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J. Phys. Chem. C 2009, 113, 2316–2321
Molecular Dynamics Simulation of DNA-Functionalized Gold Nanoparticles One-Sun Lee and George C. Schatz* Department of Chemistry, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208-3113 ReceiVed: October 23, 2008; ReVised Manuscript ReceiVed: December 10, 2008
Molecular dynamics methods have been used to study a 2 nm gold nanoparticle that is functionalized with four single stranded DNAs at the atomistic level. The DNA strands, which are attached to the [111] faces of a 201 atom truncated octahedral gold particle with a -S(CH2)6- linker, are found to be perpendicular to the surface of the particle, with the alkane chain lying on the surface. There are no significant hydrogen bonding interactions between the adsorbed ss-DNAs during the simulation. Even though the expected radius would be 49 Å (3.4 Å per base) for a Watson-Crick DNA structure, the simulation with 0.5 M salt shows a radius of about 29 Å (2.2 Å per base), which is a result that is consistent with recent experimental reports. It is also found that the sodium concentration within 30 Å of the gold particle is about 20% higher than the bulk concentration. This is consistent with an observed increase in the melting temperature of DNA when many functionalized gold particles are hybridized together. I. Introduction DNA-functionalized and DNA-linked gold nanoparticles (DNA-NPs) have many unique properties including optical, thermodynamic, and structural.1-3 Thiol-modified ss-DNAs of different lengths can be chemically adsorbed on the surface of gold particles, and in past work a wide range of DNAfunctionalized gold nanoparticles (diameters 2-250 nm4-6) have been used in applications to DNA and protein detection, including the ability to differentiate complementary target ssDNAs from those with single mismatches with selectivity and sensitivity that often exceeds what can be obtained using fluorescence-based assays. DNA-NPs also can be used as elemental building blocks in materials synthesis, and oligonucleotide coated gold nanoparticles have been used for intracellular gene regulation.7 Recently, Park et al. and Nykypanchuk et al. independently reported the self-assembly of DNANPs into different crystal structures8,9 that can be controlled by the choice of base-pair sequence. The free end of DNA that is on a gold particle has a linker region, and this linker directs the self-assembly by binding to a complementary linker region on another gold particle. However, the atomic structure of DNANPs is not known, and this has proven to be a hindrance in understanding how this system functions. In this paper, we report molecular dynamics (MD) simulations of DNA-NPs at the atomistic level. A truncated octahedron structure composed of 201 gold atoms (diameter ∼ 1.8 nm) is used for the core of the gold nanoparticle, and four ss-DNAs are attached to the [111] faces of the particle (see Figure 1a). Two different choices of single-stranded DNA are developed and simulated: one has four ss-DNAs, where each ss-DNA is composed of ten adenine bases (Au4A10 in Figure 1b), and the other has four ss-DNAs, where each ss-DNA is composed of ten thymine bases (Au4T10 in Figure 1c). This system has a comparable size to the DNA-NPs reported by Lee et al. recently.5 They reported a method to isolate DNA functionalized 2-nm particles, yielding a surface coverage of 64.8 ( 6.4 pmol/ cm2. This is similar to the surface coverage 74 pmol/cm2 for the structures we generated. We performed 8 ns MD simulations * Corresponding author.
and scrutinized the structural features of the DNA-NPs. The ss-DNA is found to be perpendicular to the surface of the gold particle in these simulations, and the adenine bases have a more rigid stacked structure than the thymine bases. The effective radius of the DNA-NPs is found to be about 29 Å and is independent of base composition. This value is comparable with recent experimental reports for DNA-functionalized NPs.4,10-12 The concentration of sodium ions around the gold particle is about 20% higher than the bulk concentration, which is consistent with previous estimates from our group.13,14 To the best of our knowledge, this is the first simulation that has determined the structural features of DNA-NPs at the atomistic level. II. Methods It has been shown that gold nanoparticles form discrete energetically optimal structures that adopt a face-centered cubic lattice with a truncated octahedral motif.15,16 While this picture is probably modified upon binding of the particle to thiolate ligands,17-19 these details are not likely to play a role in the present application. Thus, we choose a truncated octahedral gold nanoparticle composed of 201 gold atoms for this study (Figure 1). This gold nanoparticle has eight [111] surfaces and six [100] surfaces. Four ss-DNA strands, each composed of ten nucleotides, are linked to the center of the [111] surfaces on the gold nanoparticle using a six-carbon alkylthiolate linker (Figure 1a). The four [111] surfaces that are chosen for adsorption of the ss-DNAs are symmetrically distributed around the particle. These [111] surfaces are colored in red in Figure 1a. We developed two DNA-NPs: (i) each ss-DNA is composed of ten adenines (Au4A10 in Figure 1b), and (ii) each ss-DNA is composed of ten thymines (Au4T10 in Figure 1c). This structure corresponds to a coverage of 74 pmol/cm2, which is comparable to the system used in a previous experiment (64.8 ( 6.4 pmol/ cm2).5 The initial helical parameters of the ss-DNAs are adapted from the canonical B-DNA structure. This starting structure of the ss-DNA is developed using the x-leap module implemented in the AMBER package.20 The interactions between the gold atoms are described by Lennard-Jones potentials where the parameters (σ ) 2.569 Å
10.1021/jp8094165 CCC: $40.75 2009 American Chemical Society Published on Web 01/21/2009
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Figure 1. (a) Schematic structure of DNA-NP. The gold particle has a truncated octahedron structure with 201 gold atoms. The diameter of the gold particle is about 1.8 Å. A ss-DNA is linked to the center of the [111] surface of the gold particle using the -S(CH2)6 group. Four ss-DNAs are linked to the gold particle, and the [111] surface used for the adsorption of ss-DNA is colored in red. Only one ss-DNA is shown for clarity. (b) Gold nanoparticle with four ss-DNAs of 10 adenine bases and (c) 10 thymine bases.
and ε ) 0.458 eV) are taken from the literature.21 The force field parameters for the alkylthiol are taken from the work of Hautman and Klein,22 while the parameters from CHARMm are used for ss-DNA.23 An energy minimized structure of DNA-NPs (Au4A10 or Au4T10 in Figure 1) was solvated in a water box using the SOLVATE24 module implemented in VMD.25 Periodic boundary conditions were used corresponding to a box of dimensions of 100 × 100 × 100 Å3. This box was filled with 30626 water molecules based on the modified TIP3P potential.23,26 To neutralize the system, 40 Na+ ions are added. In addition to these sodium ions, another 272 Na+ and Cl- ions are added to make the concentration of each ion 0.5 M. This choice matches what has been used previously,13 and an additional 5000 steps of energy minimization were applied to the solvated system to remove the high-energy contacts. Molecular dynamics simulations were carried out using NAMD2.27 A 1 ns molecular dynamics simulation at 300 K with a NVT ensemble was performed to equilibrate the system. During the equilibration, the position of the gold atoms is fixed with harmonic constraints. In the production period, the system was simulated for 8 ns using the NVT ensemble and Langevin dynamics at a temperature of 300 K with a damping coefficient γ ) 5 ps-1.28,29 No atomic coordinates were constrained during the production period. Full electrostatics was employed using the particle-mesh Ewald method with a 1 Å grid width.30 Nonbonded interactions were calculated using a group-based cutoff with a switching function and were updated every five time steps. Covalent bonds involving hydrogen were held rigid using the SHAKE algorithm,31 allowing a 2 fs time step. Atomic coordinates were saved every 1 ps for the trajectory analysis.
III. Results and Discussion We first consider the conformational changes in the ss-DNA during the MD simulations. The canonical structure of B-DNA is used as a reference for the trajectory analysis. Obviously, this is an arbitrary choice, as the structure of ss-DNA is not expected to be the same as that of B-DNA.32 Equation 1 is used for calculating the root-mean-square deviation (rmsd) after translation and minimization of a given structure relative to the reference structure, where xi and xicanon are the coordinates of the ith atom of a structure of ss-DNA and the structure of canonical B-DNA. M is the number of atoms in each ss-DNA excluding hydrogen atoms and the atoms in the -S(CH2)6- group. The fluctuation in the rmsd of each ss-DNA of Au4A10 and Au4T10 with time is shown in Figure 2a and b. In both cases, the value of the rmsd becomes constant after 4 ns. For Au4A10, the average of the rmsd after 4 ns is 5.6 ( 1.2 Å, whereas it is 6.7 ( 1.5 Å for Au4T10.
[
M
∑|
|
]
1 RMSD(x, xcanon) ) x - xicanon 2 M i)1 i
1⁄2
(1)
Snapshots of the Au4A10 and Au4T10 structures at times t ) 2, 4, 6, and 8 ns are shown in Figure 2c and d. All ss-DNAs are perpendicular to the surface of the gold nanoparticle, and there is no significant hydrogen bonding interaction between ss-DNAs during the MD simulation. However, the -S(CH2)6group lies flat on the surface of the gold nanoparticle even though its starting structure is away from the surface. The detailed structure of the -S(CH2)6- group is shown in Figure 3. Note that although the four -S(CH2)6- groups are parallel to the surface of the gold nanoparticle in Au4A10, there is no significant
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Lee and Schatz
Figure 2. Root mean standard deviation (rmsd) of each ss-DNA of (a) Au4A10 and (b) Au4T10. The system is equilibrated after 4 ns in both nanoparticles. Snapshots of (c) Au4A10 and (d) Au4T10 at time steps t ) 2, 4, 6, and 8 ns. During the simulation, all the ss-DNAs are perpendicular to the surface of the gold nanoparticle.
contact between each ss-DNA and the surface in Au4A10. However, a few bases next to the -S(CH2)6- group of one ssDNA are on the gold surface in Au4T10. The other three ssDNAs have no significant interaction with the surface. We can conclude that the -S(CH2)6- group does not contribute to the radius of the DNA-NPs even though the length of the -S(CH2)6group is about 9 Å. To scrutinize the stacked structure of the bases, we monitored the center-center distance between neighboring bases. The centroid is used as the center of a base. The centroid of adenine is defined by the four nitrogen atoms (N1, N3, N7, and N9) and five carbon atoms (C2, C4, C5, C6, and C8) that are part of the purine ring.33 For the definition of the centroid of thymine, the two nitrogen atoms (N1 and N3) and four carbon atoms (C2, C4, C5, and C6) of the pyrimidine ring are used. The distribution of center-center distance between neighboring bases is shown in Figure 4. The canonical value of the center-center distance for B-DNA is drawn as the blue line. In Au4A10, more than 60% of the distribution is within 1 Å of the canonical value. However, less than 40% is within 1 Å of the canonical value in
Au4T10. Therefore, base-base stacking is maintained better between adenine (purine) bases than between thymine (pyrimidine) bases. This is consistent with previous results obtained in both experiments and ab initio calculations. For example, in an analysis of crystal structures, Mizutani et al. found that the purine ring gives rise to a strong π-π stacking both in solution and in the solid state, whereas the pyrimidine ring does not show this interaction.34 They prepared two nonnatural amino acids with nucleobases differing in ring structure to obtain evidence for the specificity of the π-π interaction. In the crystal structures, the molecule containing the adenine residue shows intra- and intermolecular π-π stacking, whereas the molecule containing the uracil residue does not have any stacking interaction. This result agrees well with ab initio calculations for stacked bases that were reported by Sponer et al.35 They performed MP2/6-31G* calculations on 10 stacked base pairs. They used 10-30 geometries per base pair to determine the stacking energy dependence on the twist, displacement, and vertical separation of the stacked bases. They also included geometries from B- and Z-DNA crystal structures. According
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Figure 4. Distribution of neighboring base-base distances for (a) Au4A10 and (b) Au4T10. The distance is defined as the distance between the centers of neighboring bases. The distance of canonical B-DNA is shown as a blue line in each case for comparison.
Figure 3. Conformation of the -S(CH2)6- group at time t ) 8 ns. The -S(CH2)6- group is in red, and ss-DNA is in gray. Gold atoms are depicted as green spheres. (a) The -S(CH2)6- groups are laid on the surface of Au4A10, but all of the ss-DNAs of Au4A10 are away from the surface. (b) The -S(CH2)6- groups are laid flat on the surface of Au4T10, and three of the nucleotides next to the -S(CH2)6- of one of the ss-DNAs are also flat on the surface. However, the other three ssDNA are away from the surface.
to their calculation, they found that the most stable stacked pair is the guanyl dimer, and the least stable is the uracil dimer. To further characterize the DNA-gold structures, the radial distribution function (gAuP(r)) of phosphorus atoms relative to the center of the gold particle has been calculated during the last 1 ns of the production period. The results are presented in Figure 5, with separate curves provided for each DNA. The figure shows that, for both Au4A10 and Au4T10, the first peak appears at around 11 Å. This is consistent with Figure 3, showing that the -S(CH2)6- group is laid flat on the surface of the gold particle so that the first base next to the -S(CH2)6- is close to the surface of the gold particle. Note that one of the four peaks in Figure 5b (the black curve) is higher than the other peaks. This is because three bases next to the -S(CH2)6group on one of the ss-DNA strands of Au4T10 are adsorbed on the surface of the gold particle, as shown Figure 3b. This suggests that there is some extra room on the gold particle structures that we have constructed, and indeed in the experiments of Lee et al.,5 it was estimated that on-average there are five DNAs on each 2 nm particle. To calculate the effective radius of the DNA-NPs, the radius of gyration (RG) is introduced. The radius of gyration is defined in eq 2, where NP is the number of phosphorus atoms, 〈 · · · 〉 denotes a time average, rP is the position vector of the
Figure 5. Radial distribution function (gAuP(r)) of the phosphorus atom relative to the center of the gold particle for (a) Au4A10 and (b) Au4T10. gAuP(r) of each of four ss-DNAs is shown separately in blue, red, green, and black lines. The schematic representation for the distance between the center of the gold particle and the phosphorus atom is shown in the inset.
phosphorus atom, and rG is the position vector of the center of the gold particle.
2320 J. Phys. Chem. C, Vol. 113, No. 6, 2009
RG2 )
1 NP + 1
〈
NP
∑ (rfP - rfG)2
P)0
〉
Lee and Schatz
(2)
Since the rise per base for double strand B-DNA is 3.4 Å, the length of the -S(CH2)6- group is about 9 Å, and the radius of the gold particle in our simulation is about 9 Å, the expected radius of DNA-NP with a stretched conformation of DNA would be about 49 Å. However, during the last 1 ns of the production period, the value of RG is found to be 28.4 ( 2.3 Å for Au4A10 and 28.9 ( 5.7 Å for Au4T10. These values are based on calculations of RG for each of the four ss-DNA on each particle. All statistical uncertainties are (1σ (one standard deviation). Since the radius of the gold particle is about 9 Å, we can determine an empirical equation for the radius of the DNANPs using eq 3. Here Nbase is the number of bases per ss-DNA and rAu is the radius of the gold particle. Since the -S(CH2)6group is flat on the surface of the gold particle (see Figure 3), it is assumed that the -S(CH2)6- group does not contribute to the radius of the DNA-NP. Moreover, since the first base next to the -S(CH2)6- group is close to the surface of the gold particle as shown in Figure 3, (Nbase - 1) is used instead of Nbase in eq 3.
RG ≈ 2.2(Nbase - 1) + rAu (in Å)
nanoparticles bind to a complimentary DNA sequence linker and form an aggregate with high selectivity and sensitivity. When the aggregate is heated, it undergoes reversible melting within a narrow temperature range (3 K), whereas the range is about 20 K for melting of the same DNA in bulk solution. The melting temperature is also higher than the bulk melting temperature by a few degrees. Jin et al. analyzed the parameters that affect the melting temperature of DNA-NP aggregates.14 They reported that the higher the ss-DNA coverage density on the surface of the gold particle, the higher the melting temperature and the sharper the melting profile. They also reported that the addition of salt stabilizes the nanoparticle aggregates. More recently, Long et al. reported molecular dynamics simulations of the ion distribution near DNA clusters.13 They found that the local net charge fraction (φ) of DNA clusters containing two or four DNA duplexes is higher than φ of an isolated DNA duplex. In our simulation, we calculated the number density of sodium ions within r ) 30 Å from the center of gold particle. This distance was chosen to be close to Rg, so the number density refers to ions that are in the volume occupied by the ssDNA. The number density of sodium ions is calculated using eq 4.
(3)
This result indicates that the rise per base is 2.2 Å, which is significantly smaller than the 3.4 Å rise per base in double stranded B-DNA. There are a number of recent measurements which are consistent with this result. Hill et al. reported an empirical equation for the diameter of DNA-NPs using smallangle X-ray scattering for a face centered cubic crystal.10 According to their report, the diameter of DNA-NPs is proportional to 2.55 (Å) × x, where x is the number of bases between the gold particles. This result is consistent with equation 3; however, we note that it refers to a mixture of double and single strand DNAs, so it is not exactly a comparable situation. Moreover, the ss-DNA adsorbed on a gold nanoparticle adopts different conformations depending on the experimental conditions, including the content of DNA, the length of DNA, and coverage.36 A more direct comparison with experiment is provided by the work of Park et al., who reported the conformational change of ss-DNA adsorbed on gold nanoparticles upon treatment with 6-mercapto-1-hexanol (MCH).12 They found that MCH displaces noncovalent base adsorption on the gold surface, resulting in changes in the conformation of ss-DNA from flat on the surface to perpendicular to it. This leads to a change in the effective radius of the DNA-NPs (as measured by the electrophoresis mobility) that is proportional to ∼1.9 (Å) × x, where x is the number of bases. In related work, Parak et al. and Pellegrino et al. also reported an effective diameter for DNA-NP using electrophoretic mobility measurements and a Ferguson analysis.4,11 Parak et al. used thiol-modified ss-DNAs of varying length (8-135 bases) adsorbed on a 10 nm diameter gold particle, and they found that short ss-DNAs are oriented perpendicular to the surface of gold.4 However, the effective diameter of DNANPs is strongly affected by the evaluation method according to the study of Pellegrino et al.11 They reported different sets of effective diameters depending on the evaluation method. The effective diameter obtained from the Ferguson method is proportional to 2.6 (Å) × x, where x is the number of bases. According to a recent study by Park et al., the Ferguson analysis37,38 is a reliable method for analyzing both the size and charge of DNA-NPs with diameter less than 20 nm.39 It has been found that DNA-NPs can be used to detect specific DNA sequences.1,3 To do this, the ss-DNA functionalized gold
F(r) )
〈ni(ri)〉 V
(4)
Here F(r) is the number density and V is the volume of a sphere with a radius of 30 Å minus the volume of the gold particle. 〈ni(ri)〉 is the number of particles averaged over time, as shown in eq 5, where T is the total time for the sampling. T
〈ni(ri)〉 )
∑
1 n (r (τ)) T τ)1 i i
(5)
The distribution of number density of sodium atoms (normalized to its bulk value) during the last 1 ns of the production period is shown in Figure 6. The average value of the normalized number density relative to 0.5 M bulk concentration is 1.24 ( 0.06 for Au4A10 and 1.18 ( 0.06 for Au4T10. Thus, the concentration around the gold particle is about 20% higher than the bulk concentration. This is a larger increase than we find for a single ss-DNA under the same conditions (only a 5% increase is found for a spherical cavity around the DNA), so evidently there are cooperative interactions between the ssDNAs when attached to a gold particle. As reported by Jin et al., the melting temperature of DNA that is linked to gold is increased by increasing the salt concentration. As a consequence, the binding (the reverse process of melting of DNA) temperature of DNA also increased. From our simulation, we can conclude that the higher concentration of sodium around the gold particle provides an environment for increasing the binding temperature of DNA that is linked to a gold particle. According to a previous study in our group,13 the relation between melting temperature of DNA and Na+ concentration is
∆T (K) ) -15.8 ln(C1/C2)
(6)
where C1 is the bulk concentration of ion and C2 is the concentration of Na+ ions in the vicinity of DNA. Since the sodium concentration around the gold particle is increased by 20% relative to the bulk concentration in our simulation, it corresponds to an increase in the melting temperature of DNA by ∼3 K. Of course, duplex DNA is needed to observe melting, so this number is not directly relevant to the experiments. However, the ion concentration increase, and therefore the melting temperature increase, is likely to be
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Figure 6. Distribution of number of sodium atoms around the gold particle within 30 Å of (a) Au4A10 and (b) Au4T10. The schematic representation of DNA-NP and sodium atoms within 30 Å from the center of the gold particle is shown.
larger if duplex is modeled, so this will be important to consider in future work. IV. Conclusion In this paper, we report MD simulations for DNA-functionalized gold nanoparticles at the atomistic level. The ss-DNAs are found to be perpendicular to the surface of the gold particle, whereas the -S(CH2)6- group which links the ss-DNA to the surface of gold is parallel to the surface. We obtained an effective radius of DNA-NPs using the radius of gyration, and the effective radius is about 29 Å for the two compositions of ss-DNA that we studied. This leads to a 2.2 Å increment per base, which is in the range of estimates provided by experiment (1.9-2.6 Å) and considerably shorter than the 3.4 Å increment for a Watson-Crick structure. We also found that the sodium concentration around the gold particle is increased by 20% relative to the bulk concentration. This increase in sodium concentration provides an environment for increasing the melting temperature DNA, which is what is found in the experiments for DNA-linked gold nanoparticle aggregates. Acknowledgment. This research was supported by National Science Foundation (Grant CHE-0550497), by the NSEC Center at Northwestern (NSF Grant EEC-0647560), and by the Northwestern Center for Cancer Nanobiotechnology Excellence (1 U54 CA119341-01).
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JP8094165
