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The assembly of DNA-programmable colloidal crystals is presented, where the sizes of nanoparticles used vary from 5 to 80 nm and the lattice parameters of the resulting crystals vary from 25 to 225 nm. A predictable and mathematically definable relationship between particle size and DNA length is demonstrated to dictate the assembly and crystallization processes, creating a set of design rules for DNA-based nanoscale assembly.
In 1996, we introduced the concept of using DNA and its programmable recognition properties to guide the assembly of polyvalent DNA nanoconjugates into macroscopic materials. Over the past decade, we[3-7] and others[2,8-10] have developed methods for using DNA nanoconjugates to realize ordered arrangements of small clusters and highly crystalline extended architectures. Through this work, we have begun to define the design rules for synthesizing nanoparticle structures from DNA where one can envision and realize a particle lattice through the appropriate use of nanoparticle and DNA building blocks. In principle, the approach lends itself to many particle sizes and different lengths of DNA interconnects, thereby providing a new construction kit for realizing a wide array of nanoparticle-based three-dimensional architectures. The ability to assemble crystalline lattices with control over both nanoparticle size and interparticle distance would represent a major advance for nanotechnology, as the physical properties of nanomaterials are highly dependent upon both their size and surrounding environment.[11-15] However, changing the dimensions of nanomaterials used in the assembly process also alters the manner in which the materials behave by changing the relative magnitudes and types of fundamental forces driving assembly. As such, design rules need to be established that take these differences into account to develop a complete understanding of DNA-based particle assembly. Herein, we report a set of experiments that demonstrate that there are predictable and mathematically definable relationships between particle size and DNA length that dictate the assembly and crystallization processes. These experiments allow us to define a “zone of crystallization”, wherein we can understand, explain and control the biomolecular forces driving the formation of colloidal crystals with programmable variation of both crystal lattice parameters and nanoparticle size.
Gold nanoparticles (AuNPs) ~5 to ~80 nm in diameter were densely functionalized with alkylthiol-modified oligonucleotides according to established procedures. (All DNA sequences can be found in the supporting information.) DNA linker strands were then added to these DNA-functionalized AuNPs to induce AuNP aggregation (Figure 1b). The 3′ end of each linker contained an 18-mer sequence complementary to the 3′ end of the AuNP-bound DNA, while the 5′ end contained a short, self-complementary 5′CGCG3′ sequence that induced particle aggregation.
To vary the length of the DNA linkers (and thereby control the distance between nanoparticles in an aggregate), a spacer sequence, consisting of modular “blocks” of a repeated 40-base DNA segment, was placed in-between the particle-recognition sequence and the 5′CGCG3′ sequence. DNA length was controlled by varying the number of blocks in each linker strand—we have previously determined that there is an approximate 0.255 nm rise per base pair for the DNA linkers, meaning that each block adds ~10 nm to the overall length of a single DNA strand. Each of these sections (particle recognition sequence, 5′CGCG3′ sequence and each individual block spacer) was separated by a single unpaired “flexor” base, which has been shown to be important in the formation of DNA-AuNP crystals.[3-5] A 40-base DNA strand complementary to the block region (added in a 1:1 ratio with the number of blocks in the linker strand's sequence) was hybridized to the linker strands prior to combining them with the DNA-AuNPs. This was done both to increase linker rigidity and to make this design conform with previously established crystallization schemes.[3-5] DNA-AuNPs were crystallized by adding linkers to the nanoparticle solutions and heating the resulting aggregates to a few degrees below their melting temperature (the temperature at which the DNA-AuNPs would dissociate).
Face-centered cubic (FCC) colloidal crystals were obtained with control over nanoparticle components and lattice parameters on a diverse length scale—the nanoparticle sizes range from 5 to almost 80 nm in diameter (Fig. 2, Fig. S1-S8), and the unit cell edge lengths of the crystals range from ~25 to 225 nm. Resulting crystal sizes varied, with the average domain size being 1.5 μm in diameter, corresponding to ~102-105 AuNPs/crystal, depending on unit cell dimensions (Table S4), and the largest crystal being approximately 2.6 μm.
All of the calculated lattice parameters for these crystals are within ~10% of predicted values—most systems deviate from prediction by less than 5%, indicating that the crystal lattice parameters are tailorable over the entire size regime studied and that the unit cell edge lengths can be predicted using our previous model. Furthermore, the lattice parameters can be moderately controlled via changes in solution temperature, as they were controllably and reversibly expanded by as much as 8% with only a 20 °C increase in temperature (Fig. S10). Because the DNA sequences used to assemble NPs have synthetically variable numbers of base pairs connecting them, each of which contributes 0.255 nm to the distance between nanoparticles, this gives us nanometer-scale precision over the assembled crystal structures.
Significantly, not all of the DNA-linker and AuNP combinations we designed formed well-defined crystal structures (Fig. 3). Indeed, the data can be clearly delineated into three distinct realms, where the total DNA length is significantly longer, of comparable length, or significantly shorter than the nanoparticles' diameter—only the middle region leads to well-formed crystalline aggregates. The boundaries of this “zone of crystallization” are of fundamental interest, as they allow for explanation of the DNA behavior that leads to ordered nanoparticle assemblies.
The fact that crystals are not formed at low DNA length to AuNP diameter ratios (grey squares, upper left of Fig. 3) can be understood by making a comparison between the polydispersity of the AuNPs and the flexibility of the DNA strands (Fig. 4a). dsDNA exhibits length-dependent flexibility with a persistence length of ~50 nm. Thus, longer DNA linkers have greater variation in the distance between the AuNP surface and the 5′CGCG3′ recognition units (ΔL, Fig. 4a). The data (Fig. 4b, calculations can be found in the supporting information) show that crystals form in systems where the values of ΔL are equivalent to or greater than the variability in nanoparticle size (ΔD, calculated as the size polydispersity of a given NP solution), but not when the opposite is true. In a system where particle size dispersity is greater than DNA flexibility, a well-ordered crystal is no longer the most thermodynamically favorable state. We project that this is because the energetic penalties associated with the DNA stretching and/or bending in order to direct the assembly of non-uniform AuNPs into a uniform lattice are too great to provide significant net enthalpic energy benefit.[17, 18]
This thermodynamic trade-off does not explain the upper limit to the length of DNA strands that can be used for each nanoparticle size (grey squares, bottom right of Fig. 3), however. Longer DNA linkers, with their increased flexibility, would not suffer the enthalpic penalties mentioned above, indicating that the limiting factor for crystal formation with longer DNA lengths may be kinetic, rather than thermodynamic. To form an ordered crystal, the DNA ligands holding nanoparticles together must go through a process of de- and re-hybridization to transition from an initially disordered structure to their most ordered crystalline state.[5, 19] The rate at which these binding events occur can be defined by a kon and koff for the DNA ligands, where maximum rearrangement occurs when the values of kon and koff are both high, but kon>koff. The weak, polyvalent nature of the DNA-AuNP hybridization scheme is critical for this reorganization process, as the weak binding of individual linker recognition units allows for high values of koff, while the high local concentration of DNA on the surface of the nanoparticles inflates the value of kon. The combined effect of these high kon and koff rates results in “mobile” nanoparticles within an aggregate, where repositioning of the DNA-AuNPs is possible.
To determine the relative kon and koff values for these nanoparticle systems, an effective concentration (Ceff) for the DNA linker recognition units within an aggregate was determined—calculations can be found in the supporting material. Ceff is defined as the number of linker recognition units per particle, divided by the limited volume in which they exist, due to localized confinement of DNAs that are tethered to the surface of an AuNP. Values of 1/Tm were plotted against values of ln(Ceff), where Tm is the temperature at which an aggregate dissociates. These values exist in a linear relationship (Fig. 4c) and can be used to determine the thermodynamic constants (ΔH° and ΔS°) associated with DNA duplex formation. Based on the data calculated in Fig. 4c, the ΔH° value for DNA hybridization is -141.9 kJmol-1—this is within 6.7% variance from previously established literature values for this 5′CGCG3′ sequence, indicating that this is indeed an accurate model.
Using these data, plots of calculated kon and koff values show reasonable agreement with experimental Tm values for the systems studied. When the kon of a system is less than 6×103 s-1, no crystals are observed. This indicates that, at the temperatures immediately below dehybridization of the linker-linker overlap for these systems, there is not enough thermal energy to induce restructuring of the nanoparticles on an appreciable time scale. However, when the kon of a system is greater than 1×104 s-1, the rates of DNA de- and re-hybridization are fast enough to induce restructuring in the aggregate at temperatures slightly below Tm. (In-between these values, some systems are able to restructure while others are not—these data are discussed in more detail in the supporting information.) These kinetic data explain the results at the bottom right of Fig. 3, where systems with large DNA length to AuNP diameter ratios are unable to transition from disordered aggregates to ordered crystals—it is in these systems that the lowest rates of kon are observed.
In conclusion, we have determined that there is a definable relationship between DNA length and particle size in the DNA-directed assembly of nanoparticles. This discovery enables not only a better understanding of the fundamental forces driving the crystallization process, but also the formation of colloidal crystals with tailorable features including interparticle distance, particle size, degree of filled space, and unit cell lattice parameters. The method we have developed to model DNA strands constrained on surfaces of NPs and predict their assembly behavior provides a basis for future exploration into the interactions of DNA and nanoscale objects, and we project that these methodologies can be extended to studies of nanoparticles with different shapes and compositions. These discoveries will serve as a template for future nanoparticle crystallization efforts, allowing for the formation of crystals with controllable and tunable physical properties.
**We acknowledge George Schatz for helpful discussions regarding the theoretical calculations of DNA flexibility and relative DNA concentrations in aggregates. C. A. M. acknowledges the NSF-NSEC and the AFOSR for grant support. He also is grateful for a NIH Director's Pioneer Award and an NSSEF Fellowship from the DoD. R. J. M. acknowledges Northwestern University for a Ryan Fellowship. M. R. J. acknowledges Northwestern University for a Ryan Fellowship and the NSF for a Graduate Research Fellowship. K. L. Y. acknowledges the NSF and the NDSEG for graduate fellowships. Portions of this work were performed at the DuPont-Northwestern-Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company and the State of Illinois. Use of the APS was supported by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.
Robert J. Macfarlane, Department of Chemistry, Northwestern University, 2190 Campus Drive, Evanston, IL 60201.
Matthew R. Jones, Department of Materials Science, Northwestern University, 2190 Campus Drive, Evanston, IL 60201.
Andrew J. Senesi, Department of Chemistry, Northwestern University, 2190 Campus Drive, Evanston, IL 60201.
Kaylie L. Young, Department of Chemistry, Northwestern University, 2190 Campus Drive, Evanston, IL 60201.
Byeongdu Lee, X-ray Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439.
Jinsong Wu, Department of Materials Science, Northwestern University, 2190 Campus Drive, Evanston, IL 60201.
Prof. Chad A. Mirkin, Department of Chemistry, Northwestern University, 2190 Campus Drive, Evanston, IL 60201, Department of Materials Science, Northwestern University, 2190 Campus Drive, Evanston, IL 60201.