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Lipid-Coated Microdroplet Array for in Vitro Protein Synthesis Toshihisa Osaki,†,‡,§ Satoko Yoshizawa,‡ Ryuji Kawano,† Hirotaka Sasaki,† and Shoji Takeuchi*,†,‡,§ †
Kanagawa Academy of Science and Technology, Japan Laboratory for Integrated Micro and Mechatronic Systems, CNRS-IIS,UMI 2820, The University of Tokyo, Japan § Institute of Industrial Science, The University of Tokyo, Japan ‡
bS Supporting Information ABSTRACT: Monitoring complex biological assays such as in vitro protein synthesis over long periods in micrometer-sized cavities of poly(dimethyl siloxane) (PDMS) microfluidic devices requires a strategy that solves the adsorption and absorption problems on PDMS surfaces. In this study, we developed a technique that instantaneously arrays aqueous microdroplets coated with a phospholipid membrane within a single microfluidic device. The simple lipid bilayer coating effectively inhibits the adsorption of proteins and DNA, whereas the encapsulation of the droplet reduces the area in contact with the PDMS surface, resulting in decreased absorption in part. Although the size becomes smaller during the first few hours, a lipid-coated microdroplet array demonstrated a temporal stability of more than 20 h and a size uniformity of CV 3% in the device. Furthermore, we succeeded in expressing a green fluorescent protein by confining an in vitro translation system in the microdroplets, which was confirmed by scanning the fluorescence spectrum of the droplets, demonstrating that the lipid coat secured the synthetic reaction from the adsorption problem.
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ontinuous technical advances have made in vitro protein synthesis a valuable tool for proteomic analysis.13 The major advantages are that the system synthesizes only the target protein from the added gene without contaminating unwanted substances, and, in principle, the target can be any protein, including one with cytotoxicity. Moreover, it is able to express more than one species of protein concurrently, which is generally difficult for in vivo systems. Currently, the issues related to in vitro synthesis concern protein folding and post-translational modifications,4 for which high throughput and functional analysis techniques will be required. One of the key technologies for meeting these challenges is the miniaturization and integration of the system, which facilitates the collection of statistical and quantitative data under various conditions.58 Although several previous studies used water-in-oil droplets or lipid vesicles for in vitro protein expression,710 it is difficult to control the size uniformity and the traceability of such mobile microcavities simultaneously. We consider that a potential solution will be a poly(dimethyl siloxane) (PDMS) microfluidic device that has been commonly used for various miniaturized platforms because it easily realizes the rapid prototyping of cavity designs for the system at the micrometer-length scale.1113 However, minimizing the scale increases the surface area to volume ratio, amplifying the interfacial phenomena at the PDMS surface; i.e., the adsorption and absorption problems become prominent.1416 Since protein synthesis using an in vitro translation system involves multiple reactions, changes in concentration of the biological components due to the adsorption and/or absorption may strongly affect the yield of protein synthesis. In addition, the absorbent property of PDMS can quickly dehydrate the aqueous r 2011 American Chemical Society
buffer in the microcavities that prevents long-term protein expression. Few solutions have been reported that simultaneously reduce these two problems. The use of synthetic polymer grafts, self-assembled monolayers with silane derivatives, and soluble protein and lipid bilayer precoating are examples of solutions that inhibit the adsorption by hydrophilic surface modification.1720 However, instead of preventing the absorption, the use of a hydrophilic coating on the PDMS surface induces the absorption of the aqueous solution. Likewise, suppressing the absorption by hydrophobic treatments will increase the adsorption. Therefore, there does not seem to be a simple way to overcome both problems using just one coating technique.21,22 Accordingly, we integrate arrayed microchambers within a PDMS microfluidic device, designing for in vitro protein expression. In order to suppress the adsorption/absorption problem, we take advantage of the amphiphilic characteristics of lipids. We also were concerned with the uniformity in the chamber volume and the traceability of each chamber. Figure 1 is the conceptual diagram. First, the lipid is used for coating the PDMS surface with a supported bilayer membrane23,24 to prevent the nonspecific adsorption of biological molecules (Figure 1b). Second, we induce droplet formation at the microchambers by introducing hexadecane to the channel (Figure 1c,d). In the absence of the lipid bilayer coating, the hexadecane simply leaves the aqueous solution at the microchambers,25,26 but with the bilayer, the Received: September 2, 2010 Accepted: March 7, 2011 Published: March 18, 2011 3186
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Figure 1. Microfluidic device for formation of an array of lipid membrane-coated (LM-coated) microdroplets. (ad) Schematic diagrams of the LM-coated microdroplet formation mechanism, which takes advantage of autonomous reassembling of lipid molecules at the wateroil interface. (e) Top view of the developed device. Microchambers are located at both sides of a straight main channel.
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immersed in Milli-Q water (Millipore, Japan) before use to maintain hydrophilic channel surfaces. The infusion of reagents was performed by suction using syringes. Air-tight syringes were connected to the outlets of the channels via Teflon tubes, and the reagents were deposited at the inlets. The suction rate was controlled by a syringe pump (Harvard Apparatus, MA). We used an inverted confocal laser scanning microscopy system (SP5, Leica Microsystems, Japan) for fluorescence observations. All of the experiments were performed at room temperature (23 ( 1 °C, with humidity controlled below 60%). An extrusion method was used to prepare the lipid vesicle suspension for the surface coating.27,28 First, we evaporated the chloroform from a lipid solution (1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC) by placing it under vacuum for at least 3 h. We then added 3-(N-morpholino)propanesulfonic acid (MOPS) buffer (100 mM KCl with 10 mM MOPS, pH 7) and adjusted the concentration to 5 mg/mL. After 15 min of sonication, the lipid suspension was repeatedly extruded through a 100 nm-pore polycarbonate film (Avanti Polar Lipids, AL). The obtained vesicle suspension was kept under refrigeration and used within 2 weeks. We mixed 1 wt % of a fluorescent lipid (1,2-dipalmitoylsn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) ammonium salt, Rhod-DPPE) into the DOPC solution before the solvent evaporation when visualizing the lipid membrane with fluorescence. An in vitro protein synthesis system (RTS 500, Roche Applied Science) was used for the GFP expression experiments. All of the reagents were kept on ice and mixed right before use. For the microfluidic-device experiments, 5 μL of the mixture was infused in the channel. At the same time, ca. 10 μL of the mixture was incubated on a glass slide to observe the expression as a control. In this case, the evaporation of the reagent was prevented using a silicone rubber seal and cover glass. The lipids were obtained from Avanti Polar Lipids, AL, USA. The in vitro protein synthesis system, which was based on E. coli lysate, was purchased from Roche Applied Science, IN, USA. The following reagents were also purchased: BSA (crude bovine serum albumin, also labeled with fluorescein and tetramethylrhodamine, Sigma-Aldrich, MO, USA), IgG (Alexa Fluor 488 goat antimouse immunoglobulin G, Invitrogen, CA, USA), λDNA (bacteriophage λcI857 Sam7, Takara Bio, Japan), SYBR Green I (Takara Bio, Japan), and recombinant GFP (rGFP, Roche Diagnostics, Switzerland). All of the chemicals were used without further purification.
hydrophobic hexadecane will slip into the chambers along the amphiphilic and fluidic lipid coating. Since the formed droplets will reduce the contact area with the PDMS walls, the absorption of the aqueous solution will decrease (Figure 1d). Additionally, the lipid membrane continues suppressing the adsorption even after the hexadecane infusion as the lipid covers the in vitro aqueous system during the entire process. The proposed method will concurrently produce an array of microdroplets coated with lipid membranes and allow in situ monitoring over a long period of time. In the following sections, we first present the efficiency of the phospholipid coating in the adsorption of biomolecules. Next, we explain the microdroplet formation in a microfluidic device. Finally, we show the potential of our platform by discussing a demonstration of the in vitro expression of green fluorescent protein (GFP).
’ RESULTS AND DISCUSSION
’ EXPERIMENTAL SECTION The device consisted of a straight main channel with arrayed microchambers, as shown in Figure 1e. The width of the channel was 60 μm, while the chambers had widths and depths of 15 and 20 μm, respectively. The height of the channel and chambers was 20 μm. The entrance to each chamber was deliberately tapered to facilitate the phase separation of water and oil. The volume of each microchamber was 6 pL. The PDMS device was fabricated using a common soft lithography process.11,12 Briefly, we patterned a SU8 photoresist film (Nipopon Kayaku, Japan, spincoated on a Si-wafer) using UV lithography. A PDMS replica was obtained from the SU8 mold and bonded with a glass slide by oxygen-plasma treatment (Samco, Japan). The device was kept
Formation of Lipid-Coated Microdroplet Array. This work revealed a method for autonomously forming microdroplets coated with lipids using the following simple procedure, in combination with the microfluidic device described above. First, we coated the microfluidic channel with a supported lipid bilayer membrane (sLB). We chose the vesicle fusion technique.27,29 After injecting the DOPC lipid vesicle suspension (1 mg/mL, 10 μL, 12 μL/min), we found that the vesicles adsorbed and fused at the walls, floor, and ceiling of the PDMS/glass channel, and a supported DOPC bilayer was formed within a few minutes.30,31 Figure 2a shows the formed sLB labeled with a red fluorescent dye (Rhod-DPPE, see also Supporting Information). As an index of the bilayer quality, we examined the lateral mobility of the lipid molecules on the bilayer using the FRAP (fluorescence recovery after photobleaching) technique.28 The 3187
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Figure 2. (a) Confocal microscopic image of a supported lipid bilayer membrane formed on the surface of the microfluidic device. Scale bar: 20 μm. (b) Recovery curve of fluorescence intensity at a circular photobleached spot. The insets are the bleached/recovered images. The spot size was 5 μm in diameter. Lateral diffusion coefficient was estimated by the approach of Soumpasis.32.
estimated diffusion coefficient on a glass surface, which was 1.3 ( 0.4 μm2/s (n > 10), agrees with the sLB values previously reported.33,34 From the recovery curve, we also calculated the immobile fraction of the formed membrane. The average fraction was 5 ( 3%, which indicates that defects were rare in the sLB. We also confirmed sLB formation on PDMS experimentally (data not shown).30 The self-assembling mechanism of the bilayer formation ensured thorough coverage of the surfaces. Although minor pinholes/disorders might have existed, the coating perfectly followed the shape of the microchannels and did not aggregate at the edges or corners. Figure 3 demonstrates how effectively the sLB inhibited the nonspecific adsorption of biological molecules. We chose BSA, IgG, and λDNA for the adsorbents and compared the amounts adsorbed on three surfaces: the sLB coating, nontreated surface, and BSA coating (experimental details can be found in Supporting Information). As shown in Figure 3a,b, the lipid bilayer remarkably suppressed the adsorption of proteins. The effect was much better than that of the BSA coating. As reported in a recent theoretical study,35 the efficiency of the sLB coating probably comes from the lateral fluidity of the membrane structure and the zwitterionic group in the molecule. It should be noted that the pH of the MOPS buffer (pH 7) was close to the isoelectric point of IgG (pI 59.5), where the adsorption usually increases.36,37 We also found that the bilayer blocked the adsorption of λDNA (Figure 3c,d). The sLB coating substantially inhibited the adsorption, making it possible to handle biomolecules in a microfluidic device without hindrance,20,30,38 even though the coating technique is fairly simple, easy-to-use, reliable, and inexpensive. Second, following the sLB coating, we replaced the lipidcontaining solution in the channel with a desired reagent. As shown in the adsorption experiments, the sLB coating was sufficiently stable for this solution exchange. We infused the in vitro translation system for the demonstration in the GFP Expression in Lipid-Coated Microdroplet Array section. Lipid membrane-coated (LM-coated) microdroplets were immediately formed at the microchambers by the infusion of hexadecane solvent to the channel. Figure 4a shows the sum of the confocal images with the labeled lipids illuminated, demonstrating the microdroplet shape. In addition, the hollow centers of the droplets in Figure 4b confirm that the lipids encapsulated the droplets. We found that the autonomous encapsulation of an aqueous solution by the lipid membrane occurred when the hexadecane accessed the chambers. The mechanism will be as
Figure 3. (a) Comparison of BSA (FITC-labeled, 1 mg/mL) adsorption on the supported lipid bilayer (sLB) coating and on the BSA coating. Fluorescence intensity was normalized by the nontreated glass data. Adsorption period: 1 h. (b) The same comparison of IgG (Alexa488-labeled, 1 mg/mL) adsorption on the sLB and BSA coatings. (c) Confocal microscopic image of 0.1 mg/mL λDNA adsorption on the sLB coating (top), with the profile shown by the dashed line in the image (bottom). After 1 h of incubation, the adsorbed λDNA was stained by SYBR Green I. (d) The same adsorption study on the bare PDMS/glass surface. The bright, stretched DNA strings were observed in parallel to the flow direction (left to right). The peaks at the fluorescence profile marked by the arrowheads correspond to the adsorbed DNA molecules.
follows: the bilayer, two layers with lipid molecules, hides its hydrophobic acyl chains to the inside when coming into contact with the hydrophilic PDMS/glass wall and an aqueous buffer (Figure 1b). The exchanged hydrophobic hexadecane, however, squeezes between the layers and splits the bilayer into two monolayers (Figure 1c). In other words, the hexadecane induces the reassembly of the bilayer into monolayers. This insertion of hexadecane also occurs in the microchambers, with the result that the portion of the aqueous solution in the chambers is wrapped in a lipid monolayer (Figure 1d). It should be noted that this encapsulation does not occur without a supported bilayer such as the BSA coating; instead, the aqueous phase is simply isolated at the chamber (see Supporting Information).9,26 GFP Expression in Lipid-Coated Microdroplet Array. Here, we present the successful results of the GFP synthesis in the LMcoated microdroplets. We first prepared the DOPC sLB on the channels and chambers. Then, prior to infusing the in vitro translation system, we sequentially infused N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES) buffer (50 mM, pH 7.6) and a buffer for a translation reaction complemented with amino acids, energy substrates, and nucleotides (feeding solution prepared according to the RTS500 system manufacturer’s instructions) to flush the extra lipid vesicles and potassium ions and adjust the ambient conditions for gene expression. Since the translation system contains high concentrations of protein factors, such gradual substitutions of the buffers were performed to avoid any precipitations caused by drastic change. The flow rate was 12 μL/min, and the volume was 30 μL for the buffers and 3188
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Figure 5. (a) Fluorescence spectrum of the expressed GFP in LMcoated microdroplet, (b) compared with that of an rGFP aqueous solution (1.5 μM). Ex: 488 nm/Em: 495550 nm. Lipids were unlabeled to eliminate the disturbance of the GFP spectrum. The inset is a confocal microscopic image of the GFP (24 h expression for a microdroplet). Scale bar: 5 μm.
Figure 4. LM-coated microdroplets arrayed in microchambers of the microfluidic device. (a) Stacked confocal image of the microdroplets illuminated by Rhod-DPPE and (b) an image slice of the bottom row 2 h after droplet formation. (c) Fluorescence from expressed GFP in the microdroplets and (d) its bright field image. Lipids were nonlabeled in this case, not to overlap with the fluorescence of GFP. Incubation: 5 h. Scale bars: 20 μm.
10 μL for the feeding solution, respectively. The GFP gene was mixed with the translation system right before the infusion (5 μL, 0.5 μL/min). Finally, we injected hexadecane (10 μL, 0.5 μL/min) into the channel, resulting in the formation of microdroplets with the reagents at the chambers. We restrained the flow rate of the translation system and the hexadecane in order to steadily infuse the fluids with the higher viscosities. Figure 4c shows the GFP expression within the LM-coated microdroplets. The images were taken 5 h after mixing in the gene. Although their size became smaller over time, the microdroplets remained at the microchambers for more than 20 h, and we were able to follow the expression of GFP. Likewise, we attempted the GFP expression with the BSA-coated device and the noncoating (bare PDMS/glass) device. With both devices, however, the PDMS absorbed the aqueous solution in the microchambers, which induced the intrusion of hexadecane, and we were not able to monitor the expression within an hour (see Supporting Information). On the other hand, we found that the shrinkage of the LM-coated microdroplets stopped after a few hours and the volume remained constant for up to 24 h (Figure 6 inset). We assume that the existence of the lipid membrane and its droplet shape reduced the area of contact between the aqueous solution and the wall, thereby suppressing the absorption. The size of the microdroplets was fairly reproducible at around 10 μm by controlling the flow rate of the hexadecane and the geometry of the channel/chambers. Under the best conditions, a CV (coefficient of variation) below 3% (n > 60) was achieved for the droplet diameter (Figure 4d). We believe that this is one of the most straightforward methods to
Figure 6. Time course of the GFP expression in LM-coated microdroplet (filled) and in the control condition (open). The dashed line is the detection limit of the intensity (background). The inset represents shrinkage of the microdroplets over time. /: The standard deviation in the control was evaluated from the plateau values between 10 and 24 h (n = 6).
obtain arrayed microdroplets with a uniform size in a single device. Next, we confirmed whether the GFP expression occurred in the LM-coated microdroplets, by scanning the fluorescence spectra. Figure 5 compares the spectra at the microdroplet (incubated for 24 h) with that of a commercial rGFP solution. The characteristic peak at 505 nm in the droplets corresponds with the rGFP spectrum, while it did not appear at the droplets incubated without the GFP gene (data not shown). We therefore conclude that the GFP expression successfully proceeded in the microdroplets and the fluorescence came primarily from the expressed GFP. Figure 6 shows the fluorescence intensity accompanying the increase in the GFP expression in the microdroplets, together with the control condition (see Experimental Section). The confocal z-plane was adjusted for both results to compare the fluorescence intensity values (5 μm above the floor surface). The fluorescence from GFP became detectable in the microdroplets after 1 to 2 h of incubation, which was faster than in the control. 3189
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Analytical Chemistry We consider that the kinetics of the reaction may be changed in the droplets by the volume reduction for the first hour (Figure 6 inset). At the early stage of the reaction, the condensation of the reagents would favorably work in the microdroplets, resulting in acceleration of the GFP expression. The low incubation temperature of 23 ( 1 °C and the detection limit of the fluorescence also led the time delay. Meanwhile, the fluorescence intensity steadily increased in the microdroplets until 20 h because the condensation may slow the diffusion of molecules and reduce the chance of a series of the synthetic reactions. It should be noted that the traceability of the individual droplets was permitted to follow the time course of the expression with such different conditions. Finally, we estimated the concentration of the expressed GFP. The fluorescence intensity was calibrated against the commercial rGFP concentration. After 20 h of expression, the GFP concentration was roughly 1800 nM in the LM-coated droplets and 700 nM in the control. Although the apparent concentration was higher in the droplets, the actual yield was overestimated: the yield has to be standardized using the initial volume of the encapsulated reagent, i.e., the volume of a microchamber. Since the volume ratio of a droplet to the chamber is ca. 0.17, the corrected concentration per microchamber was 300 nM, that was about half of the batch results. As discussed above, slower diffusion of the reagents would depress the reaction rate in the condensed droplets and probably resulted in the lower yield. Therefore, the yield problem may be solved by optimizing the reagent’s concentration in the translation system. On the other hand, the higher fluorescence intensity from the droplets will provide a better signal-to-noise ratio. As clearly seen in the above results, we succeeded in GFP expression in a PDMS microfluidic device. We consider that one of the key components of this success was the supported lipid bilayer, which was easily formed and effectively prevented the adsorption of the translation system during the injection of the solution. Another key was the microdroplet formation with the LM-coat, which stabilized the system for such a long period of time.
’ CONCLUSIONS In this study, we formed an array of lipid membrane-coated microdroplets using a single microfluidic device. The droplet formation was realized simply by consecutive injections of water and oil phases into the device, whose surface was precoated by a supported lipid bilayer membrane. We discovered that the droplets were easily arrayed in the microchambers with a uniform size and were stable for more than several hours. By encapsulating an in vitro translation system, we were also able to monitor GFP expression in the droplets. These results demonstrated that our platform will be useful for simultaneous and rapid screening of various in vitro protein synthesis systems, including functional analyses such as the detection of gene activity or chemical substances at the single molecule level, by taking advantage of the confined and minute space of the arrayed droplets.39 ’ ASSOCIATED CONTENT
bS
Supporting Information. (1) Figures describing the bilayer formation process. (2) Details of the adsorption experiment. (3) An example of the absorption of an aqueous solution
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by PDMS. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Address: 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan. Phone: þ81-3-5452-6650. Fax: þ81-3-5452-6649. E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors acknowledge the technical support provided by Ms. Maiko Onuki, Ms. Utae Nose, and Ms. Yoshimi Komaki. This work was partly supported by JST (Strategic International Cooperative Program), Japan. ’ REFERENCES (1) Ramachandran, N.; Hainsworth, E.; Bhullar, B.; Eisenstein, S.; Rosen, B.; Lau, A. Y.; Walter, J. C.; LaBaer, J. Science 2004, 305, 86–90. (2) Ramachandran, N.; Raphael, J. V.; Hainsworth, E.; Demirkan, G.; Fuentes, M. G.; Rolfs, A.; Hu, Y.; LaBaer, J. Nat. Methods 2008, 5, 535–538. (3) He, M.; Stoevesandt, O.; Palmer, E. A.; Khan, F.; Ericsson, O.; Taussig, M. J. Nat. Methods 2008, 5, 175–177. (4) Katzen, F.; Chang, G.; Kudlicki, W. Trends Biotechnol. 2005, 23, 150–156. (5) Kinpara, T.; Mizuno, R.; Murakami, Y.; Kobayashi, M.; Yamaura, S.; Hasan, Q.; Morita, Y.; Nakano, H.; Yamane, T.; Tamiya., E. J. Biochem. 2004, 136, 149–154. (6) Wu, N.; Zhu, Y.; Brown, S.; Oakeshott, J.; Peat, T. S.; Surjadi, R.; Easton, C.; Leech, P. W.; Sexton, B. A. Lab Chip 2009, 9, 3391–3398. (7) Tawfik, D. S.; Griffiths, A. D. Nat. Biotechnol. 1998, 16, 652–656. (8) Dittrich, P. S.; Jahnz, M.; Schwille, P. ChemBioChem 2005, 6, 811–814. (9) Ota, S.; Yoshizawa, S.; Takeuchi, S. Angew. Chem., Int. Ed. 2009, 48, 1–6. (10) Hase, M.; Yamada, A.; Hamada, T.; Baigl, D.; Yoshikawa, K. Langmuir 2007, 23, 348–352. (11) Mcdonald, J. C.; Whitesides, G. M. Acc. Chem. Res. 2002, 35, 491–499. (12) Ng, J. M. K.; Gitlin, I.; Stroock, A. D.; Whitesides, G. M. Electrophoresis 2002, 23, 3461–3473. (13) Sia, S. K.; Whitesides, G. M. Electrophoresis 2003, 24, 3563–3576. (14) Makamba, H.; Kim, J. H.; Lim, K.; Park, N.; Hahn, J. H. Electrophoresis 2003, 24, 3607–3619. (15) Mukhopadhyay, R. Anal. Chem. 2007, 79, 3248–3253. (16) Toepke, M. W.; Beebe, D. J. Lab Chip 2006, 6, 1484–1486. (17) Hu, S.; Ren, X.; Bachman, M.; Sims, C. E.; Li, G. P.; Allbritton, N. L. Anal. Chem. 2004, 76, 1865–1870. (18) Lee, S.; V€or€os, J. Langmuir 2005, 21, 11957–11962. (19) Popat, K. C.; Desai, T. A. Biosens. Bioelectron. 2004, 19, 1037–1044. (20) Yang, T.; Baryshnikova, O. K.; Mao, H.; Holden, M. A.; Cremer, P. S. J. Am. Chem. Soc. 2003, 125, 4779–4784. (21) Xu, Y.; Takai, M.; Ishihara, K. Annu. Biomed. Eng. 2010, 38, 1938–1953. (22) Ostuni, E.; Chen, C. S.; Ingber, D. E.; Whitesides, G. M. Langmuir 2001, 17, 2828–2834. (23) Tamm, L. K.; McConnell, H. M. Biophys. J. 1985, 47, 105–113. (24) Sackmann, E. Science 1996, 271, 43–48. (25) Ota, S.; Tan, W.-H.; Suzuki, H.; Takeuchi, S. IEEE Proc. MEMS 2008, 18–21. 3190
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’ NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on March 18, 2011 with an error in the affiliation Institute of Industrial Science at The University of Tokyo. The corrected version was reposted on March 23, 2011.
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