DNA Melting in Gold Nanostove Clusters - The Journal of Physical

J. Phys. Chem. C 2010, 114, 7401–7411

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DNA Melting in Gold Nanostove Clusters† Calin Hrelescu,‡,§ Joachim Stehr,‡,§ Moritz Ringler,‡,§ Ralph A. Sperling,§,| Wolfgang J. Parak,§,| Thomas A. Klar,*,§,⊥ and Jochen Feldmann‡,§ Photonics and Optoelectronics Group, Department of Physics, Ludwig-Maximilians UniVersita¨t Mu¨nchen, Amalienstrasse 54, 80799 Mu¨nchen, Germany, Center for Nano Science (CeNS), Schellingstrasse 4, 80799 Mu¨nchen, Fachbereich Physik, Philipps UniVersita¨t Marburg, Renthof 7, 35037 Marburg, Germany, and Institute of Physics, Technical UniVersity of Ilmenau, 98684 Ilmenau, Germany ReceiVed: October 10, 2009; ReVised Manuscript ReceiVed: December 11, 2009

Clusters of gold nanoparticles can be used as optically driven stoves to locally heat biological material such as DNA in biosensors or cancerous tissue in thermotherapy. Clusters of gold nanoparticles behave distinctively different from single nanoheaters as they accumulate heat in-between the individual nanoparticles. However, in very large clusters the rear nanoparticles are shed by front-lying nanoparticles such that the optothermal heating saturates with increasing cluster size. We focus on these two effects and describe the temporal and spatial development of heat generation and subsequent cooling of nanoparticle clusters excited by nanosecond laser pulses. It is found that (i) heat accumulation is most important for DNA melting assays to generate enough heat for DNA melting, (ii) shadowing effects are significant in micrometer sized nanoparticle clusters, and (iii) that DNA needs to be heated substantially above the equilibrium thermodynamic melting temperature in order to induce DNA melting by nanosecond laser pulses. 1. Introduction Gold nanoparticles (AuNPs) have proven to act as very efficient converters of optical energy into thermal energy, specifically when the optical excitation frequency is in resonance with the nanoparticle plasmon oscillation. AuNPs convert the absorbed light into thermal energy within approximately 1 ps.1,2 A single hot nanoparticle thermally equilibrates with its surrounding within the subsequent 100 ps.2,3 This effect allows for utilizing gold nanoparticles as nanoscale “stoves” within a large variety of applications: Hyperthermic destruction of cells, including the evolving field of cancer therapy,4-8 cell membrane permeabilisation,9 targeted protein denaturation,10-12 remote drug release,13-15 and photothermal interference contrast imaging16 are some of the applications reported so far. If high power femtosecond lasers are used for heating gold nanoparticles, even the breaking of thiol bonds between DNA and the AuNPs can be observed,17,18 as well as the cutting of DNA strands.19 Nanostoves have also been used to optically trigger phase transitions such as the melting of ice,20 glass/crystal transitions,21 stretching of polymers,22 local melting of lipid membranes,23 and, last but not least, dehybridization of oligonucleotides.24-26 Thermal dehybridization or melting of the DNA duplex helix is the basis of most current DNA assays because the melting temperature is determined by the base sequence.27 Some of these assays use gold nanoparticles as transducers of the information whether the DNA is in the double helix or the single strand conformation.28-30 Typically, the target DNA is mixed with a solution containing one sort of gold nanoparticles functionalized with oligonucleotides complementary to some part of the target DNA sequence and another sort of gold nanoparticles func†

Part of the “Martin Moskovits Festschrift”. * To whom correspondence should be addressed. Ludwig-Maximilians Universita¨t Mu¨nchen. § Center for Nano Science (CeNS). | Philipps Universita¨t Marburg. ⊥ Technical University of Ilmenau. ‡

tionalized with oligonucleotides complementary to some other part of the target DNA sequence. Hybridization of the oligonucleotides on the gold nanoparticles with the target DNA leads to the formation of clusters of gold nanoparticles, which can be observed optically by a pronounced change of the extinction spectrum.30 Originally, DNA melting analysis is realized by slowly increasing the temperature of the DNA containing solution by conventional heating of the whole assay solution.30,31 Recent developments use optothermal heating of the gold nanoparticles as introduced above to induce a temperature increase which is sufficient to melt the DNA. Two different schemes have been applied: Either a continuous wave laser is applied to globally heat the whole solution containing DNA linked AuNP clusters within a time frame of tens of minutes25 or even hours26 or pulsed lasers are used for DNA analysis on a millisecond time scale.24 In the latter case, only the clusters of gold nanoparticles are heated, while the surrounding solution remains in a cold state. Consequently, the totally heated volume is tiny as compared to the globally heated volume of the whole assay solution, a fact which allows for the fast, submillisecond DNA analysis. Following this idea of quickly and locally heating the DNA only, it has been proposed to use high power femtosecond lasers in order to heat single gold nanoparticles functionalized with DNA and induce DNA melting. However, in case of femtosecond lasers and single gold nanoparticles, the applied optical power needs to be that large that defunctionalization due to thiol bond breaking was observed, rather than DNA melting.17 Alternatively, thermal DNA dissection was achieved using high power lasers.19 To sum up, most experiments reported so far can be sorted in two distinct regimes: (i) the application of short, high power laser pulses to heat single gold nanoparticles causing very local destruction to thiol bonds or DNA on the nanometer length scale and (ii) the application of low power, continuous wave lasers applied to sparsely dissolved gold nanoparticles which causes global heating of the whole DNA containing

10.1021/jp9097167  2010 American Chemical Society Published on Web 01/27/2010

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solution. These two extremes have also been contrasted in some recent theoretical papers, and both of the two situations had been simulated.32-35 The ultimate question that arises is whether the intermediate regime can be of any benefit: A scenario where a limited volume of micrometer size containing an intermediate density of gold nanoparticles is hit by nanosecond laser pulses of intermediate power. While it has been speculated in a theoretical paper that in this regime “the localization [of energy] to microscale dimensions is highly difficult”,33 recent experiments have proven that nanosecond laser pulses are indeed able to induce optothermal DNA melting without DNA destruction.24 Indeed, AuNP clusters in DNA melting assays grow to the right size of some hundred nanometers up to a few micrometers in diameter and possess a gold nanoparticle density which is exactly right to allow for a collective heating effect inside the clusters to induce DNA melting without the need of ultrahigh, destructive laser powers but on a time scale short enough to allow for submillisecond DNA analysis. In this article, we focus on the numerical simulation of the temperature inside DNA linked AuNP clusters irradiated by nanosecond laser pulses. Some challenges arise which have not been considered in previous papers: The clusters of DNA grow to sizes of some hundred nanometers in diameter, so nanoparticles facing the incoming laser pulses will substantially shield light from nanoparticles in the center and on the rear side of the clusters. This effect has not been included in other simulations so far. Further, some average thermophysical properties must be found for the interior of the cluster in order to simulate heat transport correctly. Up to now, the contribution of the gold nanoparticles to the heat conductivity and heat capacity has largely been ignored because a very low nanoparticle density has been assumed. In DNA interconnected AuNP clusters, this does not hold. In section two of this paper, we will focus on these two extensions of numerical simulations. Pronounced shadowing effects are demonstrated for realistically sized DNA- AuNP clusters. In section three, results from simulations are compared with experimental data and we evidence that melting of the DNA on a microsecond time scale requires temperatures well in excess of the melting temperature known from quasi-equilibrium thermodynamical measurements such as the classical melting assay. Before turning to the numerical simulations, the millisecond DNA melting assay is briefly recalled. More details can be found in ref 24. Figure 1a shows the oligonucleotide sequences of both recognition DNA strands (blue and red 15-mer sequences) and the 30-mer target oligonucleotide (green sequence; all oligomers purchased from Metabion). For steric reasons, both recognition sequences are spaced from the thiol linker by a A15 base sequence. The gold nanoparticles (BBI International) used in this work are (10 ( 1) nm in diameter. When both types of DNA functionalized AuNPs and the target are present in the solution, clusters of AuNPs form that may easily contain up to some ten thousands of AuNPs which results in cluster diameters of up to 1 µm. The cluster diameter can be tuned by the time for which the assay is allowed to rest after the target strands are added. Typically, the clusters are 250 nm in diameter after 1 h of clustering and 800 nm after 24 h. The extinction spectrum of an unclustered assay which is kept at an elevated temperature of 60 °C (which is above the melting temperature) is shown in Figure 1b by the black line. It resembles the extinction spectrum of dissolved AuNPs. At 25 °C, which is below the 30-mer melting temperature, clusters form and the extinction spectrum shows a pronounced red shift and spectral broadening. Using a 650 nm probe laser, one can easily use the extinction at 650

Hrelescu et al.

Figure 1. (a) Sequences of AuNP linked oligonucleotide detection strands and the interconnecting target. (b) Extinction spectrum of DNA bound gold nanoparticle clusters at 25 °C (blue line) and of dispersed AuNPs at 60 °C. The green line indicates the wavelength of the pulsed heating laser of 527 nm and the red line shows the wavelength where the extinction is probed by a red laser diode and a fast photo detector. (c) Extinction of the assay solution at the probe wavelength of 650 nm versus the temperature of the assay solution. A narrow melting transition region indicates a melting temperature of 54 °C (inset).

nm as a probe signal of AuNP clustering. In a classical DNA melting assay,30 the bath temperature of the whole assay is slowly increased (typically with a rate of 1 °C/min) and the extinction at some characteristic wavelength is monitored. An example is given in Figure 1c. The melting threshold at 54 °C is easily observed, whereby the sharpness of the transition of only 3 °C (inset) is due to cooperative or percolative effects.36,37 The sharpness of this transition allows for single base mismatch detection.38 The extinction overshoot observed shortly before the melting transition is reached is due to an Ostwald ripening effect.39 Small clusters dissolve while large clusters benefit, which leads to an increase in average cluster size and hence to an increased extinction. A classical melting curve such as the one shown in Figure 1c is taken by increasing the temperature of the whole assay over some tens of minutes. In contrast, the millisecond optothermal DNA assay keeps the global assay temperature at low level (e.g., 25 °C). Only the AuNP clusters are heated by a pulsed laser (frequency doubled Nd:YLF, 527 nm, green line in Figure 1b). The experimental details have been reported in ref 24. In this contribution, we now focus on details of the optothermal heating of large AuNP clusters. 2. Numerical Simulation Methods 2.1. Heat Transport Equation. Numerical simulations of optothermal heating of AuNP clusters with pulsed lasers and subsequent cooling by transport of the thermal energy into the water bath is described by the usual heat transport equation:

DNA Melting in Gold Nanostove Clusters

F(b)c r p(b) r

∂T(b, r t) ) ∇[K(b)∇T( r b, r t)] + Q(b, r t) ∂t

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(1)

where T(r b,t) is the temperature as a function of space and time, b) is the specific heat capacity, K(r b) F(r b) is the mass density, cp(r is the thermal conductivity, and Q(r b,t) is the source term of optothermal energy density generated by the pulsed laser beam. Outside the AuNP cluster (|r b| > R, the cluster radius), the material b| > R) ) 1000 kg/m3, constants of water are applied: FH2O(|r b| > R) ) 4187 J/(kg K), and KH2O(|r b| > R) ) cp,H2O(|r b| > R) ) 0 which means that 0.600 W/(m K). Further, QH2O(|r the absorption of laser light by the water and DNA surrounding the AuNP clusters is negligible compared to the absorption and heat generation by the AuNP clusters within the visible spectral range. Further, an infinite heat conductance is assumed at all interfaces throughout this work, which is reasonable because heating pulses of 260 ns duration are applied and finite heat conductance effects at surfaces of gold nanoparticles have been shown to be irrelevant on time scales longer than 1 ns.40 Inside the clusters (|r b| < R), we assume a homogeneous effective thermal medium. This is necessary because AuNP clusters in DNA melting assays can easily reach sizes of ten thousand AuNPs and more so that there is no way to numerically handle all of the details of individual gold nanoparticles, oligonucleotides and intermittent water with all their specific materials constants in a finite element solver used to solve eq 1. The outline of section 2 is as follows: section 2.2 stresses on the corrections to the dielectric constants of DNA functionalized 10 nm gold nanoparticles which arise due to surface scattering and chemical damping caused by the DNA functionalization. This enables control over a single AuNP nanostove. In section 2.3, Q(|r b| < R,t) is determined by calculating the absorption cross section of a AuNP cluster using a discrete dipole approximation method. Effective thermophysical properties F(|r b| < R), b| < R), and K(|r b| < R) are derived in section 2.4. Finally, cp(|r everything is put together in section 2.5 to solve eq 1 using the finite element solver from Comsol. The corresponding flowchart is shown in Figure 2. 2.2. Dielectric Constant of a DNA Functionalized Au Nanostove. Before the absorption and scattering properties of the AuNP clusters can be determined, the dielectric properties of individual AuNPs must be determined. For small and chemically functionalized nanoparticles, this is not trivial because additional damping effects need to be considered.41 First, plasmon polaritons in nanoparticles with diameters below 20 nm suffer from additional damping due to interaction of the electrons with the surface.41 This is usually taken into account by using an additional frequency independent damping constant in the Drude term of the dielectric function. Chemical functionalization may lead to additional damping due to trap states for electrons provided by, e.g., embedding the AuNPs in matrices or by surface functionalization, e.g., with DNA.42-45 It is not surprising that the corresponding damping constant depends on frequency, because these trap states have specific energetic levels. This additional chemical damping arises on the surface and consequently scales with the surface to volume ratio. Hence, both the small size surface scattering effect and the chemical damping effect can be taken care of by a damping term Γ1 ) A(ω)(VF/rNP) where A(ω) is a frequency dependent proportionality factor, VF is the Fermi velocity, and rNP is the nanoparticle radius. With this additional damping, the dielectric constant εfNP of a DNA functionalized nanoparticle of 10 nm diameter can be written as

εfNP(ω) ) εJC(ω) +

ωp2 ω2 - iωΓ0

-

(

ωp2

VF ω - iω Γ0 + A(ω) rNP 2

)

(2)

εJC(ω) is the empirical dielectric constant published by Johnson and Christy,46 ωp is the plasma frequency, and Γ0 is the damping in bulk gold. εfNP(ω) is empirically determined by matching the calculated Mie scattering cross section using εfNP with the measured extinction spectrum of an unclustered solution of DNA functionalized AuNPs. A Gaussian 10% variation of the AuNP size as given by the manufacturer of the AuNPs is already taken into account in the Mie calculations.47 This variation in AuNP size needs to be considered, because it causes an inhomogeneous broadening of the extinction spectrum. Figure 3 shows the results of the best fit for εfNP(ω). The dashed black line in Figure 3a shows the measured extinction spectrum of the unclustered AuNP solution. Mie calculations using the original εJC (i.e., Γ1 ) 0) but including a 10% size variation (blue line) can not at all fit the experimental data. However, when the dielectric constant as given by the green line in Figure 3b is used, an excellent fit of the calculated extinction cross section (green line in Figure 3a) and the measured extinction is obtained. We note that the largest deviation between the Johnson Christy data (blue line in Figure 3b and the fitted εfNP (green line) is observed for the imaginary part of εfNP and long wavelengths. Recently, Stoller et al. published the dielectric constant of small gold nanoparticles covered with oil.48 They found less deviation from the Johnson Christy data with the largest discrepancies for short wavelengths. However, they covered the AuNPs with nonpolar immersion oil, probably introducing only little chemical surface damping. It is reasonable to assume that the chemical damping by polar water molecules physisorbed onto the surface of the AuNPs and by the thiol bonds of the oligonucleotides result in much more severe trap states for electrons causing additional damping specifically for long wavelengths. 2.3. Extinction and Absorption Cross Sections of Clusters. 2.3.1. Discrete Dipole Approximation. The absorption, extinction and scattering cross sections of large clusters of AuNPs are deduced by following a route suggested by Schatz and coworkers.49 The discrete dipole approximation (DDA)50,51 is used to simulate light scattering by a AuNP cluster. While the original DDA is usually used to model the scattering and extinction cross sections of one homogeneous particle of arbitrary shape, Schatz and co-workers adopted the idea of discrete dipoles for DNA linked clusters of AuNPs. In their approach each single AuNP is associated with one scattering dipole. Hereby, each particle experiences the sum of the incoming field and the fields scattered off all other (N - 1) particles. This leads to a matrix equation

b Ab P)b Einc where b P is a 3N dimensional vector of the three-dimensional polarizations of N particles, b Einc is the corresponding 3N dimensional vector of the incoming electric field at the positions of N particles and b A is a 3N × 3N dimensional polarizability matrix given in ref 51. The extinction, absorption, and scattering cross sections can then be deduced from the polarizabilities and the electric fields51

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N

Cext )

∑

4πk bb b*inc,jb P)A P)b Einc Im(E |Einc | 2 j)1 N

Cabs )

∑[

2 3b b 4πk bj(Rj-1)*b Im(P P*) j - k PjP* j 3 |Einc | 2 j)1

(3)

Csca ) Cext - Cabs

]

(4)

(5)

We use the implementation DDSCAT by Draine and Flatau to carry out the DDA calculations.52,53 Due to the Fourier transform method used in DDSCAT, the AuNP clusters need to be modeled using a cubic lattice. Hereby, it has been shown that the details of the cubic lattice, such as whether they are sc, bcc or fcc, or even a physically reasonable lattice disorder influence the results only marginally as long as the density of gold nanoparticles is kept constant.54 Therefore and for the sake of least computational effort, we choose a simple cubic (sc) model for our simulations. 2.3.2. Cubic Lattice Resembling a AuNP Cluster. While a long-range order is certainly absent in the AuNP clusters, a short-range order is observed in small-angle X-ray scattering studies as shown by Park et al.55 In the same study it has been found from the structural scattering factors that a bcc or a fcc unit cell is most likely. On the other hand, a binary lattice is expected for short-range order because there are two sorts of AuNPs each functionalized with one of the two recognition oligomers (Figure 1a). Hence, the bcc structure is the most likely

geometry for short-range order.54 In a bcc structure, the next neighbors are situated along the diagonal of the unit cell. Let d be the distance between next neighbors and abcc the length of a unit cell, then abcc ) (2/3)d. This side length of a bcc unit cell can be translated to the side length asc of a simple cubic with the same nominal particle density to ensure that the DDSCAT calculations lead to the correct results.54 It is easily shown that asc ) [2/(323)]d = 0.916d. The remaining question is to find the right size for the nearest neighbor distance d. According to Figure 1a the center-to-center distance d of two nanoparticles has different contributions

d ) 2rNP + d30bp + 2dA15 + dthioalk

(6)

where 2rNP ) 100 Å is the diameter of the gold nanoparticles and d30bp is the contribution of the hybridized DNA of 30 base pairs (bp) length, 2dA15 is the length of the two A15 spacers at each side of the hybridized region and dthioalk is the length added by the two thioalkane linkers. It has been found by Park et al.55 that the end-to-end distance of a hybridized DNA is substantially shorter in AuNP clusters compared to DNA in water. This can be assigned to the requirement of multiple strand binding and/ or salt concentration effects. Using X-ray scattering, they found that each basepair contributes 2.5 Å to the end-to-end distance which yields d30bp ) 75 Å. The end-to-end distance of the two A15 spacers is substantially shorter for two reasons: first, unhybridized DNA has a substantially shorter persistence length than hybridized DNA and second, Adenine shows some adhesion to gold, so some back-folding of the spacer to the

Figure 2. Simulation steps of optothermal AuNP cluster heating: Right hand side: Starting from the empirical dielectric constant of gold taken form Johnson and Christy, a frequency dependent damping constant is determined to match size effects and chemical damping due to DNA functionalization. The dielectric constant is adjusted such that calculated Mie scattering sufficiently fits the experimental extinction spectra of dispersed AuNP in water. A unit cell of the cluster is then formed by considering both, the spherical functionalized AuNP and the water surrounding it. This yields an effective dielectric constant εeff of the simple cubic unit cell. The result is one scattering point dipole per unit cell of the cluster. In section 2.3 the extinction and absorption cross sections and the energy source term Q(r,t) of the cluster are calculated using the DDSCAT code. Left hand side: Effective thermophysical properties are provided in section 2.4. Finally, the material constants and the heat source term are both inserted into the heat transport equation to calculate time-resolved nanoparticle heating. For details see text.



AuNP surface may occur. Extrapolation of data which Park et al.55 found for A10 and A20 spacers allows to estimate 2dA15 ) 35 Å. Based on the same reference it is also possible to quantify the thioalkane contribution to the total length: 2dthioalk ) (16 ( 1) Å. From all these data a next neighbor distance of d ) 226 Å is obtained. As described above, a sc unit cell of length asc ) 207 Å contains the same density of AuNPs and will hence lead to the same results using the DDSCAT code as assuming a bcc unit cell with next neighbor distance d ) 226 Å. Next, an effective dielectric constant εeff for the whole AuNP cluster needs to be found which can be put into the DDSCAT algorithm (note that the DDSCAT algorithm originally expects a homogeneous medium). A simple Maxwell-Garnett type theory is too simple in this case.49 Instead, the lattice dispersion theory of Draine and Goodman is applied which relates the Mie polarizability of each (spherical) AuNP inside a unit cell to the polarizability of the whole (cubic) unit cell. An implicit term already including corrections for finite lattice spacing is given by56

RNP

3asc3(εeff - 1) 4π(εeff + 2) ) 3(εeff - 1) 2 1+ (b + εeffb2)(kd)2 - i(kd)3 4π(εeff + 2) 1 3

[

] (7)

with constants b1 ) -1.8915316 and b2 ) 0.1648469. A third correction term “S” in the original formula by Draine and Goodman56 was omitted here because the incoming light is polarized along a lattice plane resulting in S ) 0. Inverting eq 7 yields εeff. In general, the Mie polarizability should be used in the left-hand side of eq 7. However, for very small particles as in the present case (2rNP ) 10 nm) it is safe to use the Rayleigh polarizability

RNP ) rNP3

εfNP(ω) - εH2O εfNP(ω) + 2εH2O

(8)

where εH2O is the dielectric constant of water. 2.3.3. Numerical Results. Figure 4a displays the effective dielectric constants of a DNA linked AuNP cluster when eq 7 is equaled to eq 8 and inverted to yield εeff. The spectral position of the nanoparticle plasmon resonance is clearly observed, although the gold nanoparticles make up only 5.90% of the cluster volume. As a side note, one sees that the important convergence criterion for the DDA method, [|εeff|]1/2(2π/λ)aSC ≈ 0.25 < 1, is fulfilled.56 Inserting εeff into the DDSCAT algorithm yields the cross sections (eqs 3-5). They are evaluated for the specific example of a AuNP cluster of 600 nm in diameter as shown in Figure 4b. The calculated extinction spectrum (black line) is compared with experimental data from AuNP clusters. Experiments were carried out at two different temperatures, 15 and 45 °C, which are both well below the melting temperature of 54 °C and also below the onset of Ostwald ripening. In addition, Figure 4b shows the calculated absorption and scattering spectra. Scattering already takes about 1/3 of the extinction and only 2/3 is left for absorption at the excitation wavelength of 527 nm, in contrast to individual 10 nm AuNPs where scattering is absolutely negligible and the extinction and absorption cross sections are basically identical.41

Figure 3. (a) Comparison between the measured extinction of a solution containing unclustered d ) 10 nm AuNPs functionalized with DNA (dashed black line) and the calculated extinction cross section of d ) 10 nm gold nanoparticles, using the Johnson and Christy data for the dielectric constant and considering inhomogeneous broadening due to a 10% variation in particle diameter (blue line). The calculated extinction spectrum using the improved dielectric constant considering frequency dependent additional damping due to the small size effect and chemical damping is shown in green. (b) Real and imaginary part of the dielectric constant. Blue curves: Smoothed data from Johnson and Christy, green curves: fitted dielectric constants used to calculate the Mie extinction spectrum in (a), green line.

This already indicates that optothermal heating of large clusters can not be treated as a simple additive heating effect of an ensemble of 12 893 AuNPs, the number of AuNPs in a 600 nm cluster. More details will be given in section 2.5. 2.4. Effective Thermal Medium. As outlined in section 2.1, a AuNP cluster must be considered as an effective, homogeneous thermal medium, because the direct solution of eq 1 considering all individual AuNPs and the water (and DNA) inbetween is impossible with finite element solvers due to the large number of AuNPs.54 Consequently, averaged values for b| < R), and K(|r b| < R) must be found as effective F(|r b| < R), cp(|r thermophysical properties. For simplicity, we do not consider temperature dependencies of F, cp, and K inside the AuNP cluster and we neglect the resistivity of thermal transport across the gold/water interface. The latter assumption is valid because the retardation of heat flow across the gold water interface was found to be on the 100 ps time scale, even in the presence of organic molecules on the noble metal nanoparticle surface,40 while the pulse duration of the heating laser applied in our experiments was 260 ns. Let

4 πr 3 3 NP f) ) 5.90% asc3

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be the volume fraction of the sc unit cell that is occupied by the AuNP. Then the cluster density can simply be averaged by

F(| b| r < R) ) fFAu + (1 - f)FH2O

(9)

For the specific example of 10 nm AuNPs and a unit cell length of aSC ) 20.7 nm as determined in section 2.3.2 (Figure 1a), one finds F(|r b| < R) ) 2081.5 kg/m3. The heat capacity of the cluster is determined by averaging the heat capacity of gold and water (and assuming that the heat capacity of DNA is similar to that of water)

c(| b| r < R) )

cAuFAu f + cH2OFH2O(1 - f) F(| b| r < R)

(10)

For the specific example of Figure 1a one finds c(|r b| < R) ) 1963.5 J/(kg K). The effective thermal conductivity is calculated according to ref 57

1 + 2f K(| b| r < R) ) kH2O 1-f

KAu - KH2O KAu + 2KH2O KAu - KH2O

(11)

KAu + 2KH2O

For the specific example of Figure 1a one finds K(|r b| < R) ) 0.713 W/(m K). One might speculate that the tiny gold nanoparticles affect the thermophysical properties of the clusters only marginally and the material properties of plain water could be used. This certainly holds for sparsely dispersed gold nanoparticles in a macroscopic liquid droplet.35 However, the cluster density is more than doubled in the specific example

of DNA linked AuNP clusters, the specific heat capacity is reduced by 53% and the thermal conductivity is increased by 19% as compared to thermophysical properties of plain water. Additionally, one might argue that the precise lattice order of the cluster is unknown. However, we would like to point out that eqs 9-11 only depend on the volume filling fraction, but not on the details of the cluster’s crystallinity. Because only the filling fraction enters into eqs 9-11, the effective thermal medium description turns out to be as rigid against possible lattice disorder as the electrodynamic calculations turned out to be,54 as long as the density of AuNPs in the cluster is taken correctly. 2.5. Optical Energy Deposition in Micrometer Sized AuNP Clusters. The total optothermal energy deposited in a single AuNP illuminated by a laser pulse with temporally dependent intensity I0(t) is straightforwardly obtained by integrating over a full laser pulse.

WNP )

∫T I0(t)Cabs,NP(λex) dt

(12)

Cabs,NP(λex) denotes the absorption cross section of a single AuNP at the excitation wavelength. If a small number (some tens of) AuNPs with mutual distances much larger than the AuNP radius forms a cluster, then the deposited energy is very well approximated by simply multiplying the single AuNP result (eq 12) by the number of nanoparticles. This assumption is reasonable because the plasmon resonances of a few gold nanoparticles with mutual distances large compared to their radius do not couple strong enough to induce a noticeable spectral shift of the absorption cross section.39 Further, each nanoparticle extincts only a small amount of light so that the light intensity can be regarded as a constant across the entire small cluster I(t,x) ≈ I0(t). Finally, the scattering cross section is negligible for clusters of only some tens of AuNPs of 10 nm diameter. Using these assumptions, one can show that the temperature inside clusters of N AuNPs is given by34

T ) T0 + ∆TNP

rNP 2/3 N s

(13)

where T0 is the bath temperature, ∆TNP is the maximal temperature increase of a single AuNP hit by the laser pulse, and s is the average surface-to-surface distance between the nanoparticles. The number of AuNPs in a cluster of radius R is given by the division of the cluster volume by the volume of a unit cell. Hence, we can rewrite eq 13 by

T ) T0 + ∆TNP

Figure 4. (a) Effective dielectric constants of a unit cell of the AuNP cluster (black: real part, blue: imaginary part). (b) Simulated (black line) and measured extinction cross sections of AuNP clusters. The experimental data were taken at solution temperatures of 15 and 45 °C (blue and red line, respectively), both below the melting temperature. The diameter of the cluster in the calculation was assumed to be 600 nm. The calculated absorption and scattering cross sections are shown in green and yellow, respectively. At the excitation wavelength of 527 nm, absorption accounts for 65% of the extinction.

rNP 4π 2 3 saSC

2/3

( )

R2

(14)

This equation suggests that the temperature inside an optothermally heated cluster increases quadratically with the cluster radius. Two facts contribute to this quadratic behavior:34 First, the heat fluxes from different AuNPs add up and second, the light induced electric field inside a cluster is enhanced. These cooperative effects of optothermal heating of a AuNP cluster are included in eq 14, however, some important effects in large clusters such as DNA linked clusters of thousands or even ten thousands of AuNPs are not yet included. These effects are (i) a spectral shift of the plasmon resonances due to plasmon coupling effects, (ii) scattering which competes with absorption,



Q(r, t) ) Q0(t)exp[-kabs(z + √R2 - F2)]

Figure 5. (a) Cylinder coordinates used for calculating the spatial dependence of light absorption. (b) Simulations of the optothermally deposited heat in clusters of different sizes. The larger the size of the cluster, the more important is the shadowing effect. Light impinges from the left.

and (iii) shadowing of deeper lying AuNPs by AuNPs at the surface layers of the cluster. In the following, these effects will be considered. In order to solve the heat transport eq 1, the expression for the energy density Q(r,t), which is optically dumped into the cluster, is required. The total power absorbed by the cluster at each time is given by

PCL(t) ) I0(t)Cabs(λex)

(15)

This total power can also be calculated by integrating Q(|r b|,t) over the volume V of the AuNP cluster. Herewith, an optically homogeneous cluster (as it has been assumed by the cubic model) will show Lambert-Beer behavior, so that PCL reads (assuming cylindrical coordinates with the center of the coordinate system in the center of the spherical AuNP cluster of radius R, see Figure 5a)

PCL(t) )

∫V Q(b,r t) dV

) Q0(t)

∫V exp[-kabs(z + √R2 - F2)] dV (16)

whereby the absorption constant is given by kabs ) Cabs(λex.)/V. Equaling eqs 15 and 16 and executing the integral in (16) over the cluster volume yields Q0(t). Finally, the source term of energy density for eq 1 reads

(17)

Figure 5 b shows four examples of AuNP clusters of different radii. In these calculations, a Gaussian shaped laser pulse of 260 ns duration (2σ ) 260 ns), and Q0(max) ) 0.8 × 105 W/m3 is applied. The clusters are illuminated from the front-left side. In case of the small clusters 2R ) 75 nm a fairly homogeneous distribution of dumped optical energy is achieved, however, a small effect of shadowing of the rear-right side is already observed. This shadowing effect becomes more severe with evolving cluster size and even dramatic for a cluster on the micrometer scale. Keeping in mind that DNA linked AuNP clusters typically show cluster sizes up to the micrometer scale, it becomes clear that the shadowing effect must be taken seriously when optothermal heating is studied numerically. We are now ready to solve the heat transport eq 1 by inserting the effective thermophysical properties of the AuNP clusters (eqs 9-11) and the energy source term Q(r,t) as given by eq 17 and demonstrated in Figure 5b. This allows for time-resolved calculations of the transient heating of the whole cluster. In the remains of this section, numerical results are compared with the analytical calculations of Govorov et al.,34 given by eq 14. Figure 6 displays numerical results of the maximal temperature as a function of the cluster diameter. A heating laser pulse of 260 ns duration and I0 ) 2.5(kW)/(mm2) is applied and the maximally achieved temperature is shown. This maximal temperature develops near the center of the cluster and approximately 100 ns after the temporal peak of the laser pulse. The analytical result (solid line) and the numerical calculations (symbols) follow a quadratic dependence on cluster radius for cluster diameter up to approximately 150 nm. For larger clusters, however, a pronounced backwardness is observed in case of the numerical calculations. This is due to the following effects, which are not included in the analytical formula (14): First, the shadowing effect shields the AuNPs at the rear of the cluster from being illuminated (Figure 5b). Second, a substantial amount of the light interacting with the AuNP cluster is scattered rather than absorbed (Figure 4b) and finally, the plasmon resonance of the (large) cluster is red-shifted as compared to the plasmon resonance of single particles (Figure 1b), although the mutual distance between the individual AuNPs is large compared the radius.39 3. DNA Melting in DNA Bound AuNP Clusters 3.1. Experimental Extinction Transients. Prior to comparing the numerical results with the experiment, we briefly recapitulate how transient extinction signals look like in submillisecond optothermal DNA melting assays. More details are given elsewhere.24 The extinction at 650 nm (Figure 1b) is recorded using a red laser diode and a fast detector diode and oscilloscope. Recording is carried out while a 260 ns laser pulse of 527 nm wavelength hits the sample solution. A typical transient is shown in Figure 7a. Before the laser pulse arrives (t < 0), a reference extinction is recorded. A very fast and pronounced decrease of the extinction is observed upon arrival of the heating pulse. At this point we only want to note that this very fast signal is always observed, even in cases where the laser pulse energy is not sufficient to melt the DNA inside the AuNP cluster.24 This fast signal can be explained by a heat induced inflation of the AuNP cluster associated with a decrease of the extinction due to the transiently increased interparticle spacing. After this very fast dynamics, a decreased extinction signal is observed (Figure 7a). This is due to the disintegration

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Hrelescu et al.

Figure 6. Temperature of AuNP clusters after they have been stroke by a single 260 ns pulse of Ith ) 2.5 kW/mm2 as a function of cluster diameter. The analytical solution according to A. Govorov et al. is shown as solid line. Numerical simulations including shadowing and retardation effects as well as scattering losses are shown as black squares. Shadowing, scattering and retardation becomes important for cluster diameters larger than 150 nm, corresponding to 200 AuNPs of d ) 10 nm size.

Figure 8. (a) Calculated temperature distribution inside a AuNP cluster of 600 nm diameter, at different times. The cluster was illuminated with a 260 ns Gaussian laser pulse of 2.5 kW/mm2 power, centered at 400 ns. (b) Temporal transient of the temperature in the point of maximal temperature (solid blue line) and at the front of the cluster (dashed blue line). The laser pulse is given as a reference (dotted line). The horizontal dotted line represents the classical melting temperature of 54 °C. Figure 7. (a) Typical dExt/Ext signal after a heating pulse has hit the DNA assay. An ultrafast spike is followed by a microsecond dynamics. If the thermal energy is sufficient, the DNA double strands melt and the cluster disintegrates on a millisecond time scale. (b) The dExt/Ext signal at 0.5 ms as given by the red arrow in (a) versus the peak intensity of the applied optical pulse. At a given bath temperature TB the optical energy is either not sufficient to melt the DNA (sketched in c) and dExt/Ext ) 0, or IPeakis just sufficient to melt the DNA (sketched in d) or it exceeds the necessary power (sketched in e). At a specific intensity Ith the melting threshold is reached.

of the AuNP cluster after the DNA linkers have been molten by the deposited optothermal energy. For further reference, the change in extinction ((dExt)/(Ext)) is recorded 500 µs after the laser pulse was launched. Next, the cuvette is agitated in order to bring undissolved AuNP clusters into the focal area and the experiment is repeated, each time starting at the same bath temperature but applying laser pulses of different power. Figure 7b shows a plot of the dExt/Ext (t ) 500 µs) signal versus the applied optical pulse intensity. No dExt/Ext (t ) 500 µs) signal is recorded when the optical intensity is not sufficient to melt the DNA. This situation is sketched in Figure 7c. In these cases, the dExt/Ext (t ) 500 µs) versus time graph shows the ultrafast spike only, but dExt/Ext (t ) 500 µs) ) 0 for times larger than 50 µs.24 If, however, the laser power is sufficient to melt the DNA (sketched in Figure 7e), a dExt/Ext (t ) 500 µs) signal evolves. From Figure 7b one can easily deduce the threshold optical power Ith necessary to induce melting of the DNA. In the particular example shown in Figure 7, the melting threshold is determined to Ith ) 2.5 kW/mm2. Of course, Ith depends on

the initial bath temperature TB (it decreases with increasing bath temperature). It also depends on the AuNP cluster size (it decreases with increasing cluster size, though the dependence is highly nonlinear because of the shadowing effect (Figure 5b). 3.2. Dynamics of a Heating-Cooling Cycle. Figure 8a shows the spatial and temporal evolution of the temperature inside a AuNP cluster with a diameter of 600 nm. The Gaussian heating laser pulse is centered at 400 ns and shows a width of 260 ps (2σ). A bath temperature of 35 °C, and a peak power of 2.5 kW/mm2 was assumed in these calculations. Figure 8b displays the temporal profile of the temperature at the hottest point inside the nanoparticle and at the front surface of the AuNP cluster. The dashed horizontal line in Figure 8b denotes the classical melting temperature TCW ) 54°C which is indexed “CW” because the temperature in a classical melting assay is typically stepped by 1 °C per minute which is extremely slow compared to the fast optical heating regime inside optothermally heated AuNP clusters. The temporal laser pulse profile is shown for comparison as a dotted line. One finds that the temperature inside the cluster is far above TCW for roughly 1 µs. A comparison of Figure 5b (source term of optothermal energy) and the temperature distributions shown in Figure 8a shows that the hot region inside the cluster is located well inside the cluster while the region where optical energy is dumped most efficiently is on a thin cap at the cluster surface only in case of a 600 nm cluster. This indicates, that during the duration of the 260 ns heating pulse, a fast heat transport must occur. This leads to two effects: First, the surface of the AuNP cluster is cooled by the water bath already during the application of



Figure 9. Black squares: Experimental data for dExt/Ext versus IPeak, repeated from Figure 7b. Inset: Sketch of the temperature distribution inside the cluster. Red circles and line: Calculated temperature of the hottest spot inside the cluster as a function of IPeak. Orange squares and line: Calculated temperature at the cluster surface as a function of IPeak. The melting threshold intensity of 2.5 kW/mm2 corresponds to a calculated temperature of 127 °C inside the cluster and 86 °C at the surface.

the laser pulse and second, heat which is predominantly generated in the outer rim of the cluster facing the laser pulse (Figure 5b) is transported toward the center and is stored there for several 100 ns. As rule of thumb, one can calculate the time scale on which thermal energy is redistributed inside the AuNPs cluster by34

τ ) R2

c(|r| < R)F(|r| < R) k(|r| < R)

(18)

For the specific example shown in Figure 8, this yields τ ) 515 ns which is the same scale as the laser pulse duration of 260 ns. Hence, redistribution of thermal energy inside the cluster and thermal energy loss are effective already during the application of the 260 ns laser pulse. Consequently, the front surface is not the hottest area in the AuNP cluster at any time (Figure 8a), although the front surface catches the largest amount of optical energy (Figure 5b). Still, the redistribution within the AuNP cluster is not sufficiently fast to completely redistribute the thermal energy homogeneously throughout the cluster and a pronounced asymmetry of the most heated area inside the cluster remains, which means that the point of highest temperature is somewhere in between the front surface and the center of the cluster. 3.3. Microsecond DNA Melting. Solving the heat transport eq 1 allows now for the determination of the optically induced opt , as illustrated in Figure 9. The black melting temperature, TM squares repeat the experimental data from Figure 7b. Figure 9 additionally shows the calculated peak temperatures near the center of the AuNP clusters as a function of the applied laser power (red circles and red line). Additionally, the temperatures at the cluster surface facing the laser beam are shown in orange color as a function of applied laser power. The temperature inside the AuNP cluster at the threshold intensity Ith can now easily be deduced. It is seen, that T(I ) Ith) ) 126 °C inside the AuNP cluster, and T(I ) Ith) ) 86 °C at the cluster surface. At this point, it is not possible to decide whether the peak temperature inside the cluster or the surface temperature is the relevant temperature for microsecond DNA melting. If the temperature inside the cluster is the relevant temperature, then DNA denaturation would start inside the cluster, if however the surface temperature is more relevant, DNA melting would be initiated at the surface of the cluster. A good reason for the first scenario would be that DNA melts most rapidly at the area

Figure 10. Threshold laser pulse power Ith (see Figure 7) as a function of bath temperature. Red and black symbols: measurements performed with increasing or decreasing bath temperatures, respectively. No hysteresis is observed within the experimental error. For bath temperatures exceeding 54 °C (classical melting temperature of the chosen oligonucleotide sequence) the experiment can not be performed. However, close to 54 °C a finite pulse power of Ith ) 2 kW/mm2 is still required to melt the DNA. Extrapolating to Ith ) 0 kW/mm2 yields a hypothetical bath temperature of 101 °C where no extra optical power would be needed to melt DNA on a microsecond time scale.

of highest temperature. A good reason for the second scenario would be that AuNPs located at the surface are bound by a smaller number of DNA duplexes and are hence more easy to split off already at lower temperatures. Wherever DNA melting is first initiated, inside the AuNP cluster or at the surface, AuNP clusters obviously need to be heated beyond the classical melting temperature of TCW ) 54 °C in a submillisecond melting experiment. The results shown in Figure 9 display a series of experiments where the bath temperature was fixed at 35 °C. A similar series of experiments taken at a bath temperature of 15 °C yielded a threshold laser power of Ith ) 3.1 kW/mm2. Again, a comparison was made with numerical simulations. In this case, it is found that the maximal temperature inside the clusters is 130 °C and the temperature at the surface is 80 °C at Ith ) 3.1 kW/mm2 in good agreement with the previous results. This shows, that optically initiated microsecond DNA melting inside AuNP clusters is independent from the surrounding bath temperature. We want to point out that temperatures above 100 °C do not necessarily lead to the formation of water vapor on a nano- and microsecond time scale. The build up of a vapor bubble requires that the surface tension of the bubble in water needs to be overcome.10 As a consequence, explosive vapor bubble formation from superheated water sets in only above approximately 550 °C.58,59 If bubbles had formed in the present experiments, the scattering cross sections, and hence the extinction, would have increased dramatically.60 The opposite is observed in the experiments discussed in this paper: the application of the heating laser pulses is followed by a decrease of the extinction signal (Figure 7a). In the current case, the laser pulses are far too long and too weak to induce the formation of bubbles.61 Melting of the gold nanoparticles would require even more intense and/or faster laser pulses and can be excluded as well. In order to corroborate the finding that microsecond DNA melting requires temperatures in excess of the traditional “CW” melting temperatures, the threshold intensity Ith is plotted against the bath temperature TB. Figure 10 displays the results of several measurements carried out at different bath temperatures. Each time, the threshold intensity was determined as explained in Figure 7b. In order to avoid cluster-size effects (larger clusters require less optical power to induce melting), we avoided the Ostwald ripening effect in the preannealing temperature range39 and measured only up to 45 °C (Figure 1c). The red circles in

7410


Figure 10 are taken in a series of experiments with stepwise increasing bath temperature and the black squares are taken subsequently with stepwise decreasing bath temperature. No hysteresis effect is observed within experimental accuracy. The plot of Ith versus TB shows that the larger TB, the less excess optical energy is needed to initiate DNA melting. A good linearity is observed which allows for extrapolation to bath temperatures beyond the classical melting temperature of 54 °C. It seems that there is still a substantial amount of optical energy necessary to melt the DNA inside the AuNP clusters, in other words Ith . 0 at TB ) 54 °C. It is possible to estimate the temperature which is necessary to induce rapid melting of the 30 bp oligonucleotide (Figure 1a) using the data given in Figure 10. The simple question that needs to be answered is: how large must the bath temperature be such that already an infinitely weak nanosecond laser pulse is sufficient to melt the DNA. This bath temperature is, however, given by the extrapolation of the data to Ith ) 0. In this case, opt ) 101 °C (Figure 10), where the suffix “opt” denotes the TM optical melting temperature using 260 ns laser pulses. This optothermally induced melting temperature deduced by extrapolation of the Ith versus TB graph is just in between the two temperatures (maximal temperature inside- and temperature at the cluster surface) deduced in Figure 9 by calculating the temperature profile inside the cluster at the threshold intensity. All these results taken together show that the microsecond melting opt ) 100 ( 20 °C, well above temperature is in the range of TM the classical “CW” melting temperature of 54 °C. This can be readily explained by the following considerations: The temperature in a classical melting assay is typically stepped by 1 °C per minute which is extremely slow compared to the fast optical heating regime using pulsed lasers. In such a classical experiment, the DNA is always in thermal equilibrium with its surrounding. Dissociation and association rate constants depend both on temperature and at 54 °C dissociation starts to overwhelm association in the CW experiment.62 This is very different in heat-jump experiments such as the submillisecond DNA melting assay24 or ultrafast protein denaturation.10,63,64 As it has been discussed in section 3.2, the AuNP clusters store the thermal energy only for approximately 1 µs (Figure 8b). Hence, DNA melting needs to be induced on that short time scale. The only way to achieve DNA melting that rapidly is to increase the dissociation rate by increasing the temperature beyond the classical TCW.10,62,63 Optically induced temperature jump experiments on DNA have previously been carried out in aqueous solution without AuNP nanostoves and an infrared laser was used to optothermally induce DNA melting on a time scale of 50 ms.65 No increase of the melting temperature of molecular beacon type DNA was found in these experiments. This result and the results of the current contribution allow for setting limits for the melting rate of short oligonucleotides in the kinetic equilibrium. This rate must be larger than (50 ms)-1 and smaller than (1 µs)-1, which is also in accordance with earlier findings by Bonnet et al.66 4. Conclusions An oligonucleotide assay based on DNA linked AuNP clusters has been examined in detail. The AuNP clusters are optothermally heated by nanosecond laser pulses and rapid DNA melting takes place on a microsecond time scale. Subsequent to the DNA duplex dehybridization, a change of the extinction at 650 nm can be recorded on a submillisecond time scale due to the diffusive disintegration of the AuNP clusters. The temporal and spatial development of heat generation inside, and

Hrelescu et al. subsequent cooling of AuNP clusters is modeled by solving the heat transport equation numerically with finite elements. The energy source term in the heat transport equation is determined by calculating the absorption cross sections of large (100-1000 nm) AuNP clusters. A discrete dipole approximation is used and several effects characteristic for large clusters are taken into account: (i) a pronounced shadowing effect where the front lying AuNPs in the cluster shade the rear AuNPs, (ii) the spectral shift of the plasmon resonance due to the collective coupling of plasmon resonances in large clusters, and (iii) an increased amount of light scattering from the clusters as compared to dispersed AuNPs. Further, small size and chemical damping effects due to DNA functionalization has been taken care of on an empirical basis by fitting a dielectric constant for small, DNA functionalized AuNPs in order to achieve agreement between extinction measurements and calculated scattering cross sections obtained by Mie theory including inhomogeneous sizes variation of the AuNPs. Care has been taken to obtain effective thermophysical properties for the AuNP clusters. To the best of our knowledge, this work resembles the most detailed numerical survey of temperature transients inside DNA linked AuNP clusters to date. Though, the theory could be extended further: So far, we neglected the temperature dependence of the effective thermophysical properties of the AuNP cluster because in DNA melting assays the temperature ranges from 10 to 100 °C only, so that we decided to ignore temperature dependencies within this temperature range for the sake of limiting computational costs. Additionally, the heat transport equation is, strictly speaking, only valid as long as phase transitions do not occur. However, DNA melting is of course a phase transition. Therefore, it was tacitly assumed that the latent heat used for DNA melting is negligible compared to the heat capacity of the water inside the AuNP cluster, the same way it was assumed that the thermophysical properties of DNA are the same as those of water (or negligible). Simulations taking all these additional details into account are, however, beyond the scope this contribution. Two different techniques have been applied to determine the temperature which is sufficient to induce DNA melting on the short time scale of approximately 1 µs inside the AuNP clusters. Different to the “CW” melting temperature of TCW ) 54 °C, where the bath temperature is slowly increased, a melting opt ) 100 ( 20 °C is found for microsecond temperature of TM DNA melting. Hence, irradiation of DNA interlinked AuNP clusters with short laser pulses is not only an excellent tool for submillisecond DNA analysis but can also be used in DNA heat jump experiments in order to investigate the temperature dependence of DNA dissociation rates. We propose that the same technique is equally well suited to perform heat jump unfolding experiments with proteins in protein interlinked AuNPs clusters. Acknowledgment. We thank Anna Helfrich, Werner Stadler, and Stefan Niedermaier for excellent technical assistance, and Alexander Govorov, Alfons Nichtl, Dieter Heindl and Konrad Kürzinger for discussions. This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through SFB 486 and by the “Nanosystems Initiative Munich” (NIM), as well as the Bavarian Science Foundation. References and Notes (1) Ahmadi, T. S.; Logunov, S. L.; Elsayed, M. A. J. Phys. Chem. 1996, 100, 8053. (2) Perner, M.; Bost, P.; Lemmer, U.; von Plessen, G.; Feldmann, J.; Becker, U.; Mennig, M.; Schmitt, M.; Schmidt, H. Phys. ReV. Lett. 1997, 78, 2192.

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DNA Melting in Gold Nanostove Clusters - The Journal of Physical

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