology. We optically trap micrometer-sized beads internalized in cells plated on crossbow-shaped adhesive micropatterns and track their displacement following a step displacement of the cell. The local intracellular complex shear modulus is measured from the relaxation of the bead position assuming that the intracellular microenvironment of the bead obeys power-law rheology. We also analyze the data with a standard viscoelastic model and compare with the power-law approach. We show that the shear modulus decreases from the cell center to the periphery and from the cell rear to the front along the polarity axis of the micropattern. We use a variety of inhibitors to quantify the spatial contribution of the cytoskeleton, intracellular membranes, and ATP-dependent active forces to intracellular mechanics and apply our technique to differentiate normal and cancer cells.

Statistical study of biomechanics of living brain cells during growth and maturation on artificial substrates

There is increasing evidence that mechanical issues play a vital role in neuron growth and brain development. The importance of this grows as novel devices, whose material properties differ from cells, are increasingly implanted in the body. In this work, we studied the mechanical properties of rat brain cells over time and on different materials by using a high throughput magnetic tweezers system. It was found that the elastic moduli of both neurite and soma in networked neurons increased with growth. However, neurites at DIV4 exhibited a relatively high stiffness, which could be ascribed to the high outgrowth tension. The power-law exponents (viscoelasticity) of both neurites and somas of neurons decreased with culture time. On the other hand, the stiffness of glial cells also increased with maturity. Furthermore, both neurites and glia become softer when cultured on compliant substrates. Especially, the glial cells cultured on a soft substrate obviously showed a less dense and more porous actin and GFAP mesh. In addition, the viscoelasticity of both neurites and glia did not show a significant dependence on the substrates' stiffness.

The physical origins of transit time measurements for rapid, single cell mechanotyping

The mechanical phenotype or 'mechanotype' of cells is emerging as a potential biomarker for cell types ranging from pluripotent stem cells to cancer cells. Using a microfluidic device, cell mechanotype can be rapidly analyzed by measuring the time required for cells to deform as they flow through constricted channels. While cells typically exhibit deformation timescales, or transit times, on the order of milliseconds to tens of seconds, transit times can span several orders of magnitude and vary from day to day within a population of single cells; this makes it challenging to characterize different cell samples based on transit time data. Here we investigate how variability in transit time measurements depends on both experimental factors and heterogeneity in physical properties across a population of single cells. We find that simultaneous transit events that occur across neighboring constrictions can alter transit time, but only significantly when more than 65% of channels in the parallel array are occluded. Variability in transit time measurements is also affected by the age of the device following plasma treatment, which could be attributed to changes in channel surface properties. We additionally investigate the role of variability in cell physical properties. Transit time depends on cell size; by binning transit time data for cells of similar diameters, we reduce measurement variability by 20%. To gain further insight into the effects of cell-to-cell differences in physical properties, we fabricate a panel of gel particles and oil droplets with tunable mechanical properties. We demonstrate that particles with homogeneous composition exhibit a marked reduction in transit time variability, suggesting that the width of transit time distributions reflects the degree of heterogeneity in subcellular structure and mechanical properties within a cell population. Our results also provide fundamental insight into the physical underpinnings of transit measurements: transit time depends strongly on particle elastic modulus, and weakly on viscosity and surface tension. Based on our findings, we present a comprehensive methodology for designing, analyzing, and reducing variability in transit time measurements; this should facilitate broader implementation of transit experiments for rapid mechanical phenotyping in basic research and clinical settings.

Rheological properties of cells measured by optical tweezers

BACKGROUND

The viscoelastic properties of cells have been investigated by a variety of techniques. However, the experimental data reported in literature for viscoelastic moduli differ by up to three orders of magnitude. This has been attributed to differences in techniques and models for cell response as well as to the natural variability of cells.

RESULTS

In this work we develop and apply a new methodology based on optical tweezers to investigate the rheological behavior of fibroblasts, neurons and astrocytes in the frequency range from 1Hz to 35Hz, determining the storage and loss moduli of their membrane-cortex complex. To avoid distortions associated with cell probing techniques, we use a previously developed method that takes into account the influence of under bead cell thickness and bead immersion. These two parameters were carefully measured for the three cell types used. Employing the soft glass rheology model, we obtain the scaling exponent and the Young's modulus for each cell type. The obtained viscoelastic moduli are in the order of Pa. Among the three cell types, astrocytes have the lowest elastic modulus, while neurons and fibroblasts exhibit a more solid-like behavior.

CONCLUSIONS

Although some discrepancies with previous results remain and may be inevitable in view of natural variability, the methodology developed in this work allows us to explore the viscoelastic behavior of the membrane-cortex complex of different cell types as well as to compare their viscous and elastic moduli, obtained under identical and well-defined experimental conditions, relating them to the cell functions.

Implementation and application of a novel 2D magnetic twisting cytometry based on multi-pole electromagnet

We implemented a novel 2D magnetic twisting cytometry (MTC) based on a previously reported multi-pole high permeability electromagnet, in which both the strength and direction of the twisting field can be controlled. Thanks to the high performance twisting electromagnet and the heterodyning technology, the measurement frequency has been extended to the 1 kHz range. In order to obtain high remanence of the ferromagnetic beads, a separate electromagnet with feedback control was adopted for the high magnetic field polarization. Our setup constitutes the first instrument which can be operated both in MTC mode and in magnetic tweezers (MT) mode. In this work, the mechanical properties of HL-1 cardiomyocytes were characterized in MTC mode. Both anisotropy and log-normal distribution of cell stiffness were observed, which agree with our previous results measured in MT mode. The response from these living cells at different frequencies can be fitted very well by the soft glassy rheology model.

Microconstriction arrays for high-throughput quantitative measurements of cell mechanical properties

We describe a method for quantifying the mechanical properties of cells in suspension with a microfluidic device consisting of a parallel array of micron-sized constrictions. Using a high-speed charge-coupled device camera, we measure the flow speed, cell deformation, and entry time into the constrictions of several hundred cells per minute during their passage through the device. From the flow speed and the occupation state of the microconstriction array with cells, the driving pressure across each constriction is continuously computed. Cell entry times into microconstrictions decrease with increased driving pressure and decreased cell size according to a power law. From this power-law relationship, the cell elasticity and fluidity can be estimated. When cells are treated with drugs that depolymerize or stabilize the cytoskeleton or the nucleus, elasticity and fluidity data from all treatments collapse onto a master curve. Power-law rheology and collapse onto a master curve are predicted by the theory of soft glassy materials and have been previously shown to describe the mechanical behavior of cells adhering to a substrate. Our finding that this theory also applies to cells in suspension provides the foundation for a quantitative high-throughput measurement of cell mechanical properties with microfluidic devices.

Combined strategies for optimal detection of the contact point in AFM force-indentation curves obtained on thin samples and adherent cells

Atomic Force Microscopy (AFM) is a widely used tool to study cell mechanics. Current AFM setups perform high-throughput probing of living cells, generating large amounts of force-indentations curves that are subsequently analysed using a contact-mechanics model. Here we present several algorithms to detect the contact point in force-indentation curves, a crucial step to achieve fully-automated analysis of AFM-generated data. We quantify and rank the performance of our algorithms by analysing a thousand force-indentation curves obtained on thin soft homogeneous hydrogels, which mimic the stiffness and topographical profile of adherent cells. We take advantage of the fact that all the proposed algorithms are based on sequential search strategies, and show that a combination of them yields the most accurate and unbiased results. Finally, we also observe improved performance when force-indentation curves obtained on adherent cells are analysed using our combined strategy, as compared to the classical algorithm used in the majority of previous cell mechanics studies.

Imaging viscoelastic properties of live cells by AFM: power-law rheology on the nanoscale

We developed force clamp force mapping (FCFM), an atomic force microscopy (AFM) technique for measuring the viscoelastic creep behavior of live cells with sub-micrometer spatial resolution. FCFM combines force-distance curves with an added force clamp phase during tip-sample contact. From the creep behavior measured during the force clamp phase, quantitative viscoelastic sample properties are extracted. We validate FCFM on soft polyacrylamide gels. We find that the creep behavior of living cells conforms to a power-law material model. By recording short (50-60 ms) force clamp measurements in rapid succession, we generate, for the first time, two-dimensional maps of power-law exponent and modulus scaling parameter. Although these maps reveal large spatial variations of both parameters across the cell surface, we obtain robust mean values from the several hundreds of measurements performed on each cell. Measurements on mouse embryonic fibroblasts show that the mean power-law exponents and the mean modulus scaling parameters differ greatly among individual cells, but both parameters are highly correlated: stiffer cells consistently show a smaller power-law exponent. This correlation allows us to distinguish between wild-type cells and cells that lack vinculin, a dominant protein of the focal adhesion complex, even though the mean values of viscoelastic properties between wildtype and knockout cells did not differ significantly. Therefore, FCFM spatially resolves viscoelastic sample properties and can uncover subtle mechanical signatures of proteins in living cells.

Probing mechanical properties of Jurkat cells under the effect of ART using oscillating optical tweezers

Acute lymphoid leukemia is a common type of blood cancer and chemotherapy is the initial treatment of choice. Quantifying the effect of a chemotherapeutic drug at the cellular level plays an important role in the process of the treatment. In this study, an oscillating optical tweezer was employed to characterize the frequency-dependent mechanical properties of Jurkat cells exposed to the chemotherapeutic agent, artesunate (ART). A motion equation for a bead bound to a cell was applied to describe the mechanical characteristics of the cell cytoskeleton. By comparing between the modeling results and experimental results from the optical tweezer, the stiffness and viscosity of the Jurkat cells before and after the ART treatment were obtained. The results demonstrate a weak power-law dependency of cell stiffness with frequency. Furthermore, the stiffness and viscosity were increased after the treatment. Therefore, the cytoskeleton cell stiffness as the well as power-law coefficient can provide a useful insight into the chemo-mechanical relationship of drug treated cancer cells and may serve as another tool for evaluating therapeutic performance quantitatively.

Chemoenvironmental modulators of fluidity in the suspended biological cell

Biological cells can be characterized as "soft matter" with mechanical characteristics potentially modulated by external cues such as pharmaceutical dosage or fever temperature. Further, quantifying the effects of chemical and physical stimuli on a cell's mechanical response informs models of living cells as complex materials. Here, we investigate the mechanical behavior of single biological cells in terms of fluidity, or mechanical hysteresivity normalized to the extremes of an elastic solid or a viscous liquid. This parameter, which complements stiffness when describing whole-cell viscoelastic response, can be determined for a suspended cell within subsecond times. Questions remain, however, about the origin of fluidity as a conserved parameter across timescales, the physical interpretation of its magnitude, and its potential use for high-throughput sorting and separation of interesting cells by mechanical means. Therefore, we exposed suspended CH27 lymphoma cells to various chemoenvironmental conditions--temperature, pharmacological agents, pH, and osmolarity--and measured cell fluidity with a non-contact technique to extend familiarity with suspended-cell mechanics in the context of both soft-matter physics and mechanical flow cytometry development. The actin-cytoskeleton-disassembling drug latrunculin exacted a large effect on mechanical behavior, amenable to dose-dependence analysis of coupled changes in fluidity and stiffness. Fluidity was minimally affected by pH changes from 6.5 to 8.5, but strongly modulated by osmotic challenge to the cell, where the range spanned halfway from solid to liquid behavior. Together, these results support the interpretation of fluidity as a reciprocal friction within the actin cytoskeleton, with implications both for cytoskeletal models and for expectations when separating interesting cell subpopulations by mechanical means in the suspended state.

Filamin acts as a key regulator in epithelial defence against transformed cells

Recent studies have shown that certain types of transformed cells are extruded from an epithelial monolayer. However, it is not known whether and how neighbouring normal cells play an active role in this process. In this study, we demonstrate that filamin A and vimentin accumulate in normal cells specifically at the interface with Src- or RasV12-transformed cells. Knockdown of filamin A or vimentin in normal cells profoundly suppresses apical extrusion of the neighbouring transformed cells. In addition, we show in zebrafish embryos that filamin plays a positive role in the elimination of the transformed cells. Furthermore, the Rho/Rho kinase pathway regulates filamin accumulation and filamin acts upstream of vimentin in the apical extrusion. This is the first report demonstrating that normal epithelial cells recognize and actively eliminate neighbouring transformed cells and that filamin is a key mediator in the interaction between normal and transformed epithelial cells.

Dissecting the contribution of actin and vimentin intermediate filaments to mechanical phenotype of suspended cells using high-throughput deformability measurements and computational modeling

Mechanical cell properties play an important role in many basic biological functions, including motility, adhesion, proliferation and differentiation. There is a growing body of evidence that the mechanical cell phenotype can be used for detection and, possibly, treatment of various diseases, including cancer. Understanding of pathological mechanisms requires investigation of the relationship between constitutive properties and major structural components of cells, i.e., the nucleus and cytoskeleton. While the contribution of actin und microtubules to cellular rheology has been extensively studied in the past, the role of intermediate filaments has been scarcely investigated up to now. Here, for the first time we compare the effects of drug-induced disruption of actin and vimentin intermediate filaments on mechanical properties of suspended NK cells using high-throughput deformability measurements and computational modeling. Although, molecular mechanisms of actin and vimentin disruption by the applied cytoskeletal drugs, Cytochalasin-D and Withaferin-A, are different, cell softening in both cases can be attributed to reduction of the effective density and stiffness of filament networks. Our experimental data suggest that actin and vimentin deficient cells exhibit, in average, 41% and 20% higher deformability in comparison to untreated control. 3D Finite Element simulation is performed to quantify the contribution of cortical actin and perinuclear vimentin to mechanical phenotype of the whole cell. Our simulation provides quantitative estimates for decreased filament stiffness in drug-treated cells and predicts more than two-fold increase of the strain magnitude in the perinuclear vimentin layer of actin deficient cells relatively to untreated control. Thus, the mechanical function of vimentin becomes particularly essential in motile and proliferating cells that have to dynamically remodel the cortical actin network. These insights add functional cues to frequently observed overexpression of vimentin in diverse types of cancer and underline the role of vimentin targeting drugs, such as Withaferin-A, as a potent cancerostatic supplement.