nanomechanical properties of individual chondrocytes and...

Nanomechanical Properties of Individual

Chondrocytes and Their Developing Growth Factor-

Stimulated Pericellular Matrix

Laurel Nga, Han-Hwa Hungb, Alexander Spruntc,g,

Susan Chubinskayad, Christine Ortize, Alan Grodzinskya,b,c,f* aBiological Engineering Division, bCenter for Biomedical Engineering, Departments of

cMechanical Engineering, eMaterial Science & Engineering, and fElectrical Engineering and Computer Science,

Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139

and d Department of Biochemistry and Section of Rheumatology, Rush University Medical Center,

Chicago g currently at ATA Engineering, San Diego, CA

*Correspondence and requests for materials should be addressed to:

Correspondence to:

Alan J. Grodzinsky

77 Massachusetts Ave. NE47-377

Cambridge, MA 02139

Phone: (617) 253-4969

Fax: (617) 258-5239

Email : [email protected]

Keywords: cartilage, chondrocytes, nanomechanics, nanoindentation, growth factors

Word Count: 3,527 (Introduction through Discussion)

For Submission to Journal of Biomechanics as an Original Article

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ABSTRACT

The nanomechanical properties of individual cartilage cells (chondrocytes) and their aggrecan

and collagen-rich pericellular matrix (PCM) were measured via atomic force microscope

nanoindentation using probe tips of two length scales (nanosized and micron-sized). The

properties of cells freshly isolated from cartilage tissue (devoid of PCM) were compared to cells

that were cultured for selected times (up to 28 days) in 3-D alginate gels which enabled PCM

assembly and accumulation. Cells were immobilized and kept viable in pyramidal wells

microfabricated into an array on silicon chips. Due to the nonconventional but known geometry

of the microfabricated wells, Hertzian contact mechanics as well as finite element analyses were

employed to estimate apparent moduli from the force-depth curves. The effects of culture

conditions on the resulting PCM properties were also studied by comparing 10% fetal bovine

serum vs. medium containing a combination of insulin growth factor-1 (IGF-1) + osteogenic

protein-1 (OP-1). While both systems showed increases in matrix stiffness with time in culture

between days 7 to 28, the IGF-1 + OP-1 combination resulted in a higher stiffness for the cell-

PCM composite by day 28, and a higher apparent modulus of the PCM. These studies give

insight into the temporal evolution of the nanomechanical properties of the pericellar matrix

relevant to the biomechanics and mechanobiology of tissue engineered constructs for cartilage

repair.

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1.Introduction

Chondrocytes occupy only 3-5% of the volume of adult articular cartilage and, hence, do

not contribute significantly to the bulk mechanical properties of the tissue (Stockwell and

Meachim 1979). However, they are responsible for the synthesis, maintenance, and turnover of

the tissue’s extracellular matrix (ECM). Mechanical loads and deformations applied to cartilage

in vivo and in vitro are known to regulate chondrocyte synthesis and catabolic degradation of

ECM macromolecules (Fitzgerald et al., 2004;Guilak et al., 1994;Kim et al., 1994;Valhmu et al.,

1998). The mechano-regulation of chondrocyte metabolism in tissue engineering gel scaffolds

depends partly on the cell’s environment and the development stage of the newly synthesized,

cell-associated pericellular matrix (PCM)(Buschmann et al., 1995).

The 2-4µm thick PCM contains a high percentage of typeVI collagen and proteoglycans

(PGs)(Poole et al., 1992;Poole et al., 1988a) and is critically important to biochemical and

biomechanical cellular function(Petit et al., 1996).

The PCM transfers loads from the ECM to the cell and its cytoskeleton and intracellular

organelles during physiologically-induced deformations in compression, shear, and tension. Thus

the mechanical properties of individual chondrocytes with and without their PCM have been

measured using micropipette aspiration (Guilak 2000), cytoindentation (Koay et al., 2003), and

in unconfined compression (Leipzig and Athanasiou 2005). Apparent moduli of isolated

chondrocytes were reported in the range 0.6-4kPa from micropipette aspiration and compression

of cells in agarose (Freeman et al., 1994). The PCM in adult cartilage has a higher modulus than

the cell (~60-70kPa) as measured via micropipette aspiration (Alexopoulos et al., 2003;Guilak et

al., 1999), compression of chondrons in agarose (Knight et al., 2001), and AFM indentation

(Allen and Mao 2004).

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The PCM may also act as a regulator of cell signaling. Scaffolds seeded with chondrons

containing intact PCM accumulated proteoglycans and typeII collagen more rapidly than parallel

cultures of enzymatically isolated chondrocytes initially devoid of PCM (Graff et al., 2003).

Chondrocytes treated with insulin-like growth factor(IGF-1) and osteogenic protein-1(OP-1)

showed increased PCM accumulation compared to chondrocytes maintained in fetal bovine

serum(FBS) (Flechtenmacher et al., 1996;Loeser et al., 2003;McQuillan et al., 1986;Nishida et

al., 2000;van Osch et al., 1998). Architecture and morphology of this newly developing PCM

differ from adult chondron PCM as seen in immunohistochemistry of typeVI collagen which

revealed a compact structure in adult chondrons but had a diffuse appearance in immature tissue

(Lee and Loeser 1998). Taken together, efforts to create tissue engineered cartilage require

detailed understanding of pericellular microenvironments.

In this study, we examined the mechanical properties of immature bovine cartilage

chondrocytes and their newly developing PCM using atomic force microscope (AFM)-based

indentation (i.e., measurement of force, F, versus indentation depth, D, on loading and unloading

at two length scales via a nanosized tip (end-radius, Rtip~40nm) and a micron-sized tip

(Rtip~2.5µm). The use of AFM to probe the mechanical properties of individual living cells has

been reviewed (A-Hassan et al., 1998;Lehenkari et al., 2000a;Radmacher 1997) and applied in

the context of mechanotransduction (Charras and Horton 2002), disease (Chasiotis et al., 2003),

drug effects (Rotsch and Radmacher 2000), and lysis kinetics(Hategan et al., 2003). To apply

this technique to phenotypically round, nonadherent chondrocytes, we first developed

microfabricated surfaces with wells to immobilize individual cells while keeping them viable.

Freshly isolated chondrocytes, and cells released from 3D alginate gels after selected times in

culture, were immobilized on these microfabricated surfaces, and studied nanomechanically to

determine the effects of the newly developing PCM on cell-PCM stiffness. Cultures were

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supplemented with either FBS or the combination of IGF-1+OP-1 to compare the effects of these

anabolic stimulants on PCM development. The temporal evolution of cell-PCM biomechanical

properties was compared to total GAG and collagen accumulation over time in culture by

alginate-released cells. Apparent cell and PCM moduli were estimated from nanoindentation data

using Hertzian contact mechanics and finite element analyses (FEA).

2.Materials and methods

2.1 Cell isolation and culture

Chondrocytes were isolated from femoral condyle cartilage of 2-3 week old bovine

calves using sequential 0.2% pronase(Sigma) and 0.025% collagenase (Boehringer Mannheim)

digestions as described(Ragan et al., 2000). Cell viability after isolation, assessed by trypan blue

(Sigma) exclusion, was >95%. Cells were seeded at 20x106 cells/ml in 2% w/v alginate

(KelcoLVCR) in 0.9% NaCl. Beads ~3mm diameter were formed through polymerization of

droplets of alginate dispensed from a 22-gauge needle into 102mM CaCl2 solution. At selected

times in culture, cells were released from alginate beads by depolymerization in a calcium

chelator (Hauselmann et al., 1992;Petit et al., 1996), 55mM NaCitrate, as described(Masuda et

al., 2003). In one series of experiments, cell-seeded beads were maintained in hi-glucose DMEM

with 10% FBS, 20µg/ml L-ascorbic acid(Sigma), and 1% antibiotic-antimycotic(Sigma). In a

second series, cells were cultured in hi-glucose DMEM supplemented with 100ng/ml

recombinant human IGF-1 (PreproTech), 100ng/ml recombinant human OP-1 (Stryker Biotech,

Hopkinton, MA), mini-ITS (Benya and Padilla 1993)(containing 5nM insulin (Sigma) to

minimize stimulation of the IGF-1 receptor, 2µg/ml transferrin (Sigma), 2ng/ml selenous acid

(Sigma), 420/2.1µg/ml linoleic acid-albumin from bovine serum albumin (Sigma)), 55µg/ml L-

ascorbic acid), and 1% antibiotic-antimycotic. Seven alginate beads were cultured in 3ml

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medium per well (12 well plate); medium was changed every other day.

2.2 Histology and immunohistochemistry of type VI collagen

Cells released from alginate were resuspended in culture medium (1x106 cells/ml) and

fixed in 2%(v/v) glutaraldehyde solution (Polyscience) buffered with 0.05M sodium cacodylate

(Sigma), and containing 0.7%(w/v) of ruthenium hexaamine trichloride (RHT, Polyscience) to

minimize loss of PGs during fixation (Hunziker et al., 1982). Fixed cells were mounted onto

glass slides using a Cytospin (1,400rpm for 10min), air dried, and stained for sulfated-PGs

(Toluidine BlueO, Sigma) and collagen (phosphomolybdic acid followed by aniline blue

(Rowley Biochemical))(Luna 1968). In addition, cells from day39 culture were released,

mounted on glass slides, dried for 3hours, treated with 2mg/ml hyaluronidase (Sigma) in 0.1M

Tris(hydroxymethyl)aminomethane-HCl, pH 5.8, for 2.5 hours at 37°C to expose typeVI

collagen epitopes, then blocked with 5% donkey serum in PBS, pH 7.1, for 4 hours. The

antibody for typeVI collagen (Chemicon) was incubated on the slides overnight (1:10 dilution in

1% donkey serum in PBS), then incubated with a secondary rhodamine-conjugated antibody

(1:50 dilution in 1% donkey serum in PBS) for 4 hours. Slides were rinsed with PBS after each

step; fluorescently labeled cells were viewed using a Nikon TE300 microscope. Cell viability

after release was >90% as assessed using fluorescein diacetate (0.2mg/ml) and ethidium bromide

(10µg/ml) (Sigma).

2.3 Cell appearance and pericellular biochemical composition

Dimethyl methylene blue dye binding (DMMB)(Farndale et al., 1986) and

hydroxyproline(Woessner 1961) assays were used as measures of sulfated-GAG and collagen

content, respectively. Optical micrographs of cells released at each time point were obtained to

measure cell diameter and to aid in estimating PCM thickness.

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2.4 Atomic force microscope imaging

Tapping mode AFM (TMAFM) images were taken of chondrocytes adsorbed on mica

(SPI Supplies, West Chester, PA) in ambient conditions using a Multimode Nanoscope IIIa

(Veeco, Santa Barbara, CA) and Olympus AC240TS-2 rectangular Si cantilevers (k~2N/m,

Rtip<10nm).

2.5 Microfabrication of Silicon Substrates for Single Cell Immobilization

Microfabricated substrates were prepared from silicon wafers at MIT’s Microsystems

Technology Laboratory and contained an array of inverted square pyramidal wells to hold a

single cell in each well (Fig.1a,b). Substrates with well side-dimensions of 15, 18, 20, or 22µm

were designed to hold freshly isolated cells and cells with associated PCM.

2.6 Nanoindentation

Silicon substrates were cleaned in piranha solution (3:1 concentrated H2S04/H2O2(30%))

rinsed with acetone and DI water, and then immersed in DI water for 2days. Culture medium was

allowed to coat the silicon surface for 5 minutes. Then 100µl of cell suspension was dropped

onto the surface just prior to nanomechanical testing. The silicon wells, cells, and cantilever

probe tip could be visualized with a 10× optical microscope attached to the AFM (Fig. 1b). An

AFM probe tip was used to push a cell laterally into a silicon well and then to perform cycles of

nanoindentation (Fig. 1c). The cell-containing well was identified and indentation was then

repeated on the same cell using a second probe tip of different size (Fig. 1c). The Picoforce

NanoscopeIV AFM(Veeco) was used to obtain indentation (F-D) data at z-piezo displacement

rates of 200nm/s, 500nm/s, 1µm/s, 3µm/s, 5µm/s, and 10µm/s. No significant change in load-

unload hysteresis was observed up to 1µm/s. Above 1µm/s, the area enclosed by the hysteresis

loop increased in a logarithmic fashion. Therefore, to limit the contribution of cellular

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visco/poro-elastic effects to the measurements, data obtained at 1µm/s are the focus of this paper

(Appendix A). A standard Si3N4 AFM square pyramidal tip (Veeco, Rtip~50 nm, k~0.06N/m) and

a colloidal probe tip were used. The colloidal probe tip was prepared using the AFM by attaching

2.5µm radius silica beads (Bang Labs) onto tipless cantilevers (Veeco, k~0.06N/m) with low

viscosity epoxy (SPI, MBond610). Cantilever spring constants were calibrated individually by

the thermal oscillation method(Hutter and Bechhoefer 1993).

2.7 Cell stiffness

Apparent elastic moduli were estimated from the nanoindentation data using 3 models:

the Hertz model for a conical tip and a spherical (colloidal) tip, the slopes of stress/strain curves

in the small strain region, and elastic FEA simulations. Analysis of cell moduli was limited to

indentation depths less than 10% of the cell diameter, a small strain regime that minimized

artifacts introduced from substrate effects (Tsui and Pharr 1999).

FEA were carried out with ABAQUS (Providence, RI). ¼ of the tip and cell were

modeled; the well walls remained fixed in all directions, a frictionless boundary condition

between the elastic cell and rigid well wall was used, and the displacement of the tip occurred

only in the z-direction (normal to the cell) to ensure symmetry (see Appendix B for details).

2.8 Statistics

For PCM thickness and force-indentation curves of individual cells (n=5 replicate loading

cycles applied to the cell), data are reported as mean±SD. When averaging loading curves for

multiple cells, with each cell subjected to five replicate loading cycles, data are reported as

mean±SE. Changes in PCM thickness were tested using ANOVA. The effects of depth and tip

radius or culture time on indentation force were tested using two-way ANOVA. When

significant effects (p<0.05) were detected, comparisons between groups were performed using

the Tukey post hoc test.

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3. Results

3.1 Characterization of pericellular matrix

TMAFM images in air show that freshly isolated cells (day0) had no distinct PCM (Fig.

2a). After day6 (10% FBS culture), a PCM layer was clearly observed (Fig.2b is a typical image

for day11). By day18 (Figs. 2c,d), type II collagen could be identified in the PCM as reported

previously in alginate gel beads using immunohistochemistry and gel electrophoresis (Petit et al.,

1996). Here, TMAFM showed fibril diameters of 59±9nm with a prominent small banding

periodicity of 22±2nm, n=10, likely associated with the 0.4D overlap zone within the primary

D=67nm periodicity (Eyre 2005;Hodge 1967;Ortolani et al., 2000).

Images of fixed cells (Fig.3) confirmed that freshly isolated cells (day0) had no visible

accumulation of PG or collagen. By day7, PGs stained uniformly around the entire cell for both

the FBS and IGF-1+OP-1 cultures. Collagen staining was minimal for FBS but distinct for IGF-

1+OP-1 cultures, both around the cell membrane and as a diffuse halo extending outward from

the cell. By day14, PG staining increased in diameter and intensity for both cultures, and

collagen staining appeared around FBS cultured cells. By the third and fourth weeks in culture,

no substantial changes in PG staining were observed, but collagen staining increased slightly in

intensity and extent for both cultures. PG staining generally appeared greater with IGF-1+OP-1

compared to FBS at all time points. While pericellular collagen staining appeared to extend

further from the cell with IGF-1+OP-1, staining intensity remained diffuse. Cell diameter

(excluding PCM) was 7.65±0.85µm (mean±SD). PCM thickness by optical microscopy was ~3-

4µm between days7-28, and did not change significantly during this time (Fig.4a). Instances of

dividing cells sharing matrix were observed but were not used for nanoindentation. Cell viability

in gel culture remained above 80%, and chondrocytes retained their spherical phenotype

(Fig.4b).

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TypeVI collagen was visible in the PCM of FBS-(Fig.4c) and IGF-1+OP-1-cultured cells

(not shown) processed at day 39, similar to that found in related experiments with same-aged

bovine calf chondrocytes on day 7, 14, and 21 in agarose gel (DiMicco et al., 2005). Thus, these

cells were capable of synthesizing and depositing this important component of the PCM in gel

culture. Biochemical characterization showed that GAG and collagen content increased rapidly

between days 0 and 14 in both cultures (Fig.5). Between days 14-28, total collagen content did

not appear to increase in either culture; GAG content continued to increase but was lower in FBS

compared to IGF-1+OP-1 cultured cells up to day28.

3.2 Indentation of freshly isolated cells

Indentation tests performed on single freshly isolated cells (day0) using both the

nanosized and micron-sized probe tips consisted of 5 sequential loading-unloading cycles

averaged at one location at a displacement rate of 1µm/s (Fig.6). A nonlinear increase in

repulsive force with indentation depth was observed; the small standard deviations for the 5

cycles indicated reversibility of deformation after each cycle. Subsequent comparisons between

days and culture conditions utilized only the loading component of the cycle. For day0 cells, the

micron-sized probe tip produced significantly different forces than the nanosized probe tip at the

same indentation depth (p<0.05) (Fig.7). The Hertz model predicted an apparent cell modulus

between 0.7-1kPa (Appendix B). FEA simulations accounting for cell and tip geometry and

boundary conditions (Fig.8a) predicted an apparent cell modulus between 2.3-3kPa for the

micron-sized probe tip (Fig.8b) (Appendix B).

3.3 Indentation of cells with newly developing pericellular matrix

For cells in 10% FBS, both probe tips revealed stiffening of the cell-PCM composite with

time in culture up to day28 (p<0.05) (Fig.9a and b). For the nanosized probe tip, this stiffening

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with time was apparent for data in the range D>700 nm, while for the micron-sized probe tip,

stiffening was pronounced throughout most of the indentation range. Interestingly, the cell-PCM

composites were always less stiff than the freshly isolated day0 cells devoid of PCM (p<0.05)

(Fig.9a,b). For day28 cells, the nanosized and micron-sized tips showed similar nanoindentation

behavior for D<900 nm (Fig.9c), while for D>900nm, the nanosized tip force exceeded the

micron-sized tip at the same indentation depth.

Cell-PCM composites in IGF-1+OP-1 also stiffened with time, observed with nanosized

and micron-sized tips, and to a greater degree than the FBS-cultured cells (Fig.10). By day 28,

cell-PCM composites were stiffer than freshly isolated day0 cells (p<0.05)(Fig.10). A modified

FEA model of a cell with a surrounding elastic (PCM) shell, indented by the micron-sized tip,

was used to estimate apparent moduli of the PCM. Using the apparent modulus of day0 cells

with no PCM (2.75kPa, Fig.8b) the shell modulus was varied until the model output matched the

experimental data. For day21 FBS cultured cells, the shell modulus was 0.1kPa and by day28,

the shell modulus increased slightly to 0.17kPa. For the day 21 IGF-1+OP-1 cultured cells, the

shell modulus was 10× stiffer than the FBS cultured cells at 1kPa and by day28, the shell

modulus was 26× stiffer at 4.15kPa (Fig.8d). See Appendix B4 and Table A1 for more details.

4. Discussion

4.1 Mechanical properties of freshly isolated (day 0) cells

While the micron-sized probes interrogate cellular-scale properties, the small radius of

curvature of nanosized probes are expected to be more sensitive to local cellular structures such

as cytoskeletal elements and intracellular organelles. Nevertheless, the estimated modulus

measured at both length scales was of the same order. This is in contrast to previously reported

measurements on intact cartilage where the stiffness was 100× greater with a micron-sized probe

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compared to a nanosized probe (Stolz et al., 2004). Hysteresis observed during the sequential,

reversible loading/unloading cycles (Fig.6) suggested the presence of time-dependent material

behavior (see Appendix B.5 for estimates of viscoelastic properties).

4.2 Pericellular matrix development

Developing PCM was confirmed and characterized using AFM imaging, measurement of

collagen and GAG content, histological assessment of collagen and sulfated proteoglycans, and

immunofluorescence labeling of typeVI collagen. The appearance of the PCM structure (e.g. a

dense network of collagen fibrils) observed by TMAFM imaging (Fig.2) was similar to

characteristic features of protease-digested native cartilage by TEM (Jurvelin et al., 1996) and

AFM (Stolz et al., 2004). GAG and collagen accumulation with time in culture (Fig.5) were

qualitatively similar to that previously reported (Ragan et al., 2000), and the enhanced

accumulation of GAG resulting from IGF-1+OP-1 compared to FBS treatment was consistent

with previous studies (Loeser et al., 2003). Histology showed a larger collagen-stained region for

IGF-1+OP-1 compared to the FBS-fed cells, though likely more diffuse and containing less total

collagen at later times, as suggested by Fig.5b. Type VI collagen (Fig.3c), characteristic of the

PCM, appeared as a diffuse halo around cells as seen by Lee and Loeser (1998), compared to the

compact and more uniform PCM of fully developed chondrons (Poole 1997).

4.3 Mechanical properties of cells with developing PCM

Cell cultures supplemented with FBS or IGF-1+OP-1 produced cells with a developing

PCM that increased in stiffness from day7 until day28 in culture (Fig.9). While the estimated

thickness of the PCM did not change significantly after day7 (Fig.4a), GAG and collagen levels

increased substantially from day7 to day14, suggesting an increase in PCM density consistent

with increased PCM stiffness (Fig.9). However, IGF-1+OP-1 cultured cells showed increases in

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stiffness despite a leveling of PGs and collagen. One explanation may be that the PCM is

undergoing molecular organization of the small PGs and collagen, as well as collagen

crosslinking (Chang and Poole 1997;Eyre et al., 1987;Poole et al., 1988b). In addition, OP-1 has

been found to help chondrocytes retain their developing PCM after release from alginate

(Nishida et al., 2000). While the developing PCM appears to accumulate quickly in culture, the

molecular structure and collagen architecture within the PCM may not resemble that of fully

developed adult chondrons.

For the FBS fed cells, it was notable that the stiffness of the cell-PCM composite even

after day28 in culture was markedly less than that of freshly isolated cells, consistent with

formation of a soft PCM of GAG, collagen, and other matrix molecules loosely organized around

the cell membrane. As seen previously by immunofluorescence to the keratin sulfate antibody

5D4 (Lee and Loeser 1998), newly developing matrix has a diffuse appearance. Thus, the early-

time PCM structure, when probed via indentation, had an apparent modulus less than the cell

itself. Contrary to the freshly isolated cells (Fig.7), the same amount of force was generated with

the micron-sized tip and the nanosized tip up to D~900 nm (Fig.9c). One hypothesis is that the

sharp nano-tip penetrated the developing PCM layer and came into closer contact with the stiffer

cell membrane, thus generating as much force as seen by the larger micro tip, which may not

have easily penetrated the PCM and thereby sensed bulk PCM properties.

In comparison, the IGF-1+OP-1 cultured cell-PCM composites released on day28

showed a significant increase in stiffness over day0 cells with both the probe tips (Fig.10).

Because the FEA had difficulty converging at depths greater than 200nm for the nanosized tip

due to the sharpness of the tip, we focus on FEA analysis with the micron-sized tip. For the first

600nm, the shell model predicted the experimental data well and gave a PCM modulus of

0.16kPa for the day28 FBS cells (Fig.8c), a value much lower than freshly isolated cells. The

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shell model compared well to the full range of data for the IGF-1+OP-1 supplemented cells

(shown in Fig.8d for first 600nm) giving a PCM modulus of 4.15kPa, higher than that of freshly

isolated cells (2.75kPa). By comparison, the moduli of newly developing PCM for both cell

treatments was much lower than that reported for native adult chondron PCM (Allen and Mao

2004;Guilak et al., 1999) possibly due to the more mature PCM structure in adult tissue.

IGF-1 alone has been shown to increase proteoglycan content in newly developing PCM

(van Osch et al., 1998). OP-1 has also been shown to increase proteoglycan (Nishida et al., 2000)

as well as collagen synthesis and accumulation in newly developing PCM (Flechtenmacher et al.,

1996). The combination of IGF-1+OP-1 has been shown to increase cell division as well as

promote proteoglycan content in the newly developing PCM (Loeser et al., 2003). IGF-1+OP-1

treatment may cause additional modifications in PCM ultrastructure, including changes in

macromolecular packing density and organization as well as increased collagen cross-linking.

4.4 Concluding remarks

In conclusion, a microfabricated surface was created to immobilize individual

chondrocytes and their newly developing PCM to maintain a spherical phenotype during

indentation tests. Apparent cell and PCM moduli were estimated from nanoindentation data

using Hertzian contact mechanics and FEA. Temporal evolution of the cell-PCM composite in

response to IGF-1+OP-1 and FBS supplements in cell cultures showed that the former led to a

greater GAG accumulation as well as a significant increase in stiffness observed by nano-

indentation measurements, indicating perhaps are more developed PCM ultrastructure. For both

cell cultures, the developing PCM properties showed increasing stiffness over a culture period of

one month. A longer term study may reveal the kinetics by which continued increases in PCM

stiffness could lead to the properties of fully developed chondrons, such as that measured via

micropipette aspiration (Guilak et al., 1999;Jones et al., 1999) and AFM (Allen and Mao 2004).

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Acknowledgements: This work was supported by NSF-NIRT 0403903, NIH Grant AR33236,

and a Whitaker Foundation Fellowship (LN). The authors would also like to thank Dr. Eliot

Frank for contributions to viscoelastic modeling, and to the MIT Institute for Soldier

Nanotechnologies funded through the U.S Army Research Office for use of instrumentation.

5. Appendix (Supplementary Material)

Appendix A. Experimental quantification of the rate-dependence of indentation hysteresis of

individual chondrocytes

Freshly isolated cells were probed with the nanosized and micron-sized tips at indentation

rates of 200nm/s, 500nm/s, 1µm/s, 3µm/s, and 5µm/s. The area enclosed by the hysteresis loop

(e.g., Fig. 6) is related to the strain energy dissipated during cyclic loading of the cell, which is

most likely associated with viscoelastic and/or poroelastic cell behavior (Leipzig and Athanasiou

2005). The hysteresis loop area was calculated by fitting the loading and unloading curves to

polynomials, integrating, and subtracting the area under the unloading from that of the loading

curve. Hysteresis was seen at all rates and normalized to the area obtained at 1µm/s (Fig. A1). In

this study, an increase in hysteresis was not seen between 200nm/s to 1µm/s indentation rates,

indicating a pseudo-steady state within this loading regime, giving an estimated relaxation time

constant of ~1s (based on a rate of 1µm/s). A previous study involving cytoindentation of single

adult bovine chondrocytes reported a time relaxation constant of 1.32s (Koay et al., 2003).

Similar hysteresis behavior was reported previously for skeletal muscle cells for which hysteresis

did not decrease below 500nm/s (Collinsworth et al., 2002). We therefore used 1µm/s z-piezo

displacement for data collection. Hysteresis was thereby minimized in order to reduce the

contribution of cell visco- and poroelastic dissipation and thereby calculate the apparent elastic

properties of the cell (A-Hassan et al., 1998).

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Appendix B. Theoretical modeling of indentation of individual chondrocytes for the estimation of

apparent elastic moduli

B.1. Hertz model (isotropic elastic half-space)

Using the small strain region (ε<0.05) corresponding to an indentation depth up to 300

nm for the data of Fig.7, the Hertz model was used to calculate an apparent modulus for the

nanosized and micron-sized tip. The modified Hertz model of a rigid conical probe tip in contact

with an elastic material was used for the nanosized tip indentation (Radmacher 1997):

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EF D2 (1 )

tanπ αυ

=−

(A1)

where F = force (nN), D = indentation depth (µm), E = Young’s modulus (cell, kPa), υ =

Poisson’s ratio (taken as 0.4 (Freeman et al., 1994), and probe tip angle α = 35°. The Si3N4 tip

(modulus~400GPa (Petersen 1982)) can be assumed rigid compared to the cell (modulus ~1kPa).

This model gave an average modulus E = 0.85 kPa (Fig. A2a). Matching the Hertz model to the

upper and lower limits of the standard error gave a modulus range between 0.7kPa to 1.0kPa

(Table A1).

For the micron-sized tip, the Hertz model of two contacting spheres was used assuming a

rigid colloidal tip and an elastic cell (Johnson and Greenwood 1997):

3/ 22

1 2

4 11 13 (1 )

EF D

R Rν

=− +

(A2)

where R1 = radius of micron-sized tip (µm) and R2 = radius of cell = 7.65 µm. The Hertz model

compared well to the experimental data with a modulus of 1kPa (Fig. A2b). The upper and lower

limits matched the standard error with moduli of 1.12kPa and 0.82kPa, respectively.

16

The apparent moduli of 0.70 - 1.00 kPa and 0.82 - 1.12 kPa for the nanosized and

micron-sized tips, respectively, were significantly different (p<0.05, unpaired t-test). These

values are in the range between 0.65 - 2.47 kPa reported previously using micropipette aspiration

(Jones et al., 1999) and unconfined compression (Leipzig and Athanasiou 2005). Interestingly,

the apparent elastic cell moduli estimated from our nanosized tip data were significantly lower

than those estimated from the micron-sized probe tip data. Previous studies have also

emphasized differences in matrix (Stolz et al., 2004) and cellular properties (Lehenkari et al.,

2000b) measured at nano- versus and micron- length scales. Of course, all such elastic models

are based on the simplifying assumption that the cell can be represented as a homogeneous

elastic solid. It should be noted that while we assume a simple elastic model, the hysteresis seen

with both probe tips (Fig. 6) indicated that more complex viscoelastic and/or poroelastic

behavior was present. Ongoing studies are focused on estimation of poro-viscoelastic cell

parameters from these data.

B.2. Stress-strain

A stress-strain (σ-ε) curve was calculated from the force-indentation depth data of Fig. 7

using the 0 - 200 nm depth range for the micron-sized tip. The stress was calculated by dividing

force by a contact area that increased with indentation depth.

σ =FA

and 22

DR

ε = (A3)

where A = 2πR1D. A modulus of 1.96 kPa was calculated from the slope of the σ-ε curve (Fig.

A3), which was linear in this range. The Hertz model and stress-strain estimation for the micron-

sized probe tip yielded similar apparent moduli for freshly isolated chondrocytes. Due to the

complex contact interaction between the sharp nanosized tip and the cell, an accurate stress-

strain curve could not be estimated.

17

B.3. Finite element analysis: Effect of mesh density and boundary conditions

Finite element analysis was used only for the micron-sized tip as the nanosized tip

simulations had difficulty converging at depths larger than 150nm due to its small radius of

curvature relative to the indentation depth. The fixed parameters were probe tip end-radius of

2.5µm, cell diameter of 7.6 µm, and Poisson's ratio of 0.4 (Freeman et al., 1994;Jones et al.,

1999). The fitting parameter was the cell modulus. Contact between the indenter and cell was

frictionless. A 20-node quadratic brick mesh (C3D20 in ABAQUS element library) was seeded

with a higher density in the vicinity of the contact region of the probe tip where larger stresses

and strains occurred. To verify that the mesh was dense enough to obtain accurate results, two

different densities of meshes were implemented and showed agreement of the resultant F-D

curves. Boundary conditions may also influence the FEA results. The exact interaction between

the cell and well wall are unknown, so the two extremes of no-slip and frictionless boundary

conditions were implemented. Interestingly, a no-slip boundary condition between the elastic cell

and rigid wall resulted in a lower modulus (by ~25%) compared to the frictionless boundary

condition. This implies that if the wall is frictionless, then the tip has to indent more of the cell to

obtain an equally large resultant force to that of the no-slip wall, which may be due to the cell

“slipping” into the well.

B.4. Cell-PCM elastic two-layered finite element analysis

The elastic cell, 7.6µm diameter, was modeled with a modulus of 2.75kPa. The elastic

PCM was modeled as being 3.65µm thick with the modulus used as the fitting parameter. A

PCM modulus of 4.15 kPa was needed to match the experimental data, consistent with the

observation that IGF-1+OP-1 treatment produced much stiffer cells-PCM composites by day 28.

At an indentation distance of 860 nm, the cell was more deformed (0.155 µm vs. 0.014 µm)

18

when surrounded by the stiffer PCM. The softer PCM absorbed the indentation force and did not

cause cell deformation as readily as the stiffer PCM. Interestingly, the deformation of the PCM

by the tip was approximately the same for both the 0.1 kPa and 4.15 kPa PCM stiffness (0.63 µm

vs. 0.59 µm, respectively).

B.5. Viscoelastic and poroelastic models

Quasi-static viscoelastic models to predict creep and stress relaxation behavior and to

extract instantaneous and equilibrium moduli, viscosity, and a relaxation time constant have been

developed in the area of nanoindentation of polymeric films such as polystyrene, semicrystalline

polyvinyl alchohol (Cheng et al., 2005), and poly(methyl methacrylate) (PMMA), and poly

(dimethylsiloxane) (PDMS) (Oyen and Cook 2003;VanLandingham et al., 2005). A similar

approach has been used along with unconfined compression tests to estimate parameters for

individual chondrocytes (Leipzig and Athanasiou 2005;Shieh and Athanasiou 2005). By

applying small sinusoidal oscillations (2-50 nm amplitude at 0.1 - 300 Hz), dynamic viscoelastic

models have been used to calculate storage and loss moduli of PMMA and PDMA films via

nanoindentation (White et al., 2005). Dynamic testing has also been performed via AFM with a

colloidal probe tip for single cells such as fibroblasts (Mahaffy et al., 2004), alveolar epithelial

cells(Rico et al., 2005), and smooth muscle cells (Smith et al., 2005), and using a nanosized

pyramidal tip for lung epithelial cells (Alcaraz et al., 2003). In these approaches, the form of the

elastic Hertz model was extended to incorporate time-dependent behavior and thereby derive

viscoelastic material parameters. Poroelastic models, which include the spatial and temporal

dependence of fluid-solid frictional interactions and intracellular pressure gradients to

characterize time dependent cell deformation behavior, have also been used to predict the

effective equilibrium elastic modulus and the hydraulic permeability of single chondrocytes,

19

modeled as homogeneous, linear, isotropic biphasic media in unconfined compression (Leipzig

and Athanasiou 2005). The recent experimental identification of non-equilibrium intracellular

hydrostatic pressure gradients within the cytoplasm, or blebs, of filamin-depleted melanoma cells

(Charras et al., 2005) have, indeed, suggested that such poroelastic behavior may be intrinsic to

transient or dynamic cell deformation.

Motivated by the observed hysteresis in our nanoindentation experiments, we first used

the simple three-element viscoelastic solid model of Eq. (A4) (Leipzig and Athanasiou 2005) to

calculate effective viscoelastic parameters corresponding to the micron-sized tip data of Fig. 6b:

/0

0

1 1( )

tE E eE t E E E

τ−∞

∞ ∞

−= + (A4)

Using a value for the relaxed modulus, E∞ = 1 kPa, corresponding to effective equilibrium

modulus predicted from the Hertz model derived from the data of Fig. A2b, the hysteresis loop

area at a loading rate of 1 µm/s data (i.e., Fig. 6b) was reasonably well matched using parameter

values for the instantaneous modulus, E0 = 2 kPa and the time constant τ = 0.1 s. Interestingly,

these values of E∞ , E0 , and τ are all within a factor of 2-3 of those reported by Leipzig and

Athanasiou, 2003. We note, however, that these calculated values were found to vary with

loading rate, as the measured hysteresis (Fig. A1) did not increase proportionally with loading

rate. Therefore, our ongoing studies focus on extensions using dynamic viscoelastic models to

calculate frequency-dependent storage and loss moduli (G'(ω), G"(ω)) describing the relaxation

spectrum as well as poroelastic models that incorporate both time and space dependence as well

as nonlinear behavior.

20

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25

Figures

Cell solution

15 µm

AFM cantilever

chondrocyte

(b)

cell

(a)

(c)

Cell solution

15 µm

AFM cantilever

chondrocyte

(b)

cell

(a)

(c)

Fig. 1. (a) Schematic of micron-sized square pyramidal wells in a silicon substrate used for cell immobilization and nanomechanical measurements. (Indentation of chondrocytes was attempted on mica but the flat surface was not suitable as the cells rolled away from the tip.) The wells were etched with a 20% KOH solution using a silicon oxide hard mask of circles with diameters of 15, 18, 20, and 22µm. The production of inverted square pyramids from circular mask openings is a consequence of anisotropy: (100) and (110) crystal planes are etched much more quickly than (111) planes, so self-terminating features bound by (111) planes are produced, forming planes 55 degrees from the vertical (Kovacs et al., 1998). The masking oxide was thermally grown on 100 mm diameter single crystal silicon wafers and patterned with a Buffered Oxide Etch (BOE) using a photoresist mask. The photoresist was then stripped and the wafers placed in an 80°C bath of 20% KOH for ~15 min. until the etch self-terminated. The oxide mask was stripped with a second BOE and the wafer was singulated with a die-saw. The silicon surface was reusable after removal of organics with piranha solution (3:1 concentrated H2S04/H2O2(30%)) followed by heat sterilization. (b) A 10× optical microscope image of a single chondrocyte on a microfabricated silicon substrate and a 0.06 N/m Si3N4 cantilever used to maneuver an individual cell into a 15µm inverted square pyramidal Si well. (c) After the cell was seated in a well, indentation was performed with the (e.g., nanosized) tip and then repeated on the exact same cell using the micron-sized tip.

26

500 nm1 µm(c) (d)

10 µm

Cell

PCM

(a)

(b)10 µm

500 nm1 µm(c) (d)

10 µm

Cell

PCM

(a)

(b)10 µm

Fig. 2. Tapping mode amplitude AFM images in air of calf chondrocytes adsorbed on mica substrates. (a) freshly isolated (day 0), (b) chondrocyte released from alginate culture at day 11 where the PCM is clearly distinguishable from the cell body, (c) chondrocyte released from alginate culture at day 18 shows single collagen fibrils emanating out of the dense fibrillar network of the PCM, (d) a higher resolution image of the dense network which exhibit fibril diameter characteristic of type II collagen fibrils (Lodish et al., 2000). Morphological features and cell surface roughness are likely altered by their sample preparation (for a review see (Shao et al., 1996)).

27

Day 0 Day 7 Day 21 Day 28Day 14

20 µm

PGStain

CollagenStain

FBS

OpticalImage

PGStain

CollagenStain

IGF-1+

OP-1

OpticalImage

20 µm

(a)

(b)

Day 0 Day 7 Day 21 Day 28Day 14

20 µm

PGStain

CollagenStain

FBS

OpticalImage

PGStain

CollagenStain

IGF-1+

OP-1

OpticalImage

20 µm

(a)

(b)

Fig. 3. Optical microscopy images (10×) of individual living calf chondrocytes and images (40×) of fixed calf chondrocytes released from alginate at different times in culture using fixed and stained for PG and collagen (Methods). (a) FBS supplemented medium and (b) IGF-1+OP-1 supplemented medium. The top rows of (a) and (b) images were taken in culture medium. The middle rows show toluidine blue staining for PGs after day 7, which covered the entire cell surface, and extended over a larger diameter for cells cultured in IGF-1+OP-1 compared to FBS supplemented medium. The bottom rows show aniline staining for collagen, which was generally not as uniform and intense as the PG stain.

28

(a)

01

23

45

6

0 7 14 21 28 35Culture Day

PCM

Thi

ckne

ss (µ

m) FBS

IGF-1+OP-1

(c)

20 µm

(b)

FBS IGF-1+OP-1

50 µmn=26 n=26 n=18 n=18n=17

(a)

01

23

45

6

0 7 14 21 28 35Culture Day

PCM

Thi

ckne

ss (µ

m) FBS

IGF-1+OP-1

(c)

20 µm

(b)

FBS IGF-1+OP-1

50 µmn=26 n=26 n=18 n=18n=17

Fig. 4. Characterization of the PCM of living calf chondrocytes cultured in alginate using either FBS or IGF-1+OP-1 supplemented medium. (a) An increase in PCM thickness (mean ± SD) measured from optical microscope images was observed from day 0 (freshly isolated cells) up to day 7; after day 7, PCM thickness did not change significantly (ANOVA, p < 0.05; n = number of cells measured.) PCM thickness was calculated as the average diameter measured at each time point minus the average diameter of freshly isolated cells (day 0) cells divided by 2. The error bars represent one standard deviation as calculated by a pooled sample variance. (b) Fluorescein diacetate and ethidium bromide showing live (green) and dead (red) cells on day 28 indicated >80% viability (n=20). (c) Type VI collagen (immunohistochemistry) was present around both FBS (shown) and IGF-1+OP-1 fed day 39 cells.

0

50

100

150

200

0 7 14 21 28 35Culture Day

GA

G/D

NA

(µ

g/10

6 cel

ls)

FBS

IGF-1+OP-1

0

2

4

6

8

10

0 7 14 21 28 35Culture Day

Col

lage

n/D

NA

(µ

g/10

6 cel

ls)

FBS

IGF-1+OP-10

50

100

150

200

0 7 14 21 28 35Culture Day

GA

G/D

NA

(µ

g/10

6 cel

ls)

FBS

IGF-1+OP-1

0

50

100

150

200

0 7 14 21 28 35Culture Day

GA

G/D

NA

(µ

g/10

6 cel

ls)

FBS

IGF-1+OP-1

0

2

4

6

8

10

0 7 14 21 28 35Culture Day

Col

lage

n/D

NA

(µ

g/10

6 cel

ls)

FBS

IGF-1+OP-10

2

4

6

8

10

0 7 14 21 28 35Culture Day

Col

lage

n/D

NA

(µ

g/10

6 cel

ls)

FBS

IGF-1+OP-1

Fig. 5. Biochemical characterization of the PCM of calf chondrocytes released from alginate culture at designated time points corresponding to days that nanoindentation experiments were conducted. Total GAG content of the PCM (by DMMB) was higher for cells supplemented with IGF-1+OP-1 compared to FBS. However, collagen content (by hydroxyproline) was similar for both cell cultures. Data were collected from 3 alginate beads pooled per condition per time point.

29

loading

unloading

(a) (b)

0

0.4

0.8

1.2

1.6

0 400 800 1200Indentation Depth (nm)

Forc

e (n

N)

loading

unloading

0.6

1.2

1.8

2.4


Forc

e (n

N)

0

loading

unloading

(a) (b)

0

0.4

0.8

1.2

1.6


Forc

e (n

N)

loading

unloading

0.6

1.2

1.8

2.4


Forc

e (n

N)

00

0.4

0.8

1.2

1.6


Forc

e (n

N)

0

0.4

0.8

1.2

1.6


Forc

e (n

N)

loading

unloading

0.6

1.2

1.8

2.4


Forc

e (n

N)

0

loading

unloading

0.6

1.2

1.8

2.4


Forc

e (n

N)

0

Fig. 6. Typical indentation curves of individual freshly isolated (day 0) calf chondrocytes. The tip-cell contact point was identified by a running average of the slope of every group of five data points until the calculated slope was greater than zero. Each plot shows 5 loading-unloading cycles (mean ± SD) for one cell immobilized in a silicon well using a z-piezo displacement rate of 1µm/s with (a) a nanosized square pyramidal Si3N4 probe tip (Rtip ~ 40 nm) and (b) a micron-sized colloidal probe tip (Rtip ~ 2.5 µm).

0

0.5

1

1.5

2

0 200 400 600 800Indentation Depth (nm)

Forc

e (n

N)

Nanosized Tip

Micron-sized Tip

0

0.5

1

1.5

2


Forc

e (n

N)

Nanosized Tip

Micron-sized Tip

Fig. 7. Nanoindentation (loading component) of freshly isolated calf chondrocytes (day0) using both the nanosized (mean ± SE for n=25 cells with 5 loading cycles/cell, Rtip~40 nm) and micron-sized (mean ± SE for n=17 cells with 5 loading cycles/cell, Rtip~2.5 µm) probe tips. (These 17 cells were also sequentially tested using the nanosized tip.)

30

(a)

1 µm

(c)

(b)

(d)

0

0.3

0.6

0.9

1.2


Forc

e (n

N)

PCM=4.15kPa

PCM=4.70kPa

PCM=3.75kPa

0

0.3

0.6

0.9


Forc

e (n

N)

Experiment-Day 0E=3kPa

E=2.3kPaE=2.75kPa

PCM=0.14kPa

PCM=0.2kPa

PCM=0.17kPa

0

0.03

0.06

0.09


Forc

e (n

N)

(a)

1 µm1 µm

(c)

(b)

(d)

0

0.3

0.6

0.9

1.2


Forc

e (n

N)

PCM=4.15kPa

PCM=4.70kPa

PCM=3.75kPa

0

0.3

0.6

0.9

1.2


Forc

e (n

N)

PCM=4.15kPa

PCM=4.70kPa

PCM=3.75kPa

0

0.3

0.6

0.9


Forc

e (n

N)


E=2.3kPaE=2.75kPa

0

0.3

0.6

0.9


Forc

e (n

N)


E=2.3kPaE=2.75kPa

PCM=0.14kPa

PCM=0.2kPa

PCM=0.17kPa

0

0.03

0.06

0.09


Forc

e (n

N)

PCM=0.14kPa

PCM=0.2kPa

PCM=0.17kPa

0

0.03

0.06

0.09


Forc

e (n

N)

Fig. 8. (a) Elastic FEA model of nanoindentation experiment on chondrocytes with a micron-sized probe tip. (b) FEA model predictions using an apparent cell modulus of 2.75 kPa compared well to experimental data for indentation on loading of freshly isolated (day0) cells (n=17 cells, 5 loading cycles per cell) with micron-sized probe tip (Rtip=2.5µm.) (c) Using a cell modulus of 2.75 kPa, shell thickness of 3.65 µm, Rcell = 7.6 µm, and Poisson’s ratio = 0.4, the FEA shell model with a shell modulus of 0.16 kPa compared well with experimental data for day 28 FBS cultured cells (n=6 cells, 5 loading cycles per cell). (d) Using a cell modulus of 2.75kPa and a shell thickness of 3.65µm, the FEA shell model with a shell modulus of 4.15kPa compared well with the experimental data for day 28 IGF-1+OP-1 cultured cells (n=5 cells, 5 loading cycles per cell). Data are mean ± SE. Estimation of the cell modulus using FEA was limited to strains <10%. All analyses were done using a consistent indentation depth of 400. Based on the data, the modulus used in the FEA simulations was chosen to bracket the data of the force-indentation curves.

31

0

0.5

1

1.5


Forc

e (n

N)

Day 28

Day 21

Day 14

Day 0

(b)

(a)

0

0.5

1

1.5

0 500 1000 1500 2000 2500Indentation Depth (nm)

Forc

e (n

N)

Day28Day 21Day14

Day7

Day 0

(c)

0

0.2

0.4

0.6

0.8


Forc

e (n

N)

NanoSized Tip

Micro-sizedTip

Day 28

0

0.5

1

1.5


Forc

e (n

N)

Day 28

Day 21

Day 14

Day 0

(b)

0

0.5

1

1.5


Forc

e (n

N)

Day 28

Day 21

Day 14

Day 0

(b)

(a)

0

0.5

1

1.5


Forc

e (n

N)

Day28Day 21Day14

Day7

Day 0

(a)

0

0.5

1

1.5


Forc

e (n

N)

Day28Day 21Day14

Day7

Day 0

0

0.5

1

1.5


Forc

e (n

N)

Day28Day 21Day14

Day7

Day 0

(c)

0

0.2

0.4

0.6

0.8


Forc

e (n

N)

NanoSized Tip

Micro-sizedTip

Day 28

(c)

0

0.2

0.4

0.6

0.8


Forc

e (n

N)

NanoSized Tip

Micro-sizedTip

Day 28

Fig. 9. Average indentation curves (mean ± SE of 5 loading cycles per cell on n cells) on loading of individual chondrocytes with their cell associated PCM after release from alginate at different times in culture with 10% FBS. (a) From the relative slopes of the F-D curves, the stiffness of the cell-PCM composite increased steadily from day7 (n=5), to days 14 (n=4), 21 (n=5), and 28 (n=6), for the case of the nanosized probe tip (Rtip~40nm). Even by day 28, however, the stiffness of the cell-PCM composite was lower than that of freshly isolated (day0) cells devoid of PCM. (b) Similarly, F-D curves obtained with the micron-sized probe tip (Rtip~2.5µm) showed

32

stiffening of the cell-PCM composite with each week in culture, from day 14 (n=4) to days 21 (n=5) and 28 (n=7) (c) With day 28 cells, the F-D behavior with the micron-sized tip was similar to that of the nanosized tip for the first ~900 nm (nanosized probe tip: n=6; micron-sized probe tip: n=7).

33

0

0.5

1

1.5

2

2.5

3


Forc

e (n

N)

Day 21Day 28

Day28 Day 21Day 0

IGF-1+OP-1

FBS

(a)

0

0.5

1

1.5

2

2.5

3


Forc

e (n

N)

Day 28Day 21

Day 28Day 21

Day 0

IGF-1+OP-1

FBS

(b)

0

0.5

1

1.5

2

2.5

3


Forc

e (n

N)

Day 21Day 28

Day28 Day 21Day 0

IGF-1+OP-1

FBS

(a)

0

0.5

1

1.5

2

2.5

3


Forc

e (n

N)

Day 21Day 28

Day28 Day 21Day 0

IGF-1+OP-1

FBS

(a)

0

0.5

1

1.5

2

2.5

3


Forc

e (n

N)

Day 28Day 21

Day 28Day 21

Day 0

IGF-1+OP-1

FBS

(b)

0

0.5

1

1.5

2

2.5

3


Forc

e (n

N)

Day 28Day 21

Day 28Day 21

Day 0

IGF-1+OP-1

FBS

(b)

Fig. 10. Average indentation curves (mean ± SE of 5 loading cycles per cell for n cells per time point) on loading of individual calf chondrocytes with their PCM after released from alginate at different times in culture with IGF-1+OP-1 supplemented medium. (a) Nanosized probe tip (Rtip~40 nm) data compared to10% FBS data of Fig 9a; the IGF-1+OP-1 fed cells showed a marked increase in stiffness from day 21 to day 28 (n=5), and a higher force than cells in 10% FBS. (b) Micron-sized probe tip (Rtip~2.5µm) data show an increase in stiffness from day 21 (n=5) to day 28 (n=5). In contrast to FBS cells of Fig. 9, day 28 IGF-1+OP-1 cultured cells were stiffer than freshly isolated (day0) cells as measured by the micron-sized probe tip, and for the nanosized tip (a) in the range D>700 nm.

34

0

0.5

1

1.5

2

2.5

3

0.1 1 10 100z-piezo displacement rate (µm/s)

Nor

mal

ized

Hys

tere

sis NanoSized Tip

Micron-sized Tip

0

0.5

1

1.5

2

2.5

3

0.1 1 10 100z-piezo displacement rate (µm/s)

Nor

mal

ized

Hys

tere

sis NanoSized Tip

Micron-sized Tip

Fig. A1. Average hysteresis area (mean ± SE) normalized to the hysteresis area measured for cells using a displacement rate of 1µm/s with the nanosized tip (n = 6 cells, each with five sequential loading and unloading curves) and micron-sized tip (n = 4, each with five loading and unloading curves). Minimal change in hysteresis was observed between displacement rates of 200nm/s to 1µm/s.

0

0.1

0.2

0.3

0.4

0 200 400Indentation Depth (nm)

Forc

e (n

N)

E=0.70kPa

E=0.85kPa

E=1kPa

100 300

0

0.2

0.4

0.6


Forc

e (n

N)

E=0.82kPa

E=1kPa

E=1.12kPa

100 300

(a) (b)

0

0.1

0.2

0.3

0.4


Forc

e (n

N)

E=0.70kPa

E=0.85kPa

E=1kPa

100 300

0

0.2

0.4

0.6


Forc

e (n

N)

E=0.82kPa

E=1kPa

E=1.12kPa

100 300

0

0.1

0.2

0.3

0.4


Forc

e (n

N)

E=0.70kPa

E=0.85kPa

E=1kPa

100 300

0

0.1

0.2

0.3

0.4


Forc

e (n

N)

E=0.70kPa

E=0.85kPa

E=1kPa

100 300

0

0.2

0.4

0.6


Forc

e (n

N)

E=0.82kPa

E=1kPa

E=1.12kPa

100 300

0

0.2

0.4

0.6


Forc

e (n

N)

E=0.82kPa

E=1kPa

E=1.12kPa

100 300

(a) (b)

Fig. A2. Comparison of experimental data up to 400 nm indentation distance (from Fig. 7, freshly isolated calf chondrocytes) to the predictions of the Hertz model using , Rcell =7.6 µm, Poisson’s ratio=0.4, for (a) the nanosized and (b) the micron-sized tip, respectively. Indentation curves on loading (mean ± SE) taken with both the nanosized (average of 25 cells with 5 loading cycles/cell, Rtip ~ 40nm) and micron-sized (average of 17 cells with 5 loading cycles/cell, Rtip ~ 2.5µm) probe tips. Based on the data, the modulus used in the Hertz model was chosen to bracket the data of the force-indentation curves.

35

0

0.01

0.02

0.03

0.04

0.05

0 0.01

Strain

Stre

ss (k

Pa)

0.02

0

0.01

0.02

0.03

0.04

0.05

0 0.01

Strain

Stre

ss (k

Pa)

0.02

Fig. A3. Stress-strain curves for nanoindentation data shown in Fig. 7 for loading (mean ± SE) for freshly isolated calf chondrocytes (day0) taken with micron-sized probe tips (average of n=17 cells with 5 loading cycles/cell, Rtip~2.5 µm) resulting in an average E=1.96kPa with a range of 1.76-2.19 kPa .

Nanosized Probe Tip Average

SE

Interval

Micron-sized Probe Tip Average

SE

Interval Hertz Model 0.85 kPa 0.7-1 kPa 1.0 kPa 0.8-1.12 kPa Stress-Strain --- --- 1.96 kPa ---

Day 0 (Freshly Isolated Cells)

FEA --- --- 2.75 kPa 2.3-3 kPa FEA : FBS --- --- 0.1 kPa 0.07-0.12 kPa

Day 21 PCM FEA : IGF-1 +OP-1

--- --- 1.0 kPa 0.8-1.3 kPa

FEA : FBS --- 0.17 kPa 0.1-0.2 kPa Day 28 PCM FEA : IGF-1

+OP-1 --- 4.15 kPa 3.75-4.70 kPa

Table A1. Summary of apparent cell moduli obtained by comparison of experimental data of Figure 10b with three different models. For nanosized tip, a modulus could not be calculated with the stress-strain curve due to the complex contact interaction of the sharp tip radius and the cell. The FEA simulation with the nanosized tip also had trouble converging due to the probe’s small radius of curvature relative to the indentation depth. For the day 21 and day 28 cells, the cell modulus was set to 2.75kPa while the PCM was varied until the FEA F-D matched the experimental data.

36

nanomechanical properties of individual chondrocytes and...

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