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Shape Analysis of DNA−Au Hybrid Particles by Analytical Ultracentrifugation Maximilan J. Urban,†,§ Isabelle T. Holder,†,⊥ Marius Schmid,†,∥ Vanesa Fernandez Espin,‡ Jose Garcia de la Torre,‡ Jörg S. Hartig,*,† and Helmut Cölfen*,† †

Department of Chemistry, University of Konstanz, Universitätsstr. 10, 78457 Konstanz, Germany Department of Physical Chemistry, University of Murcia, 30071 Murcia, Spain

‡

S Supporting Information *

ABSTRACT: Current developments in nanotechnology have increased the demand for nanocrystal assemblies with well-defined shapes and tunable sizes. DNA is a particularly well-suited building block in nanoscale assemblies because of its scalable sizes, conformational variability, and convenient self-assembly capabilities via base pairing. In hybrid materials, gold nanoparticles (AuNPs) can be assembled into nanoparticle structures with programmable interparticle distances by applying appropriate DNA sequences. However, the development of stoichiometrically defined DNA/ NP structures is still challenging since product mixtures are frequently obtained and their purification and characterization is the rate-limiting step in the development of DNA−NP hybrid assemblies. Improvements in nanostructure fractionation and characterization techniques offer great potential for nanotechnology applications in general. This study reports the application of analytical ultracentrifugation (AUC) for the characterization of anisotropic DNA-linked metal−crystal assemblies. On the basis of transmission electron microscopy data and the DNA primary sequence, hydrodynamic bead models are set up for the interpretation of the measured frictional ratios and sedimentation coefficients. We demonstrate that the presence of single DNA strands on particle surfaces as well as the shape factors of multiparticle structures in mixtures can be quantitatively described by AUC. This study will significantly broaden the possibilities to analyze mixtures of shape-anisotropic nanoparticle assemblies. By establishing insights into the analysis of nanostructure mixtures based on fundamental principles of sedimentation, a wide range of potential applications in basic research and industry become accessible. KEYWORDS: sedimentation velocity, analytical ultracentrifugation, gold nanoparticle−DNA assembly, anisotropic nanostructures, shape analysis, bead models, self-assembly particles are detected.13−15 The resolution of this technique is so high that even ions or small molecules can be separated from their small assemblies.16,17 Single core−shell particle size distributions and molecular weights were measured precisely based on a single AUC run.18 If defined assemblies of nanostructures are wanted, DNA is a highly suitable material as it permits the generation of size- and shape-programmable structures. For example, DNA structures can be self-assembled into complex shapes,19 which can serve as templates for nanoparticle (NP) alignment.20−22 Realized structures reach from discrete DNA-linked dimers and trimers10,23−25 to larger NP helices12 and 2D NP arrays.26 DNA is a particularly well-suited building block in nanoscale

D

efined assemblies of nanoparticles have interesting properties for applications in plasmonics,1−4 ultrasensitive biosensing,5 catalysis,6 and research of energy-storage devices.7,8 The characterization and purification of such defined assemblies is often the rate-limiting step in the development of more complex structures. The characterization of nanoassembly mixtures is challenging because of the wide range of distributions in shape and size that are frequently obtained. While analysis and purification by electrophoretic methods are widely applied,9−12 the potential of centrifugation techniques is still far from being exhausted. Analytical ultracentrifugation (AUC) monitors sedimentation of the entire sample under a given centrifugal field. Species are fractionated during sedimentation according to size, density, and friction. Fractionation of the sample in the centrifugal field during the measurement enables the in situ analysis of complex samples in the size range of less than 10 nm with angstrom resolution, yielding an unrivalled statistical significance since all © 2016 American Chemical Society

Received: February 24, 2016 Accepted: July 26, 2016 Published: July 26, 2016 7418

DOI: 10.1021/acsnano.6b01377 ACS Nano 2016, 10, 7418−7427

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experimental data, in addition to the sedimentation coefficient distribution. The 2D spectrum analysis (2DSA) algorithm of Brookes and Demeler is a high-resolution and supercomputerconnected program to analyze data sets in the s and f/f 0 dimension out of one single AUC run.33 The 2DSA decomposes the experimental sedimentation velocity data into a sum of finite-element solutions to the Lamm equation, describing the noninteracting settling particles present in solution. To determine the effect of noise and the confidence limits for the determined solutes in heterogeneous samples, a stochastic Monte Carlo approach is applied during the last step of the 2DSA.35 The elucidation of structural features from the hydrodynamic information extracted from AUC can be done by beadmodeling calculations in which solution properties are computed for models composed of spherical elements. This technique, which has its roots in the classical theories for beadand-spring models of flexible polymers,36 has been extensively used in biophysics37 and is now becoming a useful tool to interpret the structure and dynamics of complex nanoparticles.38,39

assemblies because of its size, conformational variability, and self-assembly capabilities via base pairing.27 However, the synthesis of structures with a defined number of DNA molecules per particle (e.g., 1:1) in high yields is challenging because of the formation of mixtures of products.23,28 Surface area restrictions on bare particles (with typical particle sizes of 5−60 nm in plasmonic applications) are not strong enough to suppress the formation of stoichiometric mixtures of products.29 For any further use, single species have to be purified. The widely applied procedure for the synthesis of defined groupings such as dimers requires an electrophoretic purification step after the conjugation to ssDNA and a second purification step after the combination of the building blocks with one complementary DNA strand per particle.30 Electrophoretic purification of NPs modified with ssDNA requires minimum DNA lengths of 50−70 nucleotides depending on particle sizes.23,31 Taken together, these approaches generate mixtures of products in the first place that have to be analyzed and purified in order to obtain homogeneous samples. The assignment of individual species in such product mixtures has so far proven to be very complicated. Here, we present a method that enables the analysis of the conjugation and hybridization products in a single step. Sedimentation velocity/analytical ultracentrifugation (SVAUC) can measure partial concentrations of the different species formed in solution and is therefore useful during synthesis developments. Furthermore, as particles are fractionated during sedimentation, SV-AUC can be used for the development of centrifuge-based purification procedures. Sedimentation and diffusion during the measurement depend strongly on the shape of the species, which allows for the extraction of additional information.32 Recent developments in the AUC field, mainly concerning data analysis, allow for the simultaneous calculation of sedimentation and diffusion coefficients of different species present in solution.33,34 Anisotropic particles show significantly slower sedimentation and diffusion compared to their spherical counterparts due to their higher friction. The sedimentation coefficient and the diffusion coefficient are interdependent via the frictional ratio f/ f 0.31 Increasing frictional ratios are measures for anisotropic particles that deviate from a spherical shape. The frictional ratio is a dimensionless ratio of the measured frictional coefficient and that of a spherical structure of the same mass and density. Changes in the frictional ratio therefore hold important information for the in situ analysis of dynamic systems and are frequently used for the analysis of DNA or proteins.34 In comparison to biomacromolecules, the calculation of the shape factors from AUC data from nanoparticle samples is a widely unexplored field,31 with only few examples of successful shape calculations either via ellipsoids of revolution or via bead modeling. We developed a method to determine the composition of the species regarding the number of single particles and DNA building blocks based on their frictional ratios. This method can be applied to already existing AUC protocols and will further enhance the possibilities and the relevance of centrifugation techniques in the nanosciences. The shape analysis by AUC is based on the extraction of diffusion coefficients due to broadening of the sedimentation boundary during sedimentation. For such an experiment, the angular velocity should be relatively low to increase the time span in which diffusion can occur.31 Since boundary spreading from differential migration and from diffusion is different, f/f 0 can be extracted from the

RESULTS AND DISCUSSION In order to explore the possibility of analyzing mixtures of DNA−nanoparticle conjugates, we synthesized defined assemblies consisting of dsDNA linkers and AuNPs following established protocols.10 We aimed at assembling NP dimers that were generated from purified building blocks composed of NP−ssDNA (68 nucleotides) that have a single complementary DNA strand attached on the particle surface. Combinations of solutions containing particles modified with complementary ssDNA strands led to the formation of slower migrating bands in electrophoresis, as described previously (Figure 1A).10 Agarose gel electrophoresis and subsequent transmission electron microscopy (TEM) analysis (Figure 1C) from extracted gel bands showed mixtures of nanoparticle conjugates, predominantly dimers. However, observed distances between particles in the TEM analysis did not reflect the DNA length. Some reasons may include the flexibility of the utilized thiol linkers and attractive forces between particles during drying on the grid. Therefore, in situ methods that measure the shape of the particles in solution are advantageous. Moreover, the applied electrophoretic and TEM analysis was not sufficient to describe the product distribution in the complex mixtures obtained. A drawback of this protocol and protocols used by other groups for DNA−NP conjugates40 is that interparticle linkages are necessarily built from double-stranded DNA. Singlestranded DNA linkers, however, might be advantageous for many applications where nonduplex structures are needed, such as in shape-switchable elements or ligand-sensing sequences such as aptamers. Alivisatos et al. addressed this problem by the development of enzymatic ligation strategies.41 However, the mixtures resulting from single-stranded DNA-linked NPs seem to be even more complex as observed for NP conjugates connected with dsDNA (Figure 1). The main difficulty for the development of procedures for ssDNA linker incorporation by standard Au thiol chemistry is the complexity of the mixtures obtained after conjugation of divalent (i.e., thiol-modified on both ends) ssDNA. As an example for the analysis of complex DNA−NP assembly mixtures, we characterized the products obtained after conjugation of NPs with divalent DNA molecules, in this case, 7419


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with thiol groups on both 3′ and 5′ ends, by SV-AUC. The experiment was set up in a way that a control of an assembled DNA strand with only one thiol group was used as well as bare particles without any DNA. Hence, in the control sample with only one thiol group per dsDNA, structures containing only a single NP were formed. In the sample with two thiol groups, the formation of nanoparticle groupings is expected. In order to assign the expected structures to the species observed in SVAUC, respective sedimentation coefficients and frictional ratios were calculated by hydrodynamic bead modeling for all expected product species. The Au−DNA hybrids were represented as described in detail in the Methods section, by bead-and-rod models in all cases involving double-stranded DNA. The radius of the Au beads was 3.2 nm, and the rods were strings of eight nearly touching beads with a radius of 1.4 nm. The special modeling applied to the construct with single-stranded DNA is also described in the Methods section. The notation for classification of particles is “n−m”, where n is the number of gold spheres and m is the number of dsDNA connectors. In Table 1, particle 1−0 is the single (coated) gold nanoparticle. Particles 1−1 and 2−1, also named “lollipop” and “dumbbell”, are the cases presenting a unique rigid straight (S) conformation. Particle 2−1/2 is the dumbbell with a flexible single-stranded DNA linker. Particle 2−2 is a dumbbell with one extra dsDNA attached at one of the beads with a variable orientation. Particle 3−2, the “trumbbell”, has three Au beads and two dsDNA connectors. We report the results for a rigid, straight conformation, although likely, in the real system, there may be a variety of conformations with different angles between the two arms. Similarly, particle 4−3, the “tetrambbell”, has four Au particles and three dsDNA connectors; again, we report the result for a straight arrangement and the range for the variety of conformations with different disposition of the connectors. We have also considered another arrangement for the tetramer, with circular rather than linear topology, that can also present different structures, not necessarily planar, with the aspect of a bent rhomboid. As in all cases with conformational variability, we report the mean and a range of plausible values. The results of the hydrodynamic calculations are presented in Table 1 and corresponding bead structures in Figure 2. The modeled sedimentation coefficients for spherical particles are in good agreement with the experimental AUC results from model-independent ls-g*(s) analysis and the 2DSA of particles without conjugated DNA (Table 2). The calculated value for 5.5 nm sized particles (TEM) is 270 S, and the measured peak sedimentation coefficient is 263 S. Larger particle sizes will increase calculated sedimentation coefficients and may lead to better agreement. 2DSA showed species with slightly higher s values in the f/f 0 range of 1 that fit the modeled data. The apparent sedimentation coefficient distribution (g*(s), ls-g*(s)) can be determined without any knowledge about the partial specific volumes (v)̅ of the sedimenting species. The calculation of diffusion-corrected sedimentation coefficient distributions as well as the shape factor (frictional ratio) determination is only possible if the density of the sedimenting species is known. Unfortunately, v ̅ values of gold colloids are not measurable by the common method of the density oscillation tube because our investigated sample is a mixture where this measurement would only yield an average value, which is of no use in our case. On the other hand, density

Figure 1. (A) Agarose gel electrophoresis of DNA/NP conjugates. The schematic structures show different combinations of DNA (blue) and nanoparticles (red). Lane 1: 5 nm AuNP without DNA. Lane 2: AuNP bearing a single ssDNA molecule (purified sample, DNA: monothiol 3′ antisense). Lane 3: AuNP bearing a single ssDNA molecule which is complementary in DNA sequence to the sequence used in lane 2 (purified sample, DNA: monothiol 5′ sense) (3′ and 5′ indicate the position of thiol modifications). Lane 4 shows a combination of the samples from lanes 2 and 3. A slower migrating band is observed that can be assigned to dimers. Lane 5: DNA strands were annealed prior to conjugation to the AuNP. A mixture of structures is observed. The resulting structures cannot be clearly assigned by electrophoresis. (B) Data obtained by AUC of a sample that was prepared by prehybridization of DNA prior to combination with nanoparticles. Experimentally determined sedimentation profiles (yellow) were modeled (red) during data analysis (rmsd = 0.0081). The sample was measured at a centrifugation speed of 3000 rpm for approximately 13 h. Absorbance was measured at a wavelength of 520 nm. Absorbance is defined as the logarithm of the ratio of incident light (I0) to transmitted light (I). (C) TEM analysis of lane 5 (left) and of the extracted dimer band in lane 4 (right). 7420


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ACS Nano Table 1. Calculated Hydrodynamic Parameters from Bead Modeling of Different DNA−Au Structures.a particle 1−0, sphere 1−1, lollipop 2−1, dumbbell 2−1/2flex, dumbbell ssDNA 2−1/2flex, dumbbell ssDNA 2−2(M)dumbbell+DNA 3−2, trumbbell 3−2, trumbbell 4−3, tetrambbell 4−3, tetrambbell 4−4 cyclic tetramer 4−4 cyclic tetramer

S S S H L V S V S V F V

# Au

# DNA

Mw (×10−6 Da)

v ̅ (cm3/g)

1 1 2 2 2 2 3 3 4 4 4 4

0 1 1 1/2 1/2 2 2 2 3 3 2 2

0.958 1.00 1.96 1.94 1.94 2.00 2.96 2.96 3.96 3.96 4.00 4.00

0.083 0.105 0.094 0.089 0.089 0.105 0.098 0.098 0.100 0.100 0.105 0.105

s, S 271 150 243 288 233 186−200 253 246−266 261 259−295 268 240−300

aT, nm

(193) (256) (277) (268)

f/f 0

3.17 5.82 7.14 5.4 6.5 7.8−8.5 (8.18) 10.3 8.8−9.5 (9.18) 13.4 10.7−12.1 (11.4) 11.8 10.7−12.7 (11.8)

0.99 1.65 1.68 1.31 1.57 1.76−1.92 2.09 1.78−1.93 2.45 1.96−2.21 2.12 1.85−2.30

(1.85) (1.86) (2.09) (2.12)

Note: S, straight conformations; V, variable conformation; mean (typical, representative) value and range of plausible values; flexible ssDNA dumbbell, high salt (H) and low salt (L). Mw = weight average molar mass, v ̅ = partial specific volume, s = sedimentation coefficient, aT = Stokes radius, and f/f 0 = frictional ratio. a

gradient measurements, for example, are well-suited for the measurement of the density of polymers and biomolecules.42 In the case of metal nanoparticles, this method cannot be applied because no solvents with higher densities than around 3 g/mL are available for these studies. Finally, the solvent variation method, 42 which is very useful for the simultaneous determination of particle size and density distributions of latexes cannot be applied here because the density of our samples is too high to allow for a reasonable accuracy of the results which are based on sedimentation measurements in water and heavy water solvents with a small density difference compared to that of the sample and solvent. Hence, we estimated a density value for the hybrid particles in the following analysis. Errors resulting from wrong estimates will be discussed. The particles consist of a crystalline gold core with a density of 19.3 g/cm3 and a shell of stabilizing ligands. In the present case, the shell of unconjugated gold particles consists of a charged triphenylphosphine (BSPP). Using reported crystal structures for gold−triphenylphosphine complexes,43 we could estimate the density of the core−shell particles. The thickness of the phosphine ligand layer is approximately 0.6 nm according to Au−P(Ph)3 crystal structures.43

Figure 2. Snapshots of conformations of the bead models of the Au−DNA particles.

Table 2. Comparison of Modeled and Experimental AUC Parameters

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Figure 3. 2DSA results from data analysis in Ultrascan. The same particles are conjugated with different DNA strands. Different shapes are formed that are reflected in the [s]/[f/f 0] plots: (A) 68 bp monothiol DNA leads to the formation of lollipop structures; (B) dithiol DNA leads to the formation of anisotropic NP groupings. It should be noted that the DNA used in (B) contains a double strand of DNA with the following modifications: one strand contains both thiol modifications while the complementary strand does not contain any thiol modification.

range of 240−340 S and shows little variance in the f/f 0 domain. At sedimentation coefficients of about 130−220 S and higher frictional ratios, another cluster of species is found. This cluster shows little variance in the s domain but variation in the f/f 0 domain between 1.2 and 1.7. Increasing frictional ratios of 1.9−2.2 and sedimentation coefficients between 170 and 280 S are found for the third cluster of species. Species found in the region of 250 S and f/f 0 ratios of 2 show broad distributions in the sedimentation coefficient and frictional ratio domain. Molecular weight distributions show peak values in the range of 1.1 MDa for monothiol DNA and 1 and 2.3 MDa for dithiol DNA. The expected molecular weight for r = 2.7 nm Au particles with a density of 19.3 g/mL is 0.9 MDa. Therefore, it should be noted that higher molecular weights present in the sample with two thiol groups per dsDNA show the formation of particle groupings. Comparison of panels A and B of Figure 3 shows that the species at a frictional ratio of 1 appears in both graphs in approximately the same range of sedimentation coefficients. Another species that is observed in both samples is found in the range of 180−190 S values. The divalent sample with a dithiol DNA linker shows additional species that are not present in the sample with monothiol DNA. The 2DSA results show clearly different behaviors of the differently modified DNA strands. Interpretation of the s and f/f 0 values on the basis of known structural parameters of the sample is possible by hydrodynamic bead modeling. Modeled coefficients for trumbbells and tetrambbells are in this range of s and f/f 0 values (Table 1). Furthermore, in structures containing more than two DNA strands, different conformations can occur. Structures comprising three particles, for example, can adopt stretched and bent conformations. Broad distributions of the frictional ratio, sometimes called shape factor, should reflect conformational and compositional variations that lead to various shapes. To which extent the shape factor is influenced by the difference between ssDNA and dsDNA in lollipop structures remains to be explored in greater detail. In the s dimension, the experimental data lead to more defined values. Modeled molecular weights of bare particles based on density of bulk gold and diameters from high-resolution transmission electron microscoy (HR-TEM) measurements are determined

The density of hybrid nanoparticles in solution is estimated based on a core−shell model.18 The calculated density for the core−shell particles with a phosphine layer with a 0.6 nm thickness is 12.5 g/cm3, whereas bare gold has a density of 19.3 g/cm3. This value is used for the 2DSA in Ultrascan. Density differences between the different reaction products are not taken into account for the 2DSA. If a DNA strand with only one thiol group is conjugated in 0.25 equiv to gold particles, it is expected that particles bearing one or multiple DNA strands are present in solution next to a larger amount of free particles. This expectation is in agreement with results from electrophoresis and TEM analysis (data not shown). Figure 3A shows the results for the data analysis of a sample where DNA with one thiol group was conjugated to gold particles. Two main species appear in s and f/f 0 distributions. At a frictional ratio of 1, species were found to fit the experimental data in the range of 240−340 S. A second distribution of species is found at lower sedimentation coefficients and higher frictional ratios. The species are not distributed randomly between the main peaks but follow a master curve. Lollipop structures consist of a dsDNA bound to the surface of a particle. These structures are anisotropic and show higher frictional ratios in the bead model (1.65). The friction during sedimentation increases due to the deviations from a spherical shape. In the range of 1.2−1.7, significant species are found in the sample with only one thiol group. The measured sedimentation coefficient of the lollipop structures is found in the range of 130−220 S and deviates from the modeled sedimentation coefficient of 150 S. One reason for the deviation is that too small particle sizes were used for the bead modeling. This leads to a smaller molecular weight and slower predicted sedimentation of the structures. Another reason might be that the DNA is not fully hybridized to a complementary sequence. The friction of ssDNA bound to a particle is expected to be lower than that of dsDNA. A dsDNA molecule with two thiol groups is able to link two particles together, and larger structures consisting of multiple particles might form. Figure 3B shows the result for conjugation of DNA with two thiol groups on opposite termini on one strand. The 2DSA shows three main distributions of s/f/f 0 values. The species with the lowest frictional ratio lies in the 7422


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Figure 4. Calculated molecular weight distributions based on AUC data: (A) 68 bp dsDNA with a single thiol group leads to the formation of lollipop structures; (B) 68 bp dsDNA with two thiol groups leads to the formation of particle groupings. The modeled molecular weight of a 5 nm AuNP is 0.958 MDa.

to be Mw = 1 MDa. 2DSA shows significant species in the range of 1−3 MDa, with heavier species in the sample with two thiol groups per DNA strand (Figure 4). This finding is in good agreement with modeled data of larger structures and the expectations from the DNA modifications. The good agreement in the molecular weight distributions shows that the thickness of the ligand shell used in the density model on the basis of crystal structures from phosphine ligands is a good estimate. A variation in the density parameter during 2DSA has a large influence on the Mw values. Density influences molecular weight determination by AUC significantly.18 It was shown that the simultaneous determination of sedimentation and diffusion coefficients allows for the calculation of density values of spherical structures.18 By this approach, errors in frictional ratios and molecular weights, which are based on calculated v ̅ values, can be determined. In our case, strongly anisotropic shapes such as the lollipops and dumbbells do not allow for the calculation of shape-specific v ̅ values based on the method developed by Carney et al.18 To address the influence of different v ̅ values on the obtained 2DSA results, we refer to the results of the bead modeling. Considering different v ̅ values for different anisotropic structures, we have determined an error in frictional ratios on the order of 8.3−10.6% (Figures S2−S4 and Tables S2 and S3). The error in molecular weights is expected to be even larger because a 1% error in the v ̅ causes a 3% error in the molar mass. Advantages and Limitations of the Method. Without DNA staining, significant amounts of the target species are needed for statistical TEM analysis to gain evidence that the structure is present. Therefore, groupings can only be determined by statistical analysis, which does not usually take more than several thousand particles from selected areas of the grid into account. Drying effects influence the shape of DNA linkers, and cryo-EM is required for reliable interparticle distance analysis.9 In SV-AUC experiments, the sedimentation boundary is monitored via UV−vis spectroscopy, and millions of particles contribute to the measured signal. Determination of concentrations of Au−DNA hybrid structures by AUC is nevertheless limited due to unknown extinction coefficients of the different constructs. For exact determination of concentrations, the extinction coefficients of all structures would have to be determined. Sedimentation coefficients and frictional ratios reflect compositions of hybrid particles. Shape information can be derived from AUC experiments if diffusion coefficients can reliably be determined. This requires sufficient

broadening of the sedimentation boundary during the measurement. In solutions with many species presenting broad sedimentation boundaries, the diffusion coefficient determination becomes challenging.33 A broad sedimentation boundary can be interpreted in terms of diffusional broadening or in terms of broad species distributions. We have performed AUC experiments with two different mixtures of DNA−NP structures to study the influence of different compositions on the 2DSA (Figure S1 and Table S1). The observed 2DSA distributions show free NPs, lollipop structures, and dumbbell/ trumbbell structures. However, their amount is largely different as would be expected for different preparations. This shows that the experiments are reproducible concerning the kind of detected structures. Experimental parameters, for example, rotational speed and noise in the data, play important roles in the resolution limit of the 2D AUC measurements as well as the quality of parameter fitting to experimental data in the latter data analysis. Therefore, the present study gives insights in the possibilities and limitations of the application of AUC in the frictional ratio analysis of colloidal mixtures.

CONCLUSION Analytical ultracentrifugation is a well-suited method for the characterization of complex mixtures of reaction products. Simultaneous extraction of sedimentation coefficients and diffusion coefficients from a single sedimentation velocity experiment resolves multiple species present in solution. It was shown by AUC analysis that conjugation with dsDNA, bearing a single thiol modification, leads to the formation of lollipop structures that contain one dsDNA strand and one particle. The DNA−NP lollipops sediment slower than bare NPs due to an increased friction and a reduced density of the hybrid structures. Anisotropy of the structures is reflected in increased frictional ratios. The synthesis of dumbbell, trumbbell, and larger structures can be accomplished by a single DNA strand that bears two thiol modifications. However, it was shown by electrophoresis, TEM, and AUC that this is only possible if an antisense strand is present. It is hypothesized that increased rigidity of the DNA is required to circumvent the binding of both thiol groups to the same particle. Multiparticle structures were clearly identified by 2DSA of f/f 0 and s domains. Hydrodynamic bead modeling of putative structures allows for rational assessment of single peaks in 2DSA plots. Unknown particle densities were modeled based on structural information from TEM analysis and the DNA primary sequence to assess 7423


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needed for one sedimentation measurement. The wavelength for absorbance detection was determined by a wavelength scan at 1500 rpm before the sedimentation experiments. Wavelengths with an absorption value between 0.5 and 1.1 were selected for the measurement, ideally 520 nm. Absorbance was measured at radial scan intervals of 0.007 cm. Particles were centrifuged between 323 rcf (2000 rpm) and 2903 rcf (6000 rpm) at a constant temperature of 298.15 K. A grid search is performed over a range of sedimentation coefficients (1−2000 S) and frictional ratios (1−4) with a sufficiently high resolution to fit the range of solutes and reduce peak splitting.33 Grid resolution is a trade-off between computing time and information content. However, coarse grids in the s or f/f 0 dimension still resolved qualitative trends. In a first analysis step, time derivative calculation showed that a range of s values between 1 and 2000 S is appropriate. Equidistant discretization with s = 200 was chosen. Frictional ratios in a range of 1−4, with 60 discretizations, were used for data analysis. The resulting 60 × 200 grid with a total of K = 12 000 species was fitted with the 2DSA algorithm to the data using a v ̅ as stated in Table 1 for the different species. Fifty Monte Carlo iterations were conducted. A virtually random distribution of residuals consistent with noise in the data acquisition was obtained. A common v ̅ value of 0.08 cm3/g, a solvent viscosity of 0.901 mPa·s, and a solvent density of 0.99918 g/ cm3 was used during the 2DSA. The sedimentation coefficients were corrected to standard conditions at 20 °C in water. Bead Modeling (AUC). The bead-modeling strategies and computational protocols have been widely described in the literature44 and implemented in the computer programs of the HYDRO suite.45 In one of the strategies, particles can be modeled as arrays of beads that reproduce the size and shape of the particle; program HYDRO++ is intended for this purpose.46 Another approach is bead/shell modeling, in which a shell consisting of a large number of small elements (minibeads) is placed on the surface of the particle, extrapolating the resulting properties to zero minibead size. This approach makes calculations feasible for models containing nonspherical subunits and is implemented in the program HYDROSUB.47 For nonrigid particles, a simple approach that is valid for overall solution properties, particularly frictional (sedimentation and diffusion) coefficients, is the so-called rigid-body approach.48 A sample of plausible conformations is generated according to some hypotheses on the kind and extent of flexibility (this was particularly simple for the cases treated in this paper). Then the properties are calculated by averaging the values obtained for each conformation as if it were instantaneously rigid. Program MULTIHYDRO, in the HYDRO suite, is intended for such previous conformational scans, generating the structural files needed for a multistructure single-run execution of HYDRO++, which in turn produces an output file with the set of properties of each conformation that can be postprocessed with any spreadsheet. Short double-stranded DNA (dsDNA) pieces in our Au−DNA are hydrodynamically equivalent to rigid, cylindrical rods with length L (nm) = 0.34nbp, where nbp is the number of base pairs and 0.34 nm is the rise per base pair in the B-form of dsDNA.49 To be considered rigid, the contour length must be smaller than the persistence length of DNA, ca. 55 nm.50 A 68 bp dsDNA has L = 23 nm, which fulfills that condition. The hydrodynamic diameter, d, to be assigned to the cylinder has been recently estimated to be 2.3 nm.50 Thus, Au− dsDNA hybrids can be represented by “beads-and-rods” models, whose properties can be evaluated with the shell-model strategy implemented in HYDROSUB.47 Shell-model calculations are timeconsuming because the number of minibeads in the model, N, is high (up to about 2000) and computing time increases as N3. We have shown that the cylindrical rod can be safely replaced, in turn, for a linear string of beads having the same length as the cylinder and with a volume that matches that of the cylinder; this condition is satisfied with beads of having a diameter b = 1.22, d = 2.8 nm for DNA. The number of beads in the string would be the larger integer number closest to N/d, which amounts to just eight beads in the rod, with little gaps between neighbors to reach the desired length L = 23 nm. Thus,

potential sources of errors. Based on the presented results, improvements in preparative centrifugation of nanostructures and upscaling toward larger amounts of purified particle assemblies for various applications could be envisioned. A further advantage of the method is that samples can be investigated directly after synthesis without further purification, allowing a fast access to synthesis results for synthesis optimization.

METHODS Citrate-coated gold particles of nominally 5 nm diameter were purchased from Ted Pella (Redding, CA). Bis(p-sulfonatophenyl)phenylphosphine (BSPP) and thiolated DNA sequences were purchased from Sigma-Aldrich. Solvents and buffer solutions were obtained from Sigma-Aldrich. All chemicals were used as received without further purification. The DNA sequences were designed to have minimized nonspecific interactions with nanoparticles. DNA 1, dithiol, sense: 5′-S-S-C6-GTTCTCCTTTTCGCTATCTTAGTTTTTCTTCTCTATCCTCACTCCTTCTTTTTTCATTCATTCTCTCT-C3-S-S3′ DNA 2, monothiol 5′, antisense: 5′-S-S-C6-AGAGATAATGAATGAATTAAGATTGAGTAAGGATAGAGAGGAATAAATGAGATAGCTTAAAGGAGAAC-3′ DNA 3, monothiol 5′, sense: 5′-S-S-C6-GTTCTCCTTTTCGCTATCTTAGTTTTTCTTCTCTATCCTCACTCCTTCTTTTTTCATTCATTCTCTCT-3′ DNA 4, antisense: 5′-AGAGATAATGAATGAATTAAGATTGAGTAAGGATAGAGAGGAATAAATGAGATAGCTTAAAGGAGAAC-3′ Citrate particles that were used directly from the manufacturer started to precipitate at salt concentrations higher than 50 mM. After ligand exchange from citrate to BSPP, particles were stable in 120 mM NaCl/KCl solutions. The purified and phosphine-stabilized particles were stored at 4 °C for up to 3 weeks with a concentration of 2−6 μM. Synthesis of DNA/AuNP Conjugates. DNA purified by HPLC was purchased from Sigma-Aldrich and resuspended in Milli-Q water to a final concentration of 100 μM. To prepare Au−DNA conjugates, 3′, 5′, or double-thiolated DNA was mixed with BSPP-coated gold colloids in a molar ratio of typically 0.25−1 DNA equivalents per particle.40 NaCl (1 M) was added to the DNA−AuNP mixture to a final concentration of 50 mM NaCl. The mixture was incubated at room temperature for 48 h before electrophoretic purification. For the results shown in Figure 1, DNA 2 and 3 were used. For the results shown in Figures 3 and 4, DNA 1 and 4 were used. Conjugates shown in Figure 1 were prepared by separate modification of nanoparticles with DNA 2 or DNA 3 and purification of structures bearing a single ssDNA strand per AuNP. The purified NP−DNA conjugates were then combined in a 1:1 stoichiometry to form dimers. Conjugates shown in Figures 3 and 4 were prepared by adding a duplex of DNA 1 and DNA 4 to AuNPs. Electrophoresis of Au−DNA Conjugates and Nanoparticle Assemblies. Gels were prepared with 0.8−4% agarose by weight in 0.5× TBE buffer. Gels were run at 5 V/cm for 90 min. High-Resolution Transmission Electron Microscopy. HRTEM was performed on a Jeol-JEM-2200FS with 200 kV acceleration voltage and high-resolution pole piece (point resolution of 0.23 nm). Two microliters of dilute particle solution (approximately 0.5 nM) was allowed to dry on a carbon-coated copper grid for at least 1 h. TEM images were analyzed using the software ImageJ. The nanoparticle size was determined based on TEM images by calculating the mean value of 50 nanoparticles. Analytical Ultracentrifugation. AUC was performed using a Beckman Coulter XL-I with a titanium 4 place (An60Ti) or 8 place (An50Ti) rotor (Beckman Coulter). Cells were outfitted with quartz windows and titanium 12 mm path length (Nanolytics) double sector centerpieces. The reference sector of each cell was filled with 350 μL of 0.5× TBE buffer, while the sample sector was filled with 340 μL of DNA-modified gold nanoparticles as described above. Four hundred microliter particle solutions with a concentration of 70 nM were 7424


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ACS Nano we can alternatively employ simple bead models. We have tested the agreement between the shell-model and bead-model approach for a single sphere, for a “lollipop” (Au sphere with attached DNA rod) and a “dumbbell” (two Au spheres joined by a DNA rod; Figure 5). The difference in the frictional properties was always less than 2%.

A rigorous way of modeling wormlike macromolecules for hydrodynamic purposes is the discrete wormlike model,59,60 where the chain is represented by a string of N touching beads of diameter d, segment length b = d, so its the contour length Lc = Nb, and the bending flexibility is represented by a potential quadratic on the local bending angle with force constant Q = kBTP/b. This scheme has been very successfully applied to the prediction of hydrodynamic properties of a variety of wormlike macromolecules.50 In the present case, the model would include, at both ends of the DNA chain, two additional beads representing the Au nanoparticles. The model can be implemented in the general purpose program MONTEHYDRO,51 which works in the so-called rigid-body Monte Carlo approach,48 predicting plausible conformations of the flexible entity and obtaining the estimation of the observable properties as conformational averages. Regarding the parameters, the hydrodynamic diameter of ssDNA can be estimated to be d ≅1 nm. The primary output of the hydrodynamic calculations reported by HYDRO programs is the hydrodynamic radius. For translational friction, sedimentation, and diffusion, the proper radius is the Stokes radius, aT, defined as the radius of a sphere which would have the same friction coefficient as the particle under consideration. It is important to note that aT depends solely on the geometry (size, shape, or conformation) of the particlein a bead model, the position and sizes of the beads. The frictional coefficient f is then obtained from aT and the solvent viscosity η0:

Figure 5. Shell model (A) and bead model (B) of a Au−DNA−Au “dumbbell” with the dimensions mentioned in the text. The calculated hydrodynamic radii, aT, are 7.14 and 7.08 nm, respectively.

For particles with two or more DNA rods linked to the same Au bead, a variety of conformations can be presented. For such cases, a sufficiently large number (100) of conformations, determined for the orientation of the DNA rods, were generated, setting the orientations according to a random, uniform distribution. The polar angles (θ,φ) that define the orientation are generated with a random number for cos θ in (−1,+1) and a random number for φ in (0,2π), with the only restriction of avoiding bead−rod, bead−bead, and bead−rod overlapping. Thus, for such particles with conformational variability, we obtain not a single value of the hydrodynamic property but a range. For this computational scheme, our computer code MULTIHYDRO51 proved its utility: with specific lines of code for the random generation of beads-and-rods particles, it produces the structural files needed for a subsequent multistructure HYDRO++ calculation, which provides the hydrodynamic properties for each conformation in an output file that can be easily postprocessed with a spreadsheet for the final statistical calculation. For all these cases with conformational variability, we report in the Results and Discussion section a range taken as the mean plus/minus twice the standard deviation. We have included one case (particle 2−1/2 “flexible dumbbell”) in which the linker is a 68 bp ssDNA. We regard ssDNA as a wormlike chain, whose rigidity is gauged by the persistence length, P, and having a contour length, Lc, which as stated by Smith et al.52 should be 0.56 nm per nucleotide. This amounts to Lc = 68 × 0.56 = 38 nm for a single-stranded chain of 68 nucleotides. More discrepancies are found in the reported rigidity, but a commonly cited value is P ≅ 0.8 nm.52−55 Nonetheless, this parameter is doubtful because factors such as intramolecular base pairing may affect the conformational statistics. A major factor influencing the persistence length is the polyelectrolyte effect in the charged nucleotide chain. The above-mentioned value is the usual one, proper of high-salt conditions (case “H”), whereas P can be as large as ≅5 nm for very low salt conditions (case “L”).56,57 Considering that the full simulation of the conformational variability would be quite laborious, we have taken a shortcut, replacing the flexible linker by a fixed-length (rigid) linker of length L ≅ ⟨r2⟩1/2, where ⟨r2⟩ is the mean square end-to-end distance of the linker chain that for a wormlike chain can be readily calculated from the abovementioned Lc and P using the Kratky−Porod equation.58 Thus, we obtain L = 7.8 nm with P = 0.8 in the high-salt condition or L = 19 nm with P = 0.8 in the low-salt condition. The “equivalent” rigid link is modeled, as in the rigid dumbbell, as a string of nearly touching beads, whose radius is chosen by equalizing the volume of the string of beads to that of that of the ssDNA of 68 nucleotides, with M ≅ 21 000 Da. This leads to the following data: “H” case, 4 beads of radius 1.0 nm; “L” case, 12 beads of radius 0.8 nm. Then the equivalent rigid beadmodel properties are evaluated with HYDRO++.

a T = f /(6πη0) From f, the sedimentation coefficient can be evaluated as s = M(1 − vρ)/(N A f), where v ̅ is the partial specific volume (volume-to-mass ̅ ratio) of the particle, ρ is the solution density (in dilute solution, that of the aqueous buffer), and NA is Avogadro’s number. The interpretation of the 2DSA distributions obtained from the AUC measurements requires the frictional ratio f/f 0, where f 0 is the frictional coefficient of a sphere having the same volume as the particle, which can be estimated from the molecular weight and the specific volume, V = M/NA, so that ⎛ 3Mv ⎞1/3 ̅⎟ f0 = 6πη0⎜ ⎝ 4πNA ⎠ Thus ⎛ 3Mv ⎞−1/3 f ̅⎟ = a T⎜ f0 ⎝ 4πNA ⎠ so that f/f 0 can be readily evaluated from the aT results from the HYDRO programs with additional data for M and v.̅ Due to the very low concentrations of our sample, the (average) partial specific volume of our samples cannot be experimentally determined using a density oscillation tube. However, the partial specific volume of the Au−DNA constructs can be estimated as the average of those of the two components, weighted by the mass of each component: v̅ =

nAuMAu vAu ̅ + nDNA MDNA vDNA ̅ nAuMAu + nDNA MDNA

where nAu, MAu, and vA̅ u are the number of Au particles, their molecular weight, and partial specific volume, respectively, and nDNA, MDNA, and vD̅ NA are the number of DNA subunits, their molecular weight, and partial specific volume, respectively. As described, the molecular weight of the Au nanoparticles can be estimated from the radius of the bare particle, 2.7 nm, and the density of gold, 19.3 cm3/g, which leads to MAu = 9.6 × 105 Da. It has to be noted that the effective partial specific volume of the Au particle must include the appreciable contribution of the shell to the particle’s volume, so that from the volume-to-mass ratio we estimate vA̅ u = 0.083 cm3/g for the Au subunits. Molecular weight of the dsDNA, as evaluated from the sequence was MdsDNA = 42 215 Da, which gives an average molecular weight per base pair of ∼620 Da, in agreement with 7425


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ACS Nano the expected value (without cation contribution), and the partial specific volume of DNAs is in the range of vD̅ NA = 0.55−0.60 cm3/g.58 We opt for the larger volume in order to account for a slight volume expansion attributable to hydration swelling. The influence of the phosphine shell on the molecular weight of the AuNPs can be neglected due to the high molar mass of the core.

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ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b01377. Additional details, figures, and tables (PDF)

AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Present Addresses §

Max-Planck-Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany. ⊥ Life Science Consulting, Friedrichstraße 8, 78532 Tuttlingen, Germany. ∥ Coriolis Pharma, Am Klopferspitz 19, 82152 Martinsried, Germany. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We thank Rose Rosenberg for her experimental assistance with analytical ultracentrifugation. We also thank Borries Demeler, Emre Brookes, and Gary Gorbet for support during data analysis with Ultrascan III. We thank Na Liu for support. Work at the University of Murcia was supported by Grant CTQ201233717 from Ministerio de Economiá y Competitividad, including FEDER funds, and Grant QMC-19353/PI/14 from Fundación Séneca, Región de Murcia. Computing time for the calculation of the data in this paper was kindly provided by Jülich Supercomputing Centre (JSC) on the Juropa supercomputer through project HKN00. H.C. thanks the DFG (SFB 1214) for support of AUC work on anisotropic particles. REFERENCES (1) Jones, M. R.; Osberg, K. D.; Macfarlane, R. J.; Langille, M. R.; Mirkin, C. A. Templated Techniques for the Synthesis and Assembly of Plasmonic Nanostructures. Chem. Rev. 2011, 111, 3736−3827. (2) Roller, E. M.; Khorashad, L. K.; Fedoruk, M.; Schreiber, R.; Govorov, A. O.; Liedl, T. DNA-Assembled Nanoparticle Rings Exhibit Electric and Magnetic Resonances at Visible Frequencies. Nano Lett. 2015, 15, 1368−73. (3) Thacker, V. V.; Herrmann, L. O.; Sigle, D. O.; Zhang, T.; Liedl, T.; Baumberg, J. J.; Keyser, U. F. DNA Origami Based Assembly of Gold Nanoparticle Dimers for Surface-Enhanced Raman Scattering. Nat. Commun. 2014, 5, 3448. (4) Daniel, M. C.; Astruc, D. Gold Nanoparticles: Assembly, Supramolecular Chemistry, Quantum-Size-Related Properties, and Applications Toward Biology, Catalysis, and Nanotechnology. Chem. Rev. 2004, 104, 293−346. (5) Anker, J. N.; Hall, W. P.; Lyandres, O.; Shah, N. C.; Zhao, J.; Van Duyne, R. P. Biosensing With Plasmonic Nanosensors. Nat. Mater. 2008, 7, 442−53. (6) Stratakis, M.; Garcia, H. Catalysis by Supported Gold Nanoparticles: Beyond Aerobic Oxidative Processes. Chem. Rev. 2012, 112, 4469−506. 7426


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