A. Nanoparticle characterization

The relative anisotropy index, κ2, which ranges from 0 (spherical system) to 1 (line), can quantify nanoparticle ligand shell shape. Representative snapshots from simulations of the three nanoparticle designs in 0.1M NaCl solution are displayed in Fig. 1(d). Due to longer ligands, the ligand shells for NP1 and NP2 are more flexible and show greater shape deviation than the ligand shell of NP3. Measurement of the relative shape anisotropy, κ2, from simulations [Fig. 1(e), Table S2]7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. of the three nanoparticle designs shows that although all nanoparticle ligand shells are somewhat spherical with approximately the same radius of gyration (Fig. S1),7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. the anisotropy is reduced by bulky end groups (NP2) or by shortening ligand length (NP3).To characterize ligand behavior, we calculated the ligand excess free volume defined in Eq. (1), which gives the excess volume a ligand can sample due to nanoparticle curvature relative to a flat surface,6666. J. M. D. Lane and G. S. Grest, Phys. Rev. Lett. 104, 235501 (2010). https://doi.org/10.1103/PhysRevLett.104.235501 Δv=Vsphere−VflatNo.ofligandsorΔv=(13σ)[l3r2+3l2r],(1)where σ specifies the ligand grafting density, l is the ligand length, and r is the NP radius. As can be seen from Eq. (1), the ligand excess free volume increases with increasing ligand length and decreasing nanoparticle diameter (Table S2).7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. Figure 1(f) shows that NP1 and NP2 have relatively high ligand excess free volumes, while NP3 has a significantly smaller excess free volume. Decreasing ligand length and increasing the size of the NP core reduce ligand excess free volume through both r and l parameters. Simulations of AuNPs in TIP3P-water and 0.025M NaCl showed that NP1 end groups have high mobility compared to NP2 and NP3 (Fig. S2).7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. Thus, with these nanoparticle designs, the effect of nanoparticle ligand shell sphericity and ligand excess free volume on NP-RNA binding varied independently of overall nanoparticle charge and size.To accurately assess the behavior of the ligands on the surface of the nanoparticle, we performed density functional theory (DFT) simulations (for details, see Figs. S5–S9 and Tables S4 and S5).7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. We used a cluster of 20 gold atoms (Au20 NP) as a model for AuNPs and three types of ligands (Fig. S9)7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. reproducing the NP designs in Fig. 1. Our results show that the behavior of the ligands depends on the ligand length and type. The longer-chain ligands S(CH2)11-NH3+ tend to keep closer to each other as it can be seen in Fig. S9(a).7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. This happens due to attractive dispersion interactions between the ligand chains that offset the repulsive Coulombic interactions between the NH3+ groups of the ligands. The situation is somewhat different for another type of the longer-chain ligands, S(CH2)10-N(CH3)3+: these ligands tend to stay somewhat further apart from each other due to their bulkier head groups [Fig. S9(b)].7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. However, still some similarity in the alignment might be noticed between both longer-chain ligands [Figs. S9(a) and S9(b)].7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. The ligand excess free volume is slightly smaller for S(CH2)10-N(CH3)3+ ligands, which is in line with the DFT results. However, for shorter ligands, S(CH2)6-NH3+, the situation is noticeably different: not only their S-centers move away from each other on the AuNP surface, but the ligand chains move away from each other due to Coulombic repulsions between the NH3+ groups being stronger than the attractive dispersion interactions between the ligand chains [Figs. S9(c) and S9(d)].7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. These observations are in a qualitative agreement with MD simulation results, indicating that the shorter ligands experience extra mobility due to increased repulsion.

B. NP-RNA binding simulations

We then performed simulations of AuNPs’ binding and interactions with the 100-bp dsRNA in 0.1M NaCl and explicit water. Representative snapshots of final system conformations from our simulations are shown in Figs. 2(a)–2(c). We observed that while the charge and size of each NP are about the same, the final RNA conformation differs depending on NP properties. NP1 and NP2 cannot compact the dsRNA; however, RNA bends and wraps around NP3. Measurement of the RNA radius of gyration in each of the three simulations [Fig. 2(d)] reveals that NP1 and NP2 do not cause dsRNA conformational changes (RNA remains linear), but NP3 causes a reduction in the radius of gyration through bending of the RNA around the nanoparticle.Our simulations show that while the overall NP size and charge are the same, the changes in NP designs result in differing RNA final conformation. Simple theory models, however, would not predict this difference. For instance, in the wormlike chain model, atomic details are neglected, and the parameters determining bending energy are bending angle, segment length, and persistence length.67,6867. J. Langowski and D. W. Heermann, Semin. Cell Dev. Biol. 18, 659 (2007). https://doi.org/10.1016/j.semcdb.2007.08.01168. A. K. Mazur, Phys. Rev. Lett. 98, 218102 (2007). https://doi.org/10.1103/PhysRevLett.98.218102 In previously published theoretical calculations, parameters such as the Bjerrum length and charge separation along the molecule were used to calculate that 6% minimum charge neutralization of DNA, which is required for bending on a superhelical ramp similar to the nucleosome.6969. G. S. Manning J. Am. Chem. Soc. 125, 15087 (2003). https://doi.org/10.1021/ja030320t Based solely on these types of descriptors (persistence length, linear charge density, etc.), the theory would not predict any difference in the interaction of nucleic acids with three nanoparticles in this study. Thus, the subtle details of the molecular structure of the nanoparticles or nucleic acid molecules play a significant role in their interaction and behavior.We next examine the atomic details of ligand-RNA binding. The snapshots in Fig. 2 show differences in end-group binding locations; the charged groups of NP1 bind exclusively to RNA's major groove [Fig. 2(a)], while NP2 and NP3 make contact with both grooves [Figs. 2(b) and 2(c)]. Measurements of the preferred binding locations of NP ligand end groups, shown in Fig. 3, demonstrate this quantitatively. Figure 3 shows the binding location of the nitrogen on the ligand end group for each nanoparticle as a radial distribution function (a)–(c) along with a heatmap looking down the z-axis of the RNA helix [(e)–(g) for ligands attached to NPs and (i)–(l) for ligands not attached to NPs). Figure 3(h) shows a schematic of major and minor groove locations on an RNA base pair. In radial distribution plots, the red line at 0 represents the RNA's helical axis, while the black line indicates the outermost positions of the RNA's helix.We also performed control molecular dynamics simulations of ligand molecules, not attached to a nanoparticle surface, with shorter lengths (30 bp) of dsRNA. When ligands are free and not constrained in their movement by the nanoparticle, as in control simulations (Table S1),7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. the binding distribution of ligands is dependent on ligand length and hydrophobicity [Figs. 3(i)–3(l)]. Packing of the alkyl backbone prevents longer ligands from binding deep within major groove in contrast to shorter ligands. The hydrophobicity of RNA's minor groove leads to an increase in end-group binding for ligands with trimethylated end groups [N(CH3)3+] and the short alkanethiol ligands. One of the possible conclusions based on these data may suggest that an increase in ligand excess free volume allows for a more energetically favorable ligand distribution by alteration of the shape of the ligand corona, as opposed to a conformational change in the dsRNA.Binding of NP1 to RNA is consistent with our earlier simulations, where the NH3+ end groups bound inside the nucleic acid helix.3939. J. A. Nash, A. Singh, N. K. Li, and Y. G. Yingling, ACS Nano 9, 12374 (2015). https://doi.org/10.1021/acsnano.5b05684 For both smaller core NP1 and NP2, the ligands bind primarily inside RNA, as shown in radial distribution plots. However, for NP3 with a smaller ligand excess free volume, the movement of the ligands was restricted (Fig. S2)7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. and the majority of charged ligands bound to the outside of RNA. This binding to the outside of the RNA helix was associated with RNA bending. In RNA-NP systems where ligands bound inside the major groove, no RNA bending occurred.Interestingly, from the radial distribution plot, NP3 still appears to have ligands bound inside the RNA's helix [as it can be seen in Fig. 3(c)]. Examining the location of ligand binding in major and minor [Figs. 2(g), 2(h), 3(g), 3(k) and 3(l)] grooves provides more insight into this observation. Short unbound ligands travel deeper into RNA major grooves, residing closer to the RNA's helical axis. Additionally, bound ligands generally show a greater preference for the minor groove compared to free ligands.For NP3, which is the only nanoparticle that induced RNA bending, charged ligand groups do not go into RNA's major groove, as can be seen by lack of color on the heatmap on Fig. 3(g). In contrast, for NP1 and NP2 that did not induce dsRNA bending [Figs. 3(e) and 3(f)], the ligands bind inside the RNA's major groove. For NP2 and NP3, which are the more spherical nanoparticles, some ligands also contact RNA's minor groove. Also, for NP2 and NP3, where ligands bind inside the minor groove, this may be due also to increased hydrophobicity of the NP end-groups, as the RNA minor groove is more hydrophobic. Overall, RNA bending with nanoparticles is associated with the absence of ligands inside the major groove of RNA.

C. RNA bending parameters

We next examine atomic details of dsRNA. The orientation of two nucleic acid base pairs relative to one another may be described using six parameters: three are translational (shift, slide, and rise) and three are rotational (roll, tilt, and twist). The roll base pair parameter, which describes groove width and depth, has been shown to be particularly important for DNA bending.39,7039. J. A. Nash, A. Singh, N. K. Li, and Y. G. Yingling, ACS Nano 9, 12374 (2015). https://doi.org/10.1021/acsnano.5b0568470. T. J. D. Richmond and A. Curt, Nature 423, 145 (2003). https://doi.org/10.1038/nature01595 Bending of nucleic acids can be achieved through periodic variations in the roll and tilt parameters or a combination of both. Figure S3 and Table S37373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. show models of RNA bending that have been achieved through the application of periodic variation of roll and/or tilt. We built these models using the program 3DNA71,7271. X.-J. Lu and W. K. Olson, Nat. Protoc. 3, 1213 (2008). https://doi.org/10.1038/nprot.2008.10472. X.-J. Lu, Nucl. Acids Res. 31, 5108 (2003). https://doi.org/10.1093/nar/gkg680 and performed an energy minimization in implicit solvent in order to obtain energies associated with each type of bending for RNA and DNA. As shown in Table S3,7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems. the bending energies for RNA and DNA do not differ significantly. The energy penalty per base-pair is the highest for changes in the tilt base-pair parameter (4.3 and 5.2 kcal/mol for RNA and DNA, respectively) and lower for roll or combination roll-tilt bending (∼2.1–2.8 kcal/mol for all samples).Figure 4 shows axial bend, major groove width, and roll and tilt base pair parameters for dsRNA measured from each RNA-NP system simulation. For each parameter, we did a three-point smoothing average across the RNA helix in each snapshot to reduce noise from base pair movement before taking a time-average for plot values. Figure 4(a) shows that NP1 and NP2 do not cause significant bending. However, bending is higher for NP3. This bending is accompanied by a periodic variation on the major groove width [Fig. 4(b)]. Tilt showed no significant variation for any of the samples, indicating that it does not contribute greatly to RNA bending. However, Fig. 4(c) shows that bending of RNA with NP3 was associated with a periodic variation on RNA's roll parameter (bottom panel). This periodic variation was not observed for RNA with NP1 and NP2, indicating that RNA bending occurs through periodic changes in the roll parameter. Variations in roll parameter show direct correlation with RNA's major groove width. The width of the major groove is smallest for high roll angles. At lowest values, the major groove width is close to 0 Å, suggesting that RNA bending by nanoparticles can only occur when ligands are not inside the major groove. In contrast, the minor groove shows much smaller variation in width (Fig. S4).7373. See supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0002043 for detailed description of all performed MD simulations and parameters of the systems, Information on the NPs characterization, Procedure description, outcomes, and conclusions on additionally performed DFT simulations of NP-ligand systems.