Supplemental Material
Viscoelastic characterization of the retracting cytoskeleton using subcellular detachment
Sang-Hee Yoon,1,2 Chan Lee3, and Mohammad R. K. Mofrad1
1Molecular Cell Biomechanics Laboratory, Department of Bioengineering, University of California, Berkeley, CA94720, USA
2Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
3Agency for Defense Development, Yuseong P.O. Box 35, Daejeon 305-600, Korea
VISCOELASTICITY
The viscoelastic model of the retracting cytoskeleton after subcellular detachment is obtained as follows. A standard linear viscoelastic solid model (Fig. 1(b)) consisting of two springs k1, k2 and one dashpot c is employed here to quantify the viscoelastic properties of the retracting cytoskeleton of 3T3 fibroblasts. Assuming that the cytoskeleton is an isotropic and viscoelastic continuum, its stress σ and stress ε are written as
(S1)
(S2)
where the subscripts of 1 and 2 refer to elastic spring component and viscous spring component, respectively. Combining the above two equations yields
(S3)
A cell migration mechanism enables us to assume the stress and strain profiles of a cytoskeleton at STEP 1 (, relaxation phase) as follows. The initial stress at is σ0 and the strain is a Heaviside function with a jump of ε0 at due to ,
(S4)
where H(t) is a Heaviside function and δ(t) is a Dirac delta function. A linear viscoelastic equation about stress and strain can be rewritten as
(S5)
The Laplace transformation of S5 yields
(S6)
The stress σt2 at is therefore expressed as
(S7)
At STEP 2 (, creep phase) where the strain exponentially decays from ε0 to zero after subcellular detachment (), the stress is considered as an inverted Heaviside function with a jump of σt2 at ,
(S8)
Using the above two equations, a viscoelastic equation about stress and strain is represented as
(S9)
The stain profile at STEP 2 is calculated through the Laplace transformation of S9,
(S10)
Thus, the strain profile normalized with respect to ε0 is given by
(S11)
MATERIALS AND METHODS
Microfabrication process
A biological platform to detach an adherent cell at a subcellular level was microfabricated on a 4-inch Pyrex glass wafer with a thickness of 500 µm (University Wafer). After cleaning the wafer with a piranha solution of 1:1 96% sulfuric acid (H2SO4) to 30% hydrogen peroxide (H2O2) for 10 minutes, 1 µm-thick LOR resist (LOR 10A, MicroChem Corp.) was spin-coated at 4000 rpm for 40 seconds, followed by soft baking at 170˚C for 5 minutes. The second positive photoresist (S1818, Rohm and Haas Corp.) was spin-coated to be 2 µm at 4000 rpm for 40 seconds for a double-layer resist stack, followed by soft baking at 110˚C for 1 minute. Optical lithography was made to pattern the double-layer stack before e-beam evaporation, as shown in Fig. S1(a). The next was the deposition of 5 nm-thick chromium (Cr) adhesion layer and 100 nm-thick gold (Au) layer on the wafer, as shown in Fig. S1(b). After the deposition of Au and Cr layers, the wafer was immersed in an organic solvent mixture (BAKER PRS-3000 Stripper, Mallinckrodt Baker, Inc.) at 80˚C for 8 hours for gold electrode patterning, as shown in Fig. S1(c), thereby fabricating the biological platform whose gold electrode is 10 µm in width and 3 µm in neighboring gap.
Pyrex glass modification with polyethylene glycol (PEG)
A PEG-coated surface is known to show an anti-fouling behavior owing to steric repulsion between hydrated neutral PEG chain and protein.1,2 The Pyrex glass surface of a biological breadboard was coated with PEG to make it cell-resistive, as shown in Fig. S2(a). For a Pyrex glass modification with PEG, the platform was treated in an oxygen plasma chamber (PM-100 Plasma Treatment System, March Plasma Systems, Inc.) at 100 W for 30 seconds. The treated platform was incubated in 2% v/v PEG silane and 1% v/v hydrochloric acid (Fisher Scientific) dissolved in anhydrous toluene (Fisher Scientific) for 2 hours. This reaction was performed in a glove box under a nitrogen purge to avoid atmospheric moisture. After this surface-treatment, the platform was rinsed in fresh toluene and ethanol, followed by drying under nitrogen and curing at 120˚C for 2 hours. The PEG-coated platform was stored in a vacuum desiccator until RGD-terminated thiol functionalization.
Gold electrode functionalization with Arg-Gly-Asp (RGD)-terminated thiol
The gold electrodes of the biological platform were treated with a RGD-terminated thiol whose solution was synthesized by chemically combining a cyclo (Arg-Gly-Asp-d-Phe-Lys) (C27H41N9O7, MW 603.68, Peptides International, Inc.) with a dithiobis(succinimidyl undecanoate) (C30H48N2O8S2, MW 603.68, Dojindo Molecular Technologies, Inc.). A cyclo (Arg-Gly-Asp-d-Phe-Lys), c(RGDfK), was dissolved in dimethoxysulfoxide (DMSO, Sigma-Aldrich) to get 1 mM aliquot and stored at -20˚C. This reaction was made in a glove box under a nitrogen purge to prevent the c(RGDfK) from explosion to atmospheric moisture. The maximum storage period of this solution was two weeks because the peptide easily loses its characteristics (e.g. anchor for αvβ3 integrin). A dithiobis(succinimidyl undecanoate) was also stored in 1 mM aliquot in DMSO at -20˚C. This preparation was also done in a moisture-free environment. Before the gold electrode functionalization, both aliquots were warmed to room temperature in a desiccator. The c(RGDfK) aliquot was mixed with triethylamine (1% v/v, Fisher Scientific) for 5 minutes to make all primary amines of the lysine amino acid unprotonated. The same volume of the dithiobis(succinimidyl undecanoate) was added to the c(RGDfK) aliquot, and then was mixed well using a vortex mixer for 4 hours to synthesize a RGD-terminated thiol solution. For the gold electrode functionalization, the fabricated biological platform was incubated with the solution for 1 hour at room temperature to promote a spontaneous chemisorption between thiol and gold, followed by sonification in DMSO for 3 minutes, rinse in ethanol and phosphate buffered saline (PBS, Sigma-Aldrich) to eliminate all unbound RGD-terminated thiol from the gold electrodes. Thiol made a self-assembled monolayer with gold according to , thereby tethering the RGD peptide to the gold electrodes (Fig. S2(b)).
Cell culture and cell loading
Mouse fibroblast NIH 3T3 cells were cultured in the Dulbecco's modified eagle medium (DMEM, GIBCO) supplemented with 10% fetal bovine serum (FBS, GIBCO) and 1% Penicillin-Streptomycin (GIBCO) at 37˚C in a humidified 5% CO2 atmosphere. The cells were passaged every five days as follows. The cells were washed 1 time in PBS, and then trypsinized with Trypsin-EDTA solution 0.5% (1X). After centrifuging it, the cells were inoculated into a new Petri dish. The fibroblasts with a passage number of 5 to 20 were used in the experiment. Before the experiment, the surface-functionalized biological platform was placed into a Petri dish containing 5 ml of cell suspension medium with a cell concentration of about 1 × 104 cells/ml. After 1 hour, unadhered cells were removed by washing the platform in PBS, followed by replacing old cell culture medium with new one. The experiment was carried out after 24 hours of cell loading in a self-designed chamber with a humidified 5% CO2 atmosphere and at 36˚C. For subcellular detachment, a three-electrode system was used, as shown in Fig. S3.
AFM indentation
The elastic modulus of the retracting cytoskeleton of fibroblasts was measured with an Autoprobe CP atomic force microscope system (Park Science Instruments). All measurements were made at a low-indentation-speed of 10 nm/s to eliminate a viscous damping effect in quantifying the elastic modulus. The elastic modulus was determined by measuring the deflection of an AFM tip (HYDRA2R-100N, Nanoscience Instruments, Inc.) which indents the retracting cytoskeleton of fibroblasts. The AFM tip whose nominal spring constant is 0.011 N/m was calibrated so that its real spring constant was determined as 0.016±0.005 N/m, which was used in the AFM indentation in this work.
REFERENCES
1S. I. Jeon, J. H. Lee, J. D. Andrade, and P. G. De Gennes, Journal of Colloid and Interface Science 142, 149 (1991).
2T. McPherson, A. Kidane, I. Szleifer, and K. Park, Langmuir 14, 176 (1998).
FIG. S1. Microfabrication process of the biological platform. (a) Photoresist patterning by lithography. (b) Chrome and gold deposition by e-beam evaporation. (c) Gold electrode patterning by lift-off process.
FIG. S2. Surface functionalization process of the biological platform. (a) PEG modification on Pyrex glass surface. (b) RGD-terminated thiol functionalization on gold surface.
FIG. S3. Experimental setup for subcellular detachment. One part of the cell is detached from the biological platform in 1× phosphate buffered saline (PBS) with a three-electrode system.
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