Engineering DNA-Mediated Colloidal Crystallization - Langmuir (ACS

Jan 24, 2006 - DNA is a powerful and versatile tool for nanoscale self-assembly. Several researchers have assembled nanoparticles and colloids into a ...
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1991

Engineering DNA-Mediated Colloidal Crystallization Anthony J. Kim,† Paul L. Biancaniello,‡ and John C. Crocker*,† Department of Chemical and Biomolecular Engineering, Department of Physics and Astronomy, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104 ReceiVed October 27, 2005. In Final Form: December 19, 2005 DNA is a powerful and versatile tool for nanoscale self-assembly. Several researchers have assembled nanoparticles and colloids into a variety of structures using the sequence-specific binding properties of DNA. Until recently, however, all of the reported structures were disordered, even in systems where ordered colloidal crystals might be expected. We detail the experimental approach and surface preparation that we used to form the first DNA-mediated colloidal crystals, using 1 µm diameter polystyrene particles. Control experiments based on the depletion interaction clearly indicate that two standard methods for grafting biomolecules to colloidal particles (biotin/avidin and water-soluble carbodiimide) do not lead to ordered structures, even when blockers are employed that yield nominally stable, reversibly aggregating dispersions. In contrast, a swelling/deswelling-based method with poly(ethylene glycol) spacers resulted in particles that readily formed ordered crystals. The sequence specificity of the interaction is demonstrated by the crystal excluding particles bearing a noninteracting sequence. The temperature dependence of gelation and crystallization agree well with a simple thermodynamic model and a more detailed model of the effective colloidal pair interaction potential. We hypothesize that the surfaces yielded by the first two chemistries somehow hinder the particle-particle rolling required for annealing ordered structures, while at the same time not inducing a significant mean-force interaction that would alter the self-assembly phase diagram. Finally, we observe that particle crystallization kinetics become faster as the grafted-DNA density is increased, consistent with the particle-particle binding process being reaction, rather than diffusion limited.

Introduction DNA has emerged as a tool for the directed self-assembly of structures on the nanoscale. Seeman et al. have shown that it is possible to create complex, nanometer-sized self-assembled structures by using the sequence-specific binding properties of DNA.1-3 In addition, a number of groups have used the specificity of DNA hybridization to self-assemble binary mixtures of colloids or nanoparticles.4-9 The crystallization of spherical colloidal particles may be considered a prototypical example of selfassembly. It is well-known that monodisperse hard spheres dispersed in a liquid spontaneously self-assemble to form a crystalline phase when their volume fraction exceeds 0.494.10-13 Alternatively, charged colloids can crystallize at even lower volume fraction and form, depending on the ionic strength, wellordered FCC or BCC structures.14-15 Similarly, numerous * To whom correspondence should be addressed. Phone: 215-898-9188. Fax: 215-573-2093. E-mail: [email protected]. † Department of Chemical and Biomolecular Engineering. ‡ Department of Physics and Astronomy. (1) Seeman, N. C. Annu. ReV. Biophys. Biomol. Struct. 1998, 27, 225-248. (2) Winfree, E. R.; Liu, F.; Wenzler, L. A.; Seeman, N. C. Nature 1998, 394, 539-544. (3) Mao, C.; Sun, W.; Shen, Z.; Seeman, N. C. Nature 1999, 397, 144-146. (4) Mirkin, C. A.; Letsinger, R. L.; Mucic, R. C.; Storhoff, J. J. Nature 1996, 382, 607-609. (5) Mucic, R. C.; Storhoff, J. J.; Mirkin, C. A.; Letsinger, R. L. J. Am. Chem. Soc. 1998, 120, 12674-12675. (6) Milam, V. T.; Hiddessen, A. L.; Crocker, J. C.; Graves, D. J.; Hammer, D. A. Langmuir 2003, 19, 10317-10323. (7) Soto, C. M.; Srinivasan, A.; Ratna, B. R. J. Am. Chem. Soc. 2002, 124, 8508. (8) Valignat, M. P.; Theodoly, O.; Crocker, J. C.; Russel, W. B.; Chaikin, P. M. Proc. Natl. Acad. Sci. 2005, 102, 4225-4229. (9) Rogers, P. H.; Michel, E.; Bauer, C. A.; Vanderet, S.; Hansen, D.; Roberts, B. K.; Calvez, A.; Crews, J. B.; Lau, K. O.; Wood, A.; Pine, D. J.; Schwartz, P. V. Langmuir 2005, 21, 5562-5569. (10) Alder, B. J.; Wainwright, T. E. J. Chem. Phys. 1957, 27, 1208. (11) Hoover, W. G.; Ree, F. H. J. Chem. Phys. 1968, 49, 3609. (12) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340. (13) Chaikin, P. M. and Lubensky, T. C. Principles of Condensed Matter Physics; Cambridge University Press: Cambridge, U.K., 2000.

experiments and simulations have found that binary suspensions (containing a mixture of two particle sizes) can form ordered alloy structures or superlattices, often with large and highly complicated unit cells.16-17 The structure formed depends sensitively on the size ratio, the total volume fraction, and the relative numbers of small and large spheres. To date, the AB (face-centered-cubic NaCl structure), AB2 (hexagonal AlB2 structure), AB6 (body-centered-cubic C60K6 structure and cubic CaB6 structure), and AB13 (cubic NaZn13 structure) have been experimentally realized for hard-sphere systems18 and structures such as CaCu5 and MgCu2 have been identified for charged particles.19 A major challenge to forming novel colloidal alloy structures is phase separationsto a large extent, crystallization occurs to maximize free volume by forming close-packed crystal structures. If a given alloy structure does not achieve a dense enough packing, a binary suspension can lower its free energy by phase separating into two separate close-packed crystals.14,18 Tkachenko20 has studied how modification of the interactions between different species in a binary mixture can remove the phase separation instability. Simulations of a binary, ‘AB’ suspension with specific interactionsswhere A attracts B, while A and B repel others of their speciessgenerate a complex phase diagram of novel structures. Suspensions with equal number density and samesized A and B spheres give rise to alloy structures such as CsCl(BCC), NaCl(SC), and ZnS(diamond), as well as a membrane phase with square order. The possibility of forming a lattice with diamond symmetry is potentially interesting for templating photonic band gap materials.21-23 (14) Murray, C. A. MRS Bull. 1998, 23, 33-38. (15) Robbins, M. O.; Kremer, K.; Grest, G. S. J. Chem. Phys. 1988, 88, 3286. (16) Bartlett, P.; Ottewill, R. H.; Pusey, P. N. Phys. ReV. Lett. 1992, 68, 3801. (17) Eldridge, M. D.; Madden, P. A.; Frenkel, D. Nature 1993, 365, 35. (18) Hunt, N.; Jardine, R.; Bartlett, P. Phys. ReV. E 2000, 62, 900. (19) Hachisu, S.; Yoshimura, S. in Physics of Complex and Supermolecular Fluids; Safran, S. A., Clark, N. A., Eds.; Wiley: New York, 1987; pp 221-240, (20) Tkachenko, A. V. Phys. ReV. Lett. 2002, 89, 1483033.

10.1021/la0528955 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/24/2006

1992 Langmuir, Vol. 22, No. 5, 2006

Kim et al.

in Figure 1b. We also performed control experiments using the depletion interaction to assemble colloids with similar surface and buffer chemistries to those in the DNA experiments. These experiments indicate that surface effects not related to DNA can explain the lack of ordering in the literature and can be eliminated by using a colloidal surface densely covered with poly(ethylene glycol) (PEG). Last, we determine and model the temperature and DNA-density dependence of the self-assembly phase diagram and kinetics. We find that crystals only form in a rather narrow range of temperatures and have acceptably fast nucleation and growth in a small range of grafted-DNA density. Materials and Methods

Figure 1. Schematic representations of (a) our DNA-mediated selfassembly system, the interaction strength is related to the overlap of two grafted polymer layers, shaded, (b) the entropic depletion attraction, which yields a similar short-range attraction, (c) 65 nucleotide long Arm-DNA grafted to the particles. Linker-DNA allows 2 arm-DNA strands to cross-link by forming a bridge between them. Upper-DNA and Lower-DNA strands hybridize with the ArmDNA to increase its persistence length but were found to have a minimal effect on particle aggregation thermodynamics (see Materials and Methods) and were omitted from the crystallizing samples.

The preferred method for inducing such specific colloidal interactions is to use hybridization, the sequence-specific assembly of single-stranded DNA grafted onto the particles into double strands. For example, Mirkin and co-workers4,5 have used DNA to self-assemble gold nanoparticles. Similarly, Milam et al.,6 Soto et al.,7 Valignat et al.,8 and Rogers et al.9 have used DNA to self-assemble micrometer-sized colloidal particles. Despite the theoretical predictions, all the self-assembled structures formed were large aggregates or small polyhedral clusters rather than ordered alloy crystals. In some cases, the DNA-mediated aggregation was not fully reversible upon heating above the DNA dissociation temperature (melting temperature, Tm), suggesting that lack of colloidal stability or so-called nonspecific binding (NSB) was to blame. The fact that completely reversible systems also failed to crystallize suggests that irreversible binding cannot be the entire explanation. The motivation of this work is to delimit those conditions under which the DNA-mediated interaction gives rise to wellordered colloidal crystals, as well as to discuss the optimization and ultimate limitations of such DNA-mediated particle selfassembly. The lack of crystallinity reported by the early studies is difficult to interpretsthere are many unknowns regarding the expected colloidal phase diagram and the strength and kinetics of the DNA-mediated interaction, as well as the nonspecific interactions between colloids with different surface chemistries in the various buffers employed. We designed studies to separate these possible factors. We work with a ‘one-component’ system, sketched in Figure 1a, where every colloid has a DNA-mediated attraction to every other, since the phase behavior and kinetics of one-component dispersions with short-range attractions is well understood from studies of the depletion interaction,24-28 sketched (21) Braun, P. V. and Wiltzius, P. Nature 1999, 402, 603. (22) Imhof, A.; Pine, D. J. Nature 1997, 389, 948. (23) Pan, G.; Kesavamoorthy, R.; Asher, S. A. Phys. ReV. Lett. 1997, 78, 3860. (24) Yodh, A. G.; Lin, K.-H.; Crocker, J. C.; Dinsmore, A. D.; Verma, R.; Kaplan, P. D. Philos. Trans. R. Soc. London A 2001, 359, 921-937. (25) Asakura, S.; Oosawa, G. J. Chem. Phys. 1954, 22, 1255.

Materials. NeutrAvidin particles (1 µm, 1% solid) were obtained from Molecular Probes (Eugene, OR). CML (0.98 µm, carboxylated modified) and 0.106 µm CML particles (10% solid) were obtained from Seradyn (Indianapolis, IN). F-108 Pluronics were obtained from BASF. DNA oligomers were custom synthesized and HPLC purified by IDT (Coralville, IA). All chemicals were purchased from Sigma Chemical Co. (St. Louis, MO). The following abbreviations are used throughout the text: EDC (N-(3-dimethylaminopropyl)N′-ethylcarbodiimidehydrochloride), GOPTS (3-glycidyloxypropyl) trimethoxysilane), 4-NPCF (4-nitrophenol chloroformate), TEA (triethylamine), PEG (poly(ethylene glycol), average MW ) 8000), Tween20 (polyoxyethylenesorbitan monolaurate), and glycine, methylene chloride, toluene, xylene without abbreviations. BlockAid blocking solutions (in phosphate buffer pH 7.4 with 140 mM NaCl) were obtained from Molecular Probes (Eugene, OR). Quantum FITC Low Level flow cytometry standards were obtained from Bangs Laboratories, Inc. (Fishers, IN). Rectangular glass capillary tubes (Vitrotubes) were obtained from VitroCom (Mountain Lakes, NJ). UV optical adhesive were obtained from Norland (Cranbury, NJ). Phosphate-buffered saline (PBS) consisted of 150 mM sodium chloride (NaCl) and 10 mM potassium phosphate at pH 7.4. 1X TE buffer consisted of 10 mM tris-HCl pH8.0, 1 mM EDTA (ethylenediaminetetraacetic acid). MES buffer (25 mM) consisted of 25 mM 2-morpholinoethanesulfonic acid at pH 6.5. Autoclaved, deionized (DI) water (18.2 MΩ cm; Easypure Barnstead) was used throughout this study. Oligonucleotide Design. The DNA sequences were designed using a custom Metropolis Monte Carlo (MMC) routine we developed. The algorithm explores DNA sequence space to construct DNA sequences with minimal repeats and low self-affinity. In place of energy, the algorithm uses an ad hoc scoring function that considers Watson-Crick (WC) base pairing of a given sequence with itself (hairpinlike secondary structure) and with translated versions of itself and its complement. Nondesigned WC pairing segments (with up to a single internal mismatch) were weighted according to GC content and exponentially by their length. After about 104 MC steps, the lowest scoring constructed DNA sequences had minimal sequence repetition and low self-affinity with melting temperatures for all nondesigned conformations at least 15 °C below our experimental temperature range. Our bridge-forming DNA construct is shown schematically in Figure 1c. Arm-DNA is a single strand, 65 bases long, modified by either a biotin or primary amine for coupling to particles. Linkers allow particles to cross-link by hybridizing at two different Arm-DNA strands. Upper-DNA and Lower-DNA are hybridization units, 28 bases long, that provide extra persistence length. The Tm’s for the upper and lower spacer segments were above 70 °C so they remain hybridized during the experiment. These spacer segments were found to have a minimal effect on the phase behavior and were only used in the early control and gelation studies. In essence, while double-stranded DNA has a longer persistence length than single-stranded DNA, it has a shorter contour length per (26) Dinsmore, A. D.; Yodh, A. G. Phys. ReV. E 1995, 52, 4045. (27) Verma, R.; Crocker, J. C.; Lubensky, T.; Yodh, A. G. Phys. ReV. Lett. 1998, 81, 4004-4007. (28) Lin, K. H.; Crocker, J. C.; Zeri, A. C.; Yodh, A. G. Phys. ReV. Lett. 2001, 87, 8301.

Engineering DNA-Mediated Colloidal Crystallization

Langmuir, Vol. 22, No. 5, 2006 1993

Table 1. Designed DNA Sequences with Calculated Meltinga and Hairpinb Temperatures name

no. of bases

sequences (5′ to 3′)

Arm-A-DNA

65

Arm-B-DNA

65

Upper-A-DNA Upper-B-DNA Lower-A-DNA Lower-B-DNA Linker-A-DNA Linker9 Linker11 Linker12 Linker14

28 28 28 28

amine/biotin-ACTTAACTACAGCATTATCAGTCTCCGAGGCCCATTGAT TCACACACGTCTAACTTGAAATCTCT amine/biotin-AGTTCCGGACCCTCATCAGCCTGCAACACCACTTCTGACT ATACGTTCAACTTGTCTACTCTGTC CGGAGACTGATAATGCTGTAGTTAAG GTTGCAGGCTGATGAGGGTCCGGAAC GTTAGACGTGTGTGAATCAATGGGCC CAAGTTGAACGTATAGTCAGAAGTGG

18 23 25 29

AGATTTCAAAGATTTCAA AGAGATTTCAACAGAGATTTCAA AGAGATTTCAAGAGAGATTTCAAG AGAGATTTCAAGTTAGAGATTTCAAGTT

melting temp (°C)

hairpin temp (°C)

89.9

32.8

96.0

34.8

73.4 88.9 82.5 74.3

21.7 25.6 29.3 21.4

-

26.9 26.9 26.9 26.9

a

Calculated using the nearest-neighbor thermodynamic parameters from SantaLucia (ref 42) based on the mean solution DNA concentration of 300 nM and NaCl concentration of 200 mM. b Calculated using mfold from Zuker (ref 43) based on the experimental NaCl concentration of 200 mM.

base pair, leading both systems to have a rather similar interaction range and strength; as confirmed in a recent study.29 The designed DNA sequences and their computed melting and hairpin temperatures are provided in Table 1. Particle Preparation. Three different grafting methods were used to attach the Arm-DNA onto 1 µm sized particles: avidin-biotinbased, water-soluble carbodiimide (WSC)-based, and polymer swelling/deswelling-based methods. Prior to surface modification, 0.98 µm CML particles were washed five times by centrifugation and redispersion in DI water to remove any surfactants that may have been present in the manufacturer’s storage buffer. AVidin-Biotin Chemistry. NeutrAvidin particles (1 µm) were grafted with the biotin-functionalized Arm-DNA using avidin-biotin chemistry.30-31 Ten microliters of 1% NeutrAvidin particles were mixed with 8.46 µL of 65.5 nM biotin-functionalized Arm-DNA in 1X PBS to give a final volume of 100 µL. The sample was allowed to incubate overnight at room temperature. After incubating, the DNA-grafted particles were washed five times by centrifugation and redispersion in the BlockAid solution to remove excess DNA. Water-Soluble Carbodiimide (WSC) Chemistry. The aminefunctionalized Arm-DNA was grafted onto carboxyl groups of the CML particles using carbodiimide reaction chemistry.32-35 Twelve microliters of 624 µM amine-functionalized Arm-DNA was mixed with 6 µL of 10% 0.98 µm CML particles in 25 mM MES buffer, pH 6.5, to give a final volume of 300 µL. Then, 2 µL of 50 mM EDC solution was added and the sample was allowed to mix gently for 30 min at room temperature. After mixing, another addition of 2 µL of 50 mM EDC was added and mixed for 30 min. This readdition and mixing process was repeated two more times. Finally, 10 µL of 100 mM glycine solution was added and mixed for 15 min to quench residual amine reactive groups. After quenching, the DNAgrafted CML particles were washed five times by centrifugation and redispersion in 10 mM MES buffer, pH 6.5, with 0.02% Tween20 to remove excess EDC and DNA. After the fifth wash, 1X TE buffer, pH 8.0, with 0.02% Tween20 was substituted as a storage buffer. Swelling/Deswelling-Based Chemistry with PEG Modification. Three different types of PEG-ylated particles, each with different grafted Arm-DNA density, were synthesized. CML particles (0.98 µm) were grafted with the amine-functionalized Arm-DNA with PEG spacers using the polymer swelling/deswelling method as described in the literature.36-37 Briefly, 0.5 g of F108 Pluronic, 40 (29) Biancaniello, P. L.; Kim, A. J.; Crocker, J. C. Phys. ReV. Lett. 2005, 94, 058302. (30) Huang, S.-C.; Swerdlow, H.; Caldwell, K. D. Anal. Biochem. 1994, 222, 441-449. (31) Leckband, D. E.; Schmitt, F.-J.; Israelachvili, J. N.; Knoll, W. Biochemistry 1994, 33, 4611-4624. (32) Nakajima, N.; Ikada, Y. Bioconjugate Chem. 1995, 6, 123-130. (33) Grabarek, Z.; Gergely, J. Anal. Biochem. 1990, 29, 131-135. (34) Tobiesen, F. A.; Michielsen, S. J. Polym. Sci., Part A: Polym. Chem. 2002, 40, 719-728. (35) Brinkley, M. Bioconjugate Chem. 1992, 3, 2-13.

Scheme 1. Schematic Representation of Colloid PEG-ylation Processa

a Briefly, an aqueous suspension of polystyrene colloids is mixed with a soluble triblock polymer. Upon exposure to toluene, the particles swell and liquefy, allowing the triblock’s hydrophobic block to penetrate into the interior. After the toluene was stripped away, the particles resolidify, trapping the triblock polymers in their glassy polymer matrix. DNA or other species may be covalently coupled to the ends of the PEG blocks either prior to or after the swelling procedure.

mg of 4-NPCF, and 40 µL of TEA were added to methylene chloride to make up a final volume of 2 mL. The reaction, which activates the hydroxyl end groups of the PEG chains, proceeded at room temperature for 12 h, and the solvent was removed by evaporation. Once the hydroxyl end groups were activated, 65 µL of 160, 320, or 960 µM 5′-amine-modified Arm-DNA were added to 20 µL of 1% w/w activated F108 in 50 mM carbonate buffer at pH 9.5 to make up a final volume of 100 µL. The mixtures were allowed to react for 4 h at room temperature with constant mixing. We estimate that under these reaction conditions roughly 2% of the F108 molecules end up with a covalently attached Arm-DNA; the amount can be increased or decreased by adjusting the (excess) concentration of DNA during the reaction. Once the reaction was complete, we used a swelling method to attach the partially labeled F108 to colloidal particles (see Scheme 1). Specifically, 100 µL of 1% w/w Arm-DNA reacted F108 (containing a large excess of unreacted F-108 and Arm-DNA molecules), 100 µL of 10% w/w CML particles and 10 µL pf toluene were added in 1X TE buffer at pH8.0 to make up a final volume (36) Monfardini, C.; Schiavon, O.; Caliceti, P.; Morpurgo, M.; Harris, J. M.; Veronese, F. M. Bioconjugate Chem. 1996, 6, 62-69. (37) Kim, A. J.; Manoharan, V. N.; Crocker, J. C. J. Am. Chem. Soc. 2005, 127, 1592-1593.

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Figure 2. Fluorescence histogram obtained from flow cytometry for DNA-grafted particles. The fluorescent intensity curves for (a) DNA-grafted particles without FITC labeled Upper-DNA target strands (Negative), (b) DNA-grafted NeutrAvidin particles with FITC-labeled Upper-DNA target strands (NeutrAvidin-biotin), (c) DNA-grafted CML particles with FITC-labeled Upper-DNA target strands (COOH-NH2 covalent), and (d)-(f) three different DNAgrafted PEG-ylated particles with FITC-labeled Upper-DNA target strands are shown. Calculated number of DNA attached per particle for (b)-(f) are ∼10 000, ∼40000, ∼9500, ∼4000, and ∼1500 DNA/ particle, respectively.

of 1 mL. Toluene is a good solvent for polystyrene and is slightly soluble in water. As it diffuses into the polymer particles, the chains dissolve and the interior becomes fluid. We then removed the toluene by steam stripping the dispersion at atmospheric pressure. Finally, the sample was washed five times by centrifugation and redispersion in 1X TE buffer, pH 8.0, to remove excess F108, Arm-DNA, and Arm-DNA-modified F-108. Flow Cytometry. Flow cytometry experiments were run on Becton Dickinson FACScan flow cytometer (Becton Dickinson, San Jose, CA). Flow cytometry was used to quantify the number of DNA strands grafted per particle. Two microliters of 340 µM FITC-labeled Upper-DNA target strands were allowed to hybridize with 20 µL of 0.2% DNA-grafted particles (NeutrAvidin, CML, and PEG-ylated) by mixing with 1X TE buffer with 200 mM NaCl to give a final volume of 100µL. The samples were then incubated for 8 h at room temperature in the dark. Following incubation, the particles were washed five times by centrifugation and redispersion in the same buffer with 0.02% Tween20 to remove excess FITC-labeled DNA target strands. The number of DNA grafted per particle was determined using the Quantum FITC low-intensity cytometry standard. Using the reported molecules of equivalent soluble fluorescence intensity (MESF) for five bead standards, the calibration curve was constructed. By comparing to the calibration curve, the fluorescent intensity data from each sample was converted to an approximate number of DNA grafted per particle. Fluorescent intensity curves for (a) DNA-grafted particles without FITC-labeled Upper-DNA target strands (Control), (b) DNA-grafted NeutrAvidin particles with FITC-labeled Upper-DNA target strands, (c) DNA-grafted CML particles with FITC-labeled Upper-DNA target strands, and (d)-(f) three different DNA-grafted PEG-ylated particles with FITC-labeled Upper-DNA target strands are shown in Figure 2. The fluorescent intensities were translated into number of grafted DNA per particle using the calibration curve as described earlier. Once translated, the NeutrAvidin and CML particles had the graftedDNA density of ∼10 000 and ∼40 000 DNA/particle, respectively.

Kim et al. The PEG-ylated particles each had the grafted-DNA density of ∼9500, ∼4000, and ∼1500 DNA/particle, respectively. Flow cytometry was also performed on beads swelling-labeled with 4-(aminomethyl) fluorescein-modified Pluronic F108. On the basis of these experiments, a 1 µm diameter colloidal particles has a grafted density of roughly 250 000 F-108 molecules, or twice that many PEG chains, each with a MW ≈ 5000. Glass Treatment. Rectangular glass capillary tubes were treated with PEG to reduce nonspecific binding toward the particles, DNA strands, and proteins. PEG was covalently attached to the glass capillary tubes using a process that has been described in the literature.38-39 Briefly, the glass capillary tubes were incubated with 10% GOPTS in xylene for 5 h at room temperature. Following incubation, now epoxy-modified capillary tubes were washed with dry acetone and then dried in the oven. Once dried, the capillary tubes were heated to 90 °C in a PEG melt for 15 h. After 15 h, the PEG-attached capillary tubes were washed with DI water to remove unreacted PEG. DNA-Mediated Self-Assembly System Preparation. Control Samples. Control samples were prepared to determine if the DNA sequences functioned as designed and assess nonspecific adsorption between the DNA and the particles. The control samples consist of (A) DNA-grafted NeutrAvidin particles without any linkers, (B) DNA-grafted CML particles without any linkers, (C) DNA-grafted PEG-ylated particles without any linkers, (D) bare NeutrAvidin particle with FITC-labeled Upper-DNA, (E) bare CML particles with FITC-labeled Upper-DNA, and (F) bare PEG-ylated particles with FITC-labeled Upper-DNA. To prepare (A), (B), and (C), 10 µL of 1% DNA-grafted particles (NeutrAvidin, CML, and PEGylated) were each mixed with 90 µL of 1X BlockAid (A) or 1X TE buffer, pH 8.0, with 100 mM NaCl (B, C). The samples were loaded into the PEG-functionalized glass capillary tubes and incubated overnight at room temperature. To prepare (D), (E), and (F), 10 µL of bare 1% particles (NeutrAvidin, CML, and PEG-ylated) were each mixed with 90 µL of 1X BlockAid (D) or 1X TE buffer, pH 8.0, with 100 mM NaCl (E, F). Then, 2 µL of 340 µM FITC-labeled Upper-DNA strands were added to the samples and they were incubated overnight at room temperature in the dark. After incubation, they were washed five times by centrifugation and redispersion in the same buffers to remove the excess FITC-labeled Upper-DNA. After being washed, all samples were loaded into the PEGfunctionalized glass capillary tubes. Gelation Study Samples. For determination of gelation temperature, 4 µL of 10% DNA-grafted particles (NeutrAvidin, CML, and PEGylated) were mixed with 0.5 µL of 30 µM Upper-DNA, 0.5 µL of 30 µM Lower-DNA, and 1.23 µL of 30 µM linker9, linker11, linker12, and linker14 in 1X BlockAid or 1X TE buffer, pH 8.0, with 100 mM NaCl to give a final volume of 100 µL. For reversibility experiments, 1 µL of 10% DNA-grafted particles (NeutrAvidin, CML, and PEGylated) were mixed with 0.5 µL of 5 µM Upper-DNA, 0.5 µL of 5 µM Lower-DNA, and 1.4 µL of 5 µM linker11, linker12, and linker12 in1X BlockAid or 1X TE buffer, pH 8.0, with 100 mM NaCl to give a final volume of 100 µL. All samples were loaded into the PEG-functionalized capillary tubes and incubated for 8 h at 50°C. Crystallization Samples. For the NeutrAvidin system, 4 µL of 10% DNA-grafted NeutrAvidin were mixed with 0.5 µL of 30 µM Upper-DNA, 0.5 µL of 30 µM Lower-DNA, and 1.23 µL of 30 µM linker11 in 1X BlockAid to give a final volume of 80 µL. For the CML system, 4 µL of 10% DNA-grafted CML particles were mixed with 0.5 µL of 30 µM Upper-DNA, 0.5 µL of 30 µM Lower-DNA, and 1.23 µL of 30 µM linker14 in 1X TE buffer, pH 8.0, with 100 mM NaCl to give a final volume of 80 µL. For the PEG-ylated system, 4 µL of 10% DNA-grafted PEG-ylated particles were mixed with 1.23 µL of 30 µM linker14 in 1X TE buffer, pH 8.0, with 100 mM NaCl to give a final volume of 80 µL. Sample chambers were (38) Gary, D. E.; Case-Green, S. C.; Fell, T. S.; Dobson, P. J.; Southern, E. M. Langmuir 1997, 13, 2833-2842. (39) Jung, A.; Stemmler, I.; Brecht, A.; Gauglitz, G. Fresenius J. Anal.Chem. 2001, 371, 128-136.

Engineering DNA-Mediated Colloidal Crystallization prepared by loading each sample into the PEG-functionalized rectangular capillary tubes with the ends sealed with a UV optical adhesive. Once the ends were sealed, they were incubated for 10 days at a carefully regulated constant temperature where the interaction was expected to lead to crystallization. Phase-Separated Crystallization Samples. Two sets of PEG-ylated particles, non-fluorescent and fluorescent, were grafted with A-set and B-set DNA sequences, respectively, mixed and allowed to phaseseparate to demonstrate DNA programmability. A linker molecule that only binds to the A-set of DNA sequences was added to this two-component system, allowing the A component to crystallize while the B component remains fluid. Four microliters of 10% A-set DNA-grafted PEG-ylated particles were mixed with 4 µL of 10% B-set DNA-grafted PEG-ylated particles with 1.23 µL of 30 µM linker14A in 1X TE buffer pH8.0 with 100 mM NaCl to give a final volume of 80 µL. Sample chambers were prepared by loading each sample into the PEG-functionalized rectangular capillary tubes with the ends sealed with a UV optical adhesive. Once the ends were sealed, they were incubated for 10 days at a carefully regulated constant temperature where the interaction was expected to lead to crystallization. Depletion Experiment. All depletion experiments were conducted in 1X Tris-EDTA (TE), pH 8.0, buffer with 100 mM NaCl. Prior to surface modification, 0.98 µm CML particles were washed five times by centrifugation and redispersion in DI water to remove any surfactants that may have come from the manufacturer. Depletion was introduced by adding 0.106 µm ‘small’ CML spheres, which were centrifuged at 9000 rpm for 5 h to concentrate them to 33% w/w. Bare CML Particle Depletion. Small spheres and 1 µm large bare CML particles were mixed to give a final concentration of 23%, 21%, 19%, and 17% small spheres with 1% large spheres in 1X TE buffer, pH 8.0, with 100 mM NaCl. Bare NeutrAVidin Particle Depletion. One micrometer bare NeutrAvidin particles were centrifuged to concentrate them to 10% w/w. Small spheres and 1 µm large NeutrAvidin spheres were mixed to give a final concentration of 23%, 21%, 19%, and 17% small spheres with 1% large spheres in 1X TE buffer, pH 8.0, with 100 mM NaCl. Glycine-Grafted CML Particle Depletion. Glycine, a small molecule that contains a primary amine, was attached onto carboxyl groups of the 0.98 µm CML particle using the same carbodiimide chemistry described above. Once the particles were glycine-modified, small spheres and 1 µm glycine-grafted CML particles were mixed to give a final concentration of 23%, 21%, 19%, and 17% small spheres with 1% large spheres in 1X TE buffer, pH 8.0, with 100 mM NaCl. PEG-ylated Particle Depletion. F108 Pluronic was attached onto the 0.98 µm CML microspheres using the same swelling/deswelling protocol as described above. Small spheres and 1 µm PEG-ylated particles were mixed to give a final concentration of 25%, 23%, 21%, 19%, and 17% small spheres with 1% large spheres in 1X TE buffer, pH 8.0, with 100 mM NaCl.

Results and Discussion DNA-Mediated Gelation Behavior and Melting Model. Melting Model. Simple thermodynamic analysis has been widely used to calculate melting temperatures for intramolecular (hairpins) and intermolecular (hybridization between two strands) DNA in solution.40-43 For DNA-grafted particles, the melting temperature analysis differs from those systems in solution. The key differences are (A) each particle has many DNA strands that are interacting at the same time, (B) when two DNA-grafted particles interact, due to the fact that DNA strands are grafted (40) Breslauer, K. J.; Frank, R.; Blocker, H.; Marky, L. A. Proc. Natl. Acad. Sci. 1986, 83, 3746-3750. (41) Allawi, H. T.; SantaLucia, J. Biochemistry 1997, 36, 10581-10594. (42) SantaLucia, J. Proc. Natl. Acad. Sci. 1998, 95, 1460-1465. (43) Zuker, M. Curr. Opin. Struct. Biol. 2000, 10, 303-310.

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on the surface, they see much higher “local” concentration compared to the bulk solution concentration,9,29 and (C) entropic repulsion coming from DNA strands has to be considered. The interaction between the DNA-grafted particles was modeled as two coupled reactions in series:

A + L a AL AL + A a ALA where A is the Arm-DNA, L is the linker-DNA, AL is the duplex formed between the Arm-DNA and linker-DNA, and ALA is the bridging duplex formed between the two different Arm-DNA strands and linker-DNA. By assuming equilibrium and applying the laws of mass action,

K1eq )

[A]eq[L]eq [AL]eq

) e-∆G0 /kBT K2eq ) 1

[AL]eq[A]eq [ALA]eq

) e-∆G0 /kBT 2

where Keq is the equilibrium constant and [X] is the concentration of DNA strand X,

[A]eq ) [A]0 - [AL]eq - 2[ALA]eq [L]eq ) [L]0 - [AL]eq and ∆G0 is the Gibbs free energy of hybridization obtained from the nearest-neighbor model40-42 and kBT is the themal energy. This reaction network can be solved numerically to obtain the equilibrium concentrations versus temperatures. It is important to point out that the model was designed so that the solution concentration was used for [A] in the first reaction and the ‘local’ concentration was used for [A] in the second reaction. This is due to the fact that the DNA strands are tethered to the particles. Therefore, the local concentration depends only on the graftedDNA density for each particles rather than the ‘average’ DNA strands are in solution. In our systems, the ratio of local to average concentration is ∼104. The Tm was determined by finding the temperature where [ALA] and [A] became equal, assuming [L] stays constant. Control and Gelation Studies. Control samples based on the three different particle chemistries, NeutrAvidin, CML, and ∼4000 DNA/particle PEG-ylated particles, were prepared. Figure 3a shows the DNA-grafted particles incubated without any linkers. When no linkers were added, the particles stayed well dispersed and did not form aggregate structures at any temperature. This observation indicates that different Arm-DNA strands do not interact with each other. In another control, the bare particles were mixed with the FITC-labeled Upper-DNA and examined under a fluorescent microscope; no florescence was detected. This observation suggests that there are no nonspecific adsorption between the FITC-labeled Upper-DNA and the particles. Figure 3b shows the NeutrAvidin particles mixed with linker12. When the well-dispersed samples were quenched from 50 °C down to 32 °C, they became aggregate structures. However, when they were heated back up to 50 °C, aggregate structures dissociated and particles redispersed. This cooling/heating cycle was repeated several times with minimal formation of irreversible two-particle aggregates, suggesting that all three chemistries yield sensibly stable, reversible particles. When the samples were rapidly quenched from 50 °C down to 32 °C, the NeutrAvidin particles completed aggregating after ∼1 h, the CML particles completed aggregating after ∼30 min, and the PEG-ylated particles completed aggregating after ∼10 min. This result already shows that aggregation is not diffusion-limited and is significantly affected by surface chemistry.

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Figure 3. Control and reversible adhesion results. (a) All three DNA-grafted suspensions, NeutrAvidin, CML, and PEG-ylated, remain well dispersed when no linkers are added, Neutravidin shown. (b) After adding linkers 11,12, or 14, all suspensions form aggregate structures, Neutravidin with linker12 shown. Heating to 50 °C drives complete redispersion (c).

Studying the temperature-dependent gelation behavior for all three particle chemistries tested the accuracy of the melting model. Figure 4a and b shows the NeutrAvidin particles mixed with linker 9. The Tm predicted by the melting model for the linker9 was ∼32 °C, which was very close to what was observed. Figure 4c and d shows CML particles mixed with linker12. The melting model predicted the Tm to be ∼38 °C, very close to what was observed. Figure 4e and f shows PEG-ylated particles with ∼4000 DNA/particle mixed with linker12. The Tm predicted by the model was ∼37 °C, again very close to what was observed. Therefore, the thermodynamic melting model was able to predict the Tm for all three particles to within a couple degrees. In addition, there exits a very sharp transition between a dispersed “liquid” state and aggregated state.9,29 It can be seen from the figure that the same sample at approximately ∼1 °C above and below the melting temperature remained as dispersed “liquid” or formed aggregates, respectively. This sharp transition in temperature can be explained by the melting model, which

Kim et al.

describes the total number of bridges formed between particles at equilibrium to be exponentially sensitive in temperature. DNA-Mediated Colloidal Crystallization. Once the gelation/ dissociation temperature, Tm, for each suspension was estimated, we tried to crystallize samples by incubating them for up to 10 days at temperatures bracketing Tm. Eight identical chambers of each suspension were prepared and were incubated simultaneously on the block of a gradient PCR machine that maintained a constant 2 °C temperature gradient. Therefore, chambers were spaced at 0.25 °C intervals of temperature. On the basis of experience from depletion crystallization, these crystallization runs were performed at an adequate volume fraction for homogeneous nucleation using particles with a coefficient of variation (CV) value below 5% polydispersity. In practice, 0.5% starting particle volume fraction sedimented in our ∼200 µm deep chambers to form a dense layer with volume fraction >20% that did not crystallize in the absence of an attractive interaction. The NeutrAvidin samples incubated with linker11 did not crystallize even after 10 days of incubation. Similarly, the CML samples incubated for 10 days with linker14 did not crystallize either. In contrast, the PEG-ylated particles with ∼4000 DNA/ particle were able to crystallize into close-packed structures after 3 days (see Figure 5). It can be seen from the figure that the structures have a faceted shape and resemble random hexagonal close-packed (RHCP) stacked colloidal crystals. There was no apparent interaction between the particles and the chamber walls (e.g., an adsorbed layer), consistent with the expectations that there should be no attraction between the particles and the bare walls. To demonstrate that the crystals formed were truly held together by DNA hybridization, the sample was heated above its Tm to see if the particles redispersed. Figure 5 shows that when the crystallized sample was heated to 50 °C, the particles dissociated completely. This test proved that the crystal structures were formed by DNA hybridization and not by some other processes such as a convective self-assembly or hard-sphere crystallization. Another study sought to demonstrate the chemical specificity of the colloid-colloid interaction. Specifically, we mixed together two suspensions labeled with different, noninteracting DNA sequences (termed A and B) and a linker molecule that should only bind A particles together. To allow the two particle species to be distinguished, we fluorescently tagged the B particles during swelling. After being incubated for 2 days at 42.3 °C, the mixed suspension formed close-packed crystal structures, shown in bright-field microscopy in Figure 6a. When the same sample is observed in fluorescence microscopy, the crystals are clearly nonfluorescent (see Figure 6b), confirming that the growing crystal expelled the fluorescent B particles, which remained well dispersed. As before, when the sample was heated above its Tm, the crystal redispersed completely and fluorescent B particles diffused into the space (see Figure 6c). Similar specificity has previously been seen in colloidal DNA-driven colloidal aggregation.9 This is, however, the first demonstration of a chemically specific interaction being used to drive phase-separated crystallization of otherwise identical colloidal particles. Interestingly, we found the mixed suspension crystallized at about 1.0 °C lower temperature relative to a comparable, pure A suspension. We hypothesize that this slight shift in the phase behavior of the A component is caused by the A crystals being partially stabilized by the osmotic pressure of the excluded B component. Depletion Studies. Asakura and Oosawa (AO) first described the depletion interaction.25 In a mixture of two different-sized spherical particles, an ordered arrangement of large spheres can decrease the total free energy of the system by increasing the

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Figure 4. Reversible gelation for DNA-grafted NeutrAvidin, CML, and PEG-ylated particles, mixed with linker9, linker12, and linker12, respectively. Gelled Neutravidin particles were heated slowly from (a) 30 to (b) 34 °C, with redispersion occurring ∼32 °C. Gelled CML particles were heated slowly from (c) 34 to (d) 38 °C, with redispersion occurring ∼38 °C. Finally, gelled PEG-ylated particles were heated slowly from (e) 33 to (f) 37 °C, with redispersion occurring ∼37 °C.

entropy of the small spheres.24 The resulting increases in smallsphere entropy induce the so-called attractive ‘depletion’ force between the large spheres. The AO model for the pair interaction potential energy U(h) due to depletion is

U(h) ) Π∆V )

π h nk T[2aS - h]2 2aS + 3aL + 6 B 2

[

]

(1)

where h is the distance from contact between two large spheres, valid for 0 < h < 2aS, Π is the osmotic pressure applied by small spheres, ∆V is the depletion volume, aS is the radius of small spheres, aL is the radius of large spheres, n is the number density of small spheres, and kBT is the thermal energy. We performed control experiments using the depletion interaction to better understand why the DNA-grafted PEGylated particles have successfully crystallized whereas the other particles, the DNA-grafted NeutrAvidin and DNA-grafted CML, failed to crystallize. The depletion study was performed using particles with similar surface and buffer chemistries to those in the DNA experiments. These experiments indicate that surface effects not related to DNA can explain the lack of particle ordering. The gelation study indicated that all three types of DNA-grafted particles were completely reversible upon heating above the DNA dissociation temperature (Tm). Therefore, we can simply rule

out irreversible NSB, which causes particles to be stuck and never come apart, from the possible causes for lack of crystal formation. However, irreversible NSB only shows a macroscopic picture and more subtle transient NSB could exist and possibly inhibit rolling and annealing of particles. In addition, most DNAmediated self-assembly experiments are conducted at high salt concentrations because most biological molecules only work properly at the physiological condition. In contrast, most entropic and depletion crystallizations are conducted at low salt concentrations so the particles can ‘fly over’ each other due to electrostatic repulsion. Therefore, depletion studies at high salt concentrations would provide some important insight into surface properties of these particles, such as steric stability. Figure 7a shows the 0.98 µm bare CML particles depleted with 23% 0.106 µm small CML spheres. From the figure, it can be seen that they formed close-packed crystal structures under depletion. The particles depleted with 21%, and 19% small spheres also formed the same structures; however, the sample depleted with 17% small spheres did not crystallize even after one week of incubation. This observation suggests that the particles were monodisperse enough to crystallize28 and the depletion potential due to a depletant volume fraction greater than 19% was needed to form crystal structures. Using the AO model, small sphere concentrations, 23%, 21%, 19%, and 17%, were converted into

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Figure 5. Close-packed crystal structures assembled using the DNAgrafted PEG-ylated particles with ∼4000 DNA/particle. When the crystallized samples were heated to 50 °C, large crystals (b) completely redispersed (c) in less than 10 s.

depletion potentials of 2.63kBT, 2.40kBT, 2.17kBT, and 1.95kBT, respectively. The fact that crystals were only formed between 2 and 3kBT agrees well with theoretical phase diagrams and earlier experimental studies.24-28 Unlike earlier aqueous binary colloid depletion studies,24 our higher salt concentration (100 mM) corresponds to a screening length of only 1 nm, which is smaller than the effective size of our grafted PEG chains or CML brush layer. The 2-3kBT computed strength of our interaction confirms the steric nature of the repulsion in the PEG systemsearlier studies have had to increase the effective depletant diameter to account for the range of electrostatic repulsion in order to achieve agreement with AO theory. Moreover, the match between our experiments and the theoretical phase diagram also appears to rule out a weak van der Waals attraction between the spheres (due, for instance, to a too-thin polymer brush layer). Figure 7b shows the bare NeutrAvidin particles depleted with 23% 0.106 µm small CML spheres. From the figure, it can be seen that the particles formed large aggregates rather than closepacked structures under depletion. The samples depleted with 21%, 19%, and 17% small spheres also formed large aggregates. Figure 7c shows the glycine-grafted CML particles depleted with 23% 0.106 µm small CML spheres. From the figure, it can be seen that they also formed large aggregates under depletion. The samples depleted with 21%, 19%, and 17% small spheres also formed the same structures. Figure 7d shows the PEG-ylated particles with ∼4000 DNA/particle depleted with 25% 0.106 µm small CML spheres. From the figure, it can be seen that they have successfully formed close-packed crystal structures under depletion. The crystal structures have a faceted shape that resembles the random hexagonal close-packed (RHCP) stacked colloidal crystals. However, the samples depleted with 23%, 21%, 19%, and 17% small spheres did not crystallize and remained well dispersed even after one week. Just as with the DNA-mediated colloidal crystallization, only

Figure 6. Mixed suspensions of A and B particles with the A-A linker forming phase-separated crystals. (a) The bright field image shows the crystal. (b) The fluorescence illumination shows fluorescent B particles are absent from corresponding location. (c) B particles diffuse freely into the area after the crystal is melted at 50 °C.

the PEG-ylated particles successfully crystallize under depletion. The other two particles, NeutrAvidin and CML, were not able to crystallize and they formed aggregated structures. This suggests that the failure to crystallize is not an effect of the DNA itself but rather has something to do with the ability of these particles to anneal into ordered structures being dependent on the surface chemistry or nanostructure. The possible sources of the effect are constrained by the fact that the suspensions are both reversible (ruling out irreversible NSB) and aggregate at the expected temperature or depletant concentration (ruling out a strong, but reversible, confounding nonspecific attraction). One possibility is that particle-on-particle rolling is inhibited due to transient NSB or interactions on a patchy surface. For the NeutrAvidin particles, we hypothesize that rolling may have inhibited transient NSB between proteins or between proteins and the particles.44 Similarly, slow particle rolling kinetics for the glycine-modified CML particles can be explained by collapse of the polymer-brush layer. CML particles are generally synthesized using a copolymerization process between styrene (44) Cantarero, L. A.; Butler, J. E.; Osborne, J. W. Anal. Biochem. 1980, 105, 375-382.

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Figure 7. Depletion study results for (a) bare CML particles, (b) bare NeutrAvidin particles, (c) Glycine-grafted CML particles, and (d) PEG-ylated particles. All samples were mixed with 23% 0.106 µm small CML spheres. Under depletion, close-packed crystals were formed for (a) and (d), but only branched aggregates were observed for (b) and (c).

monomers and acrylic acid monomers.45 Once they are copolymerized, the hydrophilic poly(acrylic acid) (PAA) chains try to stay away from the hydrophobic polystyrene core and form this polymer-brush layer. The polymer-brush layer keeps the CML particles very stable against coagulation by providing the steric repulsion in addition to the electrostatic repulsion. The decreased stability of CML particles after carbodiimide treatment suggests collapse or thinning of this hydrophilic polymer brush. Patchiness in the remaining layer could frustrate particle-onparticle rolling by creating regions on the surface in which van der Waals or weak NSB ‘trap’ particle configurations. As the PEG-ylated particles successfully crystallize into ordered structures, we hypothesize that they have the steric stability and perhaps surface uniformity needed for rapid rolling and annealing. Future experiments studying the rolling of sterically stabilized particles in contact will be needed to resolve the issue. Interactions. In an earlier publication, we derived the interaction model for the attraction between two DNA-grafted particles,29 based on mass action and a continuum description. The goal here is to compute the time-averaged potential of mean force expected between the DNA-grafted colloidal particles. While the actual force would fluctuate significantly in time as DNA bridges formed and ruptured, we can use a continuum statistical mechanical picture to compute the time-averaged force in chemical equilibrium. We model the sphere as surrounded by a ‘cloud’ of ligands of thickness L, where L is the contour length of the grafted DNA. Near contact, these ligand clouds overlap, allowing molecular bridges to form between the particles. The pair interaction can be modeled as an attraction due to dynamically forming and breaking DNA bridges between the microspheres,

acting as entropic springs, and an entropic repulsion due to compression of the grafted DNA. If the surface-to-surface separation of the spheres is h, then the bridging attraction has range h < 2L. Since DNA density is low (i.e., 104 strands per microsphere or less), we can neglect DNA-DNA collisions. Therefore, DNA on one sphere colliding with the opposing sphere produces a repulsion with range h < L. While the enthalpy of hybridization presumably generates a transient force during helix formation,46 we neglect its contribution to the time-averaged interaction. The overlap region, where the interaction occurs, is small compared to the radius, R, of the particles. Therefore, we can compute the total interaction, repulsive and attractive, between flat plates grafted with N ligands and then convert it to the twosphere geometry using the Derjaguin approximation. If Ph(x) is the probability distribution of the height of the grafted polymer, then the entropic repulsion per unit area due to DNA compressed by the plates is47

(45) Slawinski, M.; Schellekens, M. A. J.; Meuldijk, J.; Van Herk, A. M.; German, A. L. J. Appl. Polym. Sci. 2000, 76, 1186-1196.

(46) Lee, G. U.; Chrisey, L. A.; Colton, R. J. Science 1994, 266, 771. (47) Dolan, A. K.; Edwards, F. R. S. Proc. R. Soc. London A. 1974, 337, 509.

( )

∆Fr Ω(h) ≈ -2σAkBT ln ) -kBT ln A Ω(∞)

∫0h Ph(x) dx

(2)

where Ω is the number of polymer states, σA is the surface density of Arm-DNA, and the approximation is valid at long-range. Since we are assuming that DNA-DNA interactions are negligible, Ph(x) corresponds to the height distribution of a single grafted polymer. The attractive term of the interaction is an equilibrium average over many states with one or more ligand-receptor bridges. If each ligand has the same, statistically independent probability,

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p, of forming a bridge at a given separation, then the probability no bridges form is Pfree ) (1 - p)N and the probability one or more bridges form is Pbound ) 1 - Pfree. The difference in Helmholtz free energy is

(

)

Pbound ∆Fa ) -ln 1 + ) N ln(1 - p) ≈ - Np ) - 〈n〉 (3) kBT Pfree for p , 1. Remarkably, the interaction energy is simply kBT multiplied by the average number of bridges 〈n〉 that form in chemical equilibrium at that separation. Since our DNA density permits about 50 strands to span between spheres in contact, only a few percent of the available strands need hybridize to induce the weak attractions required for crystallization. Computing the attraction using eq 3 requires the use of a mass-action law generalized for spatially nonuniform reacting ligand species.48 Inside the overlap region, DNA bridges form and break according to the chemical network described earlier. Near the melting temperature, where crystallization occurs, the intermediate AL is short-lived and the reaction may be simplified to 2A + L T ALA. If the concentration profile of the ligand clouds were uniformly distributed in the overlap region, then 〈n〉 ) exp(-∆G/kBT)/c2o)cLc2A∆V by mass-action, where cA is the concentration of Arm-DNA, cL is the concentration of LinkerDNA, ∆G is the total change in Gibbs free energy to form a single bridge, co ) 1 M is a reference concentration, and ∆V is the volume of the overlap region. In general, cA is spatially nonuniform. If we assume that the mean ligand concentration cA(x) depends only on distance from the plate surface, x, then the attraction per unit area between plates is

exp(-∆G/kBT) ∆Fa(h) ) -kBT cLσ2A 2 A c o

∫0h PA(x)PA(x - h) dx h [∫0 PA(x) dx]2

(4)

where PA(x) ) cA(x)/σA is the probability distribution of the terminal end of the grafted DNA. Equation 4 indicates the interaction potential energy is proportional to the overlap of ligand clouds surrounding particles or surfaces, reminiscent of the well-known depletion interaction.25 To compute the total pair interaction, we used the geometric parameters of DNA49,50 to model the DNA spacer conformations, described by Ph(x) and PA(x), then evaluated eqs 2 and 4 using analytical and numerical methods. DNA content, σA and cL, were measured by flow cytometry and UV spectrophotometry, respectively. ∆G ) ∆Ghyb(T) + T∆Srot includes both the hybridization free energy ∆Ghyb of the DNA from the nearest neighbor model and changes in the spheres’ rotational entropy, ∆Srot ) kB ln(〈Θb/Θf〉), due to bridge linking. Θb is the equilibrium-averaged solid angle accessible to the bridged spheres, computed using the wormlike chain model,51 and Θf is the unbridged solid angle. We modeled the single-stranded ArmDNA as tethered Gaussian coils47 with moments determined by a simple random walk simulation. Spacer contour lengths include a seven-base-length correction to account for the linker segment; this was assumed to be single-stranded in computing the repulsion,Ph(x), and double-stranded for the attraction, PA(x), otherwise these probability distributions would be identical. (48) Dutt, A. K.; Datta, A. J. Phys. Chem. 1998, 102, 7981. (49) Murphy, M. C. et al. Biophys. J. 2004, 86, 2530. (50) Hagerman, P. J. Annu. ReV. Biophys. Chem. 1988, 17, 265. (51) Bustamante, C.; Marko, J. F.; Siggia, E. D.; Smith, S. Science 1994, 265, 1599.

Figure 8. Crystallization results for the DNA-grafted PEG-ylated particles with ∼1500 DNA/particle after (a) 3 days, (b) 9 days, and the DNA-grafted PEG-ylated particles with ∼9500 DNA/particle after (c) 1 day.

We prepared several chambers of monodisperse DNA-grafted colloids, varying in temperature, linker concentration, DNA surface density, and base sequence. For every sample that crystallized, we estimated the well depth of their total pair interaction using eqs 2 and 4. At a volume fraction of 20%, the chambers that crystallized had inferred interaction well depths ranging from 1 to 6 kBT. Given that these estimates are subject to a factor of 2 systematic uncertainty associated with estimating ∆Ghyb(T) a priori with the nearest-neighbor model, our DNA interaction data are consistent with the hypothesis that crystallization occurs for interactions in the 2-3kBT range, as seen earlier for depletion-based colloidal crystallization experiments at similar volume fractions. Crystallization Kinetics. The grafted-DNA density for the PEG-ylated particles was varied to study its effect on particle crystallization kinetics. Experimental results indicate that particle crystallization kinetics become faster as the grafted-DNA density is increased, consistent with the particle-particle binding process being reaction, rather than diffusion, limited. Figure 8a-c shows crystal structures formed using the particles with the graftedDNA density of ∼1500 and ∼9500 DNA/particle. It took approximately 9 days for the particles with ∼1500 DNA/particle to form crystal structures (see Figure 8a and b). Compared to the PEG-ylated particles with ∼4000 DNA/particle, which crystal-

Engineering DNA-Mediated Colloidal Crystallization

Langmuir, Vol. 22, No. 5, 2006 2001

lized after 3 days, they were about three times slower. In contrast, the particles with ∼9500 DNA/particle were able to crystallize only after a day of incubation (see Figure 8c). When compared to the particles with ∼4000 DNA/particle, their particle crystallization kinetics were about three times faster. The number of grafted DNA of ∼9500, ∼4000, and ∼1500 DNA/particle corresponds to 1 DNA/320 nm2, 1 DNA/782 nm2, and 1 DNA/ 2,084 nm2 respectively. These numbers suggest the DNA strands are far from densely packed and that their kinetics may resemble that from a conventional two-state analysis. Simply applying the rate equation for DNA hybridization,52-54 where the association and dissociation have second order and first order kinetics, respectively, we can crudely estimate the DNA density dependence of the particle crystallization kinetics. If we find two suspensions with different DNA surface densities, σi, that have crystallized at two different temperatures, Ti, we may assume that their interaction potentials are roughly equivalent. Setting equal the potential for each case computed using eq 4 and canceling common terms yields

σ2S,1 exp

( )

( )

-∆G1 -∆G2 ) σ2S,2 exp KBT1 KBT2

(5)

or equivalently,

k+,1 k +,2 ) σ2S,2 σ2S,1Keq,1 ) σ2S,2Keq,2 ) σ2S,1 k-,1 k-,2

(6)

where Keq is the equilibrium constant, k+ is the association rate constant, and k- is the dissociation rate constant. If we assume the association rate constant, k+, to be independent of temperature, we obtain

σ2S,1 σ

2 S,2

)

k-,1 k-,2

(7)

From the above equation, when the grafted-DNA density increases by 2-fold, the dissociation rate constant at the new crystallization temperature will increase 4-fold. This equation qualitatively explains the increase in the particle crystallization kinetics when the grafted-DNA density is increased, consistent with the hypothesis that steric crowding does not significantly slow hybridization.55 In an earlier study,29 we speculated that the lower DNA density in early PEG-ylated suspensions might be related to their superior annealing characteristics relative to other suspension labeling chemistries that require higher DNA density to control NSB. The present kinetics study shows our earlier conjecture to be false: PEG-ylated particles crystallize even at the same DNA (52) Okahata, Y.; Niikura, K.; Furusawa, H.; Matsuno, H. Anal. Sci. 2000, 16, 1113-1119. (53) Morrison, L.; Stols, L. M. Biochemistry 1993, 32, 3095-3104. (54) Yguerabide, J.; Ceballos, A. Anal. Biochem. 1995, 34, 208-220. (55) Shchepinov, M. S.; Case-Green, S. C.; Southern, E. M. Nucleic Acids Res. 1997, 25, 1155-1161.

density where other chemistries do not, and higher DNA density actually speeds crystallization. In summary, it appears that the kinetics of particle-particle binding is limited by the finite reaction time of the DNA rather than the diffusion of the DNA or particles. One might wonder whether the DNA density could be increased to the point that the assembly became diffusion, rather than reaction, limited. The crystallization kinetics we observe with ∼5000 DNA per particle are roughly 100 times slower than for depletion crystallization (which may be assumed to be particle diffusionlimited). On the basis of our analysis suggesting quadratic scaling, a DNA density of 50 000 or more DNA oligonucleotides per 1 µm particle might be expected to yield diffusion-limited binding, provided that steric hindrance of hybridization did not become an issue and that the interaction strength could still be moderated to a few kBT.

Conclusions In this paper, we have investigated three different onecomponent DNA-mediated colloidal self-assembly systems. They are the NeutrAvidin, CML, and PEG-ylated particles with three different grafted-DNA densities. The thermodynamic melting model accurately predicted the melting temperatures for the particles with four different linkers (9,11,12, and 14) to within a few degrees. In addition, all three particles were completely reversible upon heating above their DNA melting temperature. However, only the PEG-ylated particles have successfully assembled into close-packed crystal structures. The other two particles, the NeutrAvidin and CML, failed to crystallize even after incubating for 10 days at their respective crystallization temperatures. Through the depletion studies, we showed that the NeutrAvidin and CML particles suffered from a transient NSB that inhibited particle rolling and annealing. In contrast, the PEGylated particles had the sufficient steric stability that allowed them to roll and anneal rapidly, which is critical for assembling crystal structures. Finally, we observed that particle crystallization kinetics became faster as the grafted-DNA density is increased, consistent with the particle-particle binding process being reaction, rather than diffusion, limited. Future work will focus on binary and multicomponent systems, where the interactions between each component will be independently ‘programmed’. For example, binary systems can be designed to phase-separate into two independent close-packed crystals or they can be designed to assemble into binary alloy crystals. One of the most exciting aspects of using DNA to selfassemble colloidal particles is the possibility of forming novel alloy crystal structures. With the knowledge that we have obtained from the one-component system, such as NSB and dependence of particle crystallization kinetics on the grafted-DNA density, we will try to assemble complex and novel 3-D alloy crystal structures. Acknowledgment. Funding for this work was provided by NSF-DMR 02-03754 and MRSEC-DMR 00-79909. The authors also thank P. Dalhaimer, V. N. Manoharan, V. T. Milam, and M.-P. Valignat for valuable discussions. LA0528955