Effect of Chain Rigidity on the Crystallization of DNA-Directed

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Effect of Chain Rigidity on the Crystallization of DNA-Directed Nanoparticle System Qiuyan Yu and Rong Wang* Department of Polymer Science and Engineering, School of Chemistry and Chemical Engineering, 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, Nanjing University, Nanjing 210023, China

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S Supporting Information *

ABSTRACT: The DNA-directed nanoparticle (DNA-NP) system provides various applications in medical diagnosis, sensing, data storage, plasmonics, and photovoltaics. We studied the influence of chain rigidity on DNA-directed nanoparticle crystallization by molecular dynamics simulation. The results showed that the rigid and flexible chains grafted on nanoparticles can be used to design ordered supramolecular structure, but the mechanisms are different. The system with rigid DNA chains can induce nanoparticles’ rearrangement into a body-centered cubic (BCC) lattice due to the DNA hybridization interactions. However, for the flexible chain system, the very low hybridization can even be ignored, yet the nanoparticles can still present BCC arrangement. For rigid chains, DNA binding interactions can induce BCC formation in a very narrow length range and are unfavorable to nanoparticle rearrangement for too long or short chains.

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rigid in experimental research3,23 where crystal structures are formed, what if the whole DNA chain becomes a flexible single-stranded DNA or flexible polymer chain? And can the flexible chains coated on the nanoparticle still induce the nanoparticle rearrange into ordered lattices? The dendronmodified gold NPs, say organic−inorganic hybrid dendrimers, were found to assemble into a highly ordered simple cubic (SC) lattice with thermotropic liquid-crystalline behavior.24 Chen et al. investigated binary mixed homopolymer-grafted nanoparticle assembly by using self-consistent field theory (SCFT) and found non-close-packed simple cubic (SC) lattice and BCC lattice.25 We employed the coarse-grained DNA model14 by the molecular dynamics (MD) method, which has been widely used to explore the crystallization, dynamic, and thermodynamic properties.15,16,26,27 In this model, the DNA is an extended stiff or flexible chain with a backbone of ns spacer beads and nl linker beads as shown in Figure 1a. For more details about the model and MD method one can refer to the Supporting Information and our previous work.16,27 Herein we consider a binary system of N (= 54) spherical nanoparticles (diameter 6σ) with equal number of type A and B nanoparticles which have the same chemical and physical properties except that they are coated with different but complementary DNA chains. The chain length NL (= ns + nl) is changed by tuning the spacer length ns with fixed nl = 3. The number of chains n is also alterable. We simulate both rigid and flexible DNA-NP systems in a cubic box of size L3 with

INTRODUCTION In nature, nucleic acids are ubiquitous due to their ability of encoding substantial information via canonical Watson−Crick base-pairing interactions. With the help of chemical methods to make synthetic oligonucleotides of arbitrary sequences, one can use specific binding interactions between single-stranded DNA (ssDNA) chains to program selective interactions between different colloidal particles.1,2 The DNA-directed nanoparticle (DNA-NP) allows the thermodynamically reversible and controllable assembly of inorganic nanoparticles into ordered supramolecular structures.3,4 It provides various applications in medical diagnosis,1 sensing,5,6 data storage,7 plasmonics,8−10 and photovoltaics.11 By tuning parameters such as surface coverage, flexible spacer region, complementary DNA strand, and nanoparticle ratio, numerous crystal structures like body-centered cubic (BCC), face-centered cubic (FCC), simple cubic (SC), hexagonal close-packed (HCP), and isostructural with the alkali−fullerene complex (Cs6C60) lattices have been successfully achieved in such systems from both experiments3,12,13 and computer simulations.14−16 The introduction of organic branching moieties in the linkers,17 ethidium bromide (EtBr),18 or Ru complex small molecule19 as a DNA intercalator, RNA,20 and protein21,22 into DNA-NP systems can be used to tune the DNA bond strength and nanoparticle interaction. There is no doubt that it is just the DNA bonds that drive the DNA-NP system assembling into ordered crystalline structure. But what if there are no DNA binding sites in the system? Can the DNA-NP systems without DNA interactions still induce the nanoparticle rearrangement into ordered lattices? As we know the spacer region of DNA chain between nanoparticle and linker binding region is a double helix and © XXXX American Chemical Society

Received: August 16, 2018 Revised: September 26, 2018

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DOI: 10.1021/acs.macromol.8b01767 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

strength constant k θ of angle bending and the length of DNA chain NL with nl = 3 at T = 1.8 (Figure 2a). For NL < 13, the

Figure 1. (a) Model of DNA chain; ns and nl are the number of coarse-grained spacer beads and linker beads, respectively. (b) Example of hybridization between two DNA-coated nanoparticles (DNA-NPs). (c) Static structure factor S(q) of BCC crystal structure. The structure factor is defined as S(q ⃗) =

1 N

∑jk e−iq ⃗(rj⃗ − rk⃗ ) , where q⃗

Figure 2. Influence of chain rigidity on the formation of BCC crystal. (a) Phase diagram of DNA-NP assembly systems by changing k θ and NL with nl = 3 at T = 1.8. (b) Hybridization percentage ph of DNA chains as a function of k θ with n = 60, nl = 3, and ns = 8 at T = 1.8. (c) Distribution of effective volume fraction ϕ in the NL−k θ phase diagram.

is the wave vector, N is the number of NPs, and r⃗j, r⃗k (j, k = 1, 2, 3, ..., N) are the positions of NPs.16

periodic boundaries. The particle volume density N [63 + (n + n )n]

s l ρ= is fixed at 0.15 where the system will not L3 be restricted and form BCC lattice easily. We start the simulation from the disordered phase (DIS) or simple cubic arrangement as the initial random configuration and find the transition toward BCC crystal structure. Simulations with different initial random configurations and for various random number have also been implemented to prevent the system is stuck in a kinetic trap, which also show that the nanoparticle arrangement at equilibrium is independent of the initial conditions. Here only two types of nanoparticle arrangement (BCC and DIS) are obtained since the ratio of two types of nanoparticles coated by different DNA sequences for the binary systems is 1:1 (Figure 1).15,26 For BCC, q1, q2, q3, q4, q5, q6, q7, q8, and q9 is equal to √2, √4, √6, √8, √10, √12, √14, √16, and √18 corresponding to crystallographic planes (101), (200), (211), (220), (301), (222), (321), (400), and (330). Our simulation results agree well with the theoretical peaks (Figure 1c). We have also simulated assembly properties of rigid and flexible DNA chain without binding site systems, where chain rigidity increases with the strength constant of the angular potential Vangle = 0.5k θ (θ − θ0)2 acting on three consecutive beads (Figures S1 and S2). Compared with the DNA with binding interaction systems, we find they have the similar crystallization range if nanoparticles are grafted by flexible chains. For rigid chains, DNA binding interactions are unfavorable to nanoparticle rearrangement for too long or short chains.

BCC crystal can be obtained easily by tuning the strength constant k θ . The reasonable explanation is that the root-meansquare end-to-end distance ⟨Re2⟩1/2 of DNA chains increases with k θ , improving the probability of contact of sticky beads; thus, the hybridization percentage ph increases (Figure 2b, red spheres) which is beneficial to the crystallization. For NL ≥ 13, it can assemble into the BCC lattice due to the excluded volume effect as long as the chain retains its flexibility (k θ < 10). Although the hybridization percentage ph increases with k θ , it is still restricted to some extent when k θ ≥ 10, where DNA chain shows a certain rigidity (Figure 2b, black squares). The hybridization percentages for NL = 17 are much less than that for NL = 11, which are so small that they can be ignored. As we know, k θ mainly influences the conformation of DNA chain; therefore, the effective volume fraction ϕ changes with k θ if we treat a DNA-NP molecule as a core−shell sphere. ϕ=

4πN (2R g + RNP)3 3L3

(1)

where Rg and RNP are the root-mean-square radius of gyration of a DNA chain and nanoparticle radius, respectively. The region of ordered structures (ϕ = 0.5−0.68) in the diagram is almost consistent with that of Figure 2a, which might be a good index for the formation of ordered structure (Figure 2c and Figure S3). The ϕ value for BCC phase area is smaller than 0.68, which is the maximum space occupancy for nonclose-packed BCC crystal. Three cases are implemented to investigate the effect of the number of DNA chains n grafted to one nanoparticle and the length of DNA chain NL by tuning the spacer number ns with

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RESULTS AND DISCUSSION To estimate the effect of the rigidity on the formation of BCC crystal, we investigate the morphologies by changing the B

DOI: 10.1021/acs.macromol.8b01767 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules fixed linker number nl = 3 on the formation of BCC crystal under different strength constant of angular potential k θ as shown in Figure 3. For k θ = 0, the chain is flexible, like a

Figure 3. Phase diagrams of DNA-NP assembly systems by changing the number of DNA chains n coated on one nanoparticle and the length of DNA chain NL with nl = 3 and T = 1.8. (a) k θ = 0, (b) k θ = 20, and (c) k θ = 100.

Figure 4. (a) Comparison of DNA-NP systems with hybridization interaction and without hybridization interaction assembly systems with rigid (k θ = 100) and flexible DNA chains (k θ = 0) by changing the length of DNA chain NL; RDBS, RDnBS, FDBS, and FDnBS on the horizontal axis represent rigid DNA with binding sites, rigid DNA with nonbinding sites, flexible DNA with binding sites, and flexible DNA with nonbinding sites, respectively. (b) Hybridization percentage ph of DNA chains as a function of the chain length NL. (c) Schematic description of DNA-NP system with the flexible and rigid chains assembly into BCC crystal lattice.

polymer coil or a single DNA chain, limiting the chain stretching and DNA hybridization between the complementary sticky beads (ph < 5%, Figure S4); thus, no BCC structure forms when NL ≤ 11 (Figure 3a). However, BCC forms even though very few hybridizations when NL > 11, probably because it can maintain the free-energy-minimized morphology as an isolated particle, just like the binary hairy particles coated by polymer brush.25 What needs to be mentioned is that the BCC arrangement still can be investigated at nl = 3 and ns = 24, i.e., NL = 27 (not shown in Figure 3a). Differently, we cannot observe the unusual non-close-packed simple cubic (SC) in our system because the ratio radius of nanoparticle R = 3σ to the chain size (root-mean-square end-to-end distance ⟨Re2⟩1/2) is greater than 1 because of the limited spacer length. If we want to make sure that SC is observable in our simulation, ⟨Re2⟩1/2 needs to be increased largely to R/⟨Re2⟩1/2 < 1 by increasing ns, which is not the focus of the present work. For k θ = 20, the BCC phase area shows a left shift and widens (Figure 3b). It is thus evident that DNA chain with certain rigidity is favorable for DNA hybridization. For k θ = 100, the BCC phase area narrows, and the rigid DNA chains induce DNA-NP into BCC only at n > 40 and NL < 15 (Figure 3c). It is not beneficial when the chains are too short (NL < 7) as the DNA hybridization probability is very low (Figure S4). Importantly, the critical grafting number (n = 35) for k θ = 0 is lower than that for k θ = 20 or 100 because the former is not dependent on DNA hybridization and not sensitive to n. This might rise from the fact that the effective volume fraction ϕ value increase with k θ (Figure S5). When ϕ > 0.68, it is impossible for DNA-NP to form a BCC lattice. We further compare the DNA-NP assembly with hybridization interaction and without hybridization interaction systems in Figure 4a. For rigid chains, DNA can induce the nanoparticle rearrangement into highly ordered lattice by the base complementarity interactions only within a narrow range (NL = 8−13); however, nanoparticles grafted by rigid chains with nonbinding sites can arrange into BCC lattice in a little wider range (NL = 7−14). This result is in good agreement

with that of Tan et al.,28 who used non-base-pairing DNA as a model ligand instead of the typical base-pairing design for programmability, long-range 2D DNA-gold nanoparticle crystals can be obtained at extremely high salt concentrations in a wide range and in a divalent salt environment. Furthermore, without the influence of Watson−Crick specific base-pairing, non-base-pairing DNA can serve as an excellent model polyelectrolyte with high monodispersity and length tunability for biophysical studies toward elucidating the interactions of polyelectrolyte brushes in more complex salt environments. To a certain extent, DNA binding interactions are unfavorable to nanoparticle rearrangement for too long or short chains. The hybridization percentage ph of DNA-NP systems with rigid chains increases with the chain length NL from 7 to 10, and then it decreases to 14% (Figure 4b). The suitable hybridization percentage for crystallization is in the range from 15% to 30%, i.e., the optimal hybridization percentage.15 Nevertheless, ph of DNA-NP with flexible chains have been shown to be much less than that with rigid chains due to the restricted linker interaction, which can even be ignored in fact. For flexible chains, it is interesting to point out that the range of BCC formation is the same for the two systems with and without binding interactions, which further proves that DNA-NP with flexible chains is just like polymer coated on particles. It shows that the mechanisms of the formation of the BCC crystal for the rigid and flexible chains are different. The former is due to the DNA hybridization interactions, whereas the latter is because of volume excluded effect where BCC arrangement of nanoparticles can maintain C

DOI: 10.1021/acs.macromol.8b01767 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules the free-energy-minimized morphology as an isolated particle25 (Figure 4c).

(4) 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. (5) Mirkin, C. Spherical Nucleic Acids: Novel Topical Agents for the Treatment of Skin Disease and Brain Cancer. Nucleic Acid Ther. 2012, 22, A10. (6) 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, 442−453. (7) Park, D. J.; Zhang, C.; Ku, J. C.; Zhou, Y.; Schatz, G. C.; Mirkin, C. A. Plasmonic Photonic Crystals Realized through DNA-programmable Assembly. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 977−981. (8) Tan, S. J.; Campolongo, M. J.; Luo, D.; Cheng, W. Building Plasmonic Nanostructures with DNA. Nat. Nanotechnol. 2011, 6, 268−276. (9) Kuzyk, A.; Schreiber, R.; Fan, Z.; Pardatscher, G.; Roller, E.; Hoegele, A.; Simmel, F. C.; Govorov, A. O.; Liedl, T. DNA-based Self-Assembly of Chiral Plasmonic Nanostructures with Tailored Optical Response. Nature 2012, 483, 311−314. (10) 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. (11) Park, S. J.; Taton, T. A.; Mirkin, C. A. Array-Based Electrical Detection of DNA with Nanoparticle Probes. Science 2002, 295, 1503−1506. (12) 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. (13) Lu, F.; Yager, K. G.; Zhang, Y.; Xin, H.; Gang, O. Superlattices Assembled through Shape-Induced Directional Binding. Nat. Commun. 2015, 6, 6912. (14) Knorowski, C.; Burleigh, S.; Travesset, A. Dynamics and Statics of DNA-Programmable Nanoparticle Self-Assembly and Crystallization. Phys. Rev. Lett. 2011, 106, 215501. (15) 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 Nanoparticle Conjugates with Molecular Dynamics Simulations. Nano Lett. 2012, 12, 2509−2514. (16) Yu, Q.; Zhang, X.; Hu, Y.; Zhang, Z.; Wang, R. Dynamic Properties of DNA-Programmable Nanoparticle Crystallization. ACS Nano 2016, 10, 7485−7492. (17) Thaner, R. V.; Eryazici, I.; Macfarlane, R. J.; Brown, K. A.; Lee, B.; Nguyen, S. T.; Mirkin, C. A. The Significance of Multivalent Bonding Motifs and “Bond Order” in DNA-Directed Nanoparticle Crystallization. J. Am. Chem. Soc. 2016, 138, 6119−6122. (18) Pal, S.; Zhang, Y.; Kumar, S. K.; Gang, O. Dynamic Tuning of DNA-Nanoparticle Superlattices by Molecular Intercalation of Double Helix. J. Am. Chem. Soc. 2015, 137, 4030−4033. (19) Seo, S. E.; Wang, M. X.; Shade, C. M.; Rouge, J. L.; Brown, K. A.; Mirkin, C. A. Modulating the Bond Strength of DNA− Nanoparticle Superlattices. ACS Nano 2016, 10, 1771−1779. (20) 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. (21) Ng, D. Y. W.; Wu, Y.; Kuan, S. L.; Weil, T. Programming Supramolecular Biohybrids as Precision Therapeutics. Acc. Chem. Res. 2014, 47, 3471−3480. (22) Mcmillan, J. R.; Brodin, J. D.; Millan, J. A.; Lee, B.; de la Cruz, M. O.; Mirkin, C. A. Modulating Nanoparticle Superlattice Structure Using Proteins with Tunable Bond Distributions. J. Am. Chem. Soc. 2017, 139, 1754−1757. (23) Macfarlane, R. J.; Jones, M. R.; Senesi, A. J.; Young, K. L.; Lee, B.; Wu, J.; Mirkin, C. A. Establishing the Design Rules for DNAMediated Colloidal Crystallization. Angew. Chem., Int. Ed. 2010, 49, 4589−4592. (24) Kanie, K.; Matsubara, M.; Zeng, X.; Liu, F.; Ungar, G.; Nakamura, H.; Muramatsu, A. Simple Cubic Packing of Gold

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CONCLUSION In summary, we have investigated the effect of stiffness of DNA chains on the crystallization of DNA-NP systems. We found both the rigid and flexible chains grafted on nanoparticles can be used to design ordered supramolecular structure, but the mechanisms are different. The former needs higher critical grafting number and shorter chains than the latter. We have also simulated assembly properties of rigid and flexible DNA chain without binding site systems. Compared with the DNA with binding interaction systems, we find they have the same crystallization range if nanoparticles are grafted by flexible chains. For rigid chains, DNA binding interactions are unfavorable to nanoparticle rearrangement for too long or short chains. By tuning the strength constant of the bending, we can obtain different DNA chains or polymers with different rigidity. In experiment, we can use different polymer chains instead of the spacer region of the DNA or whole DNA chain which maybe show different chemical or physical properties.24,29,30

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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/acs.macromol.8b01767. Details for model and methods, the calculation of DNA persistence length and root mean-square of end-to-end distance, the average hybridization percentage, and effective volume fraction as a function of chain length (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.W.). ORCID

Qiuyan Yu: 0000-0002-3792-2514 Rong Wang: 0000-0001-7525-1400 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Grants 21674047, 21474051, and 21734005) and Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT). The numerical calculations have been done on the IBM Blade cluster system in the High Performance Computing Center (HPCC) of Nanjing University.

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REFERENCES

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Macromolecules Nanoparticles through Rational Design of their Dendrimeric Corona. J. Am. Chem. Soc. 2012, 134, 808−811. (25) Chen, C.; Zhang, T.; Zhu, L.; Zhao, B.; Tang, P.; Qiu, F. Hierarchical Superstructures Assembled by Binary Hairy Nanoparticles. ACS Macro Lett. 2016, 5, 718−723. (26) 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. (27) Yu, Q.; Hu, J.; Hu, Y.; Wang, R. Significance of DNA Bond Strength in Programmable Nanoparticle Thermodynamics and Dynamics. Soft Matter 2018, 14, 2665−2670. (28) Tan, S. J.; Kahn, J. S.; Derrien, T. L.; Campolongo, M. J.; Zhao, M.; Smilgies, D.; Luo, D. Crystallization of DNA-Capped Gold Nanoparticles in High-Concentration, Divalent Salt Environments. Angew. Chem., Int. Ed. 2014, 53, 1316−1319. (29) Sato, M.; Kato, T.; Shimamoto, H.; Kamitani, K.; Ohta, N.; Hirai, T.; Takahara, A. Design of High-Density Helical Polymer Brush on Silica Nanoparticles for the Size Recognition of Fullerene Molecules. ACS Macro Lett. 2018, 7, 148−152. (30) Senesi, A. J.; Eichelsdoerfer, D. J.; Brown, K. A.; Lee, B.; Auyeung, E.; Choi, C. H. J.; Macfarlane, R. J.; Young, K. L.; Mirkin, C. A. Oligonucleotide Flexibility Dictates Crystal Quality in DNAProgrammable Nanoparticle Superlattices. Adv. Mater. 2014, 26, 7235−7240.

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DOI: 10.1021/acs.macromol.8b01767 Macromolecules XXXX, XXX, XXX−XXX