a comparative study of living cell micromechanical properties by oscillatory optical tweezers

A comparative study of living cell micromechanical properties by oscillatory

optical tweezers Ming-Tzo Wei1, Angela Zaorski2, Huseyin C. Yalcin3, Jing Wang2, Melissa Hallow3,

Samir N. Ghadiali3, Arthur Chiou1, and H. Daniel Ou-Yang2*

1Institute of Biophotonics Engineering, National Yang-Ming University, Taipei, Taiwan; 2Physics Department, 3Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA

*Corresponding author:[email protected]

Abstract: Micromechanical properties of biological cells are crucial for cells functions. Despite extensive study by a variety of approaches, an understanding of the subject remains elusive. We conducted a comparative study of the micromechanical properties of cultured alveolar epithelial cells with an oscillatory optical tweezer-based cytorheometer. In this study, the frequency-dependent viscoelasticity of these cells was measured by optical trapping and forced oscillation of either a submicron endogenous intracellular organelle (intra-cellular) or a 1.5µm silica bead attached to the cytoskeleton through trans-membrane integrin receptors (extra-cellular). Both the storage modulus and the magnitude of the complex shear modulus followed weak power-law dependence with frequency. These data are comparable to data obtained by other measurement techniques. The exponents of power-law dependence of the data from the intra- and extracellular measurements are similar; however, the differences in the magnitudes of the moduli from the two measurements are statistically significant.

©2008 Optical Society of America

OCIS codes: (170.1420) Biology; (170.1530) Cell analysis; (140.7010) Trapping; (170.4520) Optical confinement and manipulation; (350.4855) Optical tweezers or optical manipulation.

References and links

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(C) 2008 OSA 9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 8594#91263 - $15.00 USD Received 3 Jan 2008; revised 19 May 2008; accepted 22 May 2008; published 28 May 2008

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1. Introduction

Mechanical stresses on biological cells have been found to change not only the cell’s morphology, but also cell cycle, gene expression and protein production in many different systems [1-7]. Like many mechanical systems, the stress-strain relationship of biological cells depends on the mechanical integrity of the cells and the extra-cellular matrix around the cells. The mechanical properties of living cells characterized by the frequency dependence of the storage and loss modules were reported by Fabry et al., [8] who used magnetic tweezers to manipulate ferromagnetic beads attached to the cell membrane. The frequency dependence of the storage modulus (G′) was found to follow a weak power law behavior and was characterized as having soft glassy material properties. In addition, Hoffman et al. [9] utilized laser-tracking microrheometry to demonstrate that the complex shear modulus (G*) also follows a weak power law dependence with frequency.

An outstanding question is whether the cell mechanical properties measured by a probe located outside the cell faithfully reflect the intracellular mechanical properties. Due to the lack of consistencies between various existing measurements of the mechanical properties of the cells [10] and the intrinsic inhomogeneity of the cell interior [11], it is difficult to compare results obtained by different experiments on different cells. To address the question, we set out to conduct experiments that measure cell mechanical properties using probes located


exterior to the plasma membrane and naturally occurring probes embedded inside the cell. Specifically, we measured the storage and loss components of the complex shear modulus, G*(ω)=G′(ω)+iG(ω)′′, of alveolar epithelial cells using a microrheometer based on oscillatory optical tweezers [12-14]. In this technique, G*(ω) is obtained by trapping and oscillating a submicron endogenous intracellular organelle. Measurements obtained by this technique were compared with results obtained by optical forced oscillation of a 1.5 µm silica bead that was linked to the cytoskeleton through attachment with integrin receptors in the plasma membrane.

Mechanical stresses and the resulting deformations are particularly relevant in lung epithelial cells because they experience a wide variety of mechanical forces in vivo including cyclic stretching, fluid dynamic shear stress, pressure gradients and surface tension forces [7, 15-18]. We choose to study lung epithelial cells as a first step to gain a better understanding of pulmonary physiology at the cellular and molecular levels.

2. Experimental setup and methods

2.1 Cell culture

For these studies, human lung epithelial type II cells (CCL-185 from American Type Culture Collection) were cultured in Ham’s F12K cell culture medium containing 10% fetal bovine serum (FBS), antibiotics including 1ml/100ml penicillin/streptomycin (100x) and 1ml/100ml amphotericin B. Cells were seeded onto 30mm diameter cover slips placed in 6 well plates by adding 2ml of a 3×104 cells/ml solution to each well. Cells were grown under standard culture conditions (37°C, 5% CO2 and 95% air) for 24 hours to obtain a sub-confluent monolayer (~25%). Protein-A coated 1.5µm silica beads (G. KISKER GbR, Germany) were treated with the anti-integrin αV antibody (Sigma, CD51) by incubation at 50 µg per 1 mg of beads in 1x phosphate buffered saline (PBS) solution [19]. The bead solution was added to the cell culture well containing the cell-seeded cover slip. After 20 minutes of incubation with the bead solution, the well was washed with PBS solution to remove unbound beads. This process allowed the bead to adhere onto the plasma membrane by the formation of integrin-antibody linkages, as is illustrated in Fig. 1, where the contact area between the cell membrane and the bead is characterized by the bead radius “a” and the half-angle θ.

Fig. 1. A schematic diagram of the integrin anti-body coated beads attaching to the plasma membrane (bead size not to scale).

2.2 Optical tweezer-based microrheometer setup

The use of oscillatory optical tweezers to trap and oscillate a particle embedded in an elastic medium and to measure its mechanical response has been demonstrated elsewhere [12-14, 20]. Fig. 2 shows the schematic diagram of the setup of an oscillating optical tweezer-based microrheometer used in this study. The expanded beam, with a size slightly larger than the back aperture of the microscope objective OBJ to achieve an “overfill, or full numerical aperture” condition. An infrared laser (Nd:YVO4 1064nm diode-pumped solid-state cw laser, Spectra Physics) was steered by a mirror mounted on a PZT piezo-electric 2-axis (orthogonal)

Integrin Antibody

Cytoskeleton

Nucleus

αv IngetrinIntegrin Antibody

Cytoskeleton

Nucleus

αv Ingetrinαv IntegrinIntegrin Antibody

Cytoskeleton

Nucleus

αv IngetrinIntegrin Antibody

Cytoskeleton

Nucleus

αv Ingetrinαv Integrin


tip/tilt platform (S-330, Physik Instrumente) which was connected to a function generator (a built-in function of the lock-in amplifier, Stanford Research SR-830).

The 1064 nm and a 633 nm HeNe laser beams (Uniphase, 5mW) joined with a beam combiner cube into a collinear configuration were launched into the right-side-port of an inverted microscope (Olympus IX-81) via a telescope lens pair, and directed into the direction of microscope optical axis via a dichromatic mirror (not shown). An oil immersion objective lens OBJ (NA=1.3, 100X, Olympus) was used to focus both laser beams to a common focus. The 1064 nm beam was used to trap and the 633 nm beam was used to track the position of dielectric probe particles inside the sample.

Fig. 2. A schematic diagram of the experimental setup. The area enclosed by the dashed lines represents an inverted optical microscope.

The tracking beam, diffracted by the moving probe particle, was collected by the condenser CDSR (NA = 0.9) and projected onto a dual-lateral position-sensing detector (PSD: PSM2-4 and OT-301, On-Trak) where the motion of the probe particle in the transverse sample plane (X-Y plane) was tracked in real-time. An optical filter was inserted to prevent 1064 nm beam from reaching the PSD. The lock-in amplifier, fed with signals from PSD and referenced with the sinusoidal electric signal that drove the PZT-driven mirror, provided the displacement amplitude and phase shift of the trapped particle with great sensitivity.

A CCD camera was installed on the microscope left-side-port to record bright-field images. The dichromatic mirror reflected laser beams and passed visible lights from the microscope halogen lamp so that sample imaging and rheological measurements could be performed simultaneously. The lock-in amplifier, PZT-driven mirror, and the microscope (including the CCD camera) were controlled by a PC.

2.3. System calibration

We applied an oscillatory optical force to a trapped bead and analyzed the oscillatory motion of the particle to determine the viscoelastic moduli of the media. The trapped bead was forced

HalogenLamp

Optical Filter

Dichromatic MirrorPosition SensingDetector

Lock - inAmplifier

CDSR Sample

MicroscopeOBJ

CCD

PC

FunctionGenerator

Beam Combiner

Telescope

633 nm

1064 nmBeam Expander

PZT - driven mirror


to oscillate along the x direction by the oscillatory tweezers driven by the PZT-controlled mirror. For a particle embedded in a viscoelastic medium, the trapped bead experiences a Stokes drag, a force from the oscillatory optical tweezers, and a negligible force produced by the 633 nm beam. The equation of motion of the trapped bead can be written as [12-14]:

( )6 cosOTmx ax kx k A t xπη ω+ + = −⎡ ⎤⎣ ⎦�� (1)

where m and a are the mass and the radius of the bead, x is the displacement of the bead relative to its unperturbed position, η(ω) and k(ω) are the frequency dependent viscosity and elasticity of the surrounding medium, A and ω are the amplitude and angular frequency of the oscillatory trapping beam and kOT is the spring constant of the optical trap. Taking into account the very low Reynolds number of the system, i.e., 6 ax mxπη >>� ��

, we ignore the first term mx�� in Eq. (1) and derive a steady-state solution to Eq. (1) as ( , ) ( ) cos [ - ( )]x t D tω ω ω δ ω= . The displacement amplitude, D, and phase shift relative to the phase of the oscillating tweezers, δ, can be written as [14]:

( )( ) ( )2 2

6

OT

OT

AkD

k k aω

πη ω=

+ + (2)

( ) 1 6tan

OT

a

k k

πη ωδ ω − ⎛ ⎞= ⎜ ⎟+⎝ ⎠

(3)

The first step in using the tweezer-based rheometer is to determine the trap spring constant kOT by applying the above two equations for water where η(ω) is the viscosity of water, and k(ω) is zero for all frequencies. Experimental data representing the frequency-dependent amplitude D(ω) and phase shift δ(ω) of an oscillating 1.5 µm silica bead in PBS solution and the corresponding theoretical fits are depicted in Fig. 3(a) and 3(b). The spring constant kOT deduced from the best fit is 14.52 pN/µm from the amplitude data and 13.63 pN/µm from the phase data; in this case η is taken to be 0.01 poise, the viscosity of water. We also tracked the Brownian motion of the same silica bead trapped by a stationary trapping beam and analyzed its position distribution and the optical force field using Boltzmann statistics for a particle in a parabolic potential well [21-23]; the optical spring constant deduced from this experiment (data not shown) is 13.85 pN/µm. The average of the two kOT values from the oscillatory tweezers approach (14.08 pN/µm) was used for the extracellular measurements where the same 1.5 µm silica beads were used.

Fig. 3. (a) The normalized amplitude (left), and (b) the relative phase (right) vs. the oscillation frequency of a 1.5 µm diameter silica bead in an oscillatory optical tweezers. The solid dots represent the experimental data and the solid lines are the fits with the spring constant kOT as the only fitting parameter.


3. Experimental Results

3.1. Intracellular Measurements

For intra-cellular probing, we used optical tweezers to trap and oscillate an internal granule (probably a lamellar body which abundantly exist in alveolar epithelial type II cells) [25] in a configuration shown in Fig. 4(A). Fig. 4(B) shows a bright-field image of these lamellar bodies. To further characterize these lamellar bodies, we used an image analysis software (Metamorph) to determine the area (A), perimeter (P) and width (W) of each lamellar body. This data was specifically obtained by using Metamorph’s “Integrated Morphometry Analysis” routine which automatically outlines the lamellar bodies based on appropriate thresholding of the image. Once A, P and W were known, we calculated the diameter as D=4*A/P and a sphericity parameter as S=D/W. Results indicate that the mean diameter for n=24 lamellar bodies was D=1.95 µm with a 95% confidence interval of [1.87µm, 2.08µm]. In addition, the mean sphericity parameter was S=1.05 with a 95% confidence interval of [1.03, 1.09]. Therefore, we conclude that the intracellular granules used in this study (i.e. lamellar bodies) were spherical, had a uniform spatial distribution and were ~2µm in diameter.

Fig. 4. (A) A sketch of optical tweezer-based cytorheometer. Optical tweezers were used to manipulate an intracellular granular structure (lamellar body, left circle), or an extracellular anti-body coated glass bead (right circle). (B) A bright-field image of lamellar bodies that abundantly exist in alveolar epithelial type II cells.

In this case, G′ and G′′ were determined from the experimentally measured particle displacement magnitude (D) and phase shift (δ) via the following two equations [12, 13]:

( ) ( ) ( )( )

cos1

6 6OT

k AkG

a a D

ω δ ωω

π π ω⎛ ⎞

′ = = −⎜ ⎟⎝ ⎠

(4)

( ) ( ) ( )( )

sin

6OT

AkG

a D

δ ωω ωη ω

π ω⎛ ⎞

′′ = = ⎜ ⎟⎜ ⎟⎝ ⎠

(5)

Since these organelles have different optical properties from that of the silica beads, the kOT used for calculating G* must be different from the value described in Sec. 2.3. Because the radiation gradient force scales as the optical contrast: [26, 27], where nm is the index of refraction of the surrounding medium, and m is the ratio of refractive index of the particle to the medium, we rescale kOT by taking the ratio of the estimated optical contrast of the organelles [composed of 80% proteins/lipids (n~1.5) and 20% water (n=1.33)] in the cytoplasmic fluids [80% water and 20% proteins] to the optical contract of the silica bead (n=1.45) in water. The rescaling reduced the kOT to approximately 61% of the value determined from a 1.5 µm silica bead in water. We did not consider further scaling of kOT due to the particle size difference between the lamella bodies and the silica particle because the gradient force is a weak function of the particle size for particles larger than the width of the

2 2( 1) /( 2)mn m m− +

-

A) B )

Nucleus


optical trap (~0.8µm) [28]. Note all experiments in this study were performed at room temperature.

Experimental data of the viscoelastic moduli obtained by trapping and oscillating a sub-micron intracellular organelle are shown in Fig. 5. Both G′ and the magnitude of the complex modulus |G*| followed a power law relationship with frequency as shown by solid lines in Fig. 5, i.e. G′=G′0(ω/ω0)α and |G*|=G*

0(ω/ω0)β. Data similar to those shown in Figure 5 were obtained in n=5 cells. We found that the intracellular G* measurements contained significant fluctuations and G′ > G" at most frequencies. From the measurements in 5 cells the mean value of the power-law exponents were α=0.24+0.09 and β=0.28+0.05, in agreement with Hoffman et al. [9] for the intracellular measurements (β=0.26). Here we report the power-law exponents (α and β) as mean + standard deviation and have used a one-sample Kolmogorov-Smirnov test to demonstrate that the α and β values follow a normal distribution (p=0.94 and p=0.99 for α and β respectively).The scaling parameters G′0 and G*

0 were found to follow a log-normal distribution. Specifically, a one-sample Kolmogorov-Smirnov test on the log’ed G′0 and G*

0 values indicate that this data is log-normally distributed (p=0.802 and p=0.718 for G′0 and G*

0 respectively). Therefore, “log-transformed” statistics were used to calculate the mean and 95% confidence intervals. The mean value for the scaling parameter G0 at a given frequency of 10Hz (ω0=62.8 rad/s) was G′0=181 dyne/cm2, 95% confidence interval [60.5 dyne/cm2, 543 dyn/cm2] and the mean value for G*

0 at 10Hz was G*0=221 dyne/cm2, [57.9

dyne/cm2, 845 dyne/cm2].

Fig. 5. Experimental data obtained by using intracellular organelles as probes: (A) G'(ω) and G"(ω), (B) G*(ω). Solid lines represent power-law fits to G' and G*

3.2. Extracellular Measurements

To apply an extra-cellular probe, we trapped an anti-integrin αV conjugated silica bead (diameter = 1.5µm) externally attached to the plasma membrane of the lung epithelial cell (shown in Fig. 1) and oscillated the trapping beam with an amplitude of A=100 nm. We determined the viscoelasticity of the cell from the amplitude (D) and the phase shift (δ) of the oscillating bead by modifying the approach developed for a bead embedded in a homogeneous and isotropic medium (see Eqs. 4 and 5) with an approach reported by Laurent, et al. [24] which accounts for a system in which the bead under a static force is located at the interface of an aqueous medium and a viscoelastic medium. In the case here, the storage modulus G′(ω) and the loss modulus G′′(ω) of the viscoelastic medium are given by:

( ) ( )( )3

cos3 cos1

4 2sin sinOT

AkG

a D

δ ωθωπ θ θ ω

⎛ ⎞⎛ ⎞′ = + −⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(6)


( ) ( )( )

sin3

16 sinOT

AkG

a D

δ ωω

θ ω⎛ ⎞

′′ = ⎜ ⎟⎜ ⎟⎝ ⎠

(7)

Due to the lack of an accurate measurement for the subtending half-angle θ (see Fig. 1), we assume θ = π/4 in all of our calculations. Note that the choice of θ only influences the magnitude of G′ and G′′ and does not influence power-law fits (see below). Estimates of G′ and G′′ using different values of θ yield a constant multiplicative factor to the values shown in Fig. 6. For θ in the range of 30 - 90 degrees, the multiplicative factors are 2.4 – 0.36 for G' and 1.4 - 0.71 for G", respectively. Because this multiplicative factor will be significantly larger when θ is smaller than 30 degrees, we avoided trapping any beads that were only very loosely bound to the cell surface, namely, the beads that visibly moved synchronously with the oscillatory trap at low oscillatory frequencies. By doing so, we also avoided making measurements on beads that were not anchored by integrins. Experimental data obtained for G′ and G′′ using an externally attached bead is shown in Fig. 6(A). A power-law fit for the storage modulus (i.e. G′=G′0(ω/ω0)α) is shown as a solid line. The results of |G*| and power-law fit (i.e. |G*|=G*

0(ω/ω0)β) are shown in Fig. 6(B). Similar measurements were obtained in n=20 cells and the mean power-law exponents were α=0.19+0.07 and β=0.27+0.06. We have used a one-sample Kolmogorov-Smirnov test to demonstrate that the externally measured α and β values follow a normal distribution (p=0.93 and p=0.80 for α and β respectively) and report α and β values as mean + standard deviation. We note that these values are in excellent agreement with results obtained by Fabry et al. [8] (i.e. α=0.17). We also calculated G′0 and G*

0 at a frequency of 10Hz (i.e. ω0=62.8 rad/s). Similar to the internal measurements, a one-sample Kolmogorov-Smirnov test on the log’ed G′0 and G*

0 values indicate that this data is also log-normally distributed (p=0.99 and p=0.97 for G′0 and G*

0 respectively) and “log-transformed” statistics were used to calculate the mean and 95% confidence interval. For external measurements the mean values were G′0=4570 dyne/cm2, [3050 dyne/cm2, 6830 dyne/cm2] and G*

0=5080 dyne/cm2, [3410 dyne/cm2, 7570 dyne/cm2]. The mean value of G*0

agrees well with other optical tweezer based measurements on the A549 cell line [29].

Fig. 6. (A) G'(ω) and G"(ω), (B) G*(ω) probed with anti-integrin conjugated silica beads attached to the plasma membrane. Solid lines represent power-law fit to G' and G*.

4. Discussions

To compare external and internal measurements of power-law rheology, we plot the mean values of the power-law exponents (α and β) and the scaling prefactors (G′0 and G*

0) in Fig 7. Since the exponents (α and β) were normally distributed, we utilized a two-tailed independent sample student t-test to compare means. As shown in Fig. 7(A), this t-test indicates that the mean values of α and β measured internally and externally are not statistically different (p=0.18 and p=0.84 respectively). Note error bars in Fig. 7(A) represent standard deviation. In contrast, a log-transformed, two-tailed independent student t-test was used to compare mean


stiffness values (G′0 and G*0) since they were log-normally distributed. These tests indicate

that the mean values of both G′0 and G*0 measured by trapping/manipulating intrinsic

intracellular granules is significantly lower than the mean values measured by trapping/manipulating a bead externally attached to the cytoskeleton via trans-membrane integrin receptors (p=1e-7 for G′0 and p=4e-7 for G*

0, see Fig. 7(B)). Note error bars in Fig. 7(B) represent 95% confidence intervals on a log-scale. These results indicate that although both external and internal measurements yield comparable power-law relationships, the internal storage and shear modulus is lower than the moduli measured using externally bound beads. Note that uncertainties in θ cannot account for such large differences between the intra and extra cellular measurements. To our knowledge, this is the first time that measurements of G′, G′′ and G*, have been made using the same technique on both intracellular and extracellular probes. The results obtained with this technique are consistent with reported values in the literature. For example, Yamada et al. [10] used laser-tracking microrheology to track intracellular granules and reported a shear modulus of G* ~ 102 - 103 dyne/cm2 for COS7 kidney epithelial cells. In contrast, Balland et al. [29] used optical tweezers to manipulate an RGD coated bead attached to the cell membrane and reported a shear modulus of, G* ~ 700 Pa or 0.7x104 dyne/cm2. Note that although these RGD coated beads are attached to the cytoskeleton via non-specific trans-membrane receptors, these investigators could not separately analyze the storage (G′) and loss (G′′) moduli components of G*. By contrast, one significant advantage of the current study is the ability to measure both G′ and G′′ using optical tweezers and the ability to utilize an intrinsic internal probe as well as an externally attached bead. The implication of our results is that measurements made with externally attached beads might overestimate the magnitude of the internal storage and shear moduli. Although the internal measurements made in this study showed large variations from cell to cell, these variations might be indicative of the intracellular dynamics and inhomogeneity intrinsic to live cells. Moreover, it is possible that the larger moduli measured with the external beads might be partly due to the extensional stiffness and/or other mechanical properties of the plasma membrane. To investigate the role of membrane mechanics, future measurements should utilize acLDL-coated beads which bind to low-density lipoprotein receptors since these receptors are not linked to the cytoskeleton [30]. However, both external and internal measurements demonstrate power-law relationships with exponents of ~ 0.2 - 0.3 which are consistent with several previous studies [8, 9, 29]. One potential source of error and/or variance with the external measurements is the degree of actin rearrangement that occurs around the integrin-coated bead. To investigate possible actin rearrangement, we obtained a bright-field image and fluorescent image of the actin cytoskeleton using a phalloidin stain as shown in Figs. 8(A) and 8(B). These images were obtained in the same location and after 20 minutes incubation with the integrin-coated beads. This image (as well as several similar images, not shown) indicates that there is minimal local restructuring of the actin cytoskeleton near the bead. We hypothesize that this may be due to short duration of incubation (20 min).


Fig. 7. (A) Power-law exponents of G' and G* for extracellular and intracellular data. Error bars represent standard deviation and means are not statistically different. (B) Magnitudes of prefactor G'o and G*o for extracellular and intracellular data. Error bars are 95% confidence intervals on log-scale and means are statistically different (p<0.01, log-transformed t-test).

Fig. 8. (A) A bright-field image of cells with a membrane-bound bead. (B) A fluorescent image of actin cytoskeleton (phalloidin) with bead location outlined in blue. Images indicate minimal local restructuring of the actin cytoskeleton near the bead due to short duration of incubation (20 min).

5. Conclusion

We used oscillatory optical tweezers to determine the intracellular viscoelasticity of human lung epithelial cells by forced oscillation of (1) an anti-integrin αV conjugated silica bead externally attached to the plasma membrane and, (2) an endogenous intracellular granule. The two methods yielded comparable results. Specifically, the storage modulus G' and the magnitude of the complex shear modulus |G*| were found to follow weak power law dependence with the oscillation frequency in the range of f = 1 Hz ~ 1,000 Hz, which is consistent with the soft glassy behavior of cellular materials. We have demonstrated that the optical forced oscillation of external probes attached to the cytoskeleton can provide reliable measurements of “whole-cell mechanics”, however, in comparison, the intracellular oscillation of endogenous organelles may be more useful in investigating intracellular heterogeneity and temporal fluctuations.

Acknowledgments

MTW and AC were supported by the National Science Council of the Republic of China Grants NSC 95-2752-E010-001-PAE, NSC 94-2120-M-010-002, NSC 94-2627-B-010-004, NSC 94-2120-M-007-006, and 95A-C-D01-PPG-01. SNG was supported by the American Heart Association Beginning Grant-In-Aid, an NSF CAREER award and is a Parker B. Francis Fellow of Pulmonary Research. AZ, JW and HDO were supported by the National Science Foundation grants: DMR-041259, EEC-0343283, and the Lehigh Center for Optical Technologies.


a comparative study of living cell micromechanical properties by oscillatory optical tweezers

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