Uptake quantification of gold nanoparticles inside of cancer cells using high order image correlation spectroscopy

: The application of gold nanoparticles (AuNPs) in cancer therapeutics and diagnostics has recently reached a clinical level. Functional use of the AuNP in theranostics first requires effective uptake into the cells, but accurate quantification of AuNPs cellular uptake in real-time is still a challenge due to the destructive nature of existing characterization methods. The optical imaging-based quantification method is highly desirable. Here, we propose the use of high-order image correlation spectroscopy (HICS) as an optical imaging-based nanoparticle quantification technique. Coupled with dark field microscopy (DFM), a non-destructive and easy quantification method could be achieved. We demonstrate HICS analysis on 80 nm AuNPs coated with cetyltrimethylammonium bromide (CTAB) uptake in HeLa cells to calculate the percentage of aggregate species (dimer) in the total uptake and their relative scattering quantum yield inside the cells, the details of which are not available with other quantification techniques. The total particle uptake kinetics measured were in a reasonable agreement with the literature.

Because the absolute quantification methods (ICP-AES, ICP-MS, TEM) are destructive and cannot be used for real-time live-cell imaging, it is desirable to further develop the existing optical imaging methods into one that is capable of measuring uptake quantity. So far, optical imaging methods have been used as intensity integration [37,41,45,47] or spectral integration [22,32] techniques to account for the relative uptake, but these techniques are limited for AuNPs due to plasmon coupling between particles, which may reduce/enhance detected signals leading to a distortion in the estimated overall number of particles. Scattering or luminescence intensity response of aggregates of plasmonic particles is neither proportional, nor functionally defined by the number of particles within [37], which makes accurate quantification extra challenging.
where δi(x,y) is intensity fluctuation of a pixel at x and y of an image, i.e., i(x, y) − i(x, y) with i(x, y) being the pixel intensity at position (x, y), and square bracket i(x, y) representing the pixel intensity average of the entire image. The significance of the spatial autocorrelation function is that average emitter number n p in a focal volume can be measured by the magnitude of autocorrelation function g(0,0), due to the properties of the Poisson distribution of emitter statistics inside a focal volume.
If there are more than one aggregate species in the system, then the high-order autocorrelation function can be used to extract the information on aggregates, defined as [61][62][63] The values of n and m are positive integers that determine the order of the correlation. Because the contribution from aggregate intensity is higher in g n,m (0,0), it becomes a function of aggregate concentration and one can build up a series of simultaneous equations to solve individual aggregate concentration. The first 6 expressions of the g n,m (0,0) function for a Gaussian focus are shown in Eq. (4) and (5). where α i is the quantum yield (or brightness) ratio of ith species to that of a monomer, and N i is the average number of ith species in the focal volume. R is the total number of species. For example, if there are two species (R = 2) and α 2 is known (i.e., quantum yield ratio of dimer to monomer) then g 1,1 (0,0) and g 1,2 (0,0) can be simultaneously solved to extract average monomer and dimer concentrations in a focal volume (N 1 and N 2 , respectively). Alternatively, if α 2 is unknown, then g 1,3 (0,0) or g 2,2 (0,0) can be further calculated from the image, meaning that there are three simultaneous equations to solve for three unknowns (N 1 , α 2 and N 2 ). These are shown in Eq. (6). This can be further extended to higher order equations if there are more unknown species concentrations [22,26].
It is important to note that Eq. (4) and (5) simply express g n,m (0,0) in terms of number density of predetermined constituent species (i.e., R), but do not determine which species it includes up to, i.e., up to trimer (R = 3) or up to tetramer (R = 4). This can be identified by the image intensity histogram. For low concentrations, it is expected that monomer and dimer numbers dominate other aggregates, hence it is reasonable to assume two species (R = 2). In applying HICS to images of AuNPs, various emission modes, such as scattering, luminescence or even harmonic generations can be utilised. For DFM images, scattering is used as the emission process, therefore α 2 is interpreted as scattering cross-section ratio of the dimer to monomer. Dimers of 80 nm AuNPs show increase in total scattering intensity (integrated at 400-700 nm) between 2 to 4 times that of a monomer, depending on the gap distance between the nanoparticles in the dimer (calculated using finite element method, data not shown).

Simulation of HICS
First, the validity of HICS was checked by analyzing simulated DFM images of randomly distributed AuNPs. Previously, Sergeev et al [63] extensively simulated and tested the validity of HICS for bimodal distribution of emissive species, i.e., monomer/dimer or monomer/ octamer, etc., and found that HICS is only accurate when the aggregate concentration is far lower than that of monomer, i.e., 2 orders of magnitude difference, N 1 >> N n . Here, we demonstrate an improvement in the validity range of HICS. Our estimation shows that it is accurate up to comparable concentrations of monomer and oligomer, but loses accuracy when aggregate concentration is simply higher than that of monomer, i.e., N 1 < N n . We also pay close attention to the relative concentration where HICS is deemed inaccurate, which has not been properly studied before.
Methodologically, we take a similar approach to the previous work by Sergeev et al [63], i.e., bimodal distribution of monomers and dimers, but take into account the different properties of the 80 nm diameter AuNP dimers. DFM simulation images for randomly positioned particles have Gaussian spots with radius of 5 pixels in a 256 × 256 pixels image size. For dimers the mean α 2 was 4 with a variable Gaussian spread with variance σ 2 , between 0 and 4 was allowed. Gaussian random noise was added on each pixel as a background. Figure 1 The HICS analyzed values of average monomers N 1 and dimers N 2 and α 2 from 200 simulated images are extracted using Eq. (3) to 5, and are plotted as points against the input values (lines) in Fig. 1(d), (e) and (f) for different N 2 concentrations, 0.001, 0.01 and 0.1, respectively. Gaussian noise background up to 50% of the monomer intensity could be successfully subtracted using the method by Petersen et al. [55] without affecting the extracted values of N 1 , N 2 and α 2 (see Methods section in the Supplemental document for more details of noise correction). More on the signal to background noise ratio (SNR) and the particle size is discussed below. Gaussian variation of α 2 up to ± 2 did not affect the results. Beyond these points however, results were heavily distorted. In each plot in Fig. 1(d), (e) and (f), N 1 is varied between 0.001 to 10. It is clear from the figures, input and output values match almost perfectly for N 1 ≥ N 2 . Such a good agreement is a marked improvement from the previous data [63], and could be attributed to an improved algorithm used in extracting the solutions from nonlinear simultaneous equations of Eq. (6). We utilized commercial numerical package (NSolve function in Mathematica 12, Wolfram) to extract the solutions.
However, for the case where N 1 < N 2 , output values fail to match the input lines (marked by grey area in Fig. 1(e) and 1(f)). In particular, N 1 is overestimated by almost 1 order of magnitude and N 2 is underestimated by half. Such deviation could be understood from the fact that high-order correlation function g n,m (0,0) is dominated by the oligomer contribution because of the factor α m 2 (m is the order of the image, ie., m = 2, 3, 4 . . . , Eq. (6)), which makes the contribution from monomer concentration N 1 insignificant and error-prone when N 1 < N 2 . In this region, two strategies can be taken to extract the concentration information. First, HICS can identify the dominant species concentration (N 2 in this case) as N 1 in the limit N 1 << N 2 , because the contribution from monomer is insignificant. This means that the monomer concentration extracted can simply be interpreted as the dimer species. This can be seen in Fig. 1(e) and 1(f), that the N 1 points (black squares) tend towards N 2 input (red line) as N 1 → 0. Simulation over 200 images in each data point showed that more than 80% of the time N 1 correctly extracted dimer concentrations. Second, g 1,1 (0,0) (or conventionally referred to as g(0) in ICS) can be an alternative measure of the dominant dimer concentration N 2 , as the correlation function is inundated by their contribution. This is represented as the green line and green square points (N p = 1/ g(0)), which tend towards the N 2 input (red line) as N 1 → 0. Both methods extract the dominant species concentration at the cost of neglecting the monomer species concentration. We shall use such method in estimating the total uptake of particles in HeLa cells in section 4, where the concentration of dimers frequently overtakes that of monomers. This bimodal simulation results demonstrate that HICS analysis can be an accurate measure of particle concentration on either situations of concentration limits (i,e., The results shown in Fig. 1 apply to any size of particle provided the scattering SNR is high. In reality, as the particle size gets smaller, the signal strength decreases hence the SNR. Generally, scattering cross section of a sphere increases to sixth power of particle diameter (∼ d 6 ) up to 80 nm particles [65]. If the SNR is ∼ 20 of the signal from monomer of 80 nm and this is assumed to be constant, then the minimum signal required is 10% of the signal of 80 nm monomer (assuming lowest detectable SNR is 2). The minimum diameter of particle d min that will be detectable then is where d ref is the reference particle diameter (80 nm in this case). This is equal to 54.5 nm. If the SNR increases to 100, the detectable size also reduces to 41.6 nm. Typical CCD camera SNR varies between 10 ∼ 20, therefore it is reasonable to limit the detectable size to 54.5 nm. However, this could be improved using enhanced detectors.

Experimental validation of HICS on random AuNPs
We further validate the accuracy of HICS analysis for randomly distributed low-concentration AuNPs on a coverslip glass for a non-cellular environment similar to the simulated images in Section 2. We use spectrum counting method to manually count the particles and compare the results to the HICS analysis to validate the method. The spectrum identification of nanoparticle dimers and aggregates is a well-established technique in DFM. Sonnichsen et al [66] used dimer scattering spectrum and intensity change to differentiate them to monomers, and Wang et al also showed the spectral shift of aggregates for their identification inside cells [32]. This is a useful method to cross-check the aggregate numbers but is not a replacement for HICS because of the low throughput of its procedure. Briefly, AuNPs of 80 nm diameter coated with cetyltrimethylammonium bromide (CTAB) were purchased from NanoSeedz Ltd (NS-80-50, Hong Kong). AuNPs were diluted, then drop-cast and spincoated on a coverslip glass. We used commercial dark-field microscopy (Nikon Eclipse Ti-S and Nikon DS-Filc colour CCD camera) for imaging and a coupled spectrometer (SpectraPro 300i, Acton Research) for scattering spectroscopy. We selected a square region where only monomers and dimers are present for the HICS analysis. Once the images were taken, noise was subtracted and filtered for the HICS processing. Monomer and dimer spot numbers in the images were counted manually using the spectrum counting method. These are easily identified in the image due to their monomodal scattering intensity and distinct colours (SPR peak at 550 nm for monomer, 600 ∼ 700 nm for dimer). Monomer number dominated the image (∼ 80% of the spots), and the rest of the spots were identified as aggregates. Dimers have their total intensity between two to four times that of monomers (i.e., 2 < α 2 < 4) with yellow to red colour. Details of the procedures are shown in Methods section in the Supplemental document. Figure 2(a) shows a typical DFM image of randomly distributed 80 nm AuNPs where green particles are identified as monomers and orange-red spots are identified as dimers or aggregates. Figure 2(b) and (c) illustrate typical scattering spectrum of a monomer (b) and a dimer (c) measured by the spectrograph. Matching theory curves are overlaid, Mie Theory [67] for monomer and finite element method (FEM, COMSOL Multiphysics) simulation for the dimer with a gap of 7 nm in air (polarization in dimer axis). Scanning electron microscopy (SEM) images of a monomer and a dimer from the sample are also shown in the inset. The red-shift of plasmon peak is observed for dimers due to plasmon coupling [68]. Good agreement between theory and experiment is seen for both cases. In addition, dimers show an increase in the total scattering intensity, between 2 ∼ 4 times that of a monomer. Based on the spectrum measurement, monomer and dimer number could be counted from the image (spectrum counting method). Counting histogram of monomers and dimers from SEM images of larger area is shown in Fig. 2(d), which shows ∼ 20% of dimer number to that of monomer. This matched well with the spectrum counting method. Comparison between HICS analysis and spectrum counting method of total 50 images for (e) monomer number (N 1 ), (f) dimer number (N 2 ) and (g) scattering ratio dimer/monomer α 2 in the images. The red line is a guide to the eye for matching spectrum counting method to HICS analysis. Left (right) side of the red line means HICS analysis is underestimating (overestimating) the counting result.
We performed HICS analysis on the DFM images and compared with the spectrum counting method. Figure 2(e), (f) and (g) show the comparison for monomer, dimer number and α 2 from 50 DFM images. These numbers are all translated from N 1 , N 2 and α 2 extracted by HICS, and the spectrum counting method. The figures show reasonable agreement between the two methods. Typical DFM images had N 1 on the order of 0.01 (particles per beam area), and N 2 on the order of 0.001 (particles per beam area), which correspond to simulation ranges for N 1 > N 2 in Fig. 1(d), where the accuracy of HICS is high. Some underestimation of N 1 by HICS analysis in Fig. 2(e) (i.e., left side of the red line) is attributed to the monomer intensity variation, which tends to reduce the particle number estimation as the variation increases [69]. In order to see the effect of varying the α 2 , which incorporates monomer and dimer intensity variations caused by size distribution, a HICS analysis was conducted on simulated images created with a Gaussian distribution of α 2 with mean value at 3 and standard deviation of 1 (containing most of the dimer cross section variation within 2 to 4). The number variation was less than 1% for N 1 , around 10% for α 2 and around 20% for N 2 .

HICS analysis on the cellular uptake of AuNPs
After successful simulation and experimental validation, HICS analysis is extended to study cellular uptake of AuNPs in HeLa cells. Since destructive techniques (ICP-MS, ICP-AES) can only be used for ensemble averaging of cells in which single cell uptake information is buried, it is not ideal to use these techniques for correlated comparison. Instead we use spectrum counting method to build histogram of dimers and monomers on selected cells and use it to support the HICS analysis.
Briefly, HeLa cells (human cervical carcinoma) were cultured in a microslide chamber, and then a diluted solution of 80 nm spherical AuNPs coated with CTAB (NS-80-50, NanoSeedz Ltd) was diluted and added to the cultured HeLa cells and incubated for desired amount of time (0.5, 2, 4, 6, 8, 10, 24, and 48 hours), before fixing and washing. CTAB is cationic (ζ-potential ∼ +40 mV), therefore are favorably taken up by negatively charged HeLa cell membrane [45]. Confocal laser scattering microscopy (CLSM) was used to check the particle internalization (See Fig. S1 in the Supplemental document for the details). DFM, described in section 3 was used to image the cells with AuNPs for the HICS analysis. Full details of the cell preparation are provided in the Methods section in the Supplemental document. Figure 3 shows selected DFM images of AuNPs incubated in HeLa cells for different incubation times. It is clear that more particles are internalized into the cells as the incubation time increases. Higher-order aggregates of AuNPs could be observed in the cells, especially for longer hours of the uptake process. While HICS can be extended to identifying these aggregate species, in practice it requires a higher dynamic range and SNR of the image detectors because the quantum yield ratios α i for aggregates vary wildly, for example between 3 ∼ 9 for trimers, and even higher range for tetramers or pentamers. A high dynamic range generally reduces the SNR for monomers because to accommodate a high intensity variation, monomer signal enhancement must be sacrificed. For our case of using CCD detectors, optimizing the SNR meant that any aggregate signals higher than dimers were removed from the HICS analysis. Perhaps a point detection confocal microscopy approach using avalanche photodiodes with a dynamic range of ∼ 10 6 could accommodate the wide variation in intensity while keeping the SNR high.
To gauge relative concentrations of monomers and dimers inside the cells, hence be able to determine which high-order correlation functions to use in extracting parameters, we again utilized the spectrum counting method to count monomers and dimer numbers in 5 randomly selected cell images and built histograms for each incubation time. This is shown in Fig. 4. It can be seen that up to 6 hours of incubation, monomer number is larger than dimer number in the images, i.e, N 1 > N 2 . As shown by our simulations in section 2.2, for this relative concentration of monomers and dimers, HICS can be used to extract N 1 , N 2 , and α 2 with accuracy level of maximum 10% error. Beyond 6 hours, however, dimer number is larger than monomer i.e, N 1 < N 2 . In this case, 1/g 1,1 (0,0) is a better indicator of the dominant species number, dimers. We shall therefore take the g 1,1 (0,0) values in estimating the total number of dimers. The variation of α 2 in the histogram is between 1.7 and 2.5 depending on the hours, and the background noise level is less than 10% of the monomer intensity, which are within the allowed limit for HICS analysis.
The actual HICS analysis on 25 DFM cell images per data point is shown in Fig. 5. In Fig. 5(a), average monomer and dimer numbers in cells, and in Fig. 5(b), α 2 with respect to incubation time up to 6 hours are shown. It is interesting to note that as the incubation time increases, number of dimers increase while the number of monomers peaks at 4 hours and then stay steady. α 2 stays consistently within 2.6-2.7 range, which means that the coupling distance is ∼ 20 nm (FEM simulation). These numbers match reasonably well with the histogram in Fig. 4 and demonstrate the utility of HICS analysis.
In Fig. 5(c) beyond 8 hours of incubation, g 1,1 (0,0) values are extracted from 25 images (instead of g n,m (0,0) for the reason discussed above), and used it to estimate the total number of dominant species, dimers. It shows that the uptake is more or less saturated beyond 10 hours. Overall number of AuNPs are estimated from these analyses and plotted in Fig. 5(d), where the increase in uptake happens mostly in the first 10 hours, and then stay steady up to 48 hours. The large variation in total number of uptake particles per cell (Fig. 5(d)) demonstrates that individual cells behave differently in uptake of particles, which could be due to different uptake kinetics, different nanoparticle capacity or a combination of both.
The uptake half-life was measured to be 6 hours, with the uptake rate of ∼ 17 particles per hour. The average number of particles at steady-state was ∼ 250 at 48 hours. As a point of reference Chithrani et al. previously reported, for 74 nm citrate coated AuNPs at concentration of 0.02 nM, uptake half-life of 2.24 hours at the uptake rate 417 particles per hour [34,35]. The maximum uptake reported was ∼ 2988 particles per cell. Wang et al. reported 70 nm AuNPs coated with ssDNA, with a maximum uptake of ∼ 128 particles per cell [37]. Since the experimental conditions of these reports were not identical to our current study it is impossible to directly compare these values to the current results. Differences between the reports are in fact real, and a reflection of actual differences in size and concentration of the particles [34], and ligand molecules [45]. Lower uptake half-life and slower uptake rate observed in our experiment are attributed to much lower concentration in our solution (∼ 0.0076 nM), but the cationic nanoparticles (CTAB coating) improves the uptake. The saturation pattern of the uptake kinetics is nevertheless consistent with the literature report [34,35].
The current study reveals the percentage of dimerization of AuNPs during the uptake. It is clear that dimers are present at the early stages of uptake (30 mins) and the percentage of it increases from 25% (30 mins) to nearly 100% (48 hour) indicating that dimerization or oligomerization become more prevalent form of nanoparticles within the cells as the incubation time increases. Receptor-mediated endocytosis producing vesicles that contain aggregates of AuNPs are reported previously [35] and simulation showed cooperative uptake process by forming aggregates [70]. However, the percentage increase in dimers or aggregates with respect to incubation time has not been reported previously and it may indicate that simple charge-driven uptake could also drive the aggregation of particles inside the cells in an effort to maximize the uptake. Further studies in size, functionalization and concentration will be needed to understand the observation. Such details of uptake are not easily observed in other methods and the current HICS methodology is clearly advantageous.

Conclusions
A new uptake quantification method based on non-destructive optical intensity high-order moment analysis is proposed and demonstrated. We validated the HICS methodology for computer simulated DFM images of AuNPs and identified a suitable range of relative aggregate species concentration for HICS validity. Generally, if monomeric species dominate aggregate species, HICS can be used with high accuracy, but if aggregate species dominate the monomeric species, g 1,1 (0,0) value can be taken to calculate the dominant aggregate species concentration. HICS is then further validated experimentally in non-cellular environment, where a good agreement in spectrum counting method and HICS method was observed. Finally, HICS was applied and demonstrated to DFM images of CTAB coated 80 nm AuNPs in HeLa cells, incubated for various hours up to 48 hours, showing a similar uptake trend of overall number of particles. More specifically, extra information such as percentage of dimerization in incubation, or the aggregate quantum yield ratio could be extracted, which was previously not possible with the destructive methods. Increase in percentage of dimers with respect to incubation hours indicate that oligomerization and aggregation is a preferred form over monomeric form, while the cell is driving its uptake to its maximum.
While the HICS method is demonstrated for monodispersed spherical particles, its extension into different shapes for the particles, such as nanorods, could form an important future work, as more anisotropic particles become used as drug delivery agents. Their variation in coupling geometries will cause a large distribution in α 2 , and since the current form of HICS does not incorporate a variation in quantum yield this would require a different formulation to the current form. Petersen previously applied a distribution of quantum yield to the theory of ICS [69] and so this could be incorporated into HICS theory in the future. This would be highly beneficial in counting multiple nanoparticle population and their numbers inside cells.
Funding. Australian Research Council.