Deformation and nano-rheology of red blood cells: an AFM investigation

Interaction forces, deformation and nano-rheology of individual red blood cells in physiologically relevant solution conditions have been determined by colloid probe atomic force microscopy (AFM). On approach of the physically immobilised cell and silica glass spherical probe surfaces, deformation of the red blood cell was observed in the force curves. At low levels of deformation, spring constants were determined in the range 3-6 m Nm(-1), whereas for higher levels of deformation, the forces increase non-linearly and on retraction, significant force curve hysteresis is observed (i.e. lower forces upon retraction). The extent of force curve hysteresis was dependent on both the drive velocity and loading force, typical of a viscoelastic system. The response of the red blood cell has been described by viscoelastic theory, where the short and long time scale elastic moduli and relaxation times are determined, i.e. the cell's nano-rheological properties elucidated. In addition to a time independent elastic modulus of 4.0 x 10(3)Nm(-2) at low levels of deformation, time-dependent elastic moduli ranges are observed (3.5 x 10(4) to 5.5 x 10(4)Nm(-2) at intermediate levels of deformation and 1.5 x 10(5) to 3.0 x 10(5)Nm(-2) at higher levels of deformation). That is, one elastic and more than one viscoelastic response to the red blood cell deformation is evident, which is considered to reflect the cellular structure.     

Chains are more flexible under tension

The mechanical response of networks, gels, and brush layers is a manifestation of the elastic properties of the individual macromolecules. Furthermore, the elastic response of macromolecules to an applied force is the foundation of the single-molecule force spectroscopy techniques. The two main classes of models describing chain elasticity include the worm-like and freely-jointed chain models. The selection between these two classes of models is based on the assumptions about chain flexibility. In many experimental situations the choice is not clear and a model describing the crossover between these two limiting classes is therefore in high demand. We are proposing a unified chain deformation model which describes the force-deformation curve in terms of the chain bending constant K and bond length b. This model demonstrates that the worm-like and freely-jointed chain models correspond to two different regimes of polymer deformation and the crossover between these two regimes depends on the chain bending rigidity and the magnitude of the applied force. Polymer chains with bending constant K>1 behave as a worm-like chain under tension in the interval of the applied forces f ≤ Kk(B)T/b and as a freely-jointed chain for f ≥ Kk(B)T/b (k(B) is the Boltzmann constant and T is the absolute temperature). The proposed crossover expression for chain deformation is in excellent agreement with the results of the molecular dynamics simulations of chain deformation and single-molecule deformation experiments of biological and synthetic macromolecules.     

Characterization of the physical properties of model biomembranes at the nanometer scale with the atomic force microscope

Interaction forces and topography of mixed phospholipid-glycolipid bilayers were investigated by atomic force microscopy (AFM) in aqueous conditions with probes functionalized with self-assembled monolayers terminating in hydroxy groups. Short-range repulsive forces were measured between the hydroxy-terminated probe and the surface of the two-dimensional (2-D) solid-like domains of distearoyl-phosphatidylethanolamine (DSPE) and digalactosyldiglyceride (DGDG). The form and range of the short-range repulsive force indicated that repulsive hydration/steric forces dominate the interaction at separation distances of 0.3-1.0 nm after which the probe makes mechanical contact with the bilayers. At loads < 5 nN the bilayer was elastically deformed by the probe, while at higher loads plastic deformation of the bilayer was observed. Surprisingly, a short-range repulsive force was not observed at the surface of the 2-D liquid-like dioleoylphosphatidylethanolamine (DOPE) film, despite the identical head groups of DOPE and DSPE. This provides direct evidence for the influence of the structure and mechanical properties of lipid bilayers on their interaction forces, an effect which may be a major importance in the control of biological processes such as cell adhesion and membrane fusion. The step height measured between lipid domains in the AFM topographic images was larger than could be accounted for by the thickness and mechanical properties of the molecules. A direct correlation was observed between the repulsive force range over the lipid domains and the topographic contrast, which provides direct insight into the fundamental mechanisms of AFM imaging in aqueous solutions. This study demonstrates that chemically modified AFM probes can be used in combination with patterned lipid bilayers as a novel and powerful approach to characterize the nanometer scale chemical and physical properties of heterogeneous biosurfaces such as cell membranes.     

Spectroscopic Monitoring of Mechanical Forces during Protein Folding by using Molecular Force Probes

Detailed folding pathways of proteins are still largely unknown. Real‐time monitoring of mechanical forces acting in proteins during structural transitions would provide deep insights into these highly complex processes. Here, we propose two molecular force probes that can be incorporated into the protein backbone to gain insight into the magnitude and direction of mechanical forces acting in proteins during natural folding and unfolding through their optical spectroscopic response. In fact, changes in the infrared and Raman spectra are proportional to the mechanical force deforming the force probes, and the relevant bands can be intensified and shifted to a transparent window in the protein spectrum by isotopic substitution. As a result, the proposed molecular force probes can act as “force rulers”, allowing the spectroscopic observation and measurement of mechanical forces acting within the proteins under natural conditions without external perturbation.     

Optical force field mapping in microdevices

We present a method for characterizing microscopic optical force fields. Two dimensional vector force maps are generated by measuring the optical force applied to a probe particle for a grid of particle positions. The method is used to map out the force field created by the beam from a lensed fiber inside a liquid filled microdevice. We find transverse gradient forces and axial scattering forces on the order of 2 pN per 10 mW laser power which are constant over a considerable axial range (>35 microm). These findings suggest future useful applications of lensed fibers for particle guiding/sorting. The propulsion of a small particle at a constant velocity of 200 microm s(-1) is shown.     

Colloid probe AFM investigation of the influence of cross-linking on the interaction behavior and nano-rheology of colloidal droplets

The repulsive forces between a glass sphere and immobilized colloidal droplets of poly(dimethylsiloxane) (PDMS) (with various levels of internal cross-linking) have been determined in aqueous solution using colloid probe atomic force microscopy. On initial surface approach, droplet deformation is negligible and interaction forces resemble those expected for electrical double layer interaction of rigid spheres. Upon further approach, droplet flattening results in forces that deviate below rigid body electrical double layer interaction. The extent of droplet deformation has been determined in terms of the deviation from hard-sphere interaction. Droplet deformability is strongly dependent on the droplet cross-linking level and hence controlled by some combination of the bulk rheological and interfacial properties of the droplets. Droplet nano-rheology has been determined from the extent of force curve hysteresis. For liquidlike droplets, with low levels of cross-linking, no force curve hysteresis is observed and the elastic deformation may be described by a single spring constant, which is controlled by the interfacial properties. For highly cross-linked droplets, the extent of deformation is controlled by the droplet's bulk rheology rather than the interfacial properties. Upon retraction of the surfaces, force curve hysteresis is observed and is due to the viscoelastic response of the PDMS. The extent of hysteresis is dependent on the rate of approach/retraction and the loading force and has been theoretically analyzed to determine nano-rheological parameters that describe droplet relaxation processes. Elastic moduli and relaxation times of the PDMS droplets vary over several orders of magnitude as a function of cross-linking.     

A silicone-based stretchable micropost array membrane for monitoring live-cell subcellular cytoskeletal response

External forces are increasingly recognized as major regulators of cellular structure and function, yet the underlying mechanism by which cells sense forces and transduce them into intracellular biochemical signals and behavioral responses ('mechanotransduction') is largely undetermined. To aid in the mechanistic study of mechanotransduction, herein we devised a cell stretching device that allowed for quantitative control and real-time measurement of mechanical stimuli and cellular biomechanical responses. Our strategy involved a microfabricated array of silicone elastomeric microposts integrated onto a stretchable elastomeric membrane. Using a computer-controlled vacuum, this micropost array membrane (mPAM) was activated to apply equibiaxial cell stretching forces to adherent cells attached to the microposts. Using the mPAM, we studied the live-cell subcellular dynamic responses of contractile forces in vascular smooth muscle cells (VSMCs) to a sustained static equibiaxial cell stretch. Our data showed that in response to a sustained cell stretch, VSMCs regulated their cytoskeletal (CSK) contractility in a biphasic manner: they first acutely enhanced their contraction to resist rapid cell deformation ('stiffening') before they allowed slow adaptive inelastic CSK reorganization to release their contractility ('softening'). The contractile response across entire single VSMCs was spatially inhomogeneous and force-dependent. Our mPAM device and live-cell subcellular contractile measurements will help elucidate the mechanotransductive system in VSMCs and thus contribute to our understanding of pressure-induced vascular disease processes.     

On-chip measurements of cell compressibility via acoustic radiation

Measurements of mechanical properties of biological cells are of great importance because changes in these properties can be strongly associated with the progression of cell differentiation and cell diseases. Although state of the art methods, such as atomic force microscopy, optical tweezers and micropipette aspiration, have been widely used to measure the mechanical properties of biological cells, all these methods involve direct contact with the cell and the measurements could be affected by the contact or any local deformation. In addition, all these methods typically deduced the Young's modulus of the cells based on their measurements. Herein, we report a new method for fast and direct measurement of the compressibility or bulk modulus of various cell lines on a microchip. In this method, the whole cell is exposed to acoustic radiation force without any direct contact. The method exploits the formation of an acoustic standing wave within a straight microchannel. When the polystyrene beads and cells are introduced into the channel, the acoustic radiation force moves them to the acoustic pressure node and the movement speed is dependent on the compressibility. By fitting the experimental and theoretical trajectories of the beads and the cells, the compressibility of the cells can be obtained. We find that the compressibility of various cancer cells (MCF-7: 4.22 ± 0.19 × 10(-10) Pa(-1), HEPG2: 4.28 ± 0.12 × 10(-10) Pa(-1), HT-29: 4.04 ± 0.16 × 10(-10) Pa(-1)) is higher than that of normal breast cells (3.77 ± 0.09 × 10(-10) Pa(-1)) and fibroblast cells (3.78 ± 0.17 × 10(-10) Pa(-1)). This work demonstrates a novel acoustic-based method for on-chip measurements of cell compressibility, complementing existing methods for measuring the mechanical properties of biological cells.     

Motion, deformation and aggregation of two cells in a microchannel by dielectrophoresis

The dynamic behavior of two cells in a microchannel subject to a nonuniform electric field is simulated numerically by a two-fluid model in the present work. Owing to the presence of nonuniform electric field, usually the cells are polarized and then the dielectrophoresis occurs. The dielectrophoretic force induces the movement and deformation of cells in the microchannel. Meanwhile, the cell membrane develops a mechanical force to resist the cell deformation. In addition, the intercellular interaction becomes dominant when the cell-cell distance is short enough such that an intercellular force is generated. The three forces are taken into account in the two-fluid model to characterize the dynamic behavior of cells. In order to validate the present model, the cell deformation is calculated and compared with the experimental results published previously, where a quantitative agreement is achieved. It is demonstrated by simulations that the cell conductivity mainly determines the motion and deformation of cells at low frequency. Instead of the cell conductivity however, the cell permittivity plays a critical and leading role at high frequency. These phenomena are consistent with the experimental observations. Furthermore, the intercellular interaction may cause the change in the dynamic behavior of cells.     

Electromagnetophoretic force measurement of a single binding interaction between lectin and yeast cell surfaces.

A novel measurement method of the binding force between a micrometer-sized particle and a solid surface in an electrolyte solution has been established by using the electromagnetophoretic buoyancy on the particle. By this method, we investigated the binding force between a yeast cell surface and an oligosaccharide-binding protein, concanavalin A (Con A), fixed on a silica capillary wall. The force measurement was carried out up to 60 pN. In a lower surface concentration of Con A, yeast cells could be desorbed by a force less than 60 pN. However, in a higher surface concentration after treated by 1 mg ml(-1) solution, yeast cells were adsorbed with a force stronger than 60 pN. In this case, the addition of 10 mg ml(-1) D-mannose solution to the medium reduced the binding force to less than 60 pN. The observed adsorption force of yeast cells ranged within 30 - 40 pN, regardless of the interfacial amount of Con A. This force was thought to be the single binding force between a mannose group of the cell surface and an active site of Con A. Moreover, the dissociation rate constant of the single binding of yeast cell and Con A complex was determined as 4.6 x 10(-3) s(-1) and the increment of the binding distance at the transition state as 0.33 nm from the desorption kinetic experiments of yeast cell under the constant pulling conditions of 10, 20 and 30 pN. Such satisfactory results demonstrate the novel advantages of the present method.     

Cell mechanics using atomic force microscopy-based single-cell compression

We report herein the establishment of a single-cell compression method based on force measurements in atomic force microscopy (AFM). The high-resolution bright-field or confocal laser scanning microscopy guides the location of the AFM probe and then monitors the deformation of cell shape, while microsphere-modified AFM probes compress the cell and measure the force. Force and deformation profiles of living cells reveal a cubic relationship at small deformation (<30%), multiple peaks at 30-70% compression, and a rapid increase at over 80% deformation. The initial compression may be described qualitatively and quantitatively using a simple model of a nonpermeable balloon filled with incompressible fluid. Stress peaks reflect cell membrane rupture, followed by the deformation and rupture of intracellular components, beyond which the cell responses become irreversible. The Young's modulus and bending constant of living cell membranes are extracted from the balloon models, with 10-30 MPa and 17-52 kT, respectively. The initial compression of dead and fixed cells is modeled using Hertzian contact theory, assuming that the cell is a homogeneous sphere. Dead cells exhibit a cytoskeleton elasticity of 4-7.5 kPa, while fixation treatment leads to a dramatic increase in the cytoskeletal Young's modulus (150-230 kPa) due to protein cross-linking by imine bonds. These results demonstrate the high sensitivity of the single-cell compression method to the molecular-level structural changes of cells, which suggests a new generic platform for investigating cell mechanics in tissue engineering and cancer research.     

Inertial separation in a contraction-expansion array microchannel

We report a contraction-expansion array (CEA) microchannel that allows inertial size separation by a force balance between inertial lift and Dean drag forces in fluid regimes in which inertial fluid effects become significant. An abrupt change of the cross-sectional area of the channel curves fluid streams and produces a similar effect compared to Dean flows in a curved microchannel of constant cross-section, thereby inducing Dean drag forces acting on particles. In addition, the particles are influenced by inertial lift forces throughout the contraction regions. These two forces act in opposite directions each other throughout the CEA microchannel, and their force balancing determines whether the particles cross the channel, following Dean flows. Here we describe the physics and design of the CEA microfluidic device, and demonstrate complete separation of microparticles (polystyrene beads of 4 and 10 μm in diameter) and efficient exchange of the carrier medium while retaining 10 μm beads.     

Fibroblasts in three dimensional matrices: cell migration and matrix remodeling

Fibroblast-collagen matrix culture has facilitated the analysis of cell physiology under conditions that more closely resemble an in vivo-like environment compared to conventional 2-dimensional (2D) cell culture. Furthermore, it has led to significant progress in understanding reciprocal and adaptive interactions between fibroblasts and the collagen matrix, which occur in tissue. Recent studies on fibroblasts in 3-dimensional (3D) collagen matrices have revealed the importance of biomechanical conditions in addition to biochemical cues for cell signaling and migration. Depending on the surrounding mechanical conditions, cells utilize specific cytoskeletal proteins to adapt to their environment. More specifically, cells utilize microtubule dependent dendritic extensions to provide mechanical structure for matrix contraction under a low cell-matrix tension state, whereas cells in a high cell-matrix tension state utilize conventional acto-myosin activity for matrix remodeling. Results of collagen matrix contraction and cell migration in a 3D collagen matrix revealed that the use of appropriate growth factors led to promigratory and procontractile activity for cultured fibroblasts. Finally, the relationship between cell migration and tractional force for matrix remodeling was discussed.     

Specifics of change in the surface area of amorphous poly(vinyl chloride) during its inelastic deformation

A direct microscopic observation procedure was used to study the processes of deformation and shrinkage of poly(vinyl chloride) above its glass transition temperature. Prior to stretching or contraction of the polymer, its surface was decorated with a thin (10–15 nm) metal layer. As a result of subsequent deformation (shrinkage), the decoration underwent structural rearrangements, which were detected by means of direct microscopic examination. These rearrangements contain information on the mechanism of deformation of the polymer substrate. In particular, the procedure makes it possible to characterize the process of development of the interface in the polymer during deformation and the reverse process of interface contraction during the shrinkage of the material. It was found that, in the case of an increase in the interfacial area, its growth is accompanied by a growth in imperfection of the polymer surface layer. These defects can concentrate mechanical stress, thus strongly affecting the fragmentation of the metal decoration on the polymer surface. It was shown that the surface defects could be eliminated by annealing of the polymer above its glass transition temperature. The introduction of a plasticizer that decreases the glass transition temperature below the deformation temperature likewise prevents the development of these defects during an increase in the surface area of the polymer in the process of its inelastic deformation.     

Noncontact method for calibration of lateral forces in scanning force microscopy

This paper describes a noncontact calibration procedure for lateral force microscopy in air and liquids. The procedure is based on the observation that the sensitivity of a force microscope may be calibrated using the raw thermal noise spectrum of the cantilever and its known spring constant, which can be found from the same uncalibrated thermal noise spectrum using Sader's method (Rev. Sci. Instrum.1999, 70, 3967-3969). In addition to the power spectrum of the cantilever thermal noise, this noncontact calibration method only requires knowledge of the plan view dimensions of the cantilever that could be measured using an optical microscope. This method is suitable for in situ force calibration even in viscous fluids through a two-step calibration procedure, where the cantilever thermal spectra are captured both in air and in the desired liquid. The lateral calibration performed with the thermal noise technique agrees well with sensitivity values obtained by the wedge calibration procedure. The approach examined in this paper allows for complete calibration of normal and lateral forces without contacting the surface, eliminating the possibility for any tip damage or contamination during calibration.     

Light-driven directed motion of azobenzene-coated polymer nanoparticles in an aqueous medium

Azobenzene-coated polymer nanoparticles in the 16-nm-diameter range act as phototriggered nanomotors combining photo to kinetic energy conversion with optical control through light intensity gradients. The grafted dyes act as molecular propellers: their photoisomerization supplies sufficient mechanical work to propel the particles in an aqueous medium toward the intensity minima with velocities of up to 15 μm/s. It is shown that nanoparticles can be driven over tens of micrometers by translating the intensity gradients in the plane. The analysis of the particles motion demonstrates the decisive role of photoisomerization in the transport with a measured driving force that is 3 to 4 orders of magnitude higher than optical forces.     

Active transport in the light of thermodynamics of open systems

A brief thermodynamic analysis of transport processes in open systems is presented. It is shown that the concept of an active transport in the usual sense of the existence of a flow against the direction of its conjugate force is operationally unrealistic. The so-called metabolically coupled active transport has been shown to be mathematically falacious. The experimental establishment in favor of the active transport process by the use of metabolic inhibitors has been logically disproven. From this analysis it is naturally concluded that all transport processes in the living organisms can be reduced to passive ones if one recognizes all the possible potential gradients existing in the system. Assuming the existence of active transport process is as erroneous as taking for granted a vital force explaining the life phenomena. It simply indicates our lack of knowledge about the pattern of superposition of a complete set of driving forces or about the nature of a yet unknown physical driving force and the generating mechanism of such a force.     

Plane wave/pseudopotential implementation of excited state gradients in density functional linear response theory: a new route via implicit differentiation

This work presents the formalism and implementation of excited state nuclear forces within density functional linear response theory using a plane wave basis set. An implicit differentiation technique is developed for computing nonadiabatic coupling between Kohn-Sham molecular orbital wave functions as well as gradients of orbital energies which are then used to calculate excited state nuclear forces. The algorithm has been implemented in a plane wave/pseudopotential code taking into account only a reduced active subspace of molecular orbitals. It is demonstrated for the H(2) and N(2) molecules that the analytical gradients rapidly converge to the exact forces when the active subspace of molecular orbitals approaches completeness.     

Organs on microfluidic chips: A mini review

Microfluidic technology provides opportunities to create in vitro models with physiological microenvironment for cell study. Introducing the identified key aspects, including tissue-tissue interfaces, spatiotemporal chemical gradients, and dynamic mechanical forces, of living organs into the microfluidic system, “organs-on-chips” display an unprecedented application potential in a lot of biological fields such as fundamental physiological and pathophysiological research, drug efficacy and toxicity testing, and clinical diagnosis. Here, we review the recent development of organs-on-chips and briefly discuss their future challenges.     

Force–Spectrum Relations for Molecular Optical Force Probes

Force probes allow real‐time monitoring of forces acting in different regions of large molecules and are potentially suited for the investigation of structural changes occurring in macromolecules during, e. g., folding processes. 1 – 10 Such information is crucial for the understanding of mechanochemical reactivity. 2 , 3 , 6 , 7 To this end, small molecular force probes can be incorporated into large molecules. 2 , 3 , 11 – 13 Some of the available systems are based on mechanochromism, the change of the UV/Vis absorption spectrum of a molecule under mechanical stress. 1 , 14 Herein we propose the idea of using molecular force probes in which the point‐group symmetry is reduced as a result of mechanical deformation. This effect leads to significant and characteristic changes in the UV/Vis, IR, and Raman spectra of the deformed molecules, which were determined using computational methods. Beneficially, these changes are reversible and occur even if the applied forces are small.