Dynamic Properties of DNA-Programmable Nanoparticle

Jul 13, 2016 - The hexagonal close-packed (HCP) and close-packed face-centered cubic (FCC) ordered structures are identified for the systems of differ...
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Dynamic Properties of DNA-Programmable Nanoparticle Crystallization Qiuyan Yu, Xuena Zhang, Yi Hu, Zhihao Zhang, and Rong Wang* Key Laboratory of High Performance Polymer Material and Technology of Ministry of Education, State Key Laboratory of Coordination Chemistry and Collaborative Innovation Center of Chemistry for Life Sciences, Department of Polymer Science and Engineering, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China S Supporting Information *

ABSTRACT: The dynamics of DNA hybridization is very important in DNA-programmable nanoparticle crystallization. Here, coarse-grained molecular dynamics is utilized to explore the structural and dynamic properties of DNA hybridizations for a self-complementary DNA-directed nanoparticle self-assembly system. The hexagonal closepacked (HCP) and close-packed face-centered cubic (FCC) ordered structures are identified for the systems of different grafted DNA chains per nanoparticle, which are in good agreement with the experimental results. Most importantly, the dynamic crystallization processes of DNA hybridizations are elucidated by virtue of the mean square displacement, the percentage of hybridizations, and the lifetime of DNA bonds. The lifetime can be modeled by the DNA dehybridization, which has an exponential form. The lifetime of DNA bonds closely depends on the temperature. A suitable temperature for the DNA-nanoparticle crystallization is obtained in the work. Moreover, a too large volume fraction hinders the self-assembly process due to steric effects. This work provides some essential information for future design of nanomaterials. KEYWORDS: DNA, nanoparticle, crystallization, dynamic, structure achieve assemblies by the same design rules.15,16 Actually, it is the DNA bond that programs nanoparticle interactions and drives their assemblies into the ordered crystalline structure in the above studies.13 Nonetheless, we are interested in how the DNA bond induces crystallization thermodynamically and kinetically. Although theoretical models15,17 have been proposed, they are too simplified to settle crucial problems of the DNA chain conformational analysis or dynamics. In order to have a better knowledge of the factors that influence DNA base-pairing interactions and the crystallization kinetic process, it is essential to find a scale-accurate coarse-grained model that can capture the stiffness and size of different parts of the DNA chains as precisely as possible. The flanking bead model based on molecular dynamics18 is very helpful in researching the DNAbased assembly of several superlattices containing bodycentered cubic (BCC), CsCl, AlB2, Cr3Si, and more complex Cs6C60.9,19,20 We can obtain relatively stable structural information and dynamic details of the assembly process by tracking the position and velocity of NP at different time and

B

ecause the strength, length, and nature of nucleic acid bonds (Watson−Crick base-pairing interaction) between particles can be adjusted systematically by varying the nucleobase sequence, length as well as the number of DNA strands attached to nanoparticles, DNA has been the ideal ligand to direct the nanoparticle interaction.1,2 This DNAfunctionalized nanoparticle (DNA-NP) allows the thermodynamically reversible and controlled assembly of inorganic nanoparticle into supramolecular structures.1 It can be widely regarded as a programmable atom equivalent (PAE) which consists of a nanoparticle core densely functionalized by oligonucleotides with specific sequence and length through which DNA mediates interactions between nanoparticles to program macroscopic materials with novel physical and chemical properties3,4 and highly ordered structures.5−9 The rigid nanoparticle core and the oligonucleotide density impose a radial orientation of the DNA and valency to the nanoparticles. Unlike atoms having a fixed series of physical and chemical properties and bonding possibilities induced by the inherent electronic properties, these properties and bonding behaviors of PAEs can be adjusted by controlling their structures in a wide range of parameters. Anisotropic spherical organic,10 inorganic,11,12 and polymeric7 nanoparticles have been regarded as PAE cores. Even RNA13 and proteins14 can © 2016 American Chemical Society

Received: March 24, 2016 Accepted: July 13, 2016 Published: July 13, 2016 7485

DOI: 10.1021/acsnano.6b02067 ACS Nano 2016, 10, 7485−7492

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ACS Nano monitoring bond-breaking or reforming of DNA hybridizations. In previous work, several factors, such as NP size and shape and DNA length and sequence, have been taken into consideration to independently adjust each of the relevant crystallographic parameters, including particle size, periodicity, and interparticle distance.15,21 However, they mainly focus on lattice structures, ignoring dynamic properties of crystallization, which play an important role in the process of lattice formation. In this paper, therefore, we largely focus on the kinetic process of DNA-NP self-assembly and crystallization to study DNA hybridization properties by coarse-grained Molecular Dynamics (MD) simulation (Figure 1). Herein, the effects of temperature, the

Figure 2. Crystal structures obtained from MD simulation under the conditions T = 1.4, Lx × Ly × Lz = 60 × 60 × 60, η = 1.15: (a, c) hexagonal close-packed (HCP) nanoparticle lattices and facecentered cubic (FCC) nanoparticle lattices; (b, d) packing type of HCP (AB periodic layered) and FCC (ABC periodic layered).

Figure 1. Schematic illustration of the coarse-grained model for A− A self-assembly system. Top: Model of ssDNA chain. ns and nl are the number of coarse-grained space beads and linker beads, respectively. Bottom: Example of two ssDNA-NP hybridization. Each particle can bind to every other particle with equal affinity by linker−linker pairing interaction in the single-component system.

The HCP and FCC are arranged in different packing ways: the former is an AB periodic layered type whose first layer overlaps the third one (Figure 2b), and the latter is an ABC periodic layered type whose first layer overlaps the fourth one (Figure 2d), where A, B, C show the different periodic layers. Number of Grafted DNA Chains per NP. The pair radial distribution function g(r) for n = 10−80 is shown in Figure 3a, giving the probability of finding a particle (or molecule) at distance r away from a reference particle relative to that for the ideal gas distribution. DNA-NPs in the low-loading regime (i.e., n = 25−40) have hexagonal close-packed (HCP) or random hexagonal close-packed (rHCP) structures. When n = 45−55, peak positions of g(r) have a slow shift, attributed to small FCC domains. When n = 60−80, an infinite number of sharp peaks appear whose separations and heights are characteristics of the FCC lattice structure. For n < 20, it has only one shape peak (r ≈ 22 in unit of σ) at short distances, superimposed on a steady decay to a constant value at longer distances. For short distances, g(r) is zero due to the strong repulsive forces. At longer distances, g(r) tends to be the ideal gas value, indicating that there is no long-range order and it is a typical liquid for n < 20.25 As n increases, a series of sharp and wide peaks appear at larger distances, with the first peak position r0 (r0 ≈ 21.22) (Figure S1) as the average distance between nearest neighbor center-to-center nanoparticles. Theoretically, if the three linker beads of DNA chains achieve partial or complete hybridizations, r0 ≈ 2R′ − (1∼3)σ (R′ ≈ 11.4−11.9, R′ is radius of a DNA tethered nanoparticle), then r0 ≈ 19.8−22.8 with σ as the diameter of a linker bead. Our simulation results agree with the theoretical prediction. To better determine the lattice structure, we also give the structure factor S(q) of nanoparticles. Parts b and c of Figure 3 present S(q) for n = 60 and 35, respectively. From Figure 3, we

number of DNA chains attached to each NP, and volume fraction of NPs on the properties of DNA hybridizations are systematically investigated to solve the existing problems.

RESULTS AND DISCUSSION The groups of Knorowski18 and Li20 theoretically validated the experimental phase diagram of binary mixtures of DNAmediated NPs15 based on the coarse-grained model. In addition to obtaining some complicated superlattice structures by tuning the temperature, the number of DNA chains, the stoichiometric ratio of two DNA-NP types, and building blocks, they also investigated the DNA hybridization kinetics, the number of hybridizations, and DNA behavior during the assembly process,18−20 which has previously aroused extensive concern by many researchers.15,22,23 However, the attention to a selfcomplementary single-component system (called A−A system here), in which each particle can bind to every other particle with equal affinity, is absent and deserves to be studied. Herein, two different kinds of close-packed crystal structures are observed: hexagonal close-packed (HCP) and face-centeredcubic (FCC) structures where each particle has 12 nearest neighbors for different linker loadings (from n = 20 to 80, where n represents the number of DNA chains attached to a nanoparticle) by simulating the single-component self-assembly (Figure 2). Compared with the binary system, the singlecomponent system increases the probability of DNA linker− linker hybridization interactions, thus allowing for closer packing and a less significant thermodynamic difference between the HCP and FCC crystallographic arrangements.24 7486

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Figure 3. Radial distribution functions g(r), static structure factor S(q), and integral of g(r). (a) g(r) for n = 10−80. (b, c) S(q) for n = 60 and n ⇀ 1 q ) = N ⟨∑jk e−i q (R j − R k)⟩, where ⇀ = 35, respectively. The structure factor is defined as S(⇀ q is the wave vector, N is the number of NPs, Rj, Rk (j, k = 1, 2, 3, ... N) are the nanoparticle positions.. (d) Integral of g(r) for n = 15, 35, 60, representing coordination numbers Ncoor = 12 for n = 35, 60.

(311), etc.24,26 The number integral over g(r) for the first peak square corresponds to coordination numbers (Ncoor = 2∫ r004πr2ρ0g(r) dr, ρ0 is the average number density) of NP. For n > 20, a coordination number Ncoor = 12 once again determines the HCP and FCC crystal structures (Figure 3d). It is difficult to form ordered structure when n < 20, and it forms an HCP structure easily in a relatively low DNA loading regime, while FCC structure forms in a higher regime. In fact, the radius ratio of a nanoparticle and a DNA bead is 6:1. If we set the volume of a DNA bead as 1, we obtain the overall particle density ρ (including the DNA beads and the nanoparticles) easily according to the model (Figure 1):

can clearly see FCC (n = 60) and HCP (n = 35) structures. For FCC, q 1 , q 2 , q 3 , q 4 , q 5 , q 6 , q 7 , q 8 is equal to 3 , 4 , 8 , 11 , 12 , 16 , 19 , 20 , corresponding to crystallographic planes (111), (200), (220), (311), (222), (400), (331), (420). For HCP, q1, q2, q3, q4, q5, q6, q7, q8 is equal to 1, 1.061, 1.132, 1.458, 1.732, 1.879, 2, 2.031, corresponding to (010), (002), (011), (012), (110), (013), (020), (112). Our simulation result agrees with the theoretical peaks very well (Figure 3b,c). We can distinguish between the FCC crystal and other structures by comparing the relative positions of order peaks qx /q1 = 1, 4/3 , 8/3 , 11/3 corresponding to FCC crystallographic planes (200), (220), 7487

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ACS Nano ρ=

N[63 + (ns + nl)n]

(1) L3 In the Methods, we give the relevant simulation conditions, such as the DNA beads and the nanoparticles (nl = 3, ns = 8, N = 32). Therefore, the overall particle density ρ increases linearly for fixed box size. Maybe this increasing density would be the main factor inducing the transition from disorder to HCP or even to FCC. Here, we will introduce the kinetic process analysis in the following work by p(H) and f(H). p(H) is the percentage of complete hybridizations of the total DNA chains, where complete hybridizations are defined if every linker bead of a DNA strand forms a hydrogen bond, namely, within the distance of σ far away from its complementary linker bead. f(H) is the fraction of hybridizations that survive over time (i.e., all pairs of the hybridized sticky ends are recorded at time t = 0 and then are tracked with the simulation time). f(H) closely decreases exponentially with simulation time step, and the decrease rate of f(H) mirrors the rate of DNA dehybridization. It conforms the following expression

f (H) = f (H)0 + A exp( −t /τ1)

Figure 5. Total number of hybridized bead pairs n(H) in equilibrium for n = 10−100 at T = 1.4, η = 1.15, Lx × Ly × Lz = 60 × 60 × 60. The inset table displays the relative parameters of linear fit results.

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In addition, because f(H) realizes equilibrium comparatively as n increases from 10 to 80 and the rate of dehybridization is unaffected by DNA concentration,28,29 increasing the number of DNA strands can raise the rate of DNA hybridization and the lifetime τ1 distributes at (1.2 × 103)−(2.6 × 103) in units of (mσ2/ε)1/2 (Figure S2). It is slightly larger for n = 10 than for larger DNA loadings because it can easily reform DNA bonds after breaking, which also can explain the great thermal fluctuation of p(H). For 20 ≤ n ≤ 50, the effect of thermal fluctuation diminishes, promoting the process of DNA hybridization. Therefore, f(H) and τ1 have little relation to DNA loadings. However, the difference of f(H) and τ1 for 60 ≤ n ≤ 80 from n < 60 suggests dense DNA shells hinder NPs’ violent motion and allow them reorganization in the limited space, where DNA bond interaction is neither too strong nor too weak as a suitable stable interaction between DNA-NPs, inducing them assemble into perfect FCC crystals. As the number of DNA strands increases from 80 to 100, the surface of NP is full of DNA strands and the coverage reaches nearly saturated. The dense DNA shells restrict the reorganization processes and prevent NPs from arranging themselves into large and perfect domains. Macfarlane et al. have observed the reorganization of nanoparticle superlattices and obtained the same conclusions by using time-resolved synchrotron smallangle X-ray scattering in experiment.30 Although stable ⟨p(H)⟩ is found as the nanoparticle surface becomes saturated, the total number of hybridized bead pairs (Figure 5) still linearly increases as the DNA chain number increases. Therefore, more DNA linkers result in more hybridizations and promote their dynamic process, in accord with the design role of Mirkin’s group.15 Temperature. The rearrangement of DNA bonds and the thermally active hybridization are important requirements in realizing the equilibrium and long-range ordered assembly of DNA-directed systems.5,19,31 The so-called thermally active hybridization means that linkers should easily attach to and detach from their complementary counterparts because of thermal fluctuations, thus allowing them to easily escape from any kinetically trapped structure.19 It can be obviously achieved by thermal annealing, which induces partial melting or dissociation of DNA duplexes chains, allowing particles to

where f(H)0 is the fraction of hybridizations in equilibrium and A represents pre-exponential factor. τ1 reflects the lifetime of DNA bonds (in unit of (mσ2/ε)1/2) . Figure 4 shows p(H) as a function of simulation time step for different loading DNA chains. For n < 20, great thermal

Figure 4. p(H) as a function of time step for n = 10−60 at T = 1.4, η = 1.15, Lx × Ly × Lz = 60 × 60 × 60. The inset is the average percentage of hybridization ⟨p(H)⟩ after equilibrium.

fluctuation of the simulation system occurs due to the very limited DNA chain interaction, which makes NP fluctuate in the simulation box. On one hand, the average percentage of hybridizations ⟨p(H)⟩ (less than 30%) is so small that hybridization strength is not enough to serve as an appropriate stabilizing interaction between the DNA-NPs and guide them into crystallization. On the other hand, too few hybridized bead pairs (Figure 5) mean that there are not enough hydrogen bonds to counteract the thermal motion of the DNA-NPs and the system remains liquid.20 Martinez et al.27 have also explained that colloids coated with a small number of DNA strands cannot crystallize in dilute solution by Monte Carlo simulation. 7488

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ACS Nano optimize their location in order to maximize the number of DNA hybridizations.5 By very slow cooling through the melting temperature over several days, DNA-modified nanoparticle solutions can give thermodynamic products and achieve Wulff equilibrium crystal structure.31 In addition, DNA bonds between the complementary sticky ends will also form, break, and reform discontinuously at a constant temperature T because of the thermal fluctuation of the simulation system itself. Herein, both of the above controlled temperature styles are used to discuss the process of the crystallization: either starting from Tinitial = 1.5 then cooling slowly to Tfinal = 1.3 (linearly decreasing temperature) or at a constant temperature T. The dynamic process of bond-breaking and reforming is mirrored by p(H) and f(H). The crystalline process is determined by mean square displacement (MSD) of NPs as a function of the simulation time step. In Figure S3, the temperature of the system at first remains constant at T = 1.5 for 5 × 105 simulation steps to create a random conformation. As the temperature linearly decreases to T = 1.4, the MSD of NPs reaches a steady state at t = 2.0 × 107, indicating full crystallization. This annealing process helps us determine the melting temperature (Tm) and optimal annealing temperature at which DNA bonds between particles readily break and reform, leading to reorganization within the particles.30 However, it takes only 7 × 106 time steps to realize full crystallization at constant temperature T = 1.4 where the system only depends on thermal fluctuation of simulation system itself (Figure 6). The point is that in the steady state of

Figure 6. MSD of NPs and the percentage of hybridizations p(H) at constant temperature T = 1.4 for n = 60, η = 1.15, and Lx × Ly × Lz = 60 × 60 × 60.

Figure 7. (a) p(H) and (b) f(H) as a function of time steps under different temperatures; (c) lifetime τ1 of DNA bonds as a function of temperature T for n = 60, η = 1.15, Lx × Ly × Lz = 60 × 60 × 60. The inset of (c) is the average percentage of hybridization ⟨p(H)⟩ after equilibrium.

the p(H) only the average number of the hybridization ⟨p(H)⟩ is constant and bond-breaking and reforming between the sticky ends are dynamic, even when thermodynamic equilibrium has been achieved, in good agreement with the binary experimental system.20 The temperature is a crucial factor to control DNA-NP selfassembly and crystallization. Figure 7 gives p(H), f(H), and ⟨p(H)⟩ as a function of simulation time step under different temperatures, showing both p(H) and f(H) strongly depend on temperature. As T increases, the average ⟨p(H)⟩ decreases and f(H) decrease more and more quickly, indicating faster and faster rate of dehybridizations. This also accounts for the fact that the p(H) of the above annealing process increases as T decreases (Figure S3). When T is high enough (T > 1.45), the

DNA bonds break easily and the lifetime of DNA bonds τ1 is short (less than 1 × 103 (mσ2/ε)1/2), leading to a too high rate of dehybridization. f(H) reaches equilibrium quickly, and ⟨p(H)⟩ becomes lower and lower as T increases (Figure 7), which make the self-assembly occur hardly. Moreover, too few hybridized complementary bead pairs result in not enough attractive interactions to counteract the thermal motion of the system.20 Under these conditions, the system melts or remains liquid. Under relatively low temperature conditions, the rate of bond formation is larger than the rate of bond breakage, so 7489

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ACS Nano p(H) increases quickly and hybridized DNA will be predominant. The lifetime τ1 of DNA bonds is larger than 1 × 104 (mσ2/ε)1/2, allowing too many interconnecting duplexes to form, and the attraction between DNA-NPs becomes so strong that it is difficult for them to break and reform. The system is kinetically trapped either in a metastable state or an amorphous state. From Figure 7b, we can see that it becomes very difficult for the system to reach equilibrium when T ≤ 1.2, which limits the reorganization process of the assembled DNANPs into a thermodynamically favored structure. Therefore, the suitable temperature for the DNA-NP crystallization is between 1.2 and 1.45 and the lifetime τ1 ranges from 1 × 103 to 1 × 104 (mσ2/ε)1/2. Volume Fraction. The concentration of NPs is controllable in experiments but difficult in simulation, so we introduce volume fraction (η) to tune the self-assembly process of DNANPs with the aid of the size of the simulation box, based on eq 3. As the end-to-end distance (R′ = 11.4−11.9) is hardly influenced by the simulation box, the volume fraction decreases with the increase of simulation box. Figure S4 shows the dynamic hybridization process for different volume fractions. The p(H) reaches a steady platform quickly, f(H) realizes equilibrium in 2.0 × 106 time steps, and the lifetime of DNA bonds ranges from 1.3 × 103 to 2.2 × 103 (mσ2/ε)1/2, which is hardly related to the volume fraction. As η increases from 0.67 to 1.15 (Lx = Ly = Lz = 73−60), the ⟨p(H)⟩ linearly increases more quickly than for η = 1.20−2.00 (Lx = Ly = Lz = 59.8−50) and has a maximum value at η = 1.15 (Figure 8). This is

promote the formation of HCP lattice to maximize the number of DNA hybridizations, but higher loadings make for closepacked FCC structure (60 ≤ n ≤ 80). Moreover, very dense DNA shells (n ≥ 90) restrict the reorganization processes and prevent NPs from arranging themselves into large and perfect domains. The thermally active hybridization induces the sticky ends to attach to and detach from their complementary counterparts, allowing them to easily escape from any kinetically trapped structure. As the temperature increases, ⟨p(H)⟩ decreases. The rate of dehybridizations speeds up more and more quickly, and the rate of hybridizations is affected slightly. The lifetime τ1 of DNA bonds is closely related to the temperature, but there is little dependency on the number of DNA chains per nanoparticle and the volume fraction. When T ≤ 1.2, the interaction between complementary bead pairs is too strong to induce the crystallization and τ1 ≥ 1 × 104 (τ1 in unit of (mσ2/ ε)1/2), but when T ≥ 1.45, the interaction is too weak to induce the crystallization and τ1 ≤ 1 × 103. When 1.2 ≤ T ≤ 1.45, 1 × 103 ≤ τ1 ≤ 1 × 104 and it is an appropriate temperature interval for the nanoparticle crystallization because it owns neither too strong nor too weak DNA interaction. Our results are very helpful in controlling the properties of crystalline with potential applications in plasmonic metamaterials,12 energy conversion,3 medical diagnosis,32,33 and electrochemical DNA biosensors.4 Additional work is underway to better understand the kinetic process and factors of DNA-NP crystallization.

METHODS Figure 1 is the model of an A−A self-assembly system where one particle can bind to any other particle by using linkers with selfcomplementary sticky ends used to simulate directional hydrogen bond interaction between complementary base pairs (A−T, C−G). Each nanoparticle is modeled as a spherical core of radius R = 3σ where σ ≈ 2.0 nm and single-strand DNA (ssDNA) chains (with the chain number n) are distributed randomly on the NP surface. An ssDNA is modeled as spacer beads (ns) and linker beads (nl), and each bead with a diameter of σ represents about 4−7 bases.18,19 Each linker bead has an additional structure with the central bead (CT) to achieve hybridization and the flanking beads (FL) to protect CT from binding to more than one complementary bead. The diameter of each CT and FL bead is 0.6σ.18 The point is that it is difficult to simulate exact values of parameters of DNA chains and NPs, so we can only obtain some approximate parameters in the condition that the coarse-grained model can capture some relevant physical processes. Flexible DNA chains are a crucial requirement to realize crystallization,10,34,35 but excessively long flexible DNA chains easily lead to short-range ordered, even disordered assemblies due to destroying the directional interaction.5 Therefore, only eight spacer beads (about 32 bases), flexible enough to form long-range ordered structures,10 are used in our model ssDNA. Since only relatively weak DNA interactions between particles make for forming crystalline lattices of nanoparticles,34 we employed as few as three complementary linker beads (nl = 3), corresponding to approximately 12−20 base pair linkers10,18 rather than 30 or more complementary linkers. Moreover, weak interactions result in reorganization of PAEs in the lattices to break any DNA bonds easily which force particles to trap in thermodynamically unfavorable states even when they are bonding to one another, thus achieving particle reorganization into ordered superlattice.20,24,28 The system volume fraction is defined as18,19

Figure 8. Average percentage of hybridization ⟨p(H)⟩ as a function of η for T = 1.4 and n = 60.

because DNA-NPs have enough space for free motion at low η, where NPs realize reorganization by bond-breaking and bondreforming, while there exists the hindering effect in limited space for larger η. When η = 1.15, the space is optimized for reorganization process, thus achieving full crystallization and obtaining the perfect closed-packing FCC superlattice.

CONCLUSIONS We focus on the dynamic process of DNA bonds for an A−A self-complementary system by using MD simulation based on the flanking bead model of Knorowski et al.18 The number of DNA chains per nanoparticle and temperature are the main factors to control the interaction strength between the nanoparticle building blocks. The low DNA loadings can

η= 7490

4 πNR′3 3 3

L

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ACS Nano where N is the number of DNA-NPs, L is the linear size of the simulation box, and R′ is the average distance between the center of a nanoparticle and the end of the relaxed DNA chain. The harmonic spring potential is used to model the covalent bonds along the ssDNA chain with the spring constant ks = 330ε/σ2 and the native spring length r0 = 0.84σ. Vbond(r ) =

1 ks(r − r0)2 2

University (PCSIRT). The numerical calculations in this paper have been done on the IBM Blade cluster system in the High Performance Computing Center (HPCC) of Nanjing University.

REFERENCES (1) Mirkin, C. A.; Letsinger, R. L.; Mucic, R. C.; Storhoff, J. J. A DNA-Based Method for Rationally Assembling Nanoparticles into Macroscopic Materials. Nature 1996, 382, 607−609. (2) Alivisatos, A. P.; Johnsson, K. P.; Peng, X. G.; Wilson, T. E.; Loweth, C. J.; Bruchez, M. P.; Schultz, P. G. Organization of ’Nanocrystal Molecules’ using DNA. Nature 1996, 382, 609−611. (3) Sebba, D. S.; Mock, J. J.; Smith, D. R.; LaBean, T. H.; Lazarides, A. A. Reconfigurable Core-Satellite Nanoassemblies as MolecularlyDriven Plasmonic Switches. Nano Lett. 2008, 8, 1803−1808. (4) Lin, L.; Liu, Y.; Tang, L. H.; Li, J. H. Electrochemical DNA Sensor by the Assembly of Graphene and DNA-Conjugated Gold Nanoparticles with Silver Enhancement Strategy. Analyst 2011, 136, 4732−4737. (5) Lu, F.; Yager, K. G.; Zhang, Y. G.; Xin, H. L.; Gang, O. Superlattices Assembled through Shape-Induced Directional Binding. Nat. Commun. 2015, 6, 6912. (6) Nickel, B.; Liedl, T. DNA-Linked Superlattices Get into Shape. Nat. Mater. 2015, 14, 746−749. (7) Renna, L. A.; Boyle, C. J.; Gehan, T. S.; Venkataraman, D. Polymer Nanoparticle Assemblies: A Versatile Route to Functional Mesostructures. Macromolecules 2015, 48, 6353−6368. (8) O’Brien, M. N.; Jones, M. R.; Lee, B.; Mirkin, C. A. Anisotropic Nanoparticle Complementarity in DNA-Mediated Co-crystallization. Nat. Mater. 2015, 14, 833−839. (9) Zhang, X. N.; Wang, R.; Xue, G. Programming Macro-materials from DNA-Directed Self-Assembly. Soft Matter 2015, 11, 1862−1870. (10) Nykypanchuk, D.; Maye, M. M.; van der Lelie, D.; Gang, O. DNA-Guided Crystallization of Colloidal Nanoparticles. Nature 2008, 451, 549−552. (11) Zhang, C.; Macfarlane, R. J.; Young, K. L.; Choi, C. H. J.; Hao, L. L.; Auyeung, E.; Liu, G. L.; Zhou, X. Z.; Mirkin, C. A. A General Approach to DNA-Programmable Atom Quivalents. Nat. Mater. 2013, 12, 741−746. (12) Young, K. L.; Ross, M. B.; Blaber, M. G.; Rycenga, M.; Jones, M. R.; Zhang, C.; Senesi, A. J.; Lee, B.; Schatz, G. C.; Mirkin, C. A. Using DNA to Design Plasmonic Metamaterials with Tunable Optical Properties. Adv. Mater. 2014, 26, 653−659. (13) Barnaby, S. N.; Thaner, R. V.; Ross, M. B.; Brown, K. A.; Schatz, G. C.; Mirkin, C. A. Modular and Chemically Responsive Oligonucleotide “Bonds” in Nanoparticle Superlattices. J. Am. Chem. Soc. 2015, 137, 13566−13571. (14) Ng, D. Y. W.; Wu, Y. Z.; Kuan, S. L.; Weil, T. Programming Supramolecular Biohybrids as Precision Therapeutics. Acc. Chem. Res. 2014, 47, 3471−3480. (15) Macfarlane, R. J.; Lee, B.; Jones, M. R.; Harris, N.; Schatz, G. C.; Mirkin, C. A. Nanoparticle Superlattice Engineering with DNA. Science 2011, 334, 204−208. (16) Macfarlane, R. J.; O’Brien, M. N.; Petrosko, S. H.; Mirkin, C. A. Nucleic Acid-Modified Nanostructures as Programmable Atom Equivalents: Forging a New ″Table of Elements″. Angew. Chem., Int. Ed. 2013, 52, 5688−5698. (17) Tkachenko, A. V. Theory of Programmable Hierarchic SelfAssembly. Phys. Rev. Lett. 2011, 106, 255501. (18) Knorowski, C.; Burleigh, S.; Travesset, A. Dynamics and Statics of DNA-Programmable Nanoparticle Self-Assembly and Crystallization. Phys. Rev. Lett. 2011, 106, 215501. (19) Li, T. I. N. G.; Sknepnek, R.; de la Cruz, M. O. Thermally Active Hybridization Drives the Crystallization of DNA-Functionalized Nanoparticles. J. Am. Chem. Soc. 2013, 135, 8535−8541. (20) Li, T. I. N. G.; Sknepnek, R.; Macfarlane, R. J.; Mirkin, C. A.; de la Cruz, M. O. Modeling the Crystallization of Spherical Nucleic Acid

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Harmonic angle potential is used to model the stiffness of the ssDNA chain and also aligns neighboring CT beads and its flanking beads (FL) Vangle(θ ) =

1 k θ(θ − θ0)2 2

(5)

where θ represents the harmonic angle between three consecutive bead (θ0 = 180°) and the spring constant kθ = 100kbT. The short-range repulsive interactions between any other pair of beads are modeled with Weeks−Chandler−Andersen (WCA) softcore repulsive potential36 with a cutoff distance rc = 21/6σ and unit of energy ε = 1.0kbT. ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ U (r ) = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥(r ≤ r c) ⎝r⎠ ⎦ ⎣⎝ r ⎠

(6)

The attractive interactions between central beads (CT) are modeled via Lennard-Jones (LJ) potential, and the cutoff distance is rc = 2.5σ ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ ULJ = 4ε′⎢⎜ ⎟ − ⎜ ⎟ ⎥(r ≤ r c) ⎝r⎠ ⎦ ⎣⎝ r ⎠

(7)

where ε′ = 10ε = 10kbT. The MD simulation is performed in an NVT ensemble with constant number of particles, volume and temperature, and the temperature is controlled by a dissipative particle dynamics thermostat37 in a three-dimensional Lx × Ly × Lz lattice. Thirty-two NPs coated with DNA chains are placed in a periodic simulation box by applying periodic boundary conditions, thus simulating a bulk system effectively. The total number of DNA-NPs (N) is selected to be compatible with the number of NPs, necessarily creating the given number of unit cells (2 × 2 × 2).20 For simplicity, all beads are assumed to have equal mass, m = 1. Each simulation runs (1.0 × 107)− (4.0 × 107) time steps, and a time step is Δt = 0.005 τ (τ = (mσ2/ ε)1/2).

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b02067. Additional figures of radial distribution functions g(r), static structure factors S(q), and dynamic process for DNA-NP crystallization under different conditions (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We thank Prof. Jinglei Hu and Prof. Liangshun Zhang for useful discussions. This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 21474051, 21074053, and 51133002) and Program for Changjiang Scholars and Innovative Research Team in 7491

DOI: 10.1021/acsnano.6b02067 ACS Nano 2016, 10, 7485−7492

Article

ACS Nano Nanoparticle Conjugates with Molecular Dynamics Simulations. Nano Lett. 2012, 12, 2509−2514. (21) Senesi, A. J.; Eichelsdoerfer, D. J.; Macfarlane, R. J.; Jones, M. R.; Auyeung, E.; Lee, B.; Mirkin, C. A. Stepwise Evolution of DNAProgrammable Nanoparticle Superlattices. Angew. Chem., Int. Ed. 2013, 52, 6624−6628. (22) Rogers, W. B.; Crocker, J. C. Direct Measurements of DNAMediated Colloidal Interactions and Their Quantitative Modeling. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 15687−15692. (23) Sambriski, E. J.; Schwartz, D. C.; de Pablo, J. J. Uncovering Pathways in DNA Oligonucleotide Hybridization via Transition State Analysis. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 18125−18130. (24) Macfarlane, R. J.; Lee, B.; Hill, H. D.; Senesi, A. J.; Seifert, S.; Mirkin, C. A. Assembly and Organization Processes in DNA-Directed Colloidal Crystallization. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 10493−10498. (25) Leach, A. R. Molecular Modelling: Principles and Applications; Pearson Education Ltd.: London, 2001; pp310−312. (26) Zhang, Y. G.; Pal, S.; Srinivasan, B.; Vo, T.; Kumar, S.; Gang, O. Selective Transformations between Nanoparticle Superlattices via the Reprogramming of DNA-Mediated Interactions. Nat. Mater. 2015, 14, 840−847. (27) Martinez-Veracoechea, F. J.; Mladek, B. M.; Tkachenko, A. V.; Frenkel, D. Design Rule for Colloidal Crystals of DNA-Functionalized Particles. Phys. Rev. Lett. 2011, 107, 045902. (28) Macfarlane, R. J.; Jones, M. R.; Senesi, A. J.; Young, K. L.; Lee, B.; Wu, J. S.; Mirkin, C. A. Establishing the Design Rules for DNAMediated Colloidal Crystallization. Angew. Chem., Int. Ed. 2010, 49, 4589−4592. (29) Biancaniello, P. L.; Kim, A. J.; Crocker, J. C. Colloidal Interactions and Self-Assembly Using DNA Hybridization. Phys. Rev. Lett. 2005, 94, 058302. (30) Macfarlane, R. J.; Thaner, R. V.; Brown, K. A.; Zhang, J.; Lee, B.; Nguyen, S. T.; Mirkin, C. A. Importance of the DNA ″Bond″ in Programmable Nanoparticle Crystallization. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 14995−15000. (31) Auyeung, E.; Li, T. I. N. G.; Senesi, A. J.; Schmucker, A. L.; Pals, B. C.; de la Cruz, M. O.; Mirkin, C. A. DNA-Mediated Nanoparticle Crystallization into Wulff Polyhedra. Nature 2013, 505, 73−77. (32) Mirkin, C. A. The Polyvalent Gold Nanoparticle ConjugateMaterials Synthesis, Biodiagnostics, and Intracellular Gene Regulation. MRS Bull. 2010, 35, 532−539. (33) Cutler, J. I.; Auyeung, E.; Mirkin, C. A. Spherical Nucleic Acids. J. Am. Chem. Soc. 2012, 134, 1376−1391. (34) Park, S. Y.; Lytton-Jean, A. K. R.; Lee, B.; Weigand, S.; Schatz, G. C.; Mirkin, C. A. DNA-Programmable Nanoparticle Crystallization. Nature 2008, 451, 553−556. (35) Crocker, J. C. Nanomaterials: Golden Handshake. Nature 2008, 451, 528−529. (36) Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of Repulsive Forces in Determining Equilibrium Structure of Simple Liquids. J. Chem. Phys. 1971, 54, 5237−5247. (37) Groot, R. D.; Warren, P. B. Dissipative particle dynamics: Bridging the Gap between Atomistic and Mesoscopic Simulation. J. Chem. Phys. 1997, 107, 4423−4435.

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DOI: 10.1021/acsnano.6b02067 ACS Nano 2016, 10, 7485−7492