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We report on the utilization of a dual-clad optical fiber for two-photon excited fluorescence correlation spectroscopy (FCS). High excitation efficiency is obtained by sending prechirped ultrafast pulses through the single-mode core of the fiber, while the fluorescence collection efficiency is enhanced because of the larger numerical aperture of the inner cladding. We show that the utilization of a dual-clad fiber is critical for ultrasensitive two-photon fluorescence detection. Our system has the ability to detect fluorescent nanospheres as small as 12 nm in radius. Quantum dots of radius 7 nm are also measured and show excellent signal to noise ratio. The particle sizes obtained from the fiber FCS system were confirmed by measurements using a commercial dynamic light scattering (DLS) system.
©2008 Optical Society of America
1. Introduction
Fluorescence correlation spectroscopy (FCS) is a highly sensitive technique which can extract dynamical information on small particles or even single molecules from the intrinsic intensity fluctuations of the fluorescence signal in a dilute solution under thermal equilibrium. It was first introduced in 1972 by Magde et al.[1]. Beginning in the 1990s with the application of confocal and multiphoton techniques in FCS, the range of application of FCS in biophysical and biochemical research has grown rapidly [2–5]. Because of the capability of quantifying biomolecular interaction and associated kinetics, FCS has become an invaluable tool. The information accessible by FCS includes concentration and diffusion coefficients of molecules in solution, aggregation formation, transport rates, chemical reaction rates, and the photophysical properties of the molecules [6–8].
In a traditional FCS setup, a confocal or multiphoton microscope is employed. The use of bulky optical instrumentation limits the use of FCS in situ or in vivo deep inside the body. Use of a fiber-optic probe as a miniaturized microscope for simultaneous excitation and detection of fluorescence molecules provides a promising approach for those applications [9]. Various applications of fiber-optic sensors have been reported [10]. However, most of the applications only measure the fluorescence intensity. Use of a fiber probe in conducting FCS can provide dynamic information for analyzing quantities such as mobility, binding dynamics, and flow velocity of the fluorescent species at a remote site. Recently, Garai et al. reported the use of a single-mode fiber (SMF) with a mode field diameter (MFD) of 3.3um to conduct one-photon excited (1PE) fiber-optic-based FCS and used this probe to detect aggregation of the amyloid-β peptide in vitro. However, the high background, as is often the case in the 1PE scheme, limits the possibility from extending the technique to single-molecular level applications [11, 12].
The problem with the high background might be solved by applying two-photon excitation (2PE) as an alternative approach to conducting fiber-optic based FCS. One of the most important advantages of 2PE is the remarkably low background noise level because of the large separation in wavelength between the laser and the fluorescence signal. In addition, due to the quadratic dependence of the excitation efficiency on laser intensity, the excitation volume is limited to only a small region close to the fiber tip [13, 14]. The probe volume is thus reduced, compared to the 1PE case under the same geometry of the fiber probe, which is desirable for FCS. A better signal-to-noise ratio can be expected due to the combination of the reduced background and the probe volume. Other advantages of 2PE include the ability to excite multiple fluophores with a single laser line, and decreased concentration depletion because of reduced out-of-focus photobleaching, thus allowing for a longer acquisition time without affecting the experimental result [5, 15].
We have developed a two-photon optical fiber fluorescence (TPOFF) probe as a minimally invasive technique for quantifying fluorescence in solid tumors in live mice in a real-time basis as reported previously [14, 16]. This technique exploits both the advantages of fiber optics and of two-photon excitation. The enhanced detection efficiency by using dual-clad fibers (DCF) in biological applications has also been reported recently. The ability to quantify nanomolar concentration has been demonstrated [17–19]. In this report, we further investigate the capability of conducting FCS measurement with this novel dual-clad fiber probe.
2. Theory
In a typical FCS setup, a laser beam is focused into a solution under thermal equilibrium. The focused laser beam and the detection optics define the probe volume of the system. As fluorescent particles move in and out of this minute open region, the total fluorescence F(t) detected will fluctuate due to the change of the total number of molecules N(t) present in the probe volume. The temporal autocorrelation function of F(t) contains information about the average duration and amplitude of the fluctuations. The decay rate and the shape of the autocorrelation function G(τ) reveal the mechanism of the process and the dwell time of the particles in the probe volume. The magnitude of G(τ) provides information about the number density of the fluorescent molecules or particles in the probe volume. The total detected fluorescence F(t) is proportional to the number of particles in the focal volume, N(t). The normalized autocorrelation function is defined as
where δF(t)=F(t)-〈F(t)〉 is the fluctuation of the fluorescence signal F(t) at about its average value and 〈 〉 denotes an ensemble average, which for a stationary random process can be taken as a long-time average [20].
For two-photon excitation, the total detected fluorescence can be expressed as
where α is a constant proportional to the detection efficiency, the two-photon cross section, and the quantum yield of the fluophore; I0 is the average laser intensity at the geometric center of the focus; S(r⃑) is the dimensionless spatial profile of the laser beam; and δC(r⃑,t) is the fluctuation of the concentration at different points inside the probe volume.
Although in our 2PE daul-clad fiber configuration, the probe volume is determined only by the excitation profile of the laser beam propagating in the central core. The excitation profile can be calculated by taking the square of the laser beam spatial profile S(r⃑). The spatial profile of the laser beam emitted from the fiber core can be well approximated by one half of a Gaussian beam.
Because the mess of the fiber is much larger than the particles, if the interaction between the fiber tip and the particles is only collision, the collision would be quasi-elastic and the kinetic energy of the particle is conserved after the collision. Therefore the fiber surface would not affect of the speed of diffusion. Although the excitation volume is only one half of a Gaussian beam, we can consider the total probe volume as the real excited volume extending out from the core plus a imaginary volume which is the mirror image of the real excited volume, because the planar fiber surface acts as a reflecting plane to the particles. The analysis of the diffusion for the fiber FCS data can thus be carried out in the same manner as conventional 2PE-FCS. The autocorrelation function takes the following form:
where 〈N〉 is the average number of particles in the probe volume and k=w 0/ZR is the ratio of the radius of the beam waist w0 to the Rayleigh range ZR.
The beam waist and the diffusion time τd are related by
where D is the diffusion coefficient. The relation between the diffusion coefficient and the hydrodynamic radius of the particle R can be expressed by the Stokes-Einstein equation:
where kB is the Boltzmann constant, T is the temperature, and η is the viscosity of the solution. With the measured diffusion time τd, the size of the particle R can be calculated through
The probe volume V can be calculated from the laser spatial profile S(r⃑) through the relation,
where γ=∫S 4(r⃑)d r⃑ 3/∫S 2(r⃑)dr⃑ 3 represents the volume contrast defined by the geometric shape of the beam. For a radially Gaussian, axially Lorentzian profile, as is the case here, γ=3/16 [13].
From Eq. (3), one can calculate the average number of particles in the probe volume by taking the inverse of G(0). However, in the presence of high background, the relation between G(0) and N has to be modified accordingly. The total measured fluorescence is Ftot(t)=F(t)+B(t), where B(t) is the background count rate. However, only the fluctuation of the fluorescence signal F(t) from the particles contributes to G(τ). Therefore, the autocorrelation function at time zero has to be modified to
where N is the average number of particles in the probe volume and NB is the equivalent number of particles due to background fluorescence [11].
3. Methods and materials
3.1 Two-photon fiber FCS apparatus
The experimental setup is shown in Fig. 1(a). The Ti:sapphire laser (Coherent Inc., Mira 900) generates 50-fs pulses at 800 nm with a 76-MHz repetition rate. The pulse is first double-passed through a 2000 line/mm transmission grating to pre-compensate the fiber dispersion and thus optimize the peak intensity of the output pulse at the distal fiber end. The beam is coupled into the inner core of the fiber with a 40X microscope objective (NA=0.65). The size of the beam at the back aperture of the objective is adjusted to match the mode field diameter of the fiber core. The fluorescence signal is collected back through the same fiber and is separated from the excitation beam by a dichroic mirror. The fluorescence signal is filtered by two short pass filters (E750SP and E735SP, Chroma) to block the scattered laser light and a set of band-pass filters (Melles Griot D523/250, HQ510/50) for fluorescence wavelength selection. The signal is detected by a photomultiplier tube (PMT, Hamamatsu, H7422-40) and recorded by a time-correlated single photon counting (TCSPC) module (SPC-630, Becker and Hickl, GmbH) installed in a computer.
Fig. 1. (a) Experimental setup for two-photon fiber FCS. PMT, photomultiplier tube. (b) Schematic diagram of the intersection of the DCF.
3.2 Enhancement of collection efficiency by a dual-clad fiber
The DCF (P6/123DC, Liekki Corp., Finland) used in this study has an inner core diameter of 6 µm with an NA of 0.15 and an inner cladding diameter of 123 µm with an NA of 0.46. The schematic of the DCF cross-section is illustrated in Fig. 1(b). The total coupling efficiency was 69% with 49% of the output power in the core.
The key feature of the DCF is that it enables simultaneous optimization of the excitation and collection efficiencies. The 2PE efficiency is maintained by propagating ultrafast pulses through the inner single-mode core of the DCF, while the collection efficiency is improved by the high numerical aperture (NA) multimode inner cladding (outer core), which is confined with a second cladding.
The enhancement of the detected 2PE fluorescence signal by the DCF can be estimated by the NA and the size of the inner cladding. Using the equations given in ref. [17], we can calculate the ratio of the 2PE fluorescence detected by the DCF to that from a conventional SMF as a function of the inner-cladding NA, as shown in Fig. 2. The detection efficiency increases nearly quadratically with increasing inner-cladding NA.
To demonstrate the enhanced sensitivity of the DCF over the SMF, we measured 100-nM 6-carboxytetramethyl rhodamine (6-TAMRA) solution by both fibers under the same configuration. A significantly improved detection sensitivity of the DCF was obtained, as shown in Fig. 3. The DCF has a 17-fold increase in the two-photon fluorescence signal compared to the SMF. In FCS, the sensitivity is quadratically proportional to the brightness of the fluorescent particles. A 17-fold increase in the signal translates to about 290-fold increase in the signal to noise ratio in FCS measurements. In the experiments, we found that the SMF does not have enough sensitivity for two-photon fiber FCS (2P-FFCS) to detect fluorescence particles smaller than 100 nm. The adoption of a DCF is crucial for ultrasensitive detection of 2P-FFCS.
Fig. 2. Calculated enhancement of the DCF-detected signal over the SMF as a function of the NA of the inner cladding of the DCF.
Fig. 3. The power dependence of two-photon fluorescence signal obtained from the DCF (red circle) and the SMF (black square) in 100-nM 6-carboxytetramethyl rhodamine (6-TAMRA) solution. The slopes on the log-log plot are 1.93 and 2.14, respectively. The DCF shows 17-fold enhancement over the SMF.
3.3 Sample preparation
Fluorescent nanospheres were purchased from Invitrogen (FluoSpheres, Molecular Probe). The spectral absorption and emission maxima of the nanospheres were 505 nm and 515 nm, respectively, for one-photon excitation. Quantum dots (QDs) were also purchased from Invitrogen (Q21331MP, Molecular Probe). The emission maximum of the quantum dots is 565 nm.
Because of the high sensitivity of FCS in dilute solutions, any agglomerates or fluorescent impurities in the solutions can make up an appreciable fraction of the signal, obscuring correlations due to the species of interest. Therefore, the size distributions of all nanosphere samples were checked by dynamic light scattering (DLS, DynaPro, Protein-Solutions Inc.) before FCS measurements. All the samples were dissolved in MilliQ water (Millpore) unless stated otherwise. Spheres were diluted to appropriate concentrations and then sonicated for 15 minutes. After sonication, the 12 nm and 18 nm radius nanospheres and QDs were first filtered with a 0.1um syringe filter (GE water & process technology) and then with a 0.05um membrane filter (Millipore). Filtering is a critical step for accurate measurements, especially for nanospheres smaller than 50 nm [4]. All samples were confirmed to have a narrow size distribution by dynamic light scattering measurements. The measured sizes are summarized in Table 1.
4. Results and discussion
4.1 Two-photon fiber FCS measurements
The 2P-FFCS system was used to measure the diffusion (due to Brownian motion) of fluorescence nanospheres in water solutions by directly dipping the fiber tip into the solution. Figure 4 shows FCS data for diffusion measurements of quantum dots (QDs) and fluorescent nanospheres. The nominal radii of the QDs and the nanospheres provided by the manufacturer are 7 nm, 12 nm, 18 nm, 50 nm and 105 nm, respectively, which are measured by transmission electron microscopy (TEM). The FCS curves for the diffusion of these nanoparticles are shown in Fig. 4(a). The curves are normalized to better illustrate the more rapid diffusion time of smaller particles. The solid curves are the fits of the data using Eq. (3). The total output power from the fiber for all the measurements was 20 mW, except for 105-nm radius beads. The excitation power for 105-nm beads was lowered to 10 mW to avoid occasional overflow of the detection unit. The acquisition time for each set of data was ~3 minutes. The data were acquired by the FIFO (first in first out) mode (also called time-tagged time-resolved mode) in the TCSPC module, and the correlation curves were calculated afterward by software (SPCM) provided by the manufacturer. The correlation curves were calculated directly from the single photon counting trace recorded, and the resolution is limited only by the dead time of the TCSPC module, which is ~100 ns. Higher signal-to-noise ratio (SNR) can be obtained with longer acquisition time, providing the solution is well prepared and impurity free. However, even when all the samples were filtered and sonicated before measurements, the longer the experimental time, the higher the probability to observe agglomerates, especially for small nanospheres, which can affect the accuracy of the measurement significantly. Therefore, the acquisition time was kept short, but for 12- and 18-nm radius beads, the curves were averaged four times to obtain a better SNR. The average mean diffusion times obtained from the FCS curves were 41, 54, 89, 247, and 544 ms, respectively. The relation between the particle sizes and the measured diffusion times is plotted in Fig. 4(b). The solid line is the theoretical prediction from the Stokes-Einstein equation. The measured diffusion times for all the beads are consistent with the theory. The calculated MFD of the core of the DCF from the experimental data was determined to be 5.86±0.17 µm, which is close to the value given in the specification of 6 µm.
Fig. 4. (a) Fluorescence correlation curves of quantum dots (cyan diamond) and fluorescent nanospheres of radii 12 nm (black square), 18 nm (red circle), 50 nm (green upward triangle), and 105 nm (blue downward triangle). The solid curves are the corresponding fits. (b) The measured mean diffusion times versus nominal particle sizes as measured with TEM. The solid line is the theory prediction from the Stokes-Einstein relation.
4.2 Accuracy of the measurements
The sizes measured by DLS and 2P-FFCS are compared to the nominal sizes given by the manufacturer and are summarized in Table 1. Since both DLS and FCS measure the hydrodynamic radius of the particles, the comparison gives a good indication of the accuracy of the technique [7]. The manufacturer-provided nominal sizes are measured by TEM, which measures the radius of the spheres on a dry surface. From the diffusion time measured by FCS, the size of the particles can be calculated using Eq. (5a), with w0=3 µm, T=300 K and η=1.002×10-3 N s/m. The measured sizes show excellent agreement between these two methods.
Table 1. Comparison of the sphere radii determined by DLS and FCS
The magnitude of G(0) provides additional information on the accuracy of the technique. From Eq. (3), we know that G(0)-1 is proportional to the average number of molecules 〈N〉 in the probe volume. However, when the signal and background are comparable, one needs to consider the effect of background on G(0) to obtain correct measurements of sample concentrations.
The measured G(0) for 6-pM and 60-pM solutions of 50-nm beads were 0.010 and 0.0085, respectively. The reason comparable G(0) were obtained despite the 10-fold difference in the concentrations is because of the background. The background photon count rate was 1.6 kHz. The signal count rates were 440 Hz and 4.1 kHz for 6-pM and 60-pM solutions, respectively. According to Eq. (7), the deduced average numbers of particles in the probe volume were 5.5 and 51.9, respectively, which is in agreement with the concentrations used. In addition, from the knowledge of the concentration and average number of particles in the probe volume, the estimated probe volume is ~1.49×103 µm3, which matches the calculated probe volume from Eq.(6) of 1.57×103 µm3. Both the recovered concentrations and the probe volume correspond to the theoretical prediction.
In a closer investigation of the measured FCS curve and the fit in Fig. 4(a), we notice that the measured FCS curves have a little deviation from the theoretical fit. The deviation might be originated from the interaction between the particles and the fiber tip. Because the carboxylated beads are highly negatively charged and the glass tends to be negatively charged in water as well [21], the beads might be repelled when they are close to the fiber tip. Therefore, the spheres will move faster away from the fiber tip. This additional interaction might cause the faster decay rate of the FCS curve compared with free diffusion case as predicted by the model. Furthermore, the larger the particle, the more obvious the effect because of the higher surface charges, as we can see in Fig. 4(a). We are currently working on improving the model by including the effect of the fiber on the particles into consideration.
4.3 Sensitivity of the technique
One of the main motivations to conduct two-photon excited FCS is lower background noise because of easy separation of the excitation laser light from the fluorescence signal. This is especially important when using a fiber probe to do FCS because the light has to travel in a longer medium, the fiber, to reach the probe end. The longer the interaction length of the light with the medium, the more the scattered light is generated, which increases the background.
Initially, we used a low NA, 10-µm core diameter DCF (P10/123DC, NA=0.07, Thorlab) to implement 2P-FFCS; the background count rate was as low as ~60 Hz (including a dark count rate of 19 Hz). The background level was about the same as a conventional objective-based FCS system. However, due to the larger probe volume and lower excitation efficiency, that fiber did not have enough sensitivity to measure fluorescent nanospheres with a radius smaller than 50 nm. Therefore, we adopted the 6-µm core DCF to conduct 2P-FFCS measurements of nanospheres here. This fiber showed sensitivity adequate enough to measure fluorescent nanospheres as small as 12 nm in radius. Nevertheless, this fiber had a higher background count rate of ~1.6 kHz, possibly due to higher doping in the core to achieve higher NA. We investigated the power dependence of the background by putting the fiber tip into pure water in the same experimental configuration. The background photon counts versus total fiber output power is shown in Fig. 5. The slope on the log-log plot is 1.7, which indicates the majority of the background is caused by 2PE fluorescence of impurities or dopants inside the fiber. Garai et al. also observed the high background due to autofluorescence from single-mode fibers. The existence of the high background from the intrinsic fluorescence of the fiber complicated the application of a fiber-optics based FCS system to single-molecule-level measurements [11].
Fig. 5. The power dependence of the background photon counts when the fiber tip was put into pure MilliQ water. The abscissa represents the total output power at the probe end of the DCF, and the ordinate represents the detected photon counts per second. The solid line is the linear fit on the log-log plot, and the slope was found to be 1.7.
Fortunately, the use of ultrafast pulses for 2PE FCS enables additional background reduction through time-gated detection [3, 22]. A software time-gated analysis can be applied when using TCSPC for FCS measurements. This part of the work is currently underway. We find that the background can be reduced as high as 5-fold without losing a significant amount of the 2PE fluorescence signal because of the long delay time provided by the fiber.
We have demonstrated that our technique can measure fluorescent nanospheres as small as 12 nm in radius. We also demonstrated the ability to measure QDs with 7-nm radius. The SNR of the QD measurement is comparable to the 50-nm fluorescent nanosphere, which is about 40-fold brighter than the 12-nm nanosphere. No averaging was required to resolve the QDs from other size particles, which shows the potential to use QDs as fluorescent probes for in vivo fiber FCS. QD’s are known for their exceptional 2PE cross-section and photostability. There have been various applications using QD for in vivo multiphoton FCS studies [23, 24].
The main limitation to conducting two-photon FCS through a fiber is the excitation efficiency at the probe end. The 2PE efficiency, which is determined by the geometry of the fiber, is more than one order of magnitude lower than a setup with a high numerical aperture objective lens. However, in contrast to the one-photon scheme, the size of the probe volume in the 2P-FFCS is determined by the two-photon fluorescence excitation volume rather than by the collection geometry. Thus, we can further engineer the fiber tip to simultaneously reduce the probe volume and increase the excitation efficiency. Fabrication of a micro-lens at the fiber tip may be a promising way to enable the implementation of in vivo FCS measurement deeper inside the body.
5. Conclusion
To summarize, a two-photon-excitation fiber-optic-based fluorescence correlation spectroscopy system has been developed that is based on a dual-clad fiber probe. This technique exploits both the advantages of 2PE and of fiber optics. The ability to detect fluorescent nanospheres as small as 12 nm in radius has been demonstrated. We have also shown that a smaller detection size limit is achievable when quantum dots are employed as the fluorescent probe. Because of the two-photon excitation scheme, the background noise from the coherent scattering and autofluorescence of the fiber is reduced, as compared to the one-photon scheme. Our study showed that it is critical to employ a dual-clad fiber for a fiber-based two-photon FCS measurement to achieve adequate sensitivity for the measurements of fluorescent nanoparticles. Because of the pulsed 2PE scheme, multiple fluophores with different excitation maxima can be excited simultaneously and fluophores with different lifetimes can also be discerned. Thus, we envision this novel fiber sensor technique can have multidimensional detection capability and serve as a minimally-invasive diagnostic tool to detect and identify sparse amounts of disease-specific molecules in body fluids or on neoplastic cells in vivo for early screening and treatments.
Acknowledgements
The authors would like to thank the support of federal funds from the National Cancer Institute, National Institutes of Health, under awards 1 R33 CA112141 and 1 R21 RR021893.
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