We demonstrate a single molecule detection approach to further extend the detection limit of correlation spectroscopic techniques through the Second Harmonic Generation Correlation Spectroscopy (SHGCS). SHG signals with high signal-to-noise ratio (SNR) were obtained from Barium titanium oxide, BaTiO3 (BTO) nanocrystals (NCs) upon excitation by a femto-second laser fitted to the scanning confocal bench. The fluctuation of SHG signals from BTO NCs in transparent and turbid media was examined and their diffusion time and particle concentration were evaluated by autocorrelation. Proof-of-concept measurements indicate that water-dispersed BTO NCs at different concentrations yield an average diffusion time of 6.43 ± 0.68 ms and the detection limit of SHGCS was found to be at 814 ± 41 fM, approximately 100 folds below the detection limit of fluorescence correlation spectroscopy (FCS). The dynamics of BTO NCs was demonstrated in serum with high SNR and selectivity to show its potential applicability in biomedicine. High SNR and the sub-picomolar detection limit positions SHGCS as an excellent technique for ultralow single particle or single molecule experimentation in a complex medium.
© 2013 OSA
Fluorescence Correlation Spectroscopy (FCS) is a single molecule technique with demonstrated applicability to provide significant insights on diffusion dynamics, chemical thermodynamics, and kinetics of interaction [1–10] of biomolecules in confined environments. The essence of this approach is to detect fluorescence fluctuations of molecules diffusing through a focal volume in a femto liter volume. Combined with confocal microscopy, FCS provides information on concentration, diffusion time, and binding constants of diffusers at the single molecule level. Since its invention in the 1970’s [11,12], extensive efforts have been undertaken and several refinements have been proposed to improve the optics and data acquisition components to maximize the SNR and expand the applications. By cross-correlating signal fluctuation from two diffusing species, Fluorescence Cross-correlation Spectroscopy (FCCS)  has been proposed to examine interactions between two or more molecules. Scanning/probe FCS [13,14] and total-internal-reflection FCS (TIR-FCS)  have also been proposed to incorporate whole system analysis as well as in the analysis of selected optically active regions to extend the detection range to micro/milli Molar scales.
However, some limitations compound traditional FCS when probing ultralow concentrations (< 100 pM). First, the photon stability and cytotoxicity of fluorophores, such as fluorescent dyes , fluorescent nanoparticles (NPs) [16,17], and quantum dots , pose some constraints on stability. When probing ultra-low concentrations, high excitation power is frequently required to obtain high fluorescence emission rates (counts-per-second per molecule), but photobleaching or blinking effect of fluorophores could interfere with the fluorescence fluctuation arising from the diffraction limited diffusion dynamics that might affect the SNR. Second, the background signal due to autofluorescence will interfere with the fluorescence signal, especially in biological fluids such as serum or blood and can easily overwhelm the signal from fluorophores. Correlation spectroscopic methods that have the potential to detect targets at ultra-low concentrations amidst a turbid background will have significant impact in in situ biodiagnostics.
In this report, we propose a Second Harmonic Generation (SHG) Correlation Spectroscopy (SHGCS) for label-free monitoring of the diffusion dynamics of structural components with second-order nonlinearity. In this proof of concept study, we replace the fluorescent probes with barium titanate, BaTiO3 (BTO) (nanocrystals, NCs) that can generate a second harmonic wave under ultra-fast laser excitation at low powers, to develop SHGCS for potential applications in biology. SHG [19,20] can be construed as an optical nonlinearity resulting from the intrinsic asymmetric structure, where the dipole is proportional to the square of the incident electromagnetic field. SHG materials emit photons with energy doubling of its incident counterpart. When the phase-matching condition is fulfilled, SHG materials can generate coherent, non-bleaching, non-blinking signals at high emission efficiency  (which can reach 90%) with a high SNR (SHG emission spectrum can be narrowed to within 10 nm). Typical inorganic crystals , such as barium titanate (BTO), lithium niobate (LiNbO3), and lithium triborate (LiB3O5) are used to generate second harmonic light. Some biological materials, such as collagen, microtubules, and muscle myosin, are also good candidates for SHG [22–24] signal monitoring. The Second Harmonic Imaging Microscopy (SHIM) has been used to image collagen and membrane structure in live cells . Interesting applications using amphiphilic porphyrins as probes for SHIM [25,26] have also been investigated. Few inorganic materials have also been used as probes for bio-imaging. Hsieh etc. utilized BaTiO3 (BTO) nanocrystals to realize regular and holographic SHIM [27,28]; recently Pantazis extended the application of BTO nanocrystals for in vivo imaging . Significant efforts in biological imaging using SHG have also been expended; however, none address the implementation of SHG in the context of correlation spectroscopy except the recent report on realizing nonlinear correlation spectroscopy via high laser power (>200 mW) and small numerical aperture (N.A. = 0.22) objective with large size (700 nm polystyrene spheres) particles .
In this work, we utilize BTO NCs as SHG probes to demonstrate second harmonic generation correlation spectroscopy (SHGCS) in a small focal volume (~femto liter) and to provide a theoretical and experimental basis for this concept. Spatial and temporal diffusion behaviors are observed from the experiments at ultra-low concentration with high SNR.
To derive a basis for SHGCS, we start from the SHG signal fluctuation calculation within a small detection volume. SHGCS detects the fluctuation of the total SHG signal, H(t), which is generated instantly without any lifetime delay under ultra-fast (~femtosecond) laser excitation and proportional to the number of nanoparticles N(t), as a function of time, t. H(t) fluctuation occurs as a function of the number of molecules N(t) diffusing in the focal volume. In our work, relatively low concentration, for example, sub-nanomolar (~10−10 M) concentration was considered to assure single diffusers.
The temporal auto-correlation function under a constant laser excitation, can be defined by,4]. However, SHG signals are transient and stable enough for hours, thus in the SHGCS, the optical property of the diffusing SHG probes do not change when diffusing through the focal volume. Therefore consistent two-dimensional autocorrelation function can be derived as,Eq. (2) to the autocorrelation data, we can obtain the diffusion time as well as the concentration of molecules fromwhere is the effective focal volume. In our experiments, we set this value to 3.05 fL after calibrating with Rhodamine 123 .
3. Materials and methods
SHG material, Tetragonal structured BTO NCs, was gifted from Prof. Paul Bowen (Swiss Federal Institute of Technology, Lausanne, Switzerland) . The asymmetric lattice structure ensures high efficiency of the second harmonic wave generation. Dry BTO NC powder (0.01mg/100ml) was dissolved in water and the solution sonicated for about 20 minutes to obtain mono-dispersed particles, and then filtered by a 0.2 um-pore membrane three times. Cover glass was immersed in aqua regia solution overnight to attain an ion-free surface and washed with nanopure water, and dried with Argon gas before spin-coating the coverslips with BTO NCs. SHG images and correlation spectroscopy data collection were obtained based on the experimental setup detailed below.
The SHG imaging and correlation spectroscopy apparatus was constructed based on a confocal microscopy bench (Fig. 1). A Chameleon Ultra Ti-Sapphire tunable laser (Coherent Inc., CA.) operating in the 690-1020 nm wavelength range was utilized as the excitation source. The pulse width of the two-photon laser beam was set to 140 fs, the repetition rate was 80 MHz and the output laser power was tunable in the 0-2 W range using a tunable neutral density filter. In our experiments average laser power used was 0.64 mW, resulting in 8.93 GW/cm2 in laser intensity; while in ref , mean laser power was greater than 200 mW, which equals 107 GW/cm2 in intensity; and for the regular two photon FCS, excitation laser intensity is usually more than 100 GW/cm2. The modulated laser beam is expanded and then delivered by a water-immersion objective, OLYMPUS UPLANAPO 60X /1.20 (Olympus Inc.), into an inverted microscopy, Olympus IX71. Although the SHG signal from the traditional second order bulk nonlinear crystals is forward directionally favored, due to the nano-sized crystals and asymmetric morphology, the forward and backward signals are both favored for BTO NCs. In this apparatus, SHG signal was collected using the same objective in the backward detection mode, a 50 um pinhole was used to reject the background noises and the SHG was filtered using appropriate band pass filters before redirecting the signals into single photon avalanche photodiodes (SPAD) (SPCM-AQR-14, PerkinElmer Inc.).
SHG signal was collected using the time-correlated single photon counting (TCSPC) mode (Time Harp200, PicoQuant GmbH Berlin, Germany), and fitted with a single exponential function using the SymphoTime software (version, 5.13, PicoQuant).
SHG microscopy of BTO NCs on cover slips under femtosecond laser excitation is shown in Fig. 2 from different band-pass filters. The wavelength of the irradiated laser beam was set at 880 nm; therefore the theoretical wavelength of the generated SHG signals accordingly should be ~440 nm. In our experiments, considering the high efficiency of SHG, and the single photon counting module used in measurements, we set the laser power at the focal plane as 0.64 mW to avoid detector saturation. The emission filter used for SHG is 460-50 (Chroma), where 460 is the center wavelength with 50 nm as the open range for the filter. Figure 2(c) is the image of BTO NCs on cover slip, where a three-particle cluster is illustrated. A cross sectional distribution of the SHG imaging in Fig. 2(c) is illustrated in Fig. 2(b) and fitted by Gaussian peaks. Gaussian peak fitting indicates that the half width-half maximum (HWHM) of each peak is around 250 nm, which is almost at the diffraction limit of the 440 nm light. TEM images of BTO nanocrystals, Fig. 2(a), clearly show that the size of BTO nanocrystals is in the range between 30 nm and 100 nm, beyond the diffraction limit of the 440 nm light. Furthermore, the excitation intensity, and the SHG intensity will follow the relation, as shown in Fig. 2(b) (inset), the slope of with respect to is around 2, confirming the generation of the second harmonic signal.
Except for the 460-50 filter which is used to collect the SHG signal, other filters were also used to check the spectrum and high SNR of SHG. Three other different band-pass filters, 400-40, 480-10, and 520-40 (Chroma) were used to obtain scanning images. The center wavelength of these filters was 400 nm, 480 nm, and 520 nm, with band pass widths of 40 nm, 10 nm, and 40 nm, respectively. As shown in Fig. 2(d)-2(f), minimum SHG signal can pass through these filters, with intensities three to four orders of magnitude less than the SHG signal. A point to note here is that, after the signal passes through the 400-40 filter a small portion of the SHG signal remains, which yield a maximum of 4 counts/ms. In theory, the SHG signal should be in the close vicinity of twice the excitation wavelength, however, due to the relatively large size of BTO nanocrystals, which are about 30-100 nm in effective diameter, the scattering effect would be efficient enough to couple with the second harmonic generation, namely the second order hyperscattering effect, which can broaden the region of second harmonic generation .
Based on the analysis of SHG imaging, it is easy to conclude that SHG signals can be collected with high efficiency, with no saturation at a high SNR. The maximum emission of BTO NCs in Fig. 2(c) is ~1100 counts/ms, while the background counts is only 0.200 counts/ms, indicating that the SNR of SHG can reach up to 10000. Although much less signal is detected 20 nm away in the spectrum (Fig. 2(d)), the SHG signal is narrowed around 440 nm, which can be easily selected by signals from fluorophores when mixed together. Thus SHG and fluorescence spectroscopy could be integrated for imaging/sensing as a dual-mode technique. Furthermore, the high emission efficiency and SNR of BTO NCs shows that the BTO nanocrystals to be an ideal tool for performing SHG correlation spectroscopy in the single molecule realm.
Due to the unique optical properties of BTO NCs, it is easy to obtain well-shaped correlation curves from SHGCS. In SHGCS measurements, the signal collection time from the detector is set to 2 minutes for correlation analysis; the focus points are set to measure at a depth of 30 um in solution and SHG signal is collected backwardly by SPAD with respect to time. Figure 3 shows the time-traced SHG signals and correlation curves from BTO NCs at the sub-nanoMol to sub-picoMol concentration range.
By correlating the time-traced SHG signals in Fig. 3(a)-3(e), we can obtain an auto-correlation function of SHG signals, shown in Fig. 3(f)-3(j). By fitting these experimental curves using Eq. (2) (solid red line in Fig. 3(f)-3(j)) one can estimate the diffusion time and average number of nanocrystals in the focal volume. It should be noted that the current theoretical model cannot perfectly fit the correlation curve, which can be attributed to two major reasons; one is that the particle size variation can lead to the distortion of correlation curve, since the size of BTO NCs is around 30~100 nm, and the hydrodynamic diameter is about 57.4 ± 3 nm from Einstein equation (Boltzmann constant; T, temperature;viscosity of the solvent; hydrodynamic radius); the other reason is that the gradient force from the excitation laser can induce a bias on the diffusers, although it is difficult to “trap” the nanocrystals. Theoretical fitting indicates that diffusion times of BTO NCs in water solutions at different concentrations are similar, and the estimated value was 6.43 ± 0.68 ms; and the estimated concentration of BTO NCs at the different levels were 23.8 ± 5.53 pM, 13.7 ± 3.08 pM, 4.96 ± 0.88 pM, 1.98 ± 0.55 pM, and 0.81 ± 0.04 pM, respectively (Fig. 4). The estimated concentrations are in good agreement with the experimental concentrations, which are 25 pM, 12.5 pM, 5 pM, 2.5 pM, and 0.5 pM respectively. The concentration level can be directly obtained from the time-traced SHG signals in Fig. 3(a)-(e). The number of BTO NCs passing through the focal volume decreases with concentration. At a concentration of 0.5 pM, less than 10 nanocrystals pass through the focal volume within 2 min. However, upon further decreasing the BTO concentration to beyond 100 fM, the number of BTO NCs in the focal volume decreases, while the detected concentration from theoretical fitting did not change, at this point the noise begins to influence the signal from nanocrystals, limiting the system to higher amplitude values in the correlation curve. This indicates that the detection limit of SHGCS can be extended to hundreds of femto Molar, a much smaller than the regular value of dyes or nanoparticles observed from FCS measurements.
To further illustrate the robustness of SHGCS, the diffusion dynamics of BTO NCs was demonstarted in a turbid media with high selectivity. The dynamics of BTO NCs were investigated in fetal bovine serum (Atlanta Biologicals, GA), shown in Fig. 5(a)-5(c). The time-traced SHG intensity from BTO NCs in Fig. 5(a) shows that a signal with very high SNR can be recorded against the serum background. It should be noted under 880 nm ultrafast laser illumination, that high fluorescence from serum can be recorded in the wavelength range 550-700 nm. However, the use of the emission filter located at half the wavelength of 880 nm will prevent interference from media fluorescence and enable the acquisition of SHG signals for estimation of the diffusion time of BTO NCs in serum at different concentrations (Fig. 5(b), (c)). As a control for SHGCS, the dynamics of Alexa 488 in serum was investigated at different concentration by two photon FCS (Fig. 5(d)-5(f)). Under the same laser irradiation, serum can provide similar fluorescent intensity as a 10 nM Alexa 488 (Fig. 5(d)) in the wavelength range 500 nm-540 nm. From autocorrelation, the diffusion time for autofluorescing serum molecules was 0.3243 ± 0.05ms. The diffusion time of pure Alexa 488 in water was about 0.046 ± 0.002ms, however when investigating the dynamics of Alexa 488 in serum, the viscosity and background noise of serum molecules will dominate the correlation curve when the concentration of Alexa 488 is decreased (Fig. 5(e), 5(f)). Due to the narrow emission band of SHG signals and minimum fluorescence background in the emission band, SHGCS can provide unique selectivity to monitor SHG material/molecules in a turbid media.
Another key aspect of the experiment is the observation that SHGCS does not give rise to triplet states, thus the conventional triplet state dynamics observed in fluorescence correlation, does not exist. In our experiment, rhodamine 123 at 5 nM concentration was used as a control to compare FCS and SHGCS results. In the derivation of FCS theory, there is an assumption that fluorescence signals from molecules diffusing through the laser focal volume is unaltered. Although average fluorescence information is obtained from these diffusing molecules for FCS, when single molecule experiments are performed, photobleaching and triplet state transitions of the diffusers will affect the autocorrelation curve. When analyzing the fluorescence dynamics of diffusing molecules through a confocal limited spot, the emitted fluorescent photons are from radiative electron transitions originating from singlet excited state S1 to ground state S0, shown in Fig. 6(a). For most fluorophores, a triplet excited state T1 exists so that some electrons on S1 can easily transit to T1, while the transition between T1 and S0 is quantumly forbidden, thus longer time is needed for electrons at T1 to relax back to S0. Usually the time needed for transition between S1 and S0 is a few nanoseconds (Fig. 6(b)), usually referred to as the fluorescence lifetime. A single exponent decay fitting of the time-correlated single photon counting (TCSPC) data indicates that the lifetime of rhodamine 123 is 4.04 ns. While time in the microseconds scale is required for the T1-S0 transition, during which the fluorophore remains in the ‘dark’ state, and in the correlation curve a triplet dynamics effect appears, as shown in Fig. 6(c). However, this ‘triplet dynamics’ does not exist in the SHGCS due to the transient SHG emission, as shown in Fig. 6(a) and 6(b). Due to the coherent and phase-matching properties, lattice relaxation is not necessary (intra-state transition kintra in Fig. 6(a)) to compensate for the momentum mismatching during the inter-state transition k21, therefore no time is needed for electrons to relax back to the ground state. Thus no lifetime is observed expect for the instrument response time (Fig. 6(b)). Compared to FCS, SHGCS can provide a better explanation of diffusive behavior of nanoparticles in solutions under turbid conditions or when significant autofluorescence exists, because SHG signals are stable and intense, hence accurate estimation of concentration and diffusion times of the target species is possible.
Our experiments indicate that SHG using BTO NCs enabling a SHGCS technique offers exciting possibilities in turbid deep tissue and in vivo imaging and detection because of its strong signal in addition to the excitation wavelength which is in the range between 700 nm and 1000 nm. Therefore SHGCS could be an excellent tool for detecting proteins in ultra-low concentrations and even single particle detection. Besides, when functionalized with relevant biomolecules, for example, antibody targeting specific proteins in blood or specific cell surface markers, the SHG BTO probes can potentially be used to study targeting of specific cells or delivery of drugs in in vivo models.
In summary, we propose a second order harmonic generation correlation spectroscopy for monitoring subpicomolar concentrations. Due to the coherent property of SHG, the signal generation efficiency is high and so is the intensity. In our experiments, BTO nanocrystals were used as signaling probes and its diffusion characteristics in water was studied from the innate SHG signal. Theoretical fitting of SHG signals indicates that the characteristic diffusion time is about 6.43 ± 0.68 ms and the lowest detected concentration is about 0.81 ± 0.04 pM, defining the detection limit of SHGCS. Our study also demonstrated that SHG signals with hign SNR can be collected and its dynamics monitored even in a turbid media. Materials such as BTO nanocrystals, with second order nonlinearity can serve as ideal candidates for single molecule detection due to its excellent signal generation efficiency.
This work was supported in part by the National Science Foundation (Grant no. 0945771 and 0754740), the CTSI (IUPUI-Purdue) grant, and the Purdue Center for Cancer Research Innovative grant.
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