Novel dynamic rheological behavior of individual focal adhesions measured within single cells using electromagnetic pulling cytometry

Magnetic tweezers with magnetic flux density feedback control

In this work, we present a single-pole magnetic tweezers (MT) device designed for integration with substrate deformation tracking microscopy and/or traction force microscopy experiments intended to explore extracellular matrix rheology and human epidermal keratinocyte mechanobiology. Assembled from commercially available off-the-shelf electronics hardware and software, the MT device is amenable to replication in the basic biology laboratory. In contrast to conventional solenoid current-controlled MT devices, operation of this instrument is based on real-time feedback control of the magnetic flux density emanating from the blunt end of the needle core using a cascade control scheme and a digital proportional-integral-derivative (PID) controller. Algorithms that compensate for a spatially non-uniform remnant magnetization of the needle core that develops during actuation are implemented into the feedback control scheme. Through optimization of PID gain scheduling, the MT device exhibits magnetization and demagnetization response times of less than 100 ms without overshoot over a wide range of magnetic flux density setpoints. Compared to current-based control, magnetic flux density-based control allows for more accurate and precise magnetic actuation forces by compensating for temperature increases within the needle core due to heat generated by the applied solenoid currents. Near field calibrations validate the ability of the MT device to actuate 4.5 μm-diameter superparamagnetic beads with forces up to 25 nN with maximum relative uncertainties of ±30% for beads positioned between 2.5 and 40 µm from the needle tip.

Complex modulus and compliance for airway smooth muscle cells

A cell can be described as a complex viscoelastic material with structural relaxations that is modulated by thermal and chemically nonequilibrium processes. Tissue morphology and function rely upon cells' physical responses to mechanical force. We measured the frequency-dependent mechanical relaxation response of adherent human airway smooth muscle cells under adenosine triphosphate (ATP) depletion and normal ATP conditions. The frequency dependence of the complex compliance J^{*} and modulus G^{*} was measured over the frequencies 10^{-1}<f<10^{3} Hz at selected temperatures between 4<T<54^{∘}C. Our results show characteristic relaxation features which can be interpreted by the mode-coupling theory (MCT) of viscoelastic liquids. We analyze the shape of the spectra in terms of a so-called A_{4} scenario with logarithmic scaling laws. Characteristic timescales τ_{β} and τ_{α} appear with corresponding energy barriers E_{β}≈(10-20)k_{B}T and E_{α}≈(20-30)k_{B}T. We demonstrate that cells are close to a glass transition. We find that the cell becomes softer around physiological temperatures, where its surface structure is more liquid-like with a plateau modulus around 0.1-0.8 kPa compared with the more solid-like interior cytoskeletal structures with a plateau modulus 1-15 kPa. Corresponding values for the viscosity are 10^{2}-10^{3} Pa s for the surface structures closer to the membrane and 10^{4}-10^{6} Pa s for the core cytoskeletal structures.

Measurement of mechanical properties of naked cell membranes using atomic force microscope puncture test

Cell membrane defines the physical boundary of the cell, maintains their shape and volume, and meanwhile dominates the cells response to mechanical force. There are many limitations in the mechanical analysis of naked cell membrane, such as cell condition, the supporting of cytoskeleton and cytoplasm. To reduce these influences, non-supported membrane was prepared on high-ordered pore array silicon substrate. Rupture forces and Young's modulus of three non-supported membranes, red blood cell membrane, somatic cell (MDCK) membrane and phospholipids membrane, are obtained quantitatively using AFM puncture tests. Results indicate that the sequence of both rupture forces and Young's modulus of the three membranes is MDCK cell membrane > red blood cell membrane > phospholipids membrane. The determinant of naked cell membrane's mechanical properties is the constituent of membrane itself, including the quantity and distribution of membrane proteins. Focused on the distribution of membrane proteins, two proposed models of cell membrane-the semi-mosaic model of red blood cell membrane and the Protein Layer-Lipid-Protein Island (PLLPI) model of nucleated mammalian cell membrane can be used to explain the different mechanical properties of naked cell membranes.

Short-term effects of X-ray on viscoelastic properties of epithelial cells

Examining the effects of ionizing radiation on the living cell is significant due to its usage in recent centuries. Investigations into the long- and short-term effects of ionizing radiation began simultaneously with its discovery. Previous studies were done on the effects of radiation on cell DNA or the biochemical cycle based on the electromagnetic radiation wavelength, intensity, and exposure time. Considering some dependent parameters like cell communication, the differentiation and the mechanical interactions of intercellular environment, and cell mechanical properties, the effects of ionizing radiation on the viscoelastic properties of cells seem to be important. The current research investigated the short-term biomechanical effects of ionizing radiation and examined the mechanical properties of cells using magnetic tweezer cytometry with nanomagnetic particles. To evaluate these effects, cells were incubated with nanomagnetic particles and then separated into controlled and irradiated groups. A 3 mGy cm2 X-ray was radiated to the irradiated group for 0.02 s. The dishes of both groups were inserted into magnetic tweezer cytometry for applying a magnetic force pulse, and the cell membrane displacement was detected by an image processing system. The creep response of the membrane was determined for viscoelastic model curve fitting. The frequency responses of the model for both groups were calculated. The results showed that radiation could decrease cell extensibility from 0.084 ± 0.001 to 0.019 ± 0.001 µm and change the storage and loss modulus as the indicator of the viscoelastic property of the material. This research explains that radiation could affect cellular mechanical properties.

In situ determination of exerted forces in magnetic pulling cytometry

Localized application of exogenous forces on soft biomaterials and cells is often essential for the study of their response to external mechanical stimuli. Magnetic means of applying forces, particularly those based on permanent magnets and magnetic beads coupled to substrates or cells provide an accessible means of exerting forces of appropriate magnitude. The amount of force exerted, however, is often inferred from calibration performed ex situ, with typically similar but different magnetic beads. Here, we construct a simple magnetic tweezer by coupling a pencil-shaped stainless-steel probe to permanent neodymium magnets using a 3D printed adapter. We then demonstrate the in situ determination of magnetic bead pulling forces on a super-paramagnetic micro-bead coupled to a soft substrate using traction force microscopy. We determine the force exerted on the magnetic bead by the magnet probe - and thus exerted by the magnetic bead on the soft polyacrylamide substrate - as a function of the distance between the probe tip and the magnetic bead. We also show that we can determine the force exerted on a magnetic bead coupled to a cell by the changes in the traction force exerted by the cell on the soft substrate beneath. We thus demonstrate that forces of nanonewton magnitude can be locally exerted on soft substrates or cells and simultaneously determined using traction force microscopy. Application of this method for the in situ measurement of localized exogenous forces exerted on cells can also enable dissection of cellular force transmission pathways.

Magnetic field application or mechanical stimulation via magnetic microparticles does not enhance chondrogenesis in mesenchymal stem cell sheets

Using a novel magnetic field bioreactor, this work evaluated the chondrogenesis of scaffold-free human mesenchymal stem cell sheets in response to static and variable magnetic fields, as well as mechanical stimulation via 4.4 μm magnetic particles. Neither static nor variable magnetic fields generated by 1.44-1.45 T permanent magnets affected cartilage formation. Notably, magnetic field-induced mechanical stimulation by magnetic particles, which applied forces to the cells and ECM statically (4.39 pN) or cyclically (1.06-63.6 pN; 16.7 mHz), also did not affect cartilage formation.

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.

Biophysical Tools to Study Cellular Mechanotransduction

The cell membrane is the interface that volumetrically isolates cellular components from the cell's environment. Proteins embedded within and on the membrane have varied biological functions: reception of external biochemical signals, as membrane channels, amplification and regulation of chemical signals through secondary messenger molecules, controlled exocytosis, endocytosis, phagocytosis, organized recruitment and sequestration of cytosolic complex proteins, cell division processes, organization of the cytoskeleton and more. The membrane's bioelectrical role is enabled by the physiologically controlled release and accumulation of electrochemical potential modulating molecules across the membrane through specialized ion channels (e.g., Na⁺, Ca2+, K⁺ channels). The membrane's biomechanical functions include sensing external forces and/or the rigidity of the external environment through force transmission, specific conformational changes and/or signaling through mechanoreceptors (e.g., platelet endothelial cell adhesion molecule (PECAM), vascular endothelial (VE)-cadherin, epithelial (E)-cadherin, integrin) embedded in the membrane. Certain mechanical stimulations through specific receptor complexes induce electrical and/or chemical impulses in cells and propagate across cells and tissues. These biomechanical sensory and biochemical responses have profound implications in normal physiology and disease. Here, we discuss the tools that facilitate the understanding of mechanosensitive adhesion receptors. This article is structured to provide a broad biochemical and mechanobiology background to introduce a freshman mechano-biologist to the field of mechanotransduction, with deeper study enabled by many of the references cited herein.

Single cell metastatic phenotyping using pulsed nanomechanical indentations

The existing approach to characterize cell biomechanical properties typically utilizes switch-like models of mechanotransduction in which cell responses are analyzed in response to a single nanomechanical indentation or a transient pulsed stress. Although this approach provides effective descriptors at population-level, at a single-cell-level, there are significant overlaps in the biomechanical descriptors of non-metastatic and metastatic cells which precludes the use of biomechanical markers for single cell metastatic phenotyping. This study presents a new promising marker for biosensing metastatic and non-metastatic cells at a single-cell-level using the effects of a dynamic microenvironment on the biomechanical properties of cells. Two non-metastatic and two metastatic epithelial breast cell lines are subjected to a pulsed stresses regimen exerted by atomic force microscopy. The force-time data obtained for the cells revealed that the non-metastatic cells increase their resistance against deformation and become more stiffened when subjected to a series of nanomechanical indentations. On the other hand, metastatic cells become slightly softened when their mechanical microenvironment is subjected to a similar dynamical changes. This distinct behavior of the non-metastatic and metastatic cells to the pulsed stresses paradigm provided a signature for single-cell-level metastatic phenotyping with a high confidence level of ∼95%.

Creased hydrogels as active platforms for mechanical deformation of cultured cells

Cells cultured in vitro using traditional substrates often change their behavior due to the lack of mechanical deformation they would naturally experience in vivo. To mimic the in vivo mechanical environment, we design temperature-responsive hydrogels with patterned surface creases as dynamic cell stretching devices. A one-step photolithographic method is first employed to pattern integrin-binding peptides on the gel, causing single cells or several-cell clusters to adhere to the surface in registry with creases. A variety of crease patterns are prescribed on a single substrate, enabling the mechanical deformation of cultured myoblast cells with different strain states and achieving tensile strain as high as 0.2. As creases provide large amplitude local deformation of the gel surface without the need for macroscopic deformation, can be formed on gels covering a wide range of modulus, and can be actuated using a variety of stimuli, they hold the potential to enable the design of high throughput and versatile platforms for mechano-biological studies.

Biomechanics of Schlemm's canal endothelium and intraocular pressure reduction

Ocular hypertension in glaucoma develops due to age-related cellular dysfunction in the conventional outflow tract, resulting in increased resistance to aqueous humor outflow. Two cell types, trabecular meshwork (TM) and Schlemm's canal (SC) endothelia, interact in the juxtacanalicular tissue (JCT) region of the conventional outflow tract to regulate outflow resistance. Unlike endothelial cells lining the systemic vasculature, endothelial cells lining the inner wall of SC support a transcellular pressure gradient in the basal to apical direction, thus acting to push the cells off their basal lamina. The resulting biomechanical strain in SC cells is quite large and is likely to be an important determinant of endothelial barrier function, outflow resistance and intraocular pressure. This review summarizes recent work demonstrating how biomechanical properties of SC cells impact glaucoma. SC cells are highly contractile, and such contraction greatly increases cell stiffness. Elevated cell stiffness in glaucoma may reduce the strain experienced by SC cells, decrease the propensity of SC cells to form pores, and thus impair the egress of aqueous humor from the eye. Furthermore, SC cells are sensitive to the stiffness of their local mechanical microenvironment, altering their own cell stiffness and modulating gene expression in response. Significantly, glaucomatous SC cells appear to be hyper-responsive to substrate stiffness. Thus, evidence suggests that targeting the material properties of SC cells will have therapeutic benefits for lowering intraocular pressure in glaucoma.

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

Among individual cells of the same source and type, the complex shear modulus G(∗) exhibits a large log-normal distribution that is the result of spatial, temporal, and intrinsic variations. Such large distributions complicate the statistical evaluation of pharmacological treatments and the comparison of different cell states. However, little is known about the characteristic features of cell-to-cell variation. In this study, we investigated how this variation depends on the spatial location within the cell and on the actin filament cytoskeleton, the organization of which strongly influences cell mechanics. By mechanically probing fibroblasts arranged on a microarray, via atomic force microscopy, we observed that the standard deviation σ of G(∗) was significantly reduced among cells in which actin filaments were depolymerized. The parameter σ also exhibited a subcellular spatial dependence. Based on our findings regarding the frequency dependence of σ of the storage modulus G('), we proposed two types of cell-to-cell variation in G(') that arise from the purely elastic and the frequency-dependent components in terms of the soft glassy rheology model of cell deformability. We concluded that the latter inherent cell-to-cell variation can be reduced greatly by disrupting actin networks, by probing at locations within the cell nucleus boundaries distant from the cell center, and by measuring at high loading frequencies.

Rare cell isolation and analysis in microfluidics

Rare cells are low-abundance cells in a much larger population of background cells. Conventional benchtop techniques have limited capabilities to isolate and analyze rare cells because of their generally low selectivity and significant sample loss. Recent rapid advances in microfluidics have been providing robust solutions to the challenges in the isolation and analysis of rare cells. In addition to the apparent performance enhancements resulting in higher efficiencies and sensitivity levels, microfluidics provides other advanced features such as simpler handling of small sample volumes and multiplexing capabilities for high-throughput processing. All of these advantages make microfluidics an excellent platform to deal with the transport, isolation, and analysis of rare cells. Various cellular biomarkers, including physical properties, dielectric properties, as well as immunoaffinities, have been explored for isolating rare cells. In this Focus article, we discuss the design considerations of representative microfluidic devices for rare cell isolation and analysis. Examples from recently published works are discussed to highlight the advantages and limitations of the different techniques. Various applications of these techniques are then introduced. Finally, a perspective on the development trends and promising research directions in this field are proposed.

Mechanical control of morphogenesis at the shoot apex

Morphogenesis does not just require the correct expression of patterning genes; these genes must induce the precise mechanical changes necessary to produce a new form. Mechanical characterization of plant growth is not new; however, in recent years, new technologies and interdisciplinary collaborations have made it feasible in young tissues such as the shoot apex. Analysis of tissues where active growth and developmental patterning are taking place has revealed biologically significant variability in mechanical properties and has even suggested that mechanical changes in the tissue can feed back to direct morphogenesis. Here, an overview is given of the current understanding of the mechanical dynamics and its influence on cellular and developmental processes in the shoot apex. We are only starting to uncover the mechanical basis of morphogenesis, and many exciting questions remain to be answered.

Multicellular aggregates: a model system for tissue rheology

Morphogenetic processes involve cell flows. The mechanical response of a tissue to active forces is linked to its effective viscosity. In order to decouple this mechanical response from the complex genetic changes occurring in a developing organism, we perform rheometry experiments on multicellular aggregates, which are good models for tissues. We observe a cell softening behavior when submitting to stresses. As our technique is very sensitive, we were able to get access to the measurement of a yield point above which a creep regime is observed obtained for strains above 12%. To explain our rheological curves we propose a model for the cytoskeleton that we represent as a dynamic network of parallel springs, which will break under stress and reattach at null strain. Such a simple model is able to reproduce most of the important behavior of cells under strain. We highlight here the importance of considering cells as complex fluids whose properties will vary with time according to the history of applied stress.

Magnetic nanoparticles as mediators of ligand-free activation of EGFR signaling

BACKGROUND

Magnetic nanoparticles (NPs) are of particular interest in biomedical research, and have been exploited for molecular separation, gene/drug delivery, magnetic resonance imaging, and hyperthermic cancer therapy. In the case of cultured cells, magnetic manipulation of NPs provides the means for studying processes induced by mechanotransduction or by local clustering of targeted macromolecules, e.g. cell surface receptors. The latter are normally activated by binding of their natural ligands mediating key signaling pathways such as those associated with the epidermal growth factor (EGFR). However, it has been reported that EGFR may be dimerized and activated even in the absence of ligands. The present study assessed whether receptor clustering induced by physical means alone suffices for activating EGFR in quiescent cells.

METHODOLOGY/PRINCIPAL FINDINGS

The EGFR on A431 cells was specifically targeted by superparamagnetic iron oxide NPs (SPIONs) carrying either a ligand-blocking monoclonal anti-EGFR antibody or a streptavidin molecule for targeting a chimeric EGFR incorporating a biotinylated amino-terminal acyl carrier peptide moiety. Application of a magnetic field led to SPION magnetization and clustering, resulting in activation of the EGFR, a process manifested by auto and transphosphorylation and downstream signaling. The magnetically-induced early signaling events were similar to those inherent to the ligand dependent EGFR pathways. Magnetization studies indicated that the NPs exerted magnetic dipolar forces in the sub-piconewton range with clustering dependent on Brownian motion of the receptor-SPION complex and magnetic field strength.

CONCLUSIONS/SIGNIFICANCE

We demonstrate that EGFR on the cell surface that have their ligand binding-pocket blocked by an antibody are still capable of transphosphorylation and initiation of signaling cascades if they are clustered by SPIONs either attached locally or targeted to another site of the receptor ectodomain. The results suggest that activation of growth factor receptors may be triggered by ligand-independent molecular crowding resulting from overexpression and/or sequestration in membrane microdomains.

Stress transmission within the cell

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. During past decades, it has become evident that the deformable cytoskeleton (CSK), an intracellular network of various filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical responses. To understand how mechanical forces regulate cellular functions, it is necessary to first understand how the CSK develops mechanical stresses in response to applied forces, and how those stresses are propagated through the CSK where various signaling molecules are immobilized. New experimental techniques have been developed to quantify cytoskeletal mechanics, which together with new computational approaches have given rise to new theories and models for describing mechanics of living cells. In this article, we discuss current understanding of cell biomechanics by focusing on the biophysical mechanisms that are responsible for the development and transmission of mechanical stresses in the cell and their effect on cellular functions. We compare and contrast various theories and models of cytoskeletal mechanics, emphasizing common mechanisms that those theories are built upon, while not ignoring irreconcilable differences. We highlight most recent advances in the understanding of mechanotransduction in the cytoplasm of living cells and the central role of the cytoskeletal prestress in propagating mechanical forces along the cytoskeletal filaments to activate cytoplasmic enzymes. It is anticipated that advances in cell mechanics will help developing novel therapeutics to treat pulmonary diseases like asthma, pulmonary fibrosis, and chronic obstructive pulmonary disease.

Cross-link-governed dynamics of biopolymer networks

Recent experiments show that networks of stiff biopolymers cross-linked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by cross-links in such networks. We show that a single microscopic time scale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times and a shear modulus G ∼ ω(1/2) for low frequencies ω. This model quantitatively describes the measured rheology of actin networks cross-linked with α-actinin-4 over more than four decades in frequency.

Ultra-rapid activation of TRPV4 ion channels by mechanical forces applied to cell surface beta1 integrins

Integrins are ubiquitous transmembrane mechanoreceptors that elicit changes in intracellular biochemistry in response to mechanical force application, but these alterations generally proceed over seconds to minutes. Stress-sensitive ion channels represent another class of mechanoreceptors that are activated much more rapidly (within msec), and recent findings suggest that calcium influx through Transient Receptor Potential Vanilloid-4 (TRPV4) channels expressed in the plasma membrane of bovine capillary endothelial cells is required for mechanical strain-induced changes in focal adhesion assembly, cell orientation and directional migration. However, whether mechanically stretching a cell's extracellular matrix (ECM) adhesions might directly activate cell surface ion channels remains unknown. Here we show that forces applied to beta1 integrins result in ultra-rapid (within 4 msec) activation of calcium influx through TRPV4 channels. The TRPV4 channels were specifically activated by mechanical strain in the cytoskeletal backbone of the focal adhesion, and not by deformation of the lipid bilayer or submembranous cortical cytoskeleton alone. This early-immediate calcium signaling response required the distal region of the beta1 integrin cytoplasmic tail that contains a binding site for the integrin-associated transmembrane CD98 protein, and external force application to CD98 within focal adhesions activated the same ultra-rapid calcium signaling response. Local direct strain-dependent activation of TRPV4 channels mediated by force transfer from integrins and CD98 may therefore enable compartmentalization of calcium signaling within focal adhesions that is critical for mechanical control of many cell behaviors that underlie cell and tissue development.

Young's modulus of elasticity of Schlemm's canal endothelial cells

Schlemm's canal (SC) endothelial cells are likely important in the physiology and pathophysiology of the aqueous drainage system of the eye, particularly in glaucoma. The mechanical stiffness of these cells determines, in part, the extent to which they can support a pressure gradient and thus can be used to place limits on the flow resistance that this layer can generate in the eye. However, little is known about the biomechanical properties of SC endothelial cells. Our goal in this study was to estimate the effective Young's modulus of elasticity of normal SC cells. To do so, we combined magnetic pulling cytometry of isolated cultured human SC cells with finite element modeling of the mechanical response of the cell to traction forces applied by adherent beads. Preliminary work showed that the immersion angles of beads attached to the SC cells had a major influence on bead response; therefore, we also measured bead immersion angle by confocal microscopy, using an empirical technique to correct for axial distortion of the confocal images. Our results showed that the upper bound for the effective Young's modulus of elasticity of the cultured SC cells examined in this study, in central, non-nuclear regions, ranged between 1,007 and 3,053 Pa, which is similar to, although somewhat larger than values that have been measured for other endothelial cell types. We compared these values to estimates of the modulus of primate SC cells in vivo, based on images of these cells under pressure loading, and found good agreement at low intraocular pressure (8-15 mm Hg). However, increasing intraocular pressure (22-30 mm Hg) appeared to cause a significant increase in the modulus of these cells. These moduli can be used to estimate the extent to which SC cells deform in response to the pressure drop across the inner wall endothelium and thereby estimate the extent to which they can generate outflow resistance.

Mechanical Stability Determines Stress Fiber and Focal Adhesion Orientation

It is well documented in a variety of adherent cell types that in response to anisotropic signals from the microenvironment cells alter their cytoskeletal organization. Previous theoretical studies of these phenomena were focused primarily on the elasticity of cytoskeletal actin stress fibers (SFs) and of the substrate while the contribution of focal adhesions (FAs) through which the cytoskeleton is linked to the external environment has not been considered. Here we propose a mathematical model comprised of a single linearly elastic SF and two identical linearly elastic FAs of a finite size at the endpoints of the SF to investigate cytoskeletal realignment in response to uniaxial stretching of the substrate. The model also includes the contribution of the chemical potential energies of the SF and the FAs to the total potential energy of the SF-FA assembly. Using the global (Maxwell's) stability criterion, we predict stable configurations of the SF-FA assembly in response to substrate stretching. Model predictions obtained for physiologically feasible values of model parameters are consistent with experimental data from the literature. The model shows that elasticity of SFs alone can not predict their realignment during substrate stretching and that geometrical and elastic properties of SFs and FAs need to be included.

Power-law creep behavior of a semiflexible chain

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Tensegrity-based mechanosensing from macro to micro

This article is a summary of a lecture on cellular mechanotransduction that was presented at a symposium on "Cardiac Mechano-Electric Feedback and Arrhythmias" that convened at Oxford, England in April 2007. Although critical mechanosensitive molecules and cellular components, such as integrins, stretch-activated ion channels, and cytoskeletal filaments, have been shown to contribute to the response by which cells convert mechanical signals into a biochemical response, little is known about how they function in the structural context of living cells, tissues and organs to produce orchestrated changes in cell behavior in response to stress. Here, studies are reviewed that suggest our bodies use structural hierarchies (systems within systems) composed of interconnected extracellular matrix and cytoskeletal networks that span from the macroscale to the nanoscale to focus stresses on specific mechanotransducer molecules. A key feature of these networks is that they are in a state of isometric tension (i.e., experience a tensile prestress), which ensures that various molecular-scale mechanochemical transduction mechanisms proceed simultaneously and produce a concerted response. These features of living architecture are the same principles that govern tensegrity (tensional integrity) architecture, and mathematical models based on tensegrity are beginning to provide new and useful descriptions of living materials, including mammalian cells. This article reviews how the use of tensegrity at multiple size scales in our bodies guides mechanical force transfer from the macro to the micro, as well as how it facilitates conversion of mechanical signals into changes in ion flux, molecular binding kinetics, signal transduction, gene transcription, cell fate switching and developmental patterning.

Nanomagnetic actuation of receptor-mediated signal transduction

Complex cell behaviours are triggered by chemical ligands that bind to membrane receptors and alter intracellular signal transduction. However, future biosensors, medical devices and other microtechnologies that incorporate living cells as system components will require actuation mechanisms that are much more rapid, robust, non-invasive and easily integrated with solid-state interfaces. Here we describe a magnetic nanotechnology that activates a biochemical signalling mechanism normally switched on by binding of multivalent chemical ligands. Superparamagnetic 30-nm beads, coated with monovalent ligands and bound to transmembrane receptors, magnetize when exposed to magnetic fields, and aggregate owing to bead-bead attraction in the plane of the membrane. Associated clustering of the bound receptors acts as a nanomagnetic cellular switch that directly transduces magnetic inputs into physiological cellular outputs, with rapid system responsiveness and non-invasive dynamic control. This technique may represent a new actuator mechanism for cell-based microtechnologies and man-machine interfaces.

High-force magnetic tweezers with force feedback for biological applications

Magnetic micromanipulation using magnetic tweezers is a versatile biophysical technique and has been used for single-molecule unfolding, rheology measurements, and studies of force-regulated processes in living cells. This article describes an inexpensive magnetic tweezer setup for the application of precisely controlled forces up to 100 nN onto 5 microm magnetic beads. High precision of the force is achieved by a parametric force calibration method together with a real-time control of the magnetic tweezer position and current. High forces are achieved by bead-magnet distances of only a few micrometers. Applying such high forces can be used to characterize the local viscoelasticity of soft materials in the nonlinear regime, or to study force-regulated processes and mechanochemical signal transduction in living cells. The setup can be easily adapted to any inverted microscope.

Out-of-equilibrium dynamics in the cytoskeleton of the living cell

We report here measurements of rheological properties of the human airway smooth muscle cell using forced nanoscale motions of Arg-Gly-Asp RGD-coated microbeads tightly bound to the cytoskeleton. With changes of forcing amplitude, the storage modulus showed small but systematic nonlinearities, especially after treatment with a contractile agonist. In a dose-dependent manner, a large oscillatory shear applied from a few seconds up to 400 s caused the cytoskeleton matrix to soften, a behavior comparable to physical rejuvenation observed in certain inert soft materials; the stiffness remained constant for as long as the large oscillatory shear was maintained, but suddenly fell with shear cessation. Stiffness then followed a slow scale-free recovery, a phenomenon comparable to physical aging. However, acetylated low-density lipoprotein acLDL-coated microbeads, which connect mainly to scavenger receptors, did not show similar out-of-equilibrium behaviors. Taken together, these data demonstrate in the cytoskeleton of the living cell behaviors with all the same signatures as that of soft inert condensed systems. This unexpected intersection of condensed matter physics and cytoskeletal biology suggests that trapping, intermittency, and approach to kinetic arrest represent central mesoscale features linking underlying molecular events to integrative cellular functions.

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.

Tools to study cell mechanics and mechanotransduction

Analysis of how cells sense and respond to mechanical stress has been limited by the availability of techniques that can apply controlled mechanical forces to living cells while simultaneously measuring changes in cell and molecular distortion, as well as alterations of intracellular biochemistry. We have confronted this challenge by developing new engineering methods to measure and manipulate the mechanical properties of cells and their internal cytoskeletal and nuclear frameworks, and by combining them with molecular cell biological techniques that rely on microscopic analysis and real-time optical readouts of biochemical signaling. In this chapter, we describe techniques like microcontact printing, magnetic twisting cytometry, and magnetic pulling cytometry that can be systematically used to study the molecular basis of cellular mechanotransduction.

Rheological behavior of living cells is timescale-dependent

The dynamic mechanical behavior of living cells has been proposed to result from timescale-invariant processes governed by the soft glass rheology theory derived from soft matter physics. But this theory is based on experimental measurements over timescales that are shorter than those most relevant for cell growth and function. Here we report results measured over a wider range of timescales which demonstrate that rheological behaviors of living cells are not timescale-invariant. These findings demonstrate that although soft glass rheology appears to accurately predict certain cell mechanical behaviors, it is not a unified model of cell rheology under biologically relevant conditions and thus, alternative mechanisms need to be considered.

Directional memory and caged dynamics in cytoskeletal remodelling

We report directional memory of spontaneous nanoscale displacements of an individual bead firmly anchored to the cytoskeleton of a living cell. A novel method of analysis shows that for shorter time intervals cytoskeletal displacements are antipersistent and thus provides direct evidence in a living cell of molecular trapping and caged dynamics. At longer time intervals displacements are persistent. The transition from antipersistence to persistence is indicative of a time-scale for cage rearrangements and is found to depend upon energy release due to ATP hydrolysis and proximity to a glass transition. Anomalous diffusion is known to imply memory, but we show here that memory is attributed to direction rather than step size. As such, these data are the first to provide a molecular-scale physical picture describing the cytoskeletal remodelling process and its rate of progression.

Nanostructured magnetizable materials that switch cells between life and death

Development of biochips containing living cells for biodetection, drug screening and tissue engineering applications is limited by a lack of reconfigurable material interfaces and actuators. Here we describe a new class of nanostructured magnetizable materials created with a femtosecond laser surface etching technique that function as multiplexed magnetic field gradient concentrators. When combined with magnetic microbeads coated with cell adhesion ligands, these materials form microarrays of 'virtual' adhesive islands that can support cell attachment, resist cell traction forces and maintain cell viability. A cell death (apoptosis) response can then be actuated on command by removing the applied magnetic field, thereby causing cell retraction, rounding and detachment. This simple technology may be used to create reconfigurable interfaces that allow users to selectively discard contaminated or exhausted cellular sensor elements, and to replace them with new living cellular components for continued operation in future biomedical microdevices and biodetectors.

Cellular adaptation to mechanical stress: role of integrins, Rho, cytoskeletal tension and mechanosensitive ion channels

To understand how cells sense and adapt to mechanical stress, we applied tensional forces to magnetic microbeads bound to cell-surface integrin receptors and measured changes in bead displacement with sub-micrometer resolution using optical microscopy. Cells exhibited four types of mechanical responses: (1) an immediate viscoelastic response; (2) early adaptive behavior characterized by pulse-to-pulse attenuation in response to oscillatory forces; (3) later adaptive cell stiffening with sustained (>15 second) static stresses; and (4) a large-scale repositioning response with prolonged (>1 minute) stress. Importantly, these adaptation responses differed biochemically. The immediate and early responses were affected by chemically dissipating cytoskeletal prestress (isometric tension), whereas the later adaptive response was not. The repositioning response was prevented by inhibiting tension through interference with Rho signaling, similar to the case of the immediate and early responses, but it was also prevented by blocking mechanosensitive ion channels or by inhibiting Src tyrosine kinases. All adaptive responses were suppressed by cooling cells to 4 degrees C to slow biochemical remodeling. Thus, cells use multiple mechanisms to sense and respond to static and dynamic changes in the level of mechanical stress applied to integrins.