DNA-Mediated Phase Behavior of Microsphere Suspensions

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DNA-Mediated Phase Behavior of Microsphere Suspensions Paul L. Biancaniello,† John C. Crocker,‡,§ Daniel A. Hammer,‡,§,| and Valeria T. Milam*,⊥ Department of Physics and Astronomy, Department of Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, and Department of Bioengineering, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104, and School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245 ReceiVed October 2, 2006. In Final Form: NoVember 15, 2006 We have constructed a phase diagram for DNA-modified microsphere suspensions based on experimental and theoretical studies. The system is comprised of 1 µm red fluorescent colloids functionalized with strands of an identical oligonucleotide sequence and 1 µm green fluorescent colloids functionalized with the complementary sequence. Keeping the suspension composition and temperature fixed, the phase behavior of colloidal mixtures was studied as a function of salt and oligonucleotide concentration. We observed a colloidal fluid phase of dispersed, single particles at low salt concentrations and low DNA densities. We attribute this colloidal fluid phase to unfavorable hybridization conditions. With increasing salt or hybridizing oligonucleotide concentrations, we observed phase transitions of fluid f fluid + aggregates f aggregates due to an increase in duplex affinity, duplex number, or both. Computational analysis assigns a 4 kBT attraction between pairs of complementary microspheres at the destabilizing fluid f fluid + aggregates transition.

Introduction There has been considerable interest in controlling the balance of attractive and repulsive interactions that govern colloidal phase behavior. Early phase diagrams of monodisperse colloidal systems explore classical hard sphere1 or soft sphere2 repulsive interactions that result in fluid or crystalline phases. Later phase diagram studies focus on either destabilizing3-6 phase transitions (fluid f gel) or stabilizing6-8 phase transitions (gel f fluid) in suspensions due to macromolecule or nanoparticle additions. These phase transitions are key indications of the net attractive or repulsive nature of these interactions; however, variations in the structure and properties within either a single phase or a two phase region occur as a function of composition or solution conditions and indicate that subtle differences exist in the range and magnitude of these interactions. For example, the lattice parameter or center-to-center separation between colloidal particles in a colloidal crystal increases as the range of repulsive interactions increases.9,10 For attractive systems, weakly ag* To whom correspondence should be addressed. Phone: (404) 8942845. Fax: (404) 894-9140. E-mail: [email protected]. † Department of Physics and Astronomy, University of Pennsylvania. ‡ Department of Chemical and Biomolecular Engineering, University of Pennsylvania. § Institute for Medicine and Engineering, University of Pennsylvania. | Department of Bioengineering, University of Pennsylvania. ⊥ School of Materials Science and Engineering, Georgia Institute of Technology. (1) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340-342. (2) Hachisu, S.; Kobayashi, Y.; Kose, A. J. Colloid Interface Sci. 1973, 42, 342-348. (3) Imhof, A.; Dhont, J. K. G. Phys. ReV. Lett. 1995, 75, 1662-1665. (4) Ilett, S. M.; Orrock, A.; Poon, W. C. K.; Pusey, P. N. Phys. ReV. E 1995, 51, 1344-1352. (5) Dinsmore, A. D.; Yodh, A. G.; Pine, D. J. Phys. ReV. E 1995, 52, 40454057. (6) Gilchrist, J. F.; Chan, A. T.; Weeks, E. R.; Lewis, J. A. Langmuir 2005, 21, 11040-11047. (7) Ogden, A. L.; Lewis, J. A. Langmuir 1996, 12, 3413-3424. (8) Tohver, V.; Chan, A.; Sakurada, O.; Lewis, J. A. Langmuir 2001, 17, 8414-8421. (9) Ise, N.; Ito, K.; Okubo, T.; Dosho, S.; Sogami, I. J. Am. Chem. Soc. 1985, 107, 8074-8077. (10) Matsuoka, H.; Harada, T.; Kago, K.; Yamaoka, H. Langmuir 1996, 12, 5588-5594.

gregated networks7,8,11,12 in which interparticle attractions are only a few kBT in magnitude tend to exhibit a tighter packing arrangement and a relatively modest shear elastic modulus as compared to more strongly aggregated systems.6,13,14 In each of these studies, the interactions stem from nonspecific colloidal forces since they are typically long-range and do not involve specific recognition between particular pairs of adhesive moieties known as receptor-ligand pairs. Specific forces characteristic of biological receptor-ligand binding events provide a novel methodology for controlling colloidal interactions. Specific forces are often described using a lock-and-key15 analogy since these short-range interactions require contact between oriented, complementary pairs of macromolecules. While the net adhesive strength between particle surfaces can be tuned by controlling the number of bonds,16,17 biological adhesive moieties or receptor-ligand pairs typically have a fixed affinity or bond strength defined by an equilibrium association constant, Ka.18 DNA is a unique exception since the affinity between individual pairs of complementary strands can be adjusted by changing either the sequence characteristics or the solution conditions. The degree of attraction between surfaces functionalized with complementary oligonucleotides can be tuned through several variables including number of base pair matches,19-21 density of hybridizing DNA strands,22,23 and solution ionic strength.20,23,24 This ability to finely tune the affinity (11) Trappe, V.; Weitz, D. A. Phys. ReV. Lett. 2000, 85, 449-452. (12) Bevan, M. A.; Scales, P. J. Langmuir 2002, 18, 1474-1484. (13) Buscall, R.; Mills, P. D.; Goodwin, J. W.; Lawson, D. W. J. Chem. Soc., Faraday Trans. 1988, 84, 4249-4260. (14) Auzerais, F. M.; Jackson, R.; Russel, W. B.; Murphy, W. F. J. Fluid Mechanics 1990, 221, 613-639. (15) Behr, J.-P. The lock-and-key principle: the state of the arts100 years on; Wiley and Sons: New York, 1994; Vol. 1, p 325. (16) Lin, J. J.; Bates, F. S.; Hammer, D. A.; Silas, J. A. Phys. ReV. Lett. 2005, 95, 26101. (17) Hiddessen, A. L.; Weitz, D. A.; Hammer, D. A., manuscript in preparation. (18) Lauffenburger, D. A.; Linderman, J. L., Receptors: models for binding, trafficking, and signaling; Oxford University Press: New York, 1993. (19) Storhoff, J. J.; Lazarides, A. A.; Mucic, R. C.; Mirkin, C. A.; Letsinger, R. L.; Schatz, G. C. J. Am. Chem. Soc. 2000, 122, 4640-4650. (20) Milam, V. T.; Hiddessen, A. L.; Crocker, J. C.; Graves, D. J.; Hammer, D. A. Langmuir 2003, 19, 10317-10323. (21) Dillenback, L. M.; Goodrich, G. P.; Keating, C. D. Nano Lett. 2005, 6, 16-23.

10.1021/la062885j CCC: $37.00 © 2007 American Chemical Society Published on Web 01/17/2007

Phase BehaVior of Microsphere Suspensions

between colloidal particles via DNA functionalities provides an ideal system for analyzing phase behavior using well-controlled, adjustable experimental parameters. To date, experimental21,23,25,26 and modeling27-32 systems have primarily used temperature to investigate oligonucleotide-driven phase transitions in nanoparticle systems. Publications by Mirkin’s group report a sharp, temperature-dependent transition between DNA-linked and DNAstabilized gold nanoparticles as compared to oligonucleotide solutions in the absence of nanoparticles.19,23,26,33 On the basis of UV-vis absorption spectroscopy measurements within this melting range, one can conclude that the fraction of dissociated gold nanoparticles must increase with temperature. Other experimental investigations24,34-36 also use elevated temperatures to investigate the phase transition between attractive colloidal aggregates or assemblies and stable colloidal fluids for DNAfunctionalized microspheres. To the best of our knowledge, however, an experimental phase diagram mapping the range of DNA-mediated phases in a colloidal system has not yet been reported. Here, we determine the phase behavior for DNA-functionalized microspheres as a function of hybridizing strand concentration and ionic strength at a fixed temperature of 25 °C. At a constant salt concentration, this experimental system demonstrates how the propensity for DNA-mediated aggregation is affected by an incremental increase in the number of bonds, starting from one bond between microspheres. At a constant concentration of hybridizing strands, this system also explores the effects of the degree of affinity, or bond strength, between complementary sequences. Computations based on the model of Crocker et al.34,36 indicate that the fluid f fluid + aggregates transition can be fitted with a 4 kBT attractive well using a physically plausible value for the hybridization free energy. This value falls within the range reported for weakly attractive systems involving depletants7,37-39 or negligibly charged microspheres.40,41 By mapping the entire range of fluid, fluid + aggregates, and aggregates phase regions as a function of DNA and salt concentration, we identify continuous trends in the phase transitions as well as within the dual phase region to demonstrate (22) Zhang, Y.; Eniola, A. O.; Graves, D. J.; Hammer, D. A. Langmuir 2003, 19, 6905-6911. (23) Jin, R.; Wu, G.; Mirkin, C. A.; Schatz, G. C. J. Am. Chem. Soc. 2003, 125, 1643-1654. (24) Rogers, P. H.; Michel, E.; Bauer, C. A.; Vanderet, S.; Hansen, D.; Roberts, B. K.; Calvez, A.; Crews, J. B.; Lau, K. W.; Wood, A.; Pine, D. J.; Schwartz, P. V. Langmuir 2005, 21, 5562-5569. (25) Mirkin, C. A.; Letsinger, R. L.; Mucic, R. C.; Storhoff, J. J. Nature 1996, 382, 607-609. (26) Elghanian, R.; Storhoff, J. J.; Mucic, R. C.; Letsinger, R. L.; Mirkin, C. A. Science 1997, 277, 1078-1081. (27) Park, S. Y.; Stroud, D. Phys. ReV. B 2003, 67, 212202. (28) Lukatsky, D. B.; Frenkel, D. Phys. ReV. Lett. 2004, 92, 68302. (29) Lukatsky, D. B.; Frenkel, D. J. Chem. Phys. 2005, 122, 214904. (30) Pierce, F.; Sorensen, C. M.; Chakrabarti, A. Langmuir 2005, 21, 88928999. (31) Long, H.; Kudlay, A.; Schatz, G. C. J. Phys. Chem. 2006, 110, 29182926. (32) Lukatsky, D. B.; Mulder, B. M.; Frenkel, D. J. Phys.: Condens. Matter 2006, 18, 567-580. (33) Storhoff, J. J.; Elghanian, R.; Mucic, R. C.; Mirkin, C. A.; Letsinger, R. L. J. Am. Chem. Soc. 1998, 120, 1959-1964. (34) Biancaniello, P. L.; Kim, A. J.; Crocker, J. C. Phys. ReV. Lett. 2005, 94, 58302. (35) Valignat, M.-P.; Theodoly, O.; Crocker, J. C.; Russel, W. B.; Chaikin, P. M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 4225-4229. (36) Kim, A. J.; Biancaniello, P. L.; Crocker, J. C. Langmuir 2006, 22, 19912001. (37) Walz, J. Y.; Sharma, A. J. Colloid Interface Sci. 1994, 168, 485-496. (38) Mao, Y.; Cates, M. E.; Lekkerkerker, H. N. W. Phys. A 1995, 222, 1024. (39) Sharma, A.; Tan, S. N.; Walz, J. Y. J. Colloid Interface Sci. 1997, 190, 392-407. (40) Tohver, V.; Smay, J. E.; Braem, A.; Braun, P. V.; Lewis, J. A. Proc. Natl. Acad. Sci. 2001, 96, 8950-8954. (41) Chan, A.; Lewis, J. A. Langmuir 2005, 21, 8576-8579.

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Figure 1. Schematic illustrating hybridization activity within the contact zone between two complementary particle surfaces. (a) Green fluorescent microsphere is conjugated with multiple copies of sequence a, while the red fluorescent microsphere is conjugated with a fixed percentage ratio of hybridizing strand sequence a′ and nonsense strand sequence n. (b) Boxed section of the same schematic in panel a illustrates the local stretching of DNA duplexes as the positions of probe strands move from the center with radial coordinates (a,0) to the periphery of the contact zone with radial coordinates (a - s/2,y). An estimate of the projected contact area or zone is based on geometrical considerations of the particle radius, a, and the maximum stretching reported for DNA duplexes, s.

how DNA can be used to finely control the degree of attraction between complementary surfaces. Experimental Procedures Preparation of DNA-Conjugated Microspheres. Similar to our previous work,20 we used a binary suspension system in which DNAmediated attractions are favorable only between heterogeneous colloids. As shown in Figure 1, 1 µm green and red fluorescent polystyrene microspheres from Molecular Probes (Eugene, OR) were functionalized with complementary oligonucleotide sequences a and a′, respectively. Our complementary sequence design and conjugation protocol are based on the same biotin-NeutrAvidin coupling procedure from our previous work.20 All oligonucleotide sequences were purchased from Biosource (Camarillo, CA). To modify the concentration of complementary DNA strands of one colloid type, the red microspheres were functionalized with a homogeneous mixture of complementary sequence a′ and a nonsense sequence n at the following percentage ratios: 100:0, 75:25, 50:50, 33:67, 25:75, 10: 90, 1:99, and 0:100. The nonsense strand is the same sequence length as both a and a′ but is complementary to neither. All sequences are designed to have low self-affinity at 25 °C to minimize intrastrand loops and hairpin configurations that would compromise the desired interstrand hybridization events. The hybridization segment of the complementary sequences is separated from the particle surface by a six thymine base segment. The hybridization buffers (pH 7.0-7.3) range in ionic strength from 25 to 200 mM NaCl to vary the affinity between complementary sequences. To prevent nonspecific colloidal aggregation, all buffers were prepared with 1 wt % denatured bovine serum albumin and then filtered using a cellulose acetate membrane with a 0.45 µm pore size. On the basis of the estimated DNA concentration on the microspheres, the calculated solution melting

2690 Langmuir, Vol. 23, No. 5, 2007 temperature42-44 ranges from 34 °C (1% hybridizing strands; 25 mM NaCl) to 56 °C (100% hybridizing strands; 200 mM NaCl). To prepare dispersed, stock suspensions of each colloid type, DNA-functionalized microspheres were first washed 2 times in hybridization buffer of the highest salt concentration (200 mM NaCl). Aggregates remaining from the conjugation process were separated from singlets via centrifugation. To determine the number density of the remaining dispersed microspheres in the stock suspensions, 8-10 aliquots of 0.02 µL were pipetted from each suspension and spotted onto a coverslip. The total number of microspheres in each dried droplet was counted using the fluorescence mode of a Zeiss Axiovert 200 (Zeiss, Thornwood, NY) at 40×. The amount of liquid in each stock suspension was then adjusted through hybridization buffer additions (200 mM NaCl) to yield a total initial microsphere volume fraction φt,0 of 10-3. To then prepare aliquots of this fixed microsphere volume fraction, φt,0, but varying ionic strength for aggregation experiments, a 20 µL volume of suspension was washed 3 times in the desired hybridization buffer. The supernatant was carefully removed each time via pipetting to avoid removing microspheres, and the final volume of 20 µL was always checked to ensure consistency in the microsphere volume fraction, φt,0. Flow Cytometry. The surface coverage of immobilized DNA strands on the red fluorescent microspheres was quantified using flow cytometry. For these experiments, microspheres were conjugated with FITC-labeled oligonucleotides using the same protocol as the previous section. Functionalized microspheres were washed 4 times in 200 mM NaCl hybridization buffer. Cytometry experiments were run on a Becton Dickinson FACScan flow cytometer (Becton Dickinson, San Jose, CA). The number of immobilized probe strands was quantified using calibration curves derived from flow cytometry runs of Quantum FITC standards (Bangs Laboratories, Fishers, IN). These calibration curves were constructed using the reported molecules of an equivalent soluble fluorochrome (MESF) intensity for these standards as a linear function of the mean fluorescence peak channel (i.e., fluorescence intensity). From these calibration curves, the corresponding MESF value was derived from the peak fluorescence intensity for microspheres functionalized with dyelabeled oligonucleotides. From these experiments, the total number of immobilized oligonucleotides on the red fluorescent microspheres was determined to be 18 106 strands per microsphere or 5763 strands/ µm2. Preparation and Imaging of Colloidal Suspensions. Heterogeneous suspensions of the desired salt concentration were prepared by vortexing volumetric quantities of the stock suspensions to yield a mixed suspension with an equivalent number of red and green microspheres and a total initial volume fraction, φt,0, of 10-3. Approximately 10 µL of the mixture was then loaded into a microchamber consisting of two coverslips separated by a Parafilm spacer (∼0.005 in. thickness). The edge of the top coverslip was traced with a vacuum grease-loaded syringe to prevent solvent evaporation. Suspensions were examined 24-26 h after mixing using an optical microscope (Nikon Diaphot 200, Tokyo, Japan) with a plan achromat 20× objective and a black and white CCD camera (Cohu Inc., San Diego, CA). Static images were captured in phase contrast mode and analyzed using Imaq software (National Instruments, Austin, TX). For cases in which aggregation was observed, suspensions were examined at 40× or 60× in fluorescence mode using a Zeiss Axiovert 200 (Zeiss, Thornwood, NY) and a CCD camera (Cohu Inc., San Diego, CA) to confirm that aggregation occurred only between heterogeneous colloidal particles. In the phase diagram, suspensions comprised of singlets only are identified as fluid, suspensions comprised of multiple singlets and aggregates are identified as fluid + aggregates, and suspensions comprised of aggregates with three or fewer singlets within a field of view are classified as aggregates. Confocal images of select suspensions were (42) Peyret, N.; SantaLucia, J. HYTHER Version 1.0; Wayne State University: Detroit, MI; accessed April 15, 2006. (43) Peyret, N.; Seneviratne, A.; Allawi, H. T.; Santa Lucia, J. Biochemistry 1999, 38, 3468-3477. (44) SantaLucia, J., Jr. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 1460-1465.

Biancaniello et al. taken at 60× using a Bio-Rad 2000 KR-3MP system (Hercules, CA) equipped with a Nikon TE 300 fluorescence microscope.

Results and Discussion Calculation of Molar Concentration of DNA Conjugated to Microspheres. Figure 1 shows a schematic of two heterogeneous colloidal particles linked together by several DNA helices formed between complementary sequences. To calculate the concentration of DNA in the volumetric shell surrounding each microsphere, single strands of 18-mer DNA were treated as rigid rods. With a spacing of 0.59 nm between phosphate groups45 along the DNA backbone, each single strand was estimated to extend ∼10 nm normal to the particle surface. The calculated difference between the effective particle radius (physical particle radius + DNA rigid rod length) and the physical particle radius yields a DNA shell with a volume, Vshell, of 3.2 × 10-17 L per microsphere. The molar concentration of DNA within this shell surrounding each microsphere, MDNA, was thus calculated to be 0.94 mM based on the equation MDNA ) nstrands/NaVshell in which the number of strands per microsphere, nstrands, is 18 106 as determined by flow cytometry, and Na is Avogadro’s number. Calculation of Number of DNA Sequences in the Contact Zone between Microspheres. To calculate the maximum number of DNA strands between a pair of microspheres, the projected contact zone area between two curved surfaces was first calculated using the radial coordinates shown in Figure 1b. This geometrical approach takes into consideration the ability for DNA helices to stretch up to 1.7 times their normal (unstressed) length45,46 as the separation distance increases between the curved surfaces. The important parameters are the following: a, the (known) particle radius of 500 nm; s, the calculated difference between the length for the unstretched (lhyb) and maximum stretched (lhybstr) hybridization segments; and y, the calculated radius of the projected contact area. In equating s to lhybstr - lhyb, it is assumed that stretching occurs only in the double-stranded hybridization segment and not in the rod-like, single-stranded spacer segment separating the particle surface from the hybridization segment. On the basis of the reported45 0.338 nm between neighboring bases for λ DNA, lhyb here is estimated to be 3.72 nm. The maximum stretched hybridization segment length, lhybstr, is estimated to be 1.7 times lhyb or 6.32 nm based on independent force displacement studies by Cluzel et al.46 and Smith et al.45 on λ DNA. Assuming that the midpoints of all DNA duplexes are equidistant from both microsphere surfaces, then one-half of the stretched segment, s/2, or 1.30 nm will fall on either side of this midpoint. The radius of the projected contact area, y, is calculated to be xa2 - (a - s/2)2 or 0.036 µm. The projected circular contact area is thus calculated to be πy2 or 0.0041 µm2. Using the flow cytometry measurement of 5763 DNA strands/ µm2, it is estimated that each microsphere has approximately 25 DNA strands in the contact zone area. Depending on the ratio of hybridizing strands, a′, to nonsense strands, n, on the red fluorescent microspheres, the number of DNA linkages between two heterogeneous colloidal particles is estimated to range from approximately 25 (for the 100% hybridizing strand case) to at most one (for the 1% hybridizing strand case). Thus, at a given salt concentration in which the affinity between individual duplexes is fixed, the suspension system is first used to explore how the propensity for DNA-mediated aggregation is affected by an incremental increase in the number of bonds or DNA linkages between colloidal particles. A range of ionic strengths (45) Smith, S. B.; Cui, Y.; Bustamente, C. Science 1996, 271, 795-799. (46) Cluzel, P.; Lebrun, A.; Heller, C.; Lavery, R.; Viovy, J.-L.; Chatenay, D.; Caron, F. Science 1996, 271, 792-794.

Phase BehaVior of Microsphere Suspensions

Figure 2. Experimental phase diagram for DNA-functionalized microspheres showing fluid (open squares), fluid + aggregates (halffilled squares), and aggregates (filled squares) regions as a function of percentage hybridizing DNA (1-100%) and salt concentration. The plotted curve corresponds to a theoretical 4 kBT attractive well in the pairwise potential due to DNA hybridization between heterogeneous colloidal particles.

is then explored at a fixed concentration of hybridizing strands to investigate the effects of the degree of affinity or bond strength on particle aggregation. Thus, starting with a single bond between pairs of microspheres, this paper systematically examines the effects of both the number and the affinity of duplex bonds on DNA-driven colloidal aggregation. The effects of the number of DNA linkages between surfaces are examined first. Effect of Number of DNA Linkages on Phase Behavior. Figure 2 maps out the fluid, fluid + aggregates, and aggregates phase regions as a function of percentage hybridizing strands and salt concentration. A homogeneous fluid phase consisting of dispersed microspheres is observed only for the lowest salt and hybridizing DNA concentrations. Data (not shown) for 0% hybridizing strands yielded fluid phase behavior at all salt concentrations, indicating that nonspecific attractions between microspheres are negligible. In the case of 1% hybridizing strands at ionic strengths of 100 mM NaCl or less, the fluid phase behavior indicates that the affinity between complementary probe strands in a single duplex is too weak to promote adhesion between colloidal particles. For all but the lowest salt concentration (25 mM NaCl) in this ionic strength range, however, increasing the DNA concentration by 10-fold does promote the onset of DNAmediated colloidal aggregation as indicated by the fluid f fluid + aggregates phase transition in Figure 2. At 25 mM NaCl, the onset of colloidal aggregation requires an even higher percentage (33%) of hybridizing strands. While complete aggregation is not observed at either 25 or 50 mM NaCl, the degree of aggregation does increase continuously with percentage of hybridizing strands, indicating a growing number of bonds or DNA linkages adhering the microspheres together. Previously, we20 and others23 have

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attributed the absence of DNA-mediated colloidal aggregation at salt concentrations below 50 mM NaCl to dominant electrostatic repulsions, possibly resulting from an extended Debye screening length. In the case of nanoparticles with a significantly smaller contact area, the absence of DNA-mediated aggregation reported23 at low salt concentrations may also be due to the reduced number of DNA linkages possible between surfaces. For any fixed salt concentration yielding fluid phase behavior in the experimental system reported here, however, the onset of DNA-driven aggregation, as indicated by the fluid f fluid + aggregates transition, becomes more favorable by simply increasing the concentration of hybridizing DNA in the contact zone allowing more linkages to form between microsphere surfaces. The gradual increase in the degree of DNA-mediated attractions between microspheres with hybridizing strand concentration is most apparent in the two phase region in which both colloidal fluid and aggregates are present. Within the fluid + aggregates regime, micrographs indicate that growing clusters are accompanied by fewer singlet particles as the percentage of hybridizing strands increases. Figure 3 illustrates this continual increase in the degree of colloidal aggregation with hybridizing strand concentration until a fluid + aggregates f aggregates transition occurs between 33 and 50% hybridizing strands for a fixed salt concentration of 100 mM NaCl. As the concentration of hybridizing strands increases on the red fluorescent microspheres, a larger fraction of the approximately 25 DNA strands extending from a microsphere can participate in hybridization activity resulting in more bonds between surfaces. For 100 mM NaCl or higher, the observed fluid + aggregates f aggregates transition indicates that the aggregation does ultimately reach completion as the percentage of hybridizing strands increases. Overall, these observations suggest that a single DNA linkage at 100 mM NaCl or less may be too weak to promote colloidal aggregation, but at these low salt concentrations the net attraction between surfaces containing multiple weak linkages promotes the stronger adhesion necessary for aggregation. Hiddessen et al.17 report similar conclusions from kinetic studies of dimer dissociation rates for microspheres functionalized with biological adhesive moieties. Despite the low affinity of individual pairs of these adhesive moieties, reversible association between microspheres was reported only at the lowest surface densities of these functional groups. These reversible associations between colloidal particles are characteristic of weakly attractive systems.7,12,37,38,40 In the current study, the fluid f fluid + aggregates phase transition marking the change from a repulsive to a weakly attractive state also occurs at modest percentages of hybridizing strands involving approximately one to eight bonds, depending on the salt concentration. Within the fluid + aggregates coexistence region of the phase diagram reported here, the degree of aggregation steadily increases with percentage of hybridizing DNA until a second transition to a completely aggregated state occurs at 100 mM NaCl or higher.

Figure 3. Representative phase contrast micrographs of colloidal suspensions showing a continuous increase in the degree of aggregation as the percentage of hybridizing strands increases from left to right. The percentage of hybridizing strands is (a) 1%, (b) 10%, (c) 25%, and (d) 50%. The salt concentration is fixed at 100 mM NaCl.

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Figure 4. Representative phase contrast micrographs of colloidal suspensions showing a continuous increase in the degree of aggregation as the salt concentration increases from (a) 25 mM, (b) 100 mM, (c) 125 mM, to (d) 200 mM NaCl. The percentage hybridizing DNA strands is fixed at 10%.

Effect of Strength of DNA Linkages on Phase Behavior. In order to examine the effects of salt concentration, the single bond case again serves as an appropriate reference. For 1% hybridizing strands in which only one DNA linkage at most is possible, the onset of colloidal aggregation or the fluid f fluid + aggregates phase transition occurs between 100 and 125 mM NaCl. The degree of aggregation increases with further salt additions indicating that the affinity between complementary strands in a single duplex must be increasing to cause sufficient adhesion necessary for the onset of aggregation. Although the degree of aggregation does continually increase for the single duplex case with salt concentrations of 125 mM NaCl or higher, a completely aggregated state is not observed unless the percentage of hybridizing DNA exceeds 1%. The increase in affinity between complementary strands with salt additions stems from counterion screening of the negatively charged phosphate groups along the DNA backbone. This counterion or Debye screening effect reduces the range of electrostatic repulsions between oligonucleotides to allow the close proximity necessary for duplex formation. Thus, salt additions effectively increase the affinity between complementary sequences to stabilize DNA duplexes and prevent helix dissociation. Figure 4 shows that for a fixed hybridizing DNA concentration of 10%, the degree of aggregation continually increases with salt concentration. For a fixed salt concentration in which the affinity between individual duplexes is constant, the increase in the degree of colloidal aggregation with increasing hybridizing strand concentration is attributed to more oligonucleotide linkages forming between surfaces. In general, at higher DNA concentrations such as 10% (shown in Figure 4) or higher, multiple bonds are more likely to form. However, it is difficult to discern for a fixed DNA concentration above 1% if DNA-driven aggregation becomes more favorable with salt additions due to more bonds forming between surfaces, greater affinity between individual bonds, or an increase in both bond number and strength. Collective Effects of Number and Strength of DNA Linkages between Colloidal Particles. The onset of DNAdriven colloidal aggregation can result from as few as one relatively strong bond (1% hybridizing strands at 125 mM NaCl); however, the weakest individual bonds can also drive aggregation provided that multiple bonds occur (approximately eight bonds maximum for 33% hybridizing DNA at 25 mM NaCl). In general, the critical concentration of salt marking either the fluid f fluid + aggregates transition or the fluid + aggregates f aggregates transition increases with decreasing concentration of hybridizing strands. This inverse relationship between salt and DNA concentration on the fluid f fluid + aggregates phase transition indicates that, in general, DNA-driven aggregation requires a higher bond strength as the number of bonds between surfaces is reduced. Thus, either a few stronger bonds or multiple weaker bonds can collectively result in DNA-driven adhesion between surfaces. Modeling the Onset of a Weakly Aggregated Suspension. Interestingly, even for the lowest salt and hybridizing DNA

concentrations used here, the calculated solution melting temperature (Tm) exceeds the 25 °C conditions used here and indicates that hybridization between complementary oligonucleotides is favorable. However, the lack of aggregation in the fluid regime of the phase diagram indicates that the theoretical hybridization activity of oligonucleotide solutions cannot be directly compared that of DNA grafted on surfaces, even if the higher local concentration of the grafted DNA is considered in Tm calculations. Unlike soluble strands that may freely diffuse in solution to find its partner sequence, the activity of immobilized sequences is confined to the contact zone between surfaces. While confining the oligonucleotides to this interparticle gap does increase the local DNA, the actual number of DNA linkages between the curved surfaces (1-25 linkages per pair of microspheres) involves only a small fraction of the total immobilized strand population (18 106 strands per microsphere), even if microspheres are linked to several neighboring colloidal particles. The statistical mechanical approach of Biancaniello et al.34,36 is used here to analyze the time-average potential of mean force between a pair of colloidal particles functionalized with complementary DNA. Unlike these prior studies34,36 in which soluble oligonucleotides are used to cross-link DNA-functionalized microspheres, the equations below reflect DNA-mediated interactions strictly between immobilized strands. In this model, attractions arise from the dynamic formation of DNA bridges between the microspheres. Repulsions arise from compression of the grafted DNA. If the surface-to-surface separation of the spheres is h, then the attractive interactions have a range h < 2l, and repulsions have a range of h < l where l is the contour length of the grafted DNA sequence. Collisions between grafted strands are ignored because the relatively large footprint of NeutrAvidin on the microspheres results in a low surface coverage of biotinylated DNA strands (∼1.8 × 104 per microsphere). Since the overlap region between interacting DNA sequences is small as compared to the particle radius, a, the total interaction can be summed from the attractive and repulsive contributions between flat plates and then converted to the two-sphere geometry using the Derjaguin approximation. The attractive term of the interaction is an equilibrium average over many states with one or more DNA bridges. If each of the N oligonucleotides has the same statistically independent probability, p, of forming a bridge at a given separation, then the probability that no bridges form is Pfree ) (1 - p)N, and the probability that one or more bridges form is Pbound ) 1 - Pfree. For p , 1, the difference in the Helmholtz free energy can thus be computed from the following equation:34,36

(

)

Pbound ∆Fa ) -ln 1 + ) N ln(1 - p) ≈ -Np ) -〈n〉 kBT Pfree (1) If the concentration profile of DNA is uniformly distributed in the overlap region, then 〈n〉 ) (exp(-∆G}/{kBT))/co2)cA2∆V by mass-action, where cA is the concentration of grafted oligo-

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nucleotides, ∆G is the total change in Gibbs free energy to form a single bridge between particle surfaces, kB is Boltzmann’s constant, T is temperature, co ) 1 M is a reference concentration, and ∆V is the volume overlap. Since it is assumed that the mean concentration of oligonucleotides, cA(x), depends only on the distance from the plate surface, x, then the attraction per unit area between plates, A, can be calculated by the following equation: 34,36

exp(-∆G/kBT) 2 ∆Fa(h) σA ) - kBT A co

∫0 hPA(x)PA(x - h)dx h [∫0 PA(x)dx]2

(2)

where σA is the surface density of grafted oligonucleotides, and the probability distribution of the terminal end of the grafted DNA, PA(x), is equated to cA(x)/σA. 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 is calculated by47

( )

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

∫0 hPh(x)dx

(3)

where Ω is the number of polymer states. Since we are assuming that interactions between immobilized oligonucleotides are negligible, Ph(x) corresponds to the height distribution of a single grafted strand. To compute the total pair interaction, we used the geometric parameters of DNA48,49 to model the DNA spacer conformations described by Ph(x) and PA(x), then evaluated eqs 2 and 3 using analytical and numerical methods. Here, ∆G ) ∆Ghyb(T) + T∆Srot includes both the hybridization free energy, ∆Ghyb, of DNA from the nearest neighbor model as well as changes in the spheres’ rotational entropy, ∆Srot, where ∆Srot ) kB ln(〈Θb/Θf〉) due to bridge linking. Θb is the equilibrium averaged solid angle accessible to the bridged spheres, analyzed using the worm-like chain model,50 and Θf is the unbridged solid angle. The pairwise (47) Dolan, A. K.; Edwards, S. F. Proc. R. Soc. London, Ser. A 1974, 337, 509-516. (48) Hagerman, P. J. Annu. ReV. Biophys. Biophys. Chem. 1988, 17, 265-286. (49) Murphy, M. C.; Rasnik, I.; Cheng, W.; Lohman, T. M.; Ha, T. J. Biophys. 2004, 86, 2530-2537. (50) Bustamente, C.; Marko, J. F.; Siggia, E. D.; Smith, S. Science 1994, 265, 1599-1600.

interaction energy between microspheres is exponentially sensitive to the assumed value for ∆Ghyb. Single-stranded DNA is treated as a tethered Gaussian coil47 with moments determined by a simple random walk simulation. This model is intended to determine pair potentials of a few kBT in magnitude and thus is applicable to model the onset of a weakly attractive state. Within the experimental phase diagram shown in Figure 2, the onset of a weakly attractive state corresponds to the fluid f fluid + aggregates transition in which DNA-driven aggregation first becomes apparent as small clusters of microspheres appear. The phase contour marking the theoretical fluid f fluid + aggregates transition was fitted using a 4 kBT attractive potential. This potential appears to be a reasonable choice based on previous reports for weakly aggregated suspensions.7,12,37,38,40 The magnitude of ∆Ghyb was adjusted until the experimental and theoretical phase transitions matched. This fitted ∆Ghyb value is approximately 3 kBT higher than predicted a priori from the nearest-neighbor model; however, this value is only about 1.5 times the standard deviation for ∆Ghyb and is thus a reasonable approximation that captures the conditions for this first phase transition. In summary, we have systematically investigated the effects of the strength and number of DNA linkages on DNA-mediated phase behavior ranging from a fluid of repulsive colloids to aggregates of attractive colloids. We observed that the degree of aggregation was sensitive to incremental increases in the concentration of hybridizing strands or ionic strength. Although linkages are able to form between complementary sequences, the hybridization activity of the immobilized sequences differs from that of oligonucleotide solutions. In fact, for moderate to high ionic strength conditions, hybridization of only a small fraction of the immobilized sequences was sufficient to induce particle aggregation. On the other hand, although solution melting temperatures indicated favorable conditions for hybridization at lower ionic strengths, aggregation was not observed. Thus, while the calculated solution melting temperature may indicate favorable conditions for hybridization due to the relatively high local DNA concentration, the strength and number of linkages between surfaces ultimately determines if aggregation occurred. Acknowledgment. We gratefully acknowledge financial support from NASA-NAG3-2417 and NSF MRSEC DMR0520020. We also thank Ying Zhang, Anthony Kim, Amy Hiddessen, and David Graves for valuable discussions. LA062885J