The optical stretcher: a novel laser tool to micromanipulate cells

Nanomechanical characterization of red blood cells using optical tweezers

Deformation behaviours of red blood cells (RBCs) have been studied by applying stretching forces via optical tweezers. Combined with finite-element analyses (FEA), the RBCs' mechanical properties are determined quantitatively based on a best fitting between the experimental deformed geometries and the simulated counterparts. Experimentally, a silica beads attached erythrocyte is optical-mechanically stretched to different lengths. On the theoretical front, a large deformation model with Mooney-Rivlin constitutive equations has been simulated by using FEA to predict the cell deformation geometries. The numerically simulated transverse and longitudinal strains which are in a good agreement with the experimental measurements facilitate the determination of elastic constants of the cells.

Full phase and amplitude control of holographic optical tweezers with high efficiency

Recently we demonstrated the applicability of a holographic method for shaping complex wavefronts to spatial light modulator (SLM) systems. Here we examine the potential of this approach for optical micromanipulation. Since the method allows one to shape both amplitude and phase of a trapping light field independently and thus provides full control over scattering and gradient forces, it extends the possibilities of commonly used holographic tweezers systems. We utilize two cascaded phase-diffractive elements which can actually be display side-by-side on a single programmable phase modulator. Theoretically the obtainable light efficiency is close to 100%, in our case the major practical limitation arises from absorption in the SLM. We present data which demonstrate the ability to create user-defined "light pathways" for microparticles driven by transverse radiation pressure.

Fluctuations of coupled fluid and solid membranes with application to red blood cells

The fluctuation spectra and the intermembrane interaction of two membranes at a fixed average distance are investigated. Each membrane can either be a fluid or a solid membrane, and in isolation, its fluctuations are described by a bare or a wave-vector-dependent bending modulus, respectively. The membranes interact via their excluded-volume interaction; the average distance is maintained by an external, homogeneous pressure. For strong coupling, the fluctuations can be described by a single, effective membrane that combines the elastic properties. For weak coupling, the fluctuations of the individual, noninteracting membranes are recovered. The case of a composite membrane consisting of one fluid and one solid membrane can serve as a microscopic model for the plasma membrane and cytoskeleton of the red blood cell. We find that, despite the complex microstructure of bilayers and cytoskeletons in a real cell, the fluctuations with wavelengths lambda greater, similar 400 nm are well described by the fluctuations of a single, polymerized membrane (provided that there are no inhomogeneities of the microstructure). The model is applied to the fluctuation data of discocytes ("normal" red blood cells), a stomatocyte, and an echinocyte. The elastic parameters of the membrane and an effective temperature that quantifies active, metabolically driven fluctuations are extracted from the experiments.

Reconfigurable microfluidic integration of a dual-beam laser trap with biomedical applications

A dual-beam fiber laser trap, termed the optical stretcher when used to deform objects, has been combined with a capillary-based microfluidic system in order to serially trap and deform biological cells. The design allows for control over the size and position of the trap relative to the flow channel. Data is recorded using video phase contrast microscopy and is subsequently analyzed using a custom edge fitting routine. This setup has been regularly used with measuring rates of 50-100 cells/h. One such experiment is presented to compare the distribution of deformability found within a normal epithelial cell line to that of a cancerous one. In general, this microfluidic optical stretcher can be used for the characterization of cells by their viscoelastic signature. Possible applications include the cytological diagnosis of cancer and the gentle and marker-free sorting of stem cells from heterogeneous populations for therapeutic cell-based approaches in regenerative medicine.

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

A precise characterization of cell elastic properties is crucial for understanding the mechanisms by which cells sense mechanical stimuli and how these factors alter cellular functions. Optical and magnetic tweezers are micromanipulation techniques which are widely used for quantifying the stiffness of adherent cells from their response to an external force applied on a bead partially embedded within the cell cortex. However, the relationships between imposed external force and resulting bead translation or rotation obtained from these experimental techniques only characterize the apparent cell stiffness. Indeed, the value of the estimated apparent cell stiffness integrates the effect of different geometrical parameters, the most important being the bead embedding angle 2gamma, bead radius R, and cell height h. In this paper, a three-dimensional finite element analysis was used to compute the cell mechanical response to applied force in tweezer experiments and to explicit the correcting functions which have to be used in order to infer the intrinsic cell Young's modulus from the apparent elasticity modulus. Our analysis, performed for an extensive set of values of gamma, h, and R, shows that the most relevant parameters for computing the correcting functions are the embedding half angle gamma and the ratio h(u)/2R, where h(u) is the under bead cell thickness. This paper provides original analytical expressions of these correcting functions as well as the critical values of the cell thickness below which corrections of the apparent modulus are necessary to get an accurate value of cell Young's modulus. Moreover, considering these results and taking benefit of previous results obtained on the estimation of cell Young's modulus of adherent cells probed by magnetic twisting cytometry (MTC) (Ohayon, J., and Tracqui, P., 2005, Ann. Biomed. Eng., 33, pp. 131-141), we were able to clarify and to solve the still unexplained discrepancies reported between estimations of elasticity modulus performed on the same cell type and probed with MTC and optical tweezers (OT). More generally, this study may strengthen the applicability of optical and magnetic tweezers techniques by insuring a more precise estimation of the intrinsic cell Young's modulus (CYM).

Laser trapping of deformable objects

We report the trapping and manipulation of bubbles in viscous glass melts through the use of a laser. This phenomenon is observed in bubbles tens of micrometers in diameter under illumination by low numerical aperture (NA = 0.55). Once the bubble was centered on the optical axis, it was trapped and followed a lateral relocation of the laser beam. This phenomenon is explained by modifications of the bubble's shape induced by axial heating and a decrease in surface tension. It is shown that formation of a concave dimple on the bubble's front surface explains the observed laser trapping and manipulation. This mechanism of laser trapping is expected to take place in other deformable materials and can also be used to remove bubbles from melts or liquids. For this technique to be effective, the alteration of the bubble's shape should be faster than its expulsion out of the laser's point of focus.

Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy

A method for the determination of the integral refractive index of living cells in suspension by digital holographic microscopy is described. Digital holographic phase contrast images of spherical cells in suspension are recorded, and the radius as well as the integral refractive index are determined by fitting the relation between cell thickness and phase distribution to the measured phase data. The algorithm only requires information about the refractive index of the suspension medium and the image scale of the microscope system. The specific digital holographic microscopy advantage of subsequent focus correction allows a simultaneous investigation of cells in different focus planes. Results obtained from human pancreas and liver tumor cells show that the integral cellular refractive index decreases with increasing cell radius.

Asymmetric elastic properties of Dictyostelium discoideum in relation to chemotaxis

In this study we used an AFM to investigate the cytoskeletal properties of live Dictyostelium discoideum cells by measuring the local stiffness across individual living cells. We have examined differences in elastic properties of polarized and unpolarized AX3 wild type and the mutant DAip1- cells, as well as the differences in the front and rear of the cells in relation to organization of the actin cytoskeleton. We found that the average Young's modulus increases upon polarization for the thin regions of the cell and that in polarized cells, the cell front was stiffer than the cell back. We also found that AX3 cells were stiffer than DAip1- cells. This finding suggests that actin polymerization is one of the major determinants of cell motility in Dictyostelium. In addition, a thin agarose film was studied as a model system to examine the influence of the substrate of thin materials probed with the AFM.

High-throughput rheological measurements with an optical stretcher

The cytoskeleton is a major determinant of the mechanical strength and morphology of most cells. The composition and assembly state of this intracellular polymer network evolve during the differentiation of cells, and the structure is involved in many cellular functions and is characteristically altered in many diseases, including cancer. Here we exploit the deformability of the cytoskeleton as a link between molecular structure and biological function, to distinguish between cells in different states by using a laser-based optical stretcher (OS) coupled with microfluidic handling of cells. An OS is a cell-sized, dual-beam laser trap designed to nondestructively test the deformability of single suspended cells. Combined with microfluidic delivery, many cells can be measured serially in a short amount of time. With this tool it could be shown that optical deformability is sensitive enough to monitor subtle changes during the progression of cells from normal to cancerous and even a metastatic state. Stem cells can also be distinguished from more differentiated cells. The surprisingly low number of cells required for this assay reflects the tight regulation of the cytoskeleton by the cell. This suggests the possibility of using optical deformability as an inherent cell marker for basic cell biological investigation, diagnosis of disease, and sorting of stem cells from heterogeneous populations, obviating the need for external markers or special preparation. Many additional biological assays can be easily adapted to utilize this innovative physical method. This chapter details the setup and use of the microfluidic OS, the analysis and interpretation of data, and the results of a typical experiment.

An optical toolbox for total control of droplet microfluidics

The use of microfluidic drops as microreactors hinges on the active control of certain fundamental operations such as droplet formation, transport, division and fusion. Recent work has demonstrated that local heating from a focused laser can apply a thermocapillary force on a liquid interface sufficient to block the advance of a droplet in a microchannel (C. N. Baroud, J.-P. Delville, F. Gallaire and R. Wunenburger, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75(4), 046302). Here, we demonstrate the generality of this optical approach by implementing the operations mentioned above, without the need for any special microfabrication or moving parts. We concentrate on the applications to droplet manipulation by implementing a wide range of building blocks, such as a droplet valve, sorter, fuser, or divider. We also show how the building blocks may be combined by implementing a valve and fuser using a single laser spot. The underlying fundamentals, namely regarding the fluid mechanical, physico-chemical and thermal aspects, will be discussed in future publications.

Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells

We present spectral domain phase microscopy (SDPM) as a new tool for measurements at the cellular scale. SDPM is a functional extension of spectral domain optical coherence tomography that allows for the detection of cellular motions and dynamics with nanometer-scale sensitivity in real time. Our goal was to use SDPM to investigate the mechanical properties of the cytoskeleton of MCF-7 cells. Magnetic tweezers were designed to apply a vertical force to ligand-coated magnetic beads attached to integrin receptors on the cell surfaces. SDPM was used to resolve cell surface motions induced by the applied stresses. The cytoskeletal response to an applied force is shown for both normal cells and those with compromised actin networks due to treatment with Cytochalasin D. The cell response data were fit to several models for cytoskeletal rheology, including one- and two-exponential mechanical models, as well as a power law. Finally, we correlated displacement measurements to physical characteristics of individual cells to better compare properties across many cells, reducing the coefficient of variation of extracted model parameters by up to 50%.

3D finite element analysis of uniaxial cell stretching: from image to insight

Mechanical forces play an important role in many microbiological phenomena such as embryogenesis, regeneration, cell proliferation and differentiation. Micromanipulation of cells in a controlled environment is a widely used approach for understanding cellular responses with respect to external mechanical forces. While modern micromanipulation and imaging techniques provide useful optical information about the change of overall cell contours under the impact of external loads, the intrinsic mechanisms of energy and signal propagation throughout the cell structure are usually not accessible by direct observation. This work deals with the computational modelling and simulation of intracellular strain state of uniaxially stretched cells captured in a series of images. A nonlinear elastic finite element method on tetrahedral grids was applied for numerical analysis of inhomogeneous stretching of a rat embryonic fibroblast 52 (REF 52) using a simplified two-component model of a eukaryotic cell consisting of a stiffer nucleus surrounded by a softer cytoplasm. The difference between simulated and experimentally observed cell contours is used as a feedback criterion for iterative estimation of canonical material parameters of the two-component model such as stiffness and compressibility. Analysis of comparative simulations with varying material parameters shows that (i) the ratio between the stiffness of cell nucleus and cytoplasm determines intracellular strain distribution and (ii) large deformations result in increased stiffness and decreased compressibility of the cell cytoplasm. The proposed model is able to reproduce the evolution of the cellular shape over a sequence of observed deformations and provides complementary information for a better understanding of mechanical cell response.

Biomechanics approaches to studying human diseases

Nanobiomechanics has recently been identified as an emerging field that can potentially make significant contributions in the study of human diseases. Research into biomechanics at the cellular and molecular levels of some human diseases has not only led to a better elucidation of the mechanisms behind disease progression, because diseased cells differ physically from healthy ones, but has also provided important knowledge in the fight against these diseases. This article highlights some of the cell and molecular biomechanics research carried out on human diseases such as malaria, sickle cell anemia and cancer and aims to provide further important insights into the pathophysiology of such diseases. It is hoped that this can lead to new methods of early detection, diagnosis and treatment.

Cellular chemomechanics at interfaces: sensing, integration and response

Living cells are complex entities whose remarkable, emergent capacity to sense, integrate, and respond to environmental cues relies on an intricate series of interactions among the cell's macromolecular components. Defects in mechanosensing, transduction,or responses underlie many diseases such as cancers, immune disorders, cardiac hypertrophy, genetic malformations, and neuropathies. Here, we highlight micro- and nanotechnology-based tools that have been used to study how chemical and mechanical cues modulate the responses of single cells in contact with the extracellular environment. Understanding the physical aspects of these complex processes at the micro- and nanometer scale could produce profound and fundamental new insights into how the processes of cell migration, metastasis, immune function and other areas which are regulated by mechanical forces.

Cell-assisted assembly of colloidal crystallites

Many cells ingest foreign particles through a process known as phagocytosis. It now turns out that some cell types organize phagocytosed microparticles into crystalline arrays. Much like the classic crystallization of colloidal particles in a thermal bath, crystallization within the cell is driven by the spatial confinement of mutually repelling particles, in this case by the cell membrane. Cytoskeleton-driven motions exert a randomizing force, similar to but stronger than thermal forces; these motions anneal defects and purify the colloidal crystals within the cells. Bidisperse mixtures of microspheres phase separate within the cell, with the larger particles crystallizing around the nucleus and the smaller particles crystallizing around the perimeter of the large particle array. Mitochondria also participate in this kind of size segregation, which appears to be driven by membrane tension and curvature minimization. Beyond the curiosity of the phenomenon itself, cell-assisted colloidal assembly may prove useful as a new tool to study a variety of biophysical processes including cytoskeletal rearrangements, organelle-membrane interactions, the in vivo mechanics of microtubules, the cooperativity of molecular motors and intracellular traffic jams on cytoskeletal filaments.

Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam

A rigorous theory is developed to predict the radiation pressure force (RPF) exerted on a spheroid by an arbitrarily oriented and located shaped beam. Analytical expressions of RPF are derived for a homogeneous spheroid, which can be prolate or oblate, transparent or absorbing. Exemplifying calculations are performed and RPF calculations for spheroids are compared to RPF calculations for spheres. The "Optical Stretcher" is also numerically simulated to study the RPF exerted on a red blood cell during its deformation.

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.

Viscoelastic properties of individual glial cells and neurons in the CNS

One hundred fifty years ago glial cells were discovered as a second, non-neuronal, cell type in the central nervous system. To ascribe a function to these new, enigmatic cells, it was suggested that they either glue the neurons together (the Greek word "gammalambdaiotaalpha" means "glue") or provide a robust scaffold for them ("support cells"). Although both speculations are still widely accepted, they would actually require quite different mechanical cell properties, and neither one has ever been confirmed experimentally. We investigated the biomechanics of CNS tissue and acutely isolated individual neurons and glial cells from mammalian brain (hippocampus) and retina. Scanning force microscopy, bulk rheology, and optically induced deformation were used to determine their viscoelastic characteristics. We found that (i) in all CNS cells the elastic behavior dominates over the viscous behavior, (ii) in distinct cell compartments, such as soma and cell processes, the mechanical properties differ, most likely because of the unequal local distribution of cell organelles, (iii) in comparison to most other eukaryotic cells, both neurons and glial cells are very soft ("rubber elastic"), and (iv) intriguingly, glial cells are even softer than their neighboring neurons. Our results indicate that glial cells can neither serve as structural support cells (as they are too soft) nor as glue (because restoring forces are dominant) for neurons. Nevertheless, from a structural perspective they might act as soft, compliant embedding for neurons, protecting them in case of mechanical trauma, and also as a soft substrate required for neurite growth and facilitating neuronal plasticity.

Design of a novel MEMS platform for the biaxial stimulation of living cells

Micromechanical systems are increasingly being used as tools in biological applications, since their characteristic dimensions permit to operate at the same length scale of the structures under investigation. Here, we present a methodology for the design, fabrication and operation of a tool for the assessment of mechanical properties of single cells. In particular, we describe a microsystems platform to study bio-mechanical response of single living cells to in-plane biaxial stretching. The proposed device employs a new linkage design in order to obtain the displacement of the quadrants of a sliced circular plate in mutually-orthogonal directions using just one linear actuator. With this linkage geometry, the whole device has only one degree of freedom. This results in a very predictable and reliable mechanical behaviour, thereby allowing use a simple and easily available control electronics. Results of this study have relevance for the design of a powerful yet simple BioMEMS platform for the characterization of living cells as in-plane bi-axial loading simulated the conditions experienced by cells in vivo more realistically than a uniaxial stretching.

Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations

Computational approaches of multicellular assemblies have reached a stage where they may contribute to unveil the processes that underlie the organization of tissues and multicellular aggregates. In this article, we briefly review and present some new results on a number of 3D lattice free individual cell-based mathematical models of epithelial cell populations. The models we consider here are parameterized by bio-physical and cell-biological quantities on the level of an individual cell. Eventually, they aim at predicting the dynamics of the biological processes on the tissue level. We focus on a number of systems, the growth of cell populations in vitro, and the spatial-temporal organization of regenerative tissues. For selected examples we compare different model approaches and show that the qualitative results are robust with respect to many model details. Hence, for the qualitative features and largely for the quantitative features many model details do not matter as long as characteristic biological features and mechanisms are correctly represented. For a quantitative prediction, the control of the bio-physical and cell-biological parameters on the molecular scale has to be known. At this point, slide-based cytometry may contribute. It permits to track the fate of cells and other tissue subunits in time and validated the organization processes predicted by the mathematical models.

Integrated monolithic optical manipulation

We present a new approach to optical manipulation that integrates microfluidic channels directly onto semiconductor laser material creating a compact integrated optical trap that requires no alignment and is wholly portable.

Power laws in microrheology experiments on living cells: Comparative analysis and modeling

We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function J(t) of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a microbead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient Ge(omega) is retrieved. Both J(t) and Ge(omega) exhibit power law behaviors: J(t) = A0(t/t0)alpha and absolute value (Ge(omega)) = G0(omega/omega0)alpha, with the same exponent alpha approximately 0.2. This power law behavior is very robust; alpha is distributed over a narrow range, and shows almost no dependence on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors A0 and G0 appear very sensitive to these parameters. Whereas the exponents alpha are normally distributed over the cell population, the prefactors A0 and G0 follow a log-normal repartition. These results are compared with other data published in the literature. We propose a global interpretation, based on a semiphenomenological model, which involves a broad distribution of relaxation times in the system. The model predicts the power law behavior and the statistical repartition of the mechanical parameters, as experimentally observed for the cells. Moreover, it leads to an estimate of the largest response time in the cytoskeletal network: tau(m) approximately 1000 s.

Mechanical response analysis and power generation by single-cell stretching

To harvest useful information about cell response due to mechanical perturbations under physiological conditions, a cantilever-based technique was designed, which allowed precise application of arbitrary forces or deformation histories on a single cell in vitro. Essential requirements for these investigations are a mechanism for applying an automated cell force and an induced-deformation detection system based on fiber-optical force sensing and closed loop control. The required mechanical stability of the setup can persist for several hours since mechanical drifts due to thermal gradients can be eliminated sufficiently (these gradients are caused by local heating of the cell observation chamber to 37 degrees C). During mechanical characterization, the cell is visualized with an optical microscope, which enables the simultaneous observation of cell shape and intracellular morphological changes. Either the cell elongation is observed as a reaction against a constant load or the cell force is measured as a response to constant deformation. Passive viscoelastic deformation and active cell response can be discriminated. The active power generated during contraction is in the range of Pmax= 10(-16) Watts, which corresponds to 2500 ATP molecules s(-1) at 10 k(B)T/molecule. The ratio of contractive to dissipative power is estimated to be in the range of 10(-2). The highest forces supported by the cell suggest that about 10(4) molecular motors must be involved in contraction. This indicates an energy-conversion efficiency of approximately 0.5. Our findings propose that, in addition to the recruitment of cell-contractile elements upon mechanical stimulation, the cell cytoskeleton becomes increasingly crosslinked in response to a mechanical pull. Quantitative stress-strain data, such as those presented here, may be employed to test physical models that describe cellular responses to mechanical stimuli.

The Deformation of an Erythrocyte Under the Radiation Pressure by Optical Stretch

In this paper, the mechanical properties of erythrocytes were studied numerically based upon the mechanical model originally developed by Pamplona and Calladine (ASME J. Biomech. Eng., 115, p. 149, 1993) for liposomes. The case under study is the erythrocyte stretched by a pair of laser beams in opposite directions within buffer solutions. The study aims to elucidate the effect of radiation pressure from the optical laser because up to now little is known about its influence on the cell deformation. Following an earlier study by Guck et al. (Phys. Rev. Lett., 84, p. 5451, 2000; Biophys. J., 81, p. 767, 2001), the empirical results of the radiation pressure were introduced and imposed on the cell surface to simulate the real experimental situation. In addition, an algorithm is specially designed to implement the simulation. For better understanding of the radiation pressure on the cell deformation, a large number of simulations were conducted for different properties of cell membrane. Results are first discussed parametrically and then evaluated by comparing with the experimental data reported by Guck et al. An optimization approach through minimizing the errors between experimental and numerical data is used to determine the optimal values of membrane properties. The results showed that an average shear stiffness around 4.611×10-6Nm−1, when the nondimensional ratio of shear modulus to bending modulus ranges from 10 to 300. These values are in a good agreement with those reported in literature.

Light-induced deformation and instability of a liquid interface. I. Statics

We study in detail the deformations of a liquid-liquid interface induced by the electromagnetic radiation pressure of a focused cw laser beam. Using a simple linear model of static equilibrium of the interface under the effect of radiation pressure, buoyancy, and Laplace pressure, we explain the observed hump height variations for any value of the optical Bond number Bo=(omega0/lc)2 (lc is the capillary length and omega0 is the waist of the beam) in the regime of weak deformations and show that the deformations are independent of the direction of propagation of the laser. By increasing the beam power, we observe an instability of the interface leading to the formation of a long jet when the laser propagates from the more refringent phase to the less refringent one. We propose that the total internal reflection of the incident light on the highly deformed interface could be at the origin of this instability. Using a nonlinear model of static equilibrium of the interface taking account of the angular dependance of radiation pressure, we explain the measured beam power threshold of the instability P, as well as the shape of the interface deformations observed at large waists just below the instability onset. According to this model, the instability should occur when the interface slope reaches the angle of total reflection, theta(TR). We find experimentally that, just below the instability threshold, the maximum incidence angle along the interface, theta(imax), is significantly smaller than theta(TR) and that our nonlinear model does not present any instability up to theta(imax)=theta(TR). Thus, although the proposed instability model correctly predicts the instability threshold P, it fails to describe the actual instability mechanism. We finally discuss possible additional effects that could explain the instability.

Imaging and probing cell mechanical properties with the atomic force microscope

This chapter describes the use of the atomic force microscope (AFM) to probe and map out regional variations in apparent elastic properties of living cells. The importance of mechanics in the field of cell biology is becoming more widely appreciated, and the AFM has unique advantages for cell mechanics applications. However, care must be taken in the acquisition, analysis, Band interpretation of AFM indentation data. To help make this powerful technique accessible to a broad range of investigators, detailed procedures are provided for all stages of the AFM experiment from sample preparation through data analysis and visualization.

Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation

The surface stress on the real shape (biconcave disklike) of an erythrocyte under laser irradiation is theoretically studied according to the finite-difference time-domain (FDTD) method. The distribution of the surface stresses depends on the orientation of erythrocytes in the laser beam. Typically when the erythrocyte was irradiated from the side direction (the laser beam was perpendicular to the normal of the erythrocyte plane), the surface stresses were so asymmetrical and nonuniform that the magnitude of the surface stress on the back surface was three times higher than that on the front surface, and the highest-to-lowest ratio of the stress reached 16 times. For comparison, the surface stress was also calculated according to the ray optics (RO) method. The tendency of the stress distribution from the RO calculation was roughly similar to that of the FDTD method. However the RO calculation produced some unphysical results, such as the infinite stress on some surface region and the zero stress on the most parts of the erythrocyte surface, which is due to the neglecting of light diffraction. The results obtained from the FDTD calculation are believed quantitatively reliable, because the FDTD method automatically takes into account of the diffraction and interference effects of the light wave. Thus, the FDTD method is more suitable than the RO method for the stress study of erythrocytes.

Characterizing single suspended cells by optorheology

The measurement of the mechanical properties of individual cells has received much attention in recent years. In this paper we describe the application of optically induced forces with an optical stretcher to perform step-stress experiments on individual suspended fibroblasts. The conversion from creep-compliance to frequency-dependent complex shear modulus reveals characteristic viscoelastic signatures of the underlying cytoskeleton and its dynamic molecular properties. Both normal and cancerous fibroblasts display a single stress relaxation time in the observed time and frequency space that can be related to the transient binding of actin crosslinking proteins. In addition, shear modulus and steady-state viscosity of the shell-like actin cortex as the main module resisting small deformations are extracted. These values in combination with insight into the cells' architecture are used to explain their different deformability. This difference can then be exploited to distinguish normal from cancerous cells. The nature of the optical stretcher as an optical trap allows easy incorporation in a microfluidic system with automatic trapping and alignment of the cells, and thus a high measurement throughput. This carries the potential for using the microfluidic optical stretcher to investigate cellular processes involving the cytoskeleton and to diagnose diseases related to cytoskeletal alterations.

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.

Using cell potential energy to model the dynamics of adhesive biological cells

Developing a continuous mathematical model of a physical phenomenon which is based on a discrete model of the same system is not straightforward. Yet such a process is useful in illustrating the link between the individual behavior of the elements comprising a system and its macroscopic behavior. Collections of biological cells can exhibit phenomena such as pattern formation, aggregation, and invasion, and mathematics has proven useful in elucidating the underlying dynamics of these phenomena. The continuous models formulated are frequently of reaction-diffusion form, and central to their application is a knowledge of the diffusion coefficient of a collection of the elements comprising the system. Cohen and Murray [J. Math Biol. 12, 237 (1981)] developed a means of deriving this quantity which has since been largely neglected by model developers, and which is based on a knowledge of the potential energy associated with the mutual interaction between the cells. In this work, we begin by deriving the energy of interaction of biological cells modeled as adhesive, deformable spheres. In so doing, we are able to quantify the equilibrium density of a biological cell aggregate, and also obtain a quantitative estimate of the diffusion coefficient of a collection of cells modeled in this way. In so doing, we are able to use experimental data from single-cell studies of the adhesiveness and cell membrane elasticity of a biological cell to derive the diffusion coefficient of a cell mass composed of a collection of identical cells. This allows us to better inform the parameter values used in reaction-diffusion models of biological systems. We go on to apply this technique to a particular situation: modeling the dynamics of a collection of biological cells which experience strong cell-cell adhesion. In so doing, we derive a nonlinear fourth-order partial differential equation to model this system. We conclude by discussing the practical utility of this work in illuminating the link between the microscopic behavior of individual biological cells and the macroscopic behavior of the aggregate to which they give rise, and also by giving some insights into how the modeling of cell-cell adhesion may be treated mathematically.

Optical rheology of biological cells

A step stress deforming suspended cells causes a passive relaxation, due to a transiently cross-linked isotropic actin cortex underlying the cellular membrane. The fluid-to-solid transition occurs at a relaxation time coinciding with unbinding times of actin cross-linking proteins. Elastic contributions from slowly relaxing entangled filaments are negligible. The symmetric geometry of suspended cells ensures minimal statistical variability in their viscoelastic properties in contrast with adherent cells and thus is defining for different cell types. Mechanical stimuli on time scales of minutes trigger active structural responses.

Remote sensing of mechanical properties of materials using a novel ultrasound transducer and signal processing

An ultrasound-based remote sensing method to evaluate the mechanical properties of materials is presented. This method consists of a disk-shaped, piezoelectric transducer, operating at its resonance frequency, and a phase-shifted, feedback circuit. Mechanical parameters are derived by analyzing the signal contained in the phase-shifted values of the reflected signal. It is concluded that, using this novel transducer system and signal processing, remote mechanical measurements can be made. Such measurements obviate the need to apply the force-deformation approach and may be used to enable stiffness imaging.

Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence

The relationship between the mechanical properties of cells and their molecular architecture has been the focus of extensive research for decades. The cytoskeleton, an internal polymer network, in particular determines a cell's mechanical strength and morphology. This cytoskeleton evolves during the normal differentiation of cells, is involved in many cellular functions, and is characteristically altered in many diseases, including cancer. Here we examine this hypothesized link between function and elasticity, enabling the distinction between different cells, by using a microfluidic optical stretcher, a two-beam laser trap optimized to serially deform single suspended cells by optically induced surface forces. In contrast to previous cell elasticity measurement techniques, statistically relevant numbers of single cells can be measured in rapid succession through microfluidic delivery, without any modification or contact. We find that optical deformability is sensitive enough to monitor the subtle changes during the progression of mouse fibroblasts and human breast epithelial cells from normal to cancerous and even metastatic state. The surprisingly low numbers of cells required for this distinction reflect the tight regulation of the cytoskeleton by the cell. This suggests using optical deformability as an inherent cell marker for basic cell biological investigation and diagnosis of disease.

Hollow spheres as individual movable micromirrors in optical tweezers

We introduce the use of hollow micron-sized spheres with a finite-thickness glass shell as individual micromirrors operating by total internal reflection (TIR) when illuminated off-axis. We also demonstrated that this kind of spheres can be optically trapped and manipulated in two dimensions using a Gaussian beam in a conventional optical tweezers setup, which allows the precise positioning of the micromirrors at specific locations within a sample cell. This mirrors constitutes a new micro-tool in the context of the so called lab-on-a-chip.

Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria

We investigate connections between single-cell mechanical properties and subcellular structural reorganization from biochemical factors in the context of two distinctly different human diseases: gastrointestinal tumor and malaria. Although the cell lineages and the biochemical links to pathogenesis are vastly different in these two cases, we compare and contrast chemomechanical pathways whereby intracellular structural rearrangements lead to global changes in mechanical deformability of the cell. This single-cell biomechanical response, in turn, seems to mediate cell mobility and thereby facilitates disease progression in situations where the elastic modulus increases or decreases due to membrane or cytoskeleton reorganization. We first present new experiments on elastic response and energy dissipation under repeated tensile loading of epithelial pancreatic cancer cells in force- or displacement-control. Energy dissipation from repeated stretching significantly increases and the cell's elastic modulus decreases after treatment of Panc-1 pancreatic cancer cells with sphingosylphosphorylcholine (SPC), a bioactive lipid that influences cancer metastasis. When the cell is treated instead with lysophosphatidic acid, which facilitates actin stress fiber formation, neither energy dissipation nor modulus is noticeably affected. Integrating recent studies with our new observations, we ascribe these trends to possible SPC-induced reorganization primarily of keratin network to perinuclear region of cell; the intermediate filament fraction of the cytoskeleton thus appears to dominate deformability of the epithelial cell. Possible consequences of these results to cell mobility and cancer metastasis are postulated. We then turn attention to progressive changes in mechanical properties of the human red blood cell (RBC) infected with the malaria parasite Plasmodium falciparum. We present, for the first time, continuous force-displacement curves obtained from in-vitro deformation of RBC with optical tweezers for different intracellular developmental stages of parasite. The shear modulus of RBC is found to increase up to 10-fold during parasite development, which is a noticeably greater effect than that from prior estimates. By integrating our new experimental results with published literature on deformability of Plasmodium-harbouring RBC, we examine the biochemical conditions mediating increases or decreases in modulus, and their implications for disease progression. Some general perspectives on connections among structure, single-cell mechanical properties and biological responses associated with pathogenic processes are also provided in the context of the two diseases considered in this work.

The dissipative contribution of myosin II in the cytoskeleton dynamics of myoblasts

We have determined the microrheological response of the actin meshwork for individual cells. We applied oscillating forces with an optical tweezer to a micrometric bead specifically bound to the actin meshwork of C2 myoblasts, and measured the amplitude and phase shift of the induced cell deformation. For a non-perturbed single cell, we have shown that the elastic and loss moduli G' and G'' behave as power laws f (alpha) and f (beta) of the frequency f (0.01<f <50 Hz), alpha and beta being in the range 0.15-0.35. This demonstrates that the dissipation mechanisms in a single cell involve a broad and continuous distribution of relaxation times. After adding blebbistatin, an inhibitor of myosin II activity, the exponent of G' decreases to about 0.10, and G'' becomes roughly constant for 0.01<f<10 Hz. The actin meshwork appears less rigid and less dissipative than in the control experiment. This is consistent with an inhibition of ATPase and reduction of the gliding mobility of myosin II on actin filaments. In this frequency range, the actomyosin activity appears as an essential mechanism allowing the cell to adapt to an external mechanical stress.

Creep function of a single living cell

We used a novel uniaxial stretching rheometer to measure the creep function J(t) of an isolated living cell. We show, for the first time at the scale of the whole cell, that J(t) behaves as a power-law J(t) = At(alpha). For N = 43 mice myoblasts (C2-7), we find alpha = 0.24 +/- 0.01 and A = (2.4 +/- 0.3) 10(-3) Pa(-1) s(-alpha). Using Laplace Transforms, we compare A and alpha to the parameters G(0) and beta of the complex modulus G*(omega) = G(0)omega(beta) measured by other authors using magnetic twisting cytometry and atomic force microscopy. Excellent agreement between A and G(0) on the one hand, and between alpha and beta on the other hand, indicated that the power-law is an intrinsic feature of cell mechanics and not the signature of a particular technique. Moreover, the agreement between measurements at very different size scales, going from a few tens of nanometers to the scale of the whole cell, suggests that self-similarity could be a central feature of cell mechanical structure. Finally, we show that the power-law behavior could explain previous results first interpreted as instantaneous elasticity. Thus, we think that the living cell must definitely be thought of as a material with a large and continuous distribution of relaxation time constants which cannot be described by models with a finite number of springs and dash-pots.

Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro

We present a three-dimensional individual cell-based, biophysical model to study the effect of normal and malfunctioning growth regulation and control on the spatial-temporal organization of growing cell populations in vitro. The model includes explicit representations of typical epithelial cell growth regulation and control mechanisms, namely 1), a cell-cell contact-mediated form of growth inhibition; 2), a cell-substrate contact-dependent cell-cycle arrest; and 3), a cell-substrate contact-dependent programmed cell death (anoikis). The model cells are characterized by experimentally accessible biomechanical and cell-biological parameters. First, we study by variation of these cell-specific parameters which of them affect the macroscopic morphology and growth kinetics of a cell population within the initial expanding phase. Second, we apply selective knockouts of growth regulation and control mechanisms to investigate how the different mechanisms collectively act together. Thereby our simulation studies cover the growth behavior of epithelial cell populations ranging from undifferentiated stem cell populations via transformed variants up to tumor cell lines in vitro. We find that the cell-specific parameters, and in particular the strength of the cell-substrate anchorage, have a significant impact on the population morphology. Furthermore, they control the efficacy of the growth regulation and control mechanisms, and consequently tune the transition from controlled to uncontrolled growth that is induced by the failures of these mechanisms. Interestingly, however, we find the qualitative and quantitative growth kinetics to be remarkably robust against variations of cell-specific parameters. We compare our simulation results with experimental findings on a number of epithelial and tumor cell populations and suggest in vitro experiments to test our model predictions.

Reagentless identification of single bacterial spores in aqueous solution by confocal laser tweezers Raman spectroscopy

We demonstrate that optical trapping combined with confocal Raman spectroscopy using a single laser source is a powerful tool for the rapid identification of micrometer-sized particles in an aqueous environment. Optical trapping immobilizes the particle while maintaining it in the center of the laser beam path and within the laser focus, thus maximizing the collection of its Raman signals. The single particle is completely isolated from other particles and substrate surfaces, therefore eliminating any unwanted background signals and ensuring that information is collected only from the selected, individual particle. In this work, an inverted confocal Raman microscope is combined with optical trapping to probe and analyze bacterial spores in solution. Rapid, reagentless detection and identification of bacterial spores with no false positives from a complex mixed sample containing polystyrene and silica beads in aqueous suspension is demonstrated. In addition, the technique is used to analyze the relative concentration of each type of particle in the mixture. Our results show the feasibility for incorporating this technique in combination with a flow cytometric-type scheme in which the intrinsic Raman signatures of the particles are used instead of or in addition to fluorescent labels to identify cells, bacteria, and particles in a wide range of applications.

Dimensionless parameters for the design of optical traps and laser guidance systems

Optical traps are routinely used for the manipulation of neutral particles. However, optical trap design is limited by the lack of an accurate theory. The generalized Lorenz-Mie theory (GLMT) solves the scattering problem for arbitrary particle size and predicts radial forces accurately. Here we show that the GLMT predicts the observed radial and axial forces in a variety of optical manipulators. We also present a dimensionless parameter beta for the prediction of axial forces. Coupled with our correlation for radial escape forces, we now have a set of two simple correlations for the practical design of radiation-force-based systems.

Mechanical anisotropy of adherent cells probed by a three-dimensional magnetic twisting device

We describe a three-dimensional magnetic twisting device that is useful in characterizing the mechanical properties of cells. With the use of three pairs of orthogonally aligned coils, oscillatory mechanical torque was applied to magnetic beads about any chosen axis. Frequencies up to 1 kHz could be attained. Cell deformation was measured in response to torque applied via an RGD-coated, surface-bound magnetic bead. In both unpatterned and micropatterned elongated cells on extracellular matrix, the mechanical stiffness transverse to the long axis of the cell was less than half that parallel to the long axis. Elongated cells on poly-L-lysine lost stress fibers and exhibited little mechanical anisotropy; disrupting the actin cytoskeleton or decreasing cytoskeletal tension substantially decreased the anisotropy. These results suggest that mechanical anisotropy originates from intrinsic cytoskeletal tension within the stress fibers. Deformation patterns of the cytoskeleton and the nucleolus were sensitive to loading direction, suggesting anisotropic mechanical signaling. This technology may be useful for elucidating the structural basis of mechanotransduction.

Deformability-based flow cytometry

BACKGROUND

Elasticity of cells is determined by their cytoskeleton. Changes in cellular function are reflected in the amount of cytoskeletal proteins and their associated networks. Drastic examples are diseases such as cancer, in which the altered cytoskeleton is even diagnostic. This connection between cellular function and cytoskeletal mechanical properties suggests using the deformability of cells as a novel inherent cell marker.

METHODS

The optical stretcher is a new laser tool capable of measuring cellular deformability. A unique feature of this deformation technique is its potential for high throughput, with the incorporation of a microfluidic delivery of cells.

RESULTS

Rudimentary implementation of the microfluidic optical stretcher has been used to measure optical deformability of several normal and cancerous cell types. A drastic difference has been seen between the response of red blood cells and polymorphonuclear cells for a given optically induced stress. MCF-10, MCF-7, and modMCF-7 cells were also measured, showing that while cancer cells stretched significantly more (five times) than normal cells, optical deformability could even be used to distinguish metastatic cancer cells from nonmetastatic cancer cells. This trimodal distribution was apparent after measuring a mere 83 cells, which shows optical deformability to be a highly regulated cell marker.

CONCLUSIONS

Preliminary work suggests a deformability-based cell sorter similar to current fluorescence-based flow cytometry without the need for specific labeling. This could be used for the diagnosis of all diseases, and the investigation of all cellular processes, that affect the cytoskeleton.

Near-infrared surface-enhanced-Raman-scattering-mediated detection of single optically trapped bacterial spores

A novel methodology has been developed for the investigation of bacterial spores. Specifically, this method has been used to probe the spore coat composition of two different Bacillus stearothermophilus variants. This technique may be useful in many applications; most notably, development of novel detection schemes toward potentially harmful bacteria. This method would also be useful as an ancillary environmental monitoring system where sterility is of importance (i.e., food preparation areas as well as invasive and minimally invasive medical applications). This unique detection scheme is based on the near-infrared (NIR) surface-enhanced Raman scattering (SERS) from single, optically trapped, bacterial spores. The SERS spectra of bacterial spores in aqueous media have been measured using SERS substrates based on approximately 60-nm-diameter gold colloids bound to 3-aminopropyltriethoxysilane derivatized glass. The light from a 787-nm laser diode was used to trap and manipulate as well as simultaneously excite the SERS of an individual bacterial spore. The collected SERS spectra were examined for uniqueness and the applicability of this technique for the strain discrimination of Bacillus stearothermophilus spores. Comparison of normal Raman and SERS spectra reveals not only an enhancement of the normal Raman spectral features but also the appearance of spectral features absent in the normal Raman spectrum.

Rotational magnetic endosome microrheology: viscoelastic architecture inside living cells

The previously developed technique of magnetic rotational microrheology [Phys. Rev. E 67, 011504 (2003)] is proposed to investigate the rheological properties of the cell interior. An endogeneous magnetic probe is obtained inside living cells by labeling intracellular compartments with magnetic nanoparticles, following the endocytosis mechanism, the most general pathway used by eucaryotic cells to internalize substances from an extracellular medium. Primarily adsorbed on the plasma membrane, the magnetic nanoparticles are first internalized within submicronic membrane vesicles (100 nm diameter) to finally concentrate inside endocytotic intracellular compartments (0.6 microm diameter). These magnetic endosomes attract each other and form chains within the living cell when submitted to an external magnetic field. Here we demonstrate that these chains of magnetic endosomes are valuable tools to probe the intracellular dynamics at very local scales. The viscoelasticity of the chain microenvironment is quantified in terms of a viscosity eta and a relaxation time tau by analyzing the rotational dynamics of each tested chain in response to a rotation of the external magnetic field. The viscosity eta governs the long time flow of the medium surrounding the chains and the relaxation time tau reflects the proportion of solidlike versus liquidlike behavior (tau=eta/G, where G is the high-frequency shear modulus). Measurements in HeLa cells show that the cell interior is a highly heterogeneous structure, with regions where chains are embedded inside a dense viscoelastic matrix and other domains where chains are surrounded by a less rigid viscoelastic material. When one compound of the cell cytoskeleton is disrupted (microfilaments or microtubules), the intracellular viscoelasticity becomes less heterogeneous and more fluidlike, in the sense of both a lower viscosity and a lower relaxation time.