A finite element model of cell deformation during magnetic bead twisting.

Magnetic twisting cytometry probes mechanical properties of an adherent cell by applying a torque to a magnetic bead that is tightly bound to the cell surface. Here we have used a three-dimensional finite element model of cell deformation to compute the relationships between the applied torque and resulting bead rotation and lateral bead translation. From the analysis, we computed two coefficients that allow the cell elastic modulus to be estimated from measurements of either bead rotation or lateral bead translation, respectively, if the degree of bead embedding and the cell height are known. Although computed strains in proximity of the bead can be large, the relationships between applied torque and bead rotation or translation remain virtually linear up to bead rotations of 15 degrees, above which geometrical nonlinearities become significant. This appreciable linear range stands in contrast to the intrinsically nonlinear force-displacement relationship that is observed when cells are indented during atomic force microscopy. Finally, these computations support the idea that adhesive forces are sufficient to keep the bead firmly attached to the cell surface throughout the range of working torques.     

An extended modeling of the micropipette aspiration experiment for the characterization of the Young's modulus and Poisson's ratio of adherent thin biological samples: numerical and experimental studies

The micropipette aspiration (MA) experiment remains a quite widely used micromanipulation technique for quantifying the elastic modulus of cells and, less frequently, of other biological samples. However, moduli estimations derived from MA experiments are only valid if the probed sample is non-adherent to the rigid substrate. This study extends this standard formulation by taking into account the influence of the sample adhesion. Using a finite element analysis of the sample aspiration into the micropipette, we derived a new expression of the aspirated length for linear elastic materials. Our results establish that (i) below a critical value, the thickness h of the probed sample must be considered to get an accurate value of its Young's modulus (ii) this critical value depends both on the Poisson's ratio and on the sample adhesivity. Additionally, we propose a novel method which allows the computation of the intrinsic Young's modulus of the adherent probed sample from its measured apparent elasticity modulus. Thanks to the set of computational graphs we derived from our theoretical analysis, we successfully validate this method by experiments performed on polyacrylamide gels. Interestingly, the original procedure we proposed allows a simultaneous quantification of the Young's modulus and of the Poisson's ratio of the adherent gel. Thus, our revisited analysis of MA experiments extends the application domain of this technique, while contributing to decrease the dispersion of elastic modulus values obtained by this method.     

Assessment of mechanical properties of adherent living cells by bead micromanipulation: comparison of magnetic twisting cytometry vs optical tweezers

We compare the measurements of viscoelastic properties of adherent alveolar epithelial cells by two micromanipulation techniques: (i) magnetic twisting cytometry and (ii) optical tweezers, using microbeads of same size and similarly attached to F-actin. The values of equivalent Young modulus E, derived from linear viscoelasticity theory, become consistent when the degree of bead immersion in the cell is taken into account. E-values are smaller in (i) than in (ii): approximately 34-58 Pa vs approximately 29-258 Pa, probably because higher stress in (i) reinforces nonlinearity and cellular plasticity. Otherwise, similar relaxation time constants, around 2 s, suggest similar dissipative mechanisms.     

单细胞机械性能检测方法与应用研究进展

细胞机械性能与细胞的生理状态与功能存在密切联系。早期对于细胞机械性能的研究受制于技术条件,只能获得细胞群的弹性或剪切模量,使得少量异质细胞的机械表型被淹没。近年来,单细胞机械性能检测技术得到了蓬勃发展。原子力显微镜、微吸管技术、光镊与光学拉伸、磁扭转流变仪与磁镊等单细胞机械性能检测技术展现出非常高的检测精度,但检测通量相对较低。新型微流控高通量检测方法的出现使检测通量呈几何式增长,有望解决大样本快速检测的需求。本文首先综述原子力显微镜、微吸管、光镊与光学拉伸和磁扭转流变仪与磁镊等单细胞机械性能检测技术。在此基础上,重点介绍细胞过孔、剪切诱导细胞变形和拉伸诱导细胞变形3种新兴微流控高通量检测技术的工作原理及最新研究进展,探讨各类方法的优缺点。最后,本文展望单细胞机械性能检测技术的未来发展方向。     

A Prestressed Cable Network Model of the Adherent Cell Cytoskeleton

A prestressed cable network is used to model the deformability of the adherent cell actin cytoskeleton. The overall and microstructural model geometries and cable mechanical properties were assigned values based on observations from living cells and mechanical measurements on isolated actin filaments, respectively. The models were deformed to mimic cell poking (CP), magnetic twisting cytometry (MTC) and magnetic bead microrheometry (MBM) measurements on living adherent cells. The models qualitatively and quantitatively captured the fibroblast cell response to the deformation imposed by CP while exhibiting only some qualitative features of the cell response to MTC and MBM. The model for CP revealed that the tensed peripheral actin filaments provide the key resistance to indentation. The actin filament tension that provides mechanical integrity to the network was estimated at ~158 pN, and the nonlinear mechanical response during CP originates from filament kinematics. The MTC and MBM simulations revealed that the model is incomplete, however, these simulations show cable tension as a key determinant of the model response.     

Sickle cell trait human erythrocytes are significantly stiffer than normal

Atomic force microscopy (AFM) allows for high-resolution topography studies of biological cells and measurement of their mechanical properties in physiological conditions. In this work, AFM was employed to measure the stiffness of abnormal human red blood cells from human subjects with the genotype for sickle cell trait. The determined Young's modulus was compared with that obtained from measurements of erythrocytes from healthy subjects. The results showed that Young's modulus of pathological erythrocytes was approximately three times higher than in normal cells. Observed differences indicate the effect of the polymerization of sickle hemoglobin as well as possible changes in the organization of the cell cytoskeleton associated with the sickle cell trait.     

Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study

We have used optical tweezers to study the elasticity of red cell membranes; force was applied to a bead attached to a permeabilized spherical ghost and the force-extension relation was obtained from the response of a second bead bound at a diametrically opposite position. Interruption of the skeletal network by dissociation of spectrin tetramers or extraction of the actin junctions engendered a fourfold reduction in stiffness at low applied force, but only a twofold change at larger extensions. Proteolytic scission of the ankyrin, which links the membrane skeleton to the integral membrane protein, band 3, induced a similar effect. The modified, unlike the native membranes, showed plastic relaxation under a prolonged stretch. Flaccid giant liposomes showed no measurable elasticity. Our observations indicate that the elastic character is at least as much a consequence of the attachment of spectrin as of a continuous membrane-bound network, and they offer a rationale for formation of elliptocytes in genetic conditions associated with membrane-skeletal perturbations. The theory of Parker and Winlove for elastic deformation of axisymmetric shells (accompanying paper) allows us to determine the function BH(2) for the spherical saponin-permeabilized ghost membranes (where B is the bending modulus and H the shear modulus); taking the literature value of 2 x 10(-19) Nm for B, H then emerges as 2 x 10(-6) Nm(-1). This is an order of magnitude higher than the value reported for intact cells from micropipette aspiration. Reasons for the difference are discussed.     

Mechano-coupling and regulation of contractility by the vinculin tail domain

Vinculin binds to multiple focal adhesion and cytoskeletal proteins and has been implicated in transmitting mechanical forces between the actin cytoskeleton and integrins or cadherins. It remains unclear to what extent the mechano-coupling function of vinculin also involves signaling mechanisms. We report the effect of vinculin and its head and tail domains on force transfer across cell adhesions and the generation of contractile forces. The creep modulus and the adhesion forces of F9 mouse embryonic carcinoma cells (wild-type), vinculin knock-out cells (vinculin −/−), and vinculin −/− cells expressing either the vinculin head domain, tail domain, or full-length vinculin (rescue) were measured using magnetic tweezers on fibronectin-coated super-paramagnetic beads. Forces of up to 10 nN were applied to the beads. Vinculin −/− cells and tail cells showed a slightly higher incidence of bead detachment at large forces. Compared to wild-type, cell stiffness was reduced in vinculin −/− and head cells and was restored in tail and rescue cells. In all cell lines, the cell stiffness increased by a factor of 1.3 for each doubling in force. The power-law exponent of the creep modulus was force-independent and did not differ between cell lines. Importantly, cell tractions due to contractile forces were suppressed markedly in vinculin −/− and head cells, whereas tail cells generated tractions similar to the wild-type and rescue cells. These data demonstrate that vinculin contributes to the mechanical stability under large external forces by regulating contractile stress generation. Furthermore, the regulatory function resides in the tail domain of vinculin containing the paxillin-binding site.     

Sensitivity of alveolar macrophages to substrate mechanical and adhesive properties

In order to understand the sensitivity of alveolar macrophages (AMs) to substrate properties, we have developed a new model of macrophages cultured on substrates of increasing Young's modulus: (i) a monolayer of alveolar epithelial cells representing the supple (approximately 0.1 kPa) physiological substrate, (ii) polyacrylamide gels with two concentrations of bis-acrylamide representing low and high intermediate stiffness (respectively 40 kPa and 160 kPa) and, (iii) a highly rigid surface of plastic or glass (respectively 3 MPa and 70 MPa), the two latter being or not functionalized with type I-collagen. The macrophage response was studied through their shape (characterized by 3D-reconstructions of F-actin structure) and their cytoskeletal stiffness (estimated by transient twisting of magnetic RGD-coated beads and corrected for actual bead immersion). Macrophage shape dramatically changed from rounded to flattened as substrate stiffness increased from soft ((i) and (ii)) to rigid (iii) substrates, indicating a net sensitivity of alveolar macrophages to substrate stiffness but without generating F-actin stress fibers. Macrophage stiffness was also increased by large substrate stiffness increase but this increase was not due to an increase in internal tension assessed by the negligible effect of a F-actin depolymerizing drug (cytochalasine D) on bead twisting. The mechanical sensitivity of AMs could be partly explained by an idealized numerical model describing how low cell height enhances the substrate-stiffness-dependence of the apparent (measured) AM stiffness. Altogether, these results suggest that macrophages are able to probe their physical environment but the mechanosensitive mechanism behind appears quite different from tissue cells, since it occurs at no significant cell-scale prestress, shape changes through minimal actin remodeling and finally an AMs stiffness not affected by the loss in F-actin integrity.     

原子力显微镜对人羊膜上皮细胞的观察

目的:在单细胞水平上分析人羊膜上皮细胞的超微结构及其机械性能(粘弹力、杨氏模量、硬度等),为进一步认识细胞结构与功能的关系奠定基础.方法:应用原子力显微镜(AFM)高分辨率、高灵敏度的特点,对人的羊膜上皮细胞进行观察.结果:人羊膜上皮细胞呈椭圆形,由原子力显微镜力位移曲线测量系统,可得粘弹力:1034.375±294.21 pN.硬度:1.1815±0.326mN/m,杨氏模量:16.44±4.67Kpa.结论:AFM能对人羊膜上皮细胞表面超微结构清晰地成像及提供更多更确切的表面信息及机械性能,从而增加对羊膜上皮细胞的认识.     

Colloidal force spectroscopy and cell biological investigations on biomimetic polyelectrolyte multilayer coatings composed of chondroitin sulfate and heparin

To promote osteoblast adhesion and proliferation on (bio)material surfaces, biomimetic coatings resembling the natural extracellular matrix (ECM) are desirable. The glycosamino glycans (GAGs) chondroitin sulfate (CS) and heparin (HEP) are promising candidates for a biomimetic coating since they are two of the most prevalent noncollagenous biomolecules constituting the ECM. Coatings containing CS and HEP were prepared employing the "layer by layer" technique yielding polyelectrolyte multilayers (PEMs). Physicochemical and mechanical characterization of the coatings were performed by means of streaming potential measurements and colloidal force spectroscopy. The capability of the coatings to support cell adhesion, spreading, proliferation, and maintenance of an osteoblastic phenotype was assessed with SaOS osteosarcoma cells. We demonstrate that PEMs constructed from CS as the polyanion display a low Young's modulus correlated with poorly supported cell adhesion and proliferation. When the CS was adsorbed onto a stiffer polypeptide PEM basis, the Young's modulus increased, and the cell response was significantly improved. For HEP coatings an intermediate Young's modulus and moderate cell adhesion and spreading were observed. No significant changes in stiffness or cell response were detected when HEP was adsorbed onto the polypeptide film.     

Measuring single cardiac myocyte contractile force via moving a magnetic bead

One of the biggest problems of heart failure is the heart's inability to effectively pump blood to meet the body's demands, which may be caused by disease-induced alterations in contraction properties (such as contractile force and Young's modulus). Thus, it is very important to measure contractile properties at single cardiac myocyte level that can lay the foundation for quantitatively understanding the mechanism of heart failure and understanding molecular alterations in diseased heart cells. In this article, we report a novel single cardiac myocyte contractile force measurement technique based on moving a magnetic bead. The measuring system is mainly composed of 1), a high-power inverted microscope with video output and edge detection; and 2), a moving magnetic bead based magnetic force loading module. The main measurement procedures are as follows: 1), record maximal displacement of single cardiac myocyte during contraction; 2), attach a magnetic bead on one end of the myocyte that will move with myocyte during the contraction; 3), repeat step 1 and record contraction processes under different magnitudes of magnetic force loading by adjusting the magnetic field applied on the magnetic bead; and 4), derive the myocyte contractile force base on the maximal displacement of cell contraction and magnetic loading force. The major advantages of this unique approach are: 1), measuring the force without direct connections to the cell specimen (i.e., "remote sensing", a noninvasive/minimally invasive approach); 2), high sensitivity and large dynamic range (force measurement range: from pico Newton to micro Newton); 3), a convenient and cost-effective approach; and 4), more importantly, it can be used to study the contractile properties of heart cells under different levels of external loading forces by adjusting the magnitude of applied magnetic field, which is very important for studying disease induced alterations in contraction properties. Experimental results demonstrated the feasibility of proposed approach.     

IL-1beta decreases the elastic modulus of human tenocytes.

Cellular responses to mechanical stimuli are regulated by interactions with the extracellular matrix, which, in turn, are strongly influenced by the degree of cell stiffness (Young's modulus). It was hypothesized that a more elastic cell could better withstand the rigors of remodeling and mechanical loading. It was further hypothesized that interleukin-1beta (IL-1beta) would modulate intracellular cytoskeleton polymerization and regulate cell stiffness. The purpose of this study was to investigate the utility of IL-1beta to alter the Young's modulus of human tenocytes. Young's modulus is the ratio of the stress to the strain, E = stress/strain = (F/A)/(deltaL/L0), where L0 is the equilibrium length, deltaL is the length change under the applied stress, F is the force applied, and A is the area over which the force is applied. Human tenocytes were incubated with 100 pM recombinant human IL-1beta for 5 days. The Young's modulus was reduced by 27-63%. Actin filaments were disrupted in >75% of IL-1beta-treated cells, resulting in a stellate shape. In contrast, immunostaining of alpha-tubulin showed increased intensity in IL-1beta-treated tenocytes. Human tenocytes in IL-1beta-treated bioartificial tendons were more tolerant to mechanical loading than were untreated counterparts. These results indicate that IL-1beta reduced the Young's modulus of human tenocytes by disrupting the cytoskeleton and/or downregulating the expression of actin and upregulating the expression of tubulins. The reduction in cell modulus may help cells to survive excessive mechanical loading that may occur in damaged or healing tendons.     

Measurement of cell microrheology by magnetic twisting cytometry with frequency domain demodulation.

Magnetic twisting cytometry (MTC) (Wang N, Butler JP, and Ingber DE, Science 260: 1124-1127, 1993) is a useful technique for probing cell micromechanics. The technique is based on twisting ligand-coated magnetic microbeads bound to membrane receptors and measuring the resulting bead rotation with a magnetometer. Owing to the low signal-to-noise ratio, however, the magnetic signal must be modulated, which is accomplished by spinning the sample at approximately 10 Hz. Present demodulation approaches limit the MTC range to frequencies <0.5 Hz. We propose a novel demodulation algorithm to expand the frequency range of MTC measurements to higher frequencies. The algorithm is based on coherent demodulation in the frequency domain, and its frequency range is limited only by the dynamic response of the magnetometer. Using the new algorithm, we measured the complex modulus of elasticity (G*) of cultured human bronchial epithelial cells (BEAS-2B) from 0.03 to 16 Hz. Cells were cultured in supplemented RPMI medium, and ferromagnetic beads (approximately 5 microm) coated with an RGD peptide were bound to the cell membrane. Both the storage (G', real part of G*) and loss (G", imaginary part of G*) moduli increased with frequency as omega(alpha) (2 pi x frequency) with alpha approximately equal to 1/4. The ratio G"/G' was approximately 0.5 and varied little with frequency. Thus the cells exhibited a predominantly elastic behavior with a weak power law of frequency and a nearly constant proportion of elastic vs. frictional stresses, implying that the mechanical behavior conformed to the so-called structural damping (or constant-phase) law (Maksym GN, Fabry B, Butler JP, Navajas D, Tschumperlin DJ, LaPorte JD, and Fredberg JJ, J Appl Physiol 89: 1619-1632, 2000). We conclude that frequency domain demodulation dramatically increases the frequency range that can be probed with MTC and reveals that the mechanics of these cells conforms to constant-phase behavior over a range of frequencies approaching three decades.     

Quantitative measurement of changes in adhesion force involving focal adhesion kinase during cell attachment, spread, and migration

Focal adhesion kinase (FAK) is a critical protein for the regulation of integrin-mediated cellular functions and it can enhance cell motility in Madin-Darby canine kidney (MDCK) cells by hepatocyte growth factor (HGF) induction. We utilized optical trapping and cytodetachment techniques to measure the adhesion force between pico-Newton and nano-Newton (nN) for quantitatively investigating the effects of FAK on adhesion force during initial binding (5 s), beginning of spreading (30 min), spreadout (12 h), and migration (induced by HGF) in MDCK cells with overexpressed FAK (FAK-WT), FAK-related non-kinase (FRNK), as well as normal control cells. Optical tweezers was used to measure the initial binding force between a trapped cell and glass coverslide or between a trapped bead and a seeded cell. In cytodetachment, the commercial atomic force microscope probe with an appropriate spring constant was used as a cyto-detacher to evaluate the change of adhesion force between different FAK expression levels of cells in spreading, spreadout, and migrating status. The results demonstrated that FAK-WT significantly increased the adhesion forces as compared to FRNK cells throughout all the different stages of cell adhesion. For cells in HGF-induced migration, the adhesion force decreased to almost the same level (approximately 600 nN) regardless of FAK levels indicating that FAK facilitates cells to undergo migration by reducing the adhesion force. Our results suggest FAK plays a role of enhancing cell adhesive ability in the binding and spreading, but an appropriate level of adhesion force is required for HGF-induced cell migration.     

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer.

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G'(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G'(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.     

An AFM study on mechanical properties of native and dimethyl suberimidate cross-linked pericardium tissue

Changes in the stiffness of hog pericardium tissue, native and treated with dimethyl suberimidate (DMS), are investigated by atomic force microscopy (AFM). Young's modulus is calculated on the basis of the Hertz-Sneddon model. The cross-linking process increases the stiffness of the tissue. The values of Young's modulus are higher for the DMS stabilized pericardium than for the native one. We also observe that the Young's modulus of native tissue increases when the time between getting the biological material and performing the measurements is longer. This process is probably connected with natural degradation of the biological samples.     

Magnetic Tweezers for the Measurement of Twist and Torque

Single-molecule techniques make it possible to investigate the behavior of individual biological molecules in solution in real time. These techniques include so-called force spectroscopy approaches such as atomic force microscopy, optical tweezers, flow stretching, and magnetic tweezers. Amongst these approaches, magnetic tweezers have distinguished themselves by their ability to apply torque while maintaining a constant stretching force. Here, it is illustrated how such a “conventional” magnetic tweezers experimental configuration can, through a straightforward modification of its field configuration to minimize the magnitude of the transverse field, be adapted to measure the degree of twist in a biological molecule. The resulting configuration is termed the freely-orbiting magnetic tweezers. Additionally, it is shown how further modification of the field configuration can yield a transverse field with a magnitude intermediate between that of the “conventional” magnetic tweezers and the freely-orbiting magnetic tweezers, which makes it possible to directly measure the torque stored in a biological molecule. This configuration is termed the magnetic torque tweezers. The accompanying video explains in detail how the conversion of conventional magnetic tweezers into freely-orbiting magnetic tweezers and magnetic torque tweezers can be accomplished, and demonstrates the use of these techniques. These adaptations maintain all the strengths of conventional magnetic tweezers while greatly expanding the versatility of this powerful instrument.     

The Elastic Properties of the Cryptococcus neoformans Capsule

Microbial capsules are important for virulence, but their architecture and physical properties are poorly understood. The human pathogenic fungus Cryptococcus neoformans has a large polysaccharide capsule that is necessary for virulence and is the target of protective antibody responses. To study the C. neoformans capsule we developed what we believe is a new approach whereby we probed the capsular elastic properties by applying forces using polystyrene beads manipulated with optical tweezers. This method allowed us to determine the Young's modulus for the capsule in various conditions that affect capsule growth. The results indicate that the Young's modulus of the capsule decreases with its size and increases with the Ca²⁺ concentration in solution. Also, capsular polysaccharide manifests an unexpected affinity for polystyrene beads, a property that may function in attachment to host cells and environmental structures. Bead probing with optical tweezers provides a new, nondestructive method that may have wide applicability for studying the effects of growth conditions, immune components, and drugs on capsular properties.     

Constitutive material modeling of cell: a micromechanics approach

The variations in mechanical properties of cells obtained from experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work. The proposed model is developed using the Mori-Tanaka method of homogenization by treating the cell as a fiber-reinforced composite medium satisfying the continuum hypothesis. The validation of the constitutive model using finite element analysis on atomic force microscopy (AFM) and magnetic twisting cytometry (MTC) has been carried out and is found to yield good correlation with reported experimental results. It is observed from the study that as the volume fraction of the stress fiber increases, the stiffness of the cell increases and it alters the force displacement behavior for the AFM and MTC experiments. Through this model, we have also been able to find the stress fiber as a likely cause of the differences in the derived mechanical property from the AFM and MTC experiments. The correlation of the mechanical behavior of the cell with the cell composition, as obtained through this study, is an important observation in cell mechanics.