NANO LETTERS
Diffusion-Limited Patterning of Molecules in Nanofluidic Channels
2006 Vol. 6, No. 8 1735-1740
Rohit Karnik,† Kenneth Castelino,† Chuanhua Duan,† and Arun Majumdar*,†,‡,§ Department of Mechanical Engineering, UniVersity of California, Berkeley, California 94720, Department of Materials Science and Engineering, UniVersity of California, Berkeley, California 94720, and Materials Sciences DiVision, Lawrence Berkeley National Laboratory, Berkeley, California 94720 Received May 20, 2006; Revised Manuscript Received June 17, 2006
ABSTRACT Diffusion-limited patterning (DLP) is a new technique that enables patterning of labile molecular species in solution phase onto surfaces that are not easily accessible. This technique is self-aligning and is simple to implement for patterning multiple species. We demonstrated DLP by patterning alternating bands of fluorescently labeled and unlabeled streptavidin in biotin-functionalized nanofluidic channels with spatial resolution better than 1 µm. The methodology of DLP also enables experimental measurement of a unique parameter that relates molecular surface grafting density, concentration, diffusivity, and channel geometry.
Nanotechnology revolves around patterning of matter with nanometer-scale control and exploiting the unique properties that result from such patterning. A key aspect of this is patterning of different materials on surfaces, which has found important applications ranging from electronics to medicine. In particular, patterning of molecules on surfaces is important for controlled surface immobilization1 of functional molecules, control of surface properties such as surface charge and hydrophobicity,2 and assembly of nanostructures.3,4 Technologies such as microfluidics,5,6 protein and DNA microarrays,7 and various biological assays frequently use surface patterning of molecules. We are interested in patterning of biomolecules and surface charge in nanofluidic channels for biosensing and flow control.8-10 Lithographic techniques,11-13 microcontact printing, spotting, microfluidic patterning, and dip-pen techniques are among the well-known technologies for patterning molecules on surfaces14 among other techniques.15 Many of these techniques are very flexible, in that arbitrary two-dimensional patterns can be replicated or formed. However, they require specialized equipment or chemicals, require realignment at each step, or are incompatible with biomolecules. Here we present the technique of diffusion-limited patterning (DLP) that overcomes these limitations and enables molecular patterning without any specialized equipment, in a noninvasive manner on surfaces that are not easily accessible. * To whom correspondence may be addressed. E-mail:
[email protected]. † Department of Mechanical Engineering, University of California, Berkeley. ‡ Department of Materials Science and Engineering, University of California, Berkeley. § Materials Sciences Division, Lawrence Berkeley National Laboratory. 10.1021/nl061159y CCC: $33.50 Published on Web 07/21/2006
© 2006 American Chemical Society
To understand the concept of DLP, consider a surface to which species (A, B, C, etc.) can bind. DLP works if the surface is confined to a channel such that the molecules can access the surface only through the entrance of the channel (Figure 1a). A further requirement is that the reactions are irreversible and that once molecules react with the surface, the surface becomes inert to further reactions. If molecules of A are added, they will diffuse into the channel and react with the surface. If the channel height is sufficiently small, then after a short time a sharp reaction front forms (Figure 1b). The surface is saturated with A between the entrance of the channel and the reaction front and is free to react beyond the reaction front. The front progresses further into the channel with time as more molecules of A diffuse and react with the surface. Now, if the reactant A is replaced with reactant B, it will react with the surface beyond the reaction front (Figure 1c). Exposing the channel to different molecules A, B, C... that can bind to the surface results in a pattern of surface-bound molecules that can be controlled by controlling the concentrations of A, B, C... and the times for which they are allowed to diffuse into the channel (Figure 1d). Hence, the concentration history at the channel inlet is reproduced as a spatial pattern. A technique for obtaining macroscale gradients of surface properties by preparation of molecular gradients on surfaces has been presented by Chaudhury and Whitesides.16 In this method, the surface is exposed to a reactant with a concentration gradient that develops due to diffusion of the reactant and is not significantly perturbed by the reaction. DLP differs from the above technique, in that in addition to diffusion the concentration profile is determined by the
tion.20 Streptavidin has been patterned using techniques such as photoactivation,20 imprint lithography,21 and microstamping.22 Immobilization of antibodies conjugated to streptavidin with low nonspecific adsorption to a poly(ethylene glycol)biotin functionalized surface via streptavidin-biotin binding has also recently been demonstrated.23 Therefore, the streptavidin-biotin system has practical utility and is ideal for demonstration of DLP. We now calculate the expected progress of the reaction front when it is limited by diffusion. If the time scale for diffusion of streptavidin is small, the concentration of streptavidin may be assumed to vary linearly between its value at the entrance of the channel (c) to zero at the reaction front. In this case, the flux of streptavidin (J) is given by J ) AD(c/x)
(1)
where A is the channel cross-section area, D is the molecular diffusivity, and x is the distance of the reaction front from the entrance of the channel. If the perimeter of the channel cross-section is P and if streptavidin binds with a surface density γο per unit area, then the rate of consumption of streptavidin by the binding reaction is Pγo(dx/dt). Under the assumption of a quasi-steady state, the rate of consumption equals the flux of streptravidin Figure 1. Diffusion-limited patterning (DLP). (a) DLP requires a channel that is accessible to the bulk solution only from its entrance. The surface is functionalized, so that reactants can bind to the channel surface. (b) Once a reactant (red) is introduced into the bulk solution, it diffuses into the channel, forming a sharp reaction front under certain conditions. (c) When a second reactant (blue) is introduced, it reacts with the region of the channel beyond the first reactant. (d) Repeating this process with different reactants results in patterning of the reactants inside the channel.
reaction rate itself. In DLP, the increased area-to-volume ratio in nanofluidic channels results in the formation of sharp reaction fronts instead of smooth gradients and enables patterning of molecules with high spatial resolution. The rate of reaction and the patterns formed are determined by reactant flux due to diffusion; hence, we call this technique diffusion-limited patterning. Edge-spreading lithography has been used to pattern multiple alkanethiolate monolayers on gold17 and shares some similarities with DLP. In this method, different alkanethiolate molecules are serially delivered to a gold surface via silica beads and a stamp, forming concentric ring patterns. DLP differs from this technique in the method of delivery of the reactants, and is more suitable for biological applications. To demonstrate DLP, we chose the streptavidin-biotin reaction system. Streptavidin is a tetrameric protein that has four sites for binding the small molecule biotin.18 The streptavidin-biotin bond is among the strongest noncovalent interactions known, with a dissociation constant of core streptavidin19 being 4 × 10-14 M with a dissociation halflife of 2.9 days, making it an essentially irreversible reaction. Since streptavidin is homobifunctional, extremely stable, and binds to biotin with high affinity, it is commonly used for protein micropatterning mediated by biomolecular recogni1736
J ) AD(c/x) ) Pγo(dx/dt)
(2)
The solution of this equation is x2 )
( )
2DAc t ) DDLPt Pγo
DDLP ≡
2DAc Pγo
(3)
Here, we can define an experimental parameter, DDLP, with dimensions m2/s which we call the effective diffusivity in this diffusion-reaction system. Note that as opposed to the molecular diffusivity, DDLP can be controlled externally either by the channel height (2A/P) or through the bulk concentration at the channel entrance. Equation 3 shows that the progress of a sharp diffusion-limited reaction front is expected to increase with the square root of time. It is also apparent that for eq 3 to be valid, the assumption of a linear concentration gradient requires that DDLP , D. This reaction-diffusion model has been previously used for modeling the penetration and reaction of antimicrobial agents in biofilms.24 To demonstrate DLP, channels with silica walls were fabricated on fused silica wafers using a sacrificial polysilicon process.10,25 Two types of channels were fabricated: type I (as-made), and type II (enlarged). Type I channels used in the present work were identical to those in our previous work25 and were ∼35 nm in height, 3.5 µm wide, and 120 µm long. A unit consisted of 10 channels with etch holes that allowed for the sacrificial polysilicon etch and also Nano Lett., Vol. 6, No. 8, 2006
Figure 2. Nanofluidic channel device. (a) A set of channels consists of 10 channels, each 120 µm long, 3.5 µm wide, and 35 nm in height. Scale bar 10 µm. (b) Schematic cross section along the length of a channel. (c) The wafer was diced into ∼ 1 cm × 1 cm chips, each with nine sets of channels. Scale bar 100 µm.
defined the ends of the channels (Figure 2a,b). After fabrication of the channels, the wafer was diced into chips, each with nine repeating units (Figure 2c). To obtain larger (type II) channels, the 35 nm channels were etched in a 30% w/w KOH solution in water at room temperature (∼23 °C) for 30 h. The chips used for experiments were etched simultaneously in the same solution to ensure uniformity across different chips. Channel surfaces were functionalized with biotin using the same surface chemistry as our earlier work.25 For experiments with type I channels, the channels were treated with oxygen plasma at 300 W for 10 min after the sacrificial polysilicon etch, briefly rinsed in ethanol, and then immersed in a 2% v/v solution of (3-aminopropyl)trimethoxysilane (APTMS) (Gelest, Morrisville, PA) in ethanol for 1 h. Following this, the channels were rinsed with ethanol and then with water, resulting in a surface functionalized with amine groups. The channels were then treated with ∼5 mM solution of sulfosuccinimidyl 2-(biotinamido)-ethyl-1,3-dithiopropionate (NHS-SS-Biotin) (Pierce Biotechnology, Rockford, IL) in 1X phosphate buffered saline (PBS) for 30 min and rinsed with water. This resulted in biotin-functionalized channels ready for DLP experiments. We have previously characterized each step of the functionalization using conductance measurements.25 For type II channels, the channels were rinsed with deionized water after the KOH etch, rinsed with ethanol, and then similarly functionalized with APTMS followed by NHS-SS-Biotin. After functionalization with biotin, the surface of the chips was wiped with clean wipes (Kimwipe, Kimberly-Clark Professional) and a drop of unlabeled streptavidin (Molecular Probes, Eugene, OR) solution in 1X PBS was immediately placed on the channels. Wiping the surface was a critical step, since it ensured that the ends of the channels were immediately exposed to streptavidin, reducing uncertainty in measurement of time. Once the drop was placed on the chip, it was kept in a closed humidified container. After a specified amount of time, the chip was rinsed with 1X PBS and was ready for the introduction of labeled streptavidin Nano Lett., Vol. 6, No. 8, 2006
(Alexa Fluor 488 labeled streptavidin, from Molecular Probes, Eugene, OR). The channels were exposed to alternating solutions of unlabeled and labeled streptavidin, which resulted in patterned bands of streptavidin in the channels. In the first set of experiments, four chips with type I channels were simultaneously functionalized with biotin. The first chip was exposed alternately to 100 µg/mL solutions of unlabeled and labeled streptavidin for a duration of 10 min per solution. The second chip was exposed alternately to 1 mg/mL solutions of streptavidin for a duration of 5 min per solution. For the third and fourth chips, the time was increased continuously as 2, 6, 10, 14, ... min (the ratios are 1:3:5:7 ..., see discussion) in order to obtain patterns with equal width. For the second set of experiments, the chips were etched with KOH to obtain type II channels with a smaller area-to-volume ratio. Similar experiments were repeated with two chips, with the duration of the 100 µg/ mL solutions being 10 min, and that of 1 mg/mL solutions being 2 min. To examine the rate at which the reaction front progresses with time, alternating patterns of unlabeled and labeled streptavidin were obtained by exposing the chips to streptavidin solutions for equal time durations. Fluorescence images of streptavidin patterned using DLP reveal sharp bands of labeled and unlabeled streptavidin in the channels (Figure 3). The patterns are noticeably uniform across different channels and the widths of the bands decrease away from the channel ends in all cases. Assuming a diffusivity of 6 × 10-11 m2/s for streptavidin,26,27 the diffusion time scale for a diffusion length of 40 µm is 27 s. Since the time scale for dissociation of streptavidin from biotin is large, and the time scale for diffusion of streptavidin into the channel is small compared to the duration of each patterning step (2-10 min), the pattern may be assumed to be a record of the progress of the reaction front with time. Therefore, the width of each band reflects the length by which the reaction front progressed with time. The decreasing band size implies that band formation is slower if the reaction front is away from 1737
Figure 3. DLP with unlabeled and fluorescently labeled streptavidin diffusing for equal durations of time. Channels used, concentrations of streptavidin, and time durations for each step are as follows: (a) type I, 1 mg/mL, 5 min; (b) type II, 1 mg/mL, 2 min; (c) type I, 100 µg/mL, 10 min; and (d) type II, 100 µg/mL, 10 min. Scale bar 20 µm. (e) Progress of reaction front with time, shown for the above patterns. The position of the reaction front measured from the channel entrance is denoted by x, and x2 is plotted on the Y-axis for comparison with eq 3. Dashed lines passing through the origin are fit to data (symbols).
the channel entrance. Channels in Figure 3a,b were patterned using 1 mg/mL streptavidin solutions, while those in Figure 3c,d were patterned using 100 µg/mL solutions. Channels in Figure 3a,c are type I channels, while those in Figure 3b,d are larger type II channels. From Figure 3, three aspects of DLP are apparent: The reaction front progresses faster if (a) the reaction front is closer to the entrance of the channel, (b) the concentration of streptavidin is higher, and (c) the channel height is larger. Figure 3e plots x2 as a function of t and shows excellent agreement between the experiments and the predictions of eq 3. Further, the slopes of the lines are equal to DDLP in each case. This result suggests that patterning using DLP can be controlled either by varying DDLP or the time for which the channel is exposed to each reactant. For a given channel geometry and reaction, concentration and time are the only parameters that can be easily controlled. To illustrate control over patterning, we attempted to form bands of labeled and unlabeled streptavidin of equal widths. Since the reaction front progresses as the square root of time, the duration for the patterning of successive bands must be in the ratio 1:3:5:7:9... in order to obtain bands of equal width. Patterning using reaction durations of 2, 6, 10, 14, 18, and 22 min indeed resulted in bands with approximately equal 1738
Figure 4. DLP with unlabeled and fluorescently labeled streptavidin diffusing for increasing durations of time. Bands of approximately equal widths were patterned using durations of 2, 6, 10, 14, 18, and 22 min for the diffusion of each band. Channels were type I, and streptavidin concentrations of 1 mg/mL (a) and 100 µg/mL (b) were used. Scale bar 20 µm. (c) Progress of reaction front with time, shown for the above patterns. The position of the reaction front measured from the channel entrance is denoted by x, and x2 is plotted on the Y-axis for comparison with eq 3. Dashed lines passing through the origin are fit to data (symbols). Table 1. Summary of DLP Experimental Parameters
figure
time duration sequence for band formation (min)
streptavidin concn channel (mg/mL) geometry
3a 4a 3b
5, 5, 5, 5, 5, 5 2, 6, 10, 14, 18, 22 6, 6, 6, 6, 6, 6
1 1 1
type I type I type II
3c 4b 3d
10, 10, 10, 10, 10, 10 2, 6, 10, 14, 18, 22 10, 10, 10, 10, 10, 10
0.1 0.1 0.1
type I type I type II
DDLP × 1014 (m2/s) 32.8 36.4 286 (2 × 286)/ (32.8 + 36.4) ) 8.27 1.77 2.19 15.7 (2 × 15.7)/ (1.77 + 2.19) ) 7.93
width (Figure 4a,b). The progress of the reaction front (Figure 4c) again shows that x2 is proportional to t, in accordance with eq 3. To explore the dependence of DDLP on concentration, channel geometry, and surface grafting density suggested by eq 3, experimental values of DDLP for different concentrations and channel geometries are summarized in Table 1. DDLP values for type I channels with identical concentrations but different patterns (equal time and equal band size) agree within 25%, giving an indication of repeatability of DDLP in our experiments. Knowing the diffusivity of streptavidin and the channel geometry, we may estimate the surface grafting density. The experimentally observed value of DDLP is 35 × 10-14 m2/s for a bulk concentration of 1 mg/mL ) 1022 m-3. Assuming a diffusivity26,27 of 60 × 10-12 m2/s and an effective channel height of 20 nm,31 eq 3 gives a surface Nano Lett., Vol. 6, No. 8, 2006
density γo ) 3.4 × 1016 m-2, which matches closely with reported surface densities.28 While these results are in agreement with eq 3, accurate quantitative prediction of DDLP using eq 3 was not possible in our experiments. For example, eq 3 suggests that the ratio of DDLP for type I and type II channels at the same streptavidin concentrations is equal to the ratio of channel heights, other parameters being equal. It is evident from Table 1 that this ratio is approximately 8. With an effective channel height of 20 nm for type I channels and a DDLP ratio of 8, the effective and actual heights of type II channels are estimated to be 160 and 175 nm, respectively, which is within a factor of 2 of the channel height measured using SEM (Figure S2, Supporting Information). Equation 3 also suggests that DDLP is proportional to concentration. However, for type I channels for entrance concentrations of 1 and 0.1 mg/mL the measured ratio of DDLP was found to be 17.5. For type II channels this ratio is 18.2, while the expected ratio is 10. An accurate measurement and control of channel height and surface density were not possible in our experiments, which could account for the deviations from the quantitative predictions of eq 3. However, our results suggest that eq 3 is at least qualitatively valid, but further experiments with independent control and observation of each parameter are required for quantitative characterization. Once characterized, such a system could potentially be used to extract surface grafting density, channel geometry, concentration, or diffusivity, if three of the four parameters are known. For choosing other reaction systems and channel geometries for patterning, knowledge of the parameters affecting the resolution of the system would be useful. Assuming firstorder reaction kinetics, the rate of reaction per unit area is given by kc(γo - γ), where k is the association rate constant. Further assuming that the reaction is irreversible, we can show (see Supporting Information) that the DLP spatial resolution (RDLP) is approximately equal to the Thiele length29 and depends on channel geometry, reaction rate constant, diffusivity, and the surface binding density RDLP ∼ 2
x
AD ) kγoP
x
2hD ) 2 × Thiele length kγo
(4)
It is evident that a smaller channel height, faster reaction rate, and lower diffusivity result in higher spatial resolution. Using data for reaction-limited binding of streptavidin to biotin-functionalized surface,28 we estimate k ) 1.2 × 10-22 m3/s or 7.3 × 104 M-1 s-1 (see Supporting Information). DLP resolution is then estimated to be 0.76 µm for type I channels and 2.15 µm for type II channels. For comparison, antigen-antibody association rate constants are in the range 103-106 M-1 s-1.30 High-resolution images of streptavidin patterns also suggest that the patterning resolution was approximately 1 µm or better in certain cases (Figure S1, Supporting Information). However, an analysis of line intensity plots for the patterns in Figure 3 revealed RDLP values ranging from ∼1 to 2.5 µm, with no significant difference between type I and type II channels. As a reference, we measured RDLP of line intensity plots across Nano Lett., Vol. 6, No. 8, 2006
the channel width, which would be expected to have sharpness on the order of the channel height of 30 nm. However, the measured RDLP along these lines was ∼1 µm, which is indicative of the optical resolution of the microscope system. Different biotin surface densities would result in similar binding density of streptavidin,28 but different binding kinetics, which is one possible reason for the variation in RDLP. Given the limitations of our optical imaging system, the estimated RDLP is qualitatively consistent with our experimental results. In the present work, we have demonstrated DLP using the streptavidin-biotin system to pattern bands of fluorescently labeled streptavidin in nanofluidic channels. The most important requirement for patterning several molecules is the availability of a surface to which all the molecules can irreversibly bind. This condition is satisfied for multiple biolomecular species by using streptavidin conjugates that can bind to a biotinylated surface,23 which suggests that DLP could be extended for patterning multiple biomolecular species. A simple technique to pattern multiple molecular species with micrometer spatial resolution is currently lacking, and DLP could potentially fill this gap in applications such as low-density microarrays or patterning of surface properties. While we have focused on the streptavidin-biotin reaction, DLP is a universal technique that could be used with different reaction systems in diverse patterning applications. DLP could also be performed in gas phase and in other types of channel geometries such as nanopipets. DLP enables experimental observation of DDLP and RDLP, which relate the parameters of surface binding density, rate constant, concentration, channel geometry, and diffusivity in a unique combination. It suggests that in addition to patterning, DLP could be extended to measure analyte concentrations (c), diffusivity (D), surface binding density (γo), and the reaction rate constant (k). In conclusion, our work suggests that DLP could be used as a cost-effective method for biomolecular patterning and may also emerge as a new tool for studying interfacial transport phenomena and kinetics of surface reactions. Acknowledgment. We thank Kanhayalal Baheti, Tao Tong, and Robert Wang (UC Berkeley) for their help. We also thank Peidong Yang and his group for continued discussions in nanofluidics. The channels were fabricated in the Microfabrication Laboratory of the University of California, Berkeley. This research was supported by the Basic Energy Sciences, Department of Energy and the National Science Foundation. Supporting Information Available: Patterning image analysis, SEM image of channel cross section, and derivation of DLP resolution. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Zhu, H.; Snyder, M. Curr. Opin. Chem. Biol. 2003, 7, 55-63. (2) Xia, Y. N.; Qin, D.; Yin, Y. D. Curr. Opin. Colloid Interface Sci. 2001, 6, 54-64. (3) Bhat, R. R.; Fischer, D. A.; Genzer, J. Langmuir 2002, 18, 56405643. 1739
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(21) Hoff, J. D.; Cheng, L. J.; Meyhofer, E.; Guo, L. J.; Hunt, A. J. Nano Lett. 2004, 4, 853-857. (22) Hyun, J.; Zhu, Y. J.; Liebmann-Vinson, A.; Beebe, T. P.; Chilkoti, A. Langmuir 2001, 17, 6358-6367. (23) Metzger, S. W.; Natesan, M.; Yanavich, C.; Schneider, J.; Lee, G. U. J. Vacuum Sci. Technol., A 1999, 17, 2623-2628. (24) Dodds, M. G.; Grobe, K. J.; Stewart, P. S. Biotechnol. Bioeng. 2000, 68, 456-465. (25) Karnik, R.; Castelino, K.; Fan, R.; Yang, P.; Majumdar, A. Nano Lett. 2005, 5, 1638-1642. (26) Kamholz, A. E.; Schilling, E. A.; Yager, P. Biophys. J. 2001, 80, 1967-1972. (27) Arrio-Dupont, M.; Foucault, G.; Vacher, M.; Devaux, P. F.; Cribier, S. Biophys. J. 2000, 78, 901-907. (28) Jung, L. S.; Nelson, K. E.; Stayton, P. S.; Campbell, C. T. Langmuir 2000, 16, 9421-9432. (29) Leconte, M.; Martin, J.; Rakotomalala, N.; Salin, D.; Yortsos, Y. C. J. Chem. Phys. 2004, 120, 7314-7321. (30) Karlsson, R.; Michaelsson, A.; Mattsson, L. J. Immunol. Methods 1991, 145, 229-240. (31) Bound streptavidin decreases the channel height by 5 nm on either surface. Another 2.5 nm of channel height is excluded at either channel wall due to the size of streptavidin floating in the channel giving an effective channel height of 35 - 5 × 2 - 2.5 × 2 ) 20 nm (the space within a distance r of a flat surface is sterically excluded for the center of a sphere of radius r.
NL061159Y
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