Estimation of cell Young's modulus of adherent cells probed by optical and magnetic tweezers: influence of cell thickness and bead immersion

Multi-oscillation microrheology via acoustic force spectroscopy enables frequency-dependent measurements on endothelial cells at high-throughput

Active microrheology is one of the main methods to determine the mechanical properties of cells and tissue, and the modelling of these viscoelastic properties is under heavy debate with many competing approaches. Most experimental methods of active microrheology such as optical tweezers or atomic force microscopy based approaches rely on single cell measurements, and thus suffer from a low throughput. Here, we present a novel method for frequency-dependent microrheology on cells using acoustic forces which allows multiplexed measurements of several cells in parallel. Acoustic force spectroscopy (AFS) is used to generate multi-oscillatory forces in the range of pN-nN on particles attached to primary human umbilical vein endothelial cells (HUVEC) cultivated inside a microfluidic chip. While the AFS was introduced as a single-molecule technique to measure mechanochemical properties of biomolecules, we exploit the AFS to measure the dynamic viscoelastic properties of cells exposed to different conditions, such as flow shear stresses or drug injections. By controlling the force and measuring the position of the particle, the complex shear modulus G*(ω) can be measured continuously over several hours. The resulting power-law shear moduli are consistent with fractional viscoelastic models. In our experiments we confirm a decrease in shear modulus after perturbing the actin cytoskeleton via cytochalasin B. This effect was reversible after washing out the drug. Additionally, we include critical information for the usage of the new method AFS as a measurement tool showing its capabilities and limitations and we find that for performing viscoelastic measurements with the AFS, a thorough calibration and careful data analysis is crucial, for which we provide protocols and guidelines.

Translation of a Coated Rigid Spherical Inclusion in an Elastic Matrix: Exact Solution, and Implications for Mechanobiology

The displacement of relatively rigid beads within a relatively compliant, elastic matrix can be used to measure the mechanical properties of the matrix. For example, in mechanobiological studies, magnetic or reflective beads can be displaced with a known external force to estimate the matrix modulus. Although such beads are generally rigid compared to the matrix, the material surrounding the beads typically differs from the matrix in one or two ways. The first case, as is common in mechanobiological experimentation, is the situation in which the bead must be coated with materials such as protein ligands that enable adhesion to the matrix. These layers typically differ in stiffness relative to the matrix material. The second case, common for uncoated beads, is the situation in which the beads disrupt the structure of the hydrogel or polymer, leading to a region of enhanced or reduced stiffness in the neighborhood of the bead. To address both cases, we developed the first analytical solution of the problem of translation of a coated, rigid spherical inclusion displaced within an isotropic elastic matrix by a remotely applied force. The solution is applicable to cases of arbitrary coating stiffness and size of the coating. We conclude by discussing applications of the solution to mechanobiology.

Biocompatible Cantilevers for Mechanical Characterization of Zebrafish Embryos using Image Analysis

We have developed a force sensing system to continuously evaluate the mechanical elasticity of micrometer-scale (a few hundred micrometers to a millimeter) live tissues. The sensing is achieved by measuring the deflection of force sensitive cantilevers through microscopic image analysis, which does not require electrical strain gauges. Cantilevers made of biocompatible polydimethylsiloxane (PDMS) were actuated by a piezoelectric actuator and functioned as a pair of chopsticks to measure the stiffness of the specimen. The dimensions of the cantilevers were easily adjusted to match the size, range, and stiffness of the zebrafish samples. In this paper, we demonstrated the versatility of this technique by measuring the mechanical elasticity of zebrafish embryos at different stages of development. The stiffness of zebrafish embryos was measured once per hour for 9 h. From the experimental results, we successfully quantified the stiffness change of zebrafish embryos during embryonic development.

Noninvasive detection of changes in cells' cytosol conductivity by combining dielectrophoresis with optical tweezers

Cellular electrical properties are modulated by various physical and/or chemical stresses and detection of these changes is a challenging issue. Optical tweezers (OT) and dielectrophoresis (DEP) are frequently integrated to devices dedicated to the investigation of cells properties. Here we provide a technique to detect changes in cytosol conductivity of cells by using a combination of DEP and OT. The method was exemplified for the case of cells electroporation and is based on balancing the DEP force by a controlled OT force. We observed a decrease of the DEP force in the case of electroporated cells which was correlated to a decrease of cytosol conductivity by means of Clausius-Mossotti factor modeling. For highly stressing electroporation pulses, the cytosol conductivity drops to values close to those of the cells suspending medium. These results are consistent with those reported in the literature proving the robustness of our proposed sensing method.

The desmin network is a determinant of the cytoplasmic stiffness of myoblasts

BACKGROUND INFORMATION

The mechanical properties of cells are essential to maintain their proper functions, and mainly rely on their cytoskeleton. A lot of attention has been paid to actin filaments, demonstrating their central role in the cells mechanical properties, but much less is known about the participation of intermediate filament (IF) networks. Indeed the contribution of IFs, such as vimentin, keratins and lamins, to cell mechanics has only been assessed recently. We study here the involvement of desmin, an IF specifically expressed in muscle cells, in the rheology of immature muscle cells. Desmin can carry mutations responsible for a class of muscle pathologies named desminopathies.

RESULTS

In this study, using three types of cell rheometers, we assess the consequences of expressing wild-type (WT) or mutated desmin on the rheological properties of single myoblasts. We find that the mechanical properties of the cell cortex are not correlated to the quantity, nor the quality of desmin expressed. On the contrary, the overall cell stiffness increases when the amount of WT or mutated desmin polymerised in cytoplasmic networks increases. However, myoblasts become softer when the desmin network is partially depleted by the formation of aggregates induced by the expression of a desmin mutant.

CONCLUSIONS

We demonstrate that desmin plays a negligible role in the mechanical properties of the cell cortex but is a determinant of the overall cell stiffness. More particularly, desmin participates to the cytoplasm viscoelasticity.

SIGNIFICANCE

Desminopathies are associated with muscular weaknesses attributed to a disorganisation of the structure of striated muscle that impairs the active force generation. The present study evidences for the first time the key role of desmin in the rheological properties of myoblasts, raising the hypothesis that desmin mutations could also alter the passive mechanical properties of muscles, thus participating to the lack of force build up in muscle tissue.

A numerical model suggests the interplay between nuclear plasticity and stiffness during a perfusion assay

Cell deformability is a necessary condition for a cell to be able to migrate, an ability that is vital both for healthy and diseased organisms. The nucleus being the largest and stiffest organelle, it often is a barrier to cell migration. It is thus essential to characterize its mechanical behaviour. First, we numerically investigate the visco-elasto-plastic properties of the isolated nucleus during a compression test. This simulation highlights the impact of the mechanical behaviour of the nuclear lamina and the nucleoplasm on the overall plasticity. Second, a whole cell model is developed to simulate a perfusion experiment to study the possible interactions between the cytoplasm and the nucleus. We analyze and discuss the role of the lamina for a wild-type cell model, and a lamin-deficient one, in which the Young's modulus of the lamina is set to 1% of its nominal value. This simulation suggests an interplay between the cytoplasm and the nucleoplasm, especially in the lamin-deficient cell, showing the need of a stiffer nucleoplasm to maintain nuclear plasticity.

Modeling mechanical control of spindle orientation of intestinal crypt stem cells

Tissue development requires a control over the sequence of symmetric and asymmetric stem cell divisions to obtain the specific numbers of differentiated cells populating the tissue and stem cells residing in the niche. A good experimental model to study this process is the mouse intestinal crypt development, where it has been shown that stem cells follow an optimal strategy in which asymmetric division occurs only after all symmetric divisions have taken place to reach a fixed number of cells in the niche in the shortest time. Here we introduce a model of stem cell division that is able to explain the experimentally observed stem cell population dynamics by the effect of mechanical forces acting on the spindle. We also observe that the mechanically induced strategy for development is sub-optimal and crucially depends on the stiffness of the spindle. These findings highlight the crucial importance of mechanical forces for the development and maintenance of the intestinal crypt.

Influence of neighboring adherent cells on laminar flow induced shear stress in vitro-A systematic study

Cells experience forces if subjected to laminar flow. These forces, mostly of shear force character, are strongly dependent not only on the applied flow field itself but also on hydrodynamic effects originating from neighboring cells. This particularly becomes important for the interpretation of data from in vitro experiments in flow chambers without confluent cell layers. By employing numerical Finite Element Method simulations of such assemblies of deformable objects under shear flow, we investigate the occurring stress within elastic adherent cells and the influence of neighboring cells on these quantities. For this, we simulate single and multiple adherent cells of different shapes fixed on a solid substrate under laminar flow parallel to the substrate for different velocities. We determine the local stress within the cells close to the cell-substrate-interface and the overall stress of the cells by surface integration over the cell surface. Comparing each measurand in the case of a multiple cell situation with the corresponding one of single cells under identical conditions, we introduce a dimensionless influence factor. The systematic variation of the distance and angle between cells, where the latter is with respect to the flow direction, flow velocity, Young's modulus, cell shape, and cell number, enables us to describe the actual influence on a cell. Overall, we here demonstrate that the cell density is a crucial parameter for all studies on flow induced experiments on adherent cells in vitro.

Biochemical and Cellular Determinants of Renal Glomerular Elasticity

The elastic properties of renal glomeruli and their capillaries permit them to maintain structural integrity in the presence of variable hemodynamic forces. Measured by micro-indentation, glomeruli have an elastic modulus (E, Young's modulus) of 2.1 kPa, and estimates from glomerular perfusion studies suggest that the E of glomeruli is between 2 and 4 kPa. F-actin depolymerization by latrunculin, inhibition of acto-myosin contractility by blebbistatin, reduction in ATP synthesis, and reduction of the affinity of adhesion proteins by EDTA reduced the glomerular E to 1.26, 1.7, 1.5, and 1.43 kPa, respectively. Actin filament stabilization with jasplakinolide and increasing integrin affinity with Mg2+ increased E to 2.65 and 2.87 kPa, respectively. Alterations in glomerular E are reflected in commensurate changes in F/G actin ratios. Disruption of vimentin intermediate filaments by withaferin A reduced E to 0.92 kPa. The E of decellularized glomeruli was 0.74 kPa, indicating that cellular components of glomeruli have dominant effects on their elasticity. The E of glomerular basement membranes measured by magnetic bead displacement was 2.4 kPa. Podocytes and mesangial cells grown on substrates with E values between 3 and 5 kPa had actin fibers and focal adhesions resembling those of podocytes in vivo. Renal ischemia and ischemia-reperfusion reduced the E of glomeruli to 1.58 kPa. These results show that the E of glomeruli is between 2 and 4 kPa. E of the GBM, 2.4 kPa, is consistent with this value, and is supported by the behavior of podocytes and mesangial cells grown on variable stiffness matrices. The podocyte cytoskeleton contributes the major component to the overall E of glomeruli, and a normal E requires ATP synthesis. The reduction in glomerular E following ischemia and in other diseases indicates that reduced glomerular E is a common feature of many forms of glomerular injury and indicative of an abnormal podocyte cytoskeleton.

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.

Probing cytoskeletal pre-stress and nuclear mechanics in endothelial cells with spatiotemporally controlled (de-)adhesion kinetics on micropatterned substrates

The mechanical properties of living cells reflect their propensity to migrate and respond to external forces. Both cellular and nuclear stiffnesses are strongly influenced by the rigidity of the extracellular matrix (ECM) through reorganization of the cyto- and nucleoskeletal protein connections. Changes in this architectural continuum affect cell mechanics and underlie many pathological conditions. In this context, an accurate and combined quantification of the mechanical properties of both cells and nuclei can contribute to a better understanding of cellular (dys-)function. To address this challenge, we have established a robust method for probing cellular and nuclear deformation during spreading and detachment from micropatterned substrates. We show that (de-)adhesion kinetics of endothelial cells are modulated by substrate stiffness and rely on the actomyosin network. We combined this approach with measurements of cell stiffness by magnetic tweezers to show that relaxation dynamics can be considered as a reliable parameter of cellular pre-stress in adherent cells. During the adhesion stage, large cellular and nuclear deformations occur over a long time span (>60 min). Conversely, nuclear deformation and condensed chromatin are relaxed in a few seconds after detachment. Finally, our results show that accumulation of farnesylated prelamin leads to modifications of the nuclear viscoelastic properties, as reflected by increased nuclear relaxation times. Our method offers an original and non-intrusive way of simultaneously gauging cellular and nuclear mechanics, which can be extended to high-throughput screens of pathological conditions and potential countermeasures.

Buckling prevention strategies in nature as inspiration for improving percutaneous instruments: a review

A typical mechanical failure mode observed in slender percutaneous instruments, such as needles and guidewires, is buckling. Buckling is observed when the axial compressive force that is required to penetrate certain tissue types exceeds the critical load of the instrument and manifests itself by sudden lateral deflection of the instrument. In nature, several organisms are able to penetrate substrates without buckling while using apparatuses with diameters smaller than those of off-the-shelf available percutaneous needles and guidewires. In this study we reviewed the apparatuses and buckling prevention strategies employed by biological organisms to penetrate substrates such as wood and skin. A subdivision is made between buckling prevention strategies that focus on increasing the critical load of the penetration tool and strategies that focus on decreasing the penetration load of the substrate. In total, 28 buckling prevention strategies were identified and categorized. Most organisms appear to be using a combination of buckling prevention strategies simultaneously. Integration and combination of these biological buckling prevention strategies in percutaneous instruments may contribute to increasing the success rate of percutaneous interventions.

Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.

Modelling is an important tool in understanding the behaviour of biological tissues. In this paper we advocate a new modelling framework in which cells and tissues are represented by a collection of particles with associated properties. The particles interact with each other and can change their behaviour in response to changes in their environment. We demonstrate how the propose framework can be used to represent the mechanical behaviour of different tissues with much greater flexibility as compared to traditional continuum based methods.

Three-Dimensional Cell Entrapment as a Function of the Weight Percent of Peptide-Amphiphile Hydrogels

The design of scaffolds which mimic the stiffness, nanofiber structure, and biochemistry of the native extracellular matrix (ECM) has been a major objective for the tissue engineering field. Furthermore, mimicking the innate three-dimensional (3D) environment of the ECM has been shown to significantly altered cellular response compared to that of traditional two-dimensional (2D) culture. We report the development of a self-assembling, fibronectin-mimetic, peptide-amphiphile nanofiber scaffold for 3D cell culture. To form such a scaffold, 5 mol % of a bioactive PR_g fibronectin-mimetic peptide-amphiphile was mixed with 95 mol % of a diluent peptide-amphiphile (E2) whose purpose was to neutralize electrostatic interactions, increase the gelation kinetics, and promote cell survival. Atomic force microscopy verified the fibrilar structure of the gels, and the mechanical properties were characterized for various weight percent (wt %) formulations of the 5 mol % PR_g-95 mol % E2 peptide-amphiphile mixture. The 0.5 wt % formulations had an elastic modulus of 429.0 ± 21.3 Pa whereas the 1.0 wt % peptide-amphiphile hydrogels had an elastic modulus of 808.6 ± 38.1 Pa. The presence of entrapped cells in the gels decreased the elastic modulus, and the decrease was a function of cell loading. Although both formulations supported cell proliferation, the 0.5 wt % gels supported significantly greater NIH3T3/GFP fibroblast cell proliferation throughout the gels than the 1.0 wt % gels. However, compared to the 0.5 wt % formulations, the 1.0 wt % hydrogels promoted greater increases in mRNA expression and the production of fibronectin and type IV collagen ECM proteins. This study suggests that this fibronectin-mimetic scaffold holds great promise in the advancement of 3D culture applications and cell therapies.

Microcapsule mechanics: from stability to function

Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties for functional aspects. At first, assembly strategies are presented that allow control over the decisive geometrical parameters, diameter and wall thickness, which both influence the capsule's mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified. Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.

Fluorescence-based force/tension sensors: a novel tool to visualize mechanical forces in structural proteins in live cells

SIGNIFICANCE

Three signaling systems, chemical, electrical, and mechanical, ubiquitously contribute to cellular activities. There is limited information on the mechanical signaling system because of a lack of tools to measure stress in specific proteins. Although significant advances in methodologies such as atomic force microscopy and laser tweezers have achieved great success in single molecules and measuring the mean properties of cells and tissues, they cannot deal with specific proteins in live cells.

RECENT ADVANCES

To remedy the situation, we developed a family of genetically encoded optical force sensors to measure the stress in structural proteins in living cells. The sensors can be incorporated into specific proteins and are not harmful in transgenic animals. The chimeric proteins distribute and function as their wild-type counterparts, and local stress can be read out from changes in Förster resonance energy transfer (FRET).

CRITICAL ISSUES

Our original sensor used two mutant green fluorescence proteins linked by an alpha helix that served as a linking spring. Ever since, we have improved the probe design in a number of ways. For example, we replaced the helical linker with more common elastic protein domains to better match the compliance of the wild-type hosts. We greatly improved sensitivity by using the angular dependence of FRET rather than the distance dependence as the transduction mechanism, because that has nearly 100% efficiency at rest and nearly zero when stretched.

FUTURE DIRECTIONS

These probes enable researchers to investigate the roles of mechanical force in cellular activities at the level of single molecules, cells, tissues, and whole animals.

A method to measure mechanical properties of pulmonary epithelial cell layers

The lung has a huge inner alveolar surface composed of epithelial cell layers. The knowledge about mechanical properties of lung epithelia is helpful to understand the complex lung mechanics and biomechanical interactions. Methods have been developed to determine mechanical indices (e.g., tissue elasticity) which are both very complex and in need of costly equipment. Therefore, in this study, a mechanostimulator is presented to dynamically stimulate lung epithelial cell monolayers in order to determine their mechanical properties based on a simple mathematical model. First, the method was evaluated by comparison to classical tensile testing using silicone membranes as substitute for biological tissue. Second, human pulmonary epithelial cells (A549 cell line) were grown on flexible silicone membranes and stretched at a defined magnitude. Equal secant moduli were determined in the mechanostimulator and in a conventional tension testing machine (0.49 ± 0.05 MPa and 0.51 ± 0.03 MPa, respectively). The elasticity of the cell monolayer could be calculated by the volume-pressure relationship resulting from inflation of the membrane-cell construct. The secant modulus of the A549 cell layer was calculated as 0.04 ± 0.008 MPa. These findings suggest that the mechanostimulator may represent an adequate device to determine mechanical properties of cell layers.

Mechanobiology in lung epithelial cells: measurements, perturbations, and responses

Epithelial cells of the lung are located at the interface between the environment and the organism and serve many important functions including barrier protection, fluid balance, clearance of particulate, initiation of immune responses, mucus and surfactant production, and repair following injury. Because of the complex structure of the lung and its cyclic deformation during the respiratory cycle, epithelial cells are exposed to continuously varying levels of mechanical stresses. While normal lung function is maintained under these conditions, changes in mechanical stresses can have profound effects on the function of epithelial cells and therefore the function of the organ. In this review, we will describe the types of stresses and strains in the lungs, how these are transmitted, and how these may vary in human disease or animal models. Many approaches have been developed to better understand how cells sense and respond to mechanical stresses, and we will discuss these approaches and how they have been used to study lung epithelial cells in culture. Understanding how cells sense and respond to changes in mechanical stresses will contribute to our understanding of the role of lung epithelial cells during normal function and development and how their function may change in diseases such as acute lung injury, asthma, emphysema, and fibrosis.

Influence of power-law rheology on cell injury during microbubble flows

The reopening of fluid-occluded pulmonary airways generates microbubble flows which impart complex hydrodynamic stresses to the epithelial cells lining airway walls. In this study we used boundary element solutions and finite element techniques to investigate how cell rheology influences the deformation and injury of cells during microbubble flows. An optimized Prony-Dirichlet series was used to model the cells' power-law rheology (PLR) and results were compared with a Maxwell fluid model. Results indicate that membrane strain and the risk for cell injury decreases with increasing channel height and bubble speed. In addition, the Maxwell and PLR models both indicate that increased viscous damping results in less cellular deformation/injury. However, only the PLR model was consistent with the experimental observation that cell injury is not a function of stress exposure duration. Correlation of our models with experimental observations therefore highlights the importance of using PLR in computational models of cell mechanics/deformation. These computational models also indicate that altering the cell's viscoelastic properties may be a clinically relevant way to mitigate microbubble-induced cell injury.