Multipoint fluorescence correlation spectroscopy using spatial light modulator

A multipoint holographic fluorescence correlation spectroscope (MP-hFCS) was successfully developed. The validity of the MP-hFCS was demonstrated using diffusion measurements of fluorescent dye solutions and of fluorescent proteins in single cells. Furthermore, the successful detection of the nuclear transport of a green fluorescent proteintagged glucocorticoid receptor α indicates the possibility of being able to monitor directional molecular transport using the MP-hFCS. This allows multipoint analysis of the intermolecular interactions and molecular transport in living cells. Finally, the MP-hFCS can achieve multipoint diffusion measurements with high spatial and time resolution while maintaining a high photon detection sensitivity. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Fluorescence correlation spectroscopy (FCS) [1,2] is a powerful tool for measuring the dynamics of fluorescent molecules either in solution or in a living cell. For a living cell, fluorescence measurement that is non-invasive or induces little damage to the cell can be achieved. FCS can reveal the diffusion coefficient, the target molecule concentration, and the brightness of a single molecule. These parameters allow estimations of the molecular size [3], the molecular shape [4,5], the affinities of molecular interactions [6,7], and the degree of homo-multimerization [6]. However, one drawback is that measurements are generally limited to a single point because of the nature of the confocal detection system, despite the fact that different diffusion processes may be ongoing in different cellular compartments under different physiological conditions. To overcome this disadvantage, numerous multipoint diffusion measurement systems have been developed, such as the two-beam crosscorrelation method for FCS [8], single plane illumination microscopy based FCS (SPIM-FCS) [9], massively parallel FCS (mpFCS) [10], multipoint total internal reflection (M-TIR-FCS) [11], temporal image correlation spectroscopy (TICS) [12], imaging FCS [13], pair correlation functions (pCFs) [14], and raster image correlation spectroscopy (RICS) [15]. Flow velocity measurement via FCS was first demonstrated using the two-beam crosscorrelation method. A single excitation laser beam was separated into two beams using a beam splitter, and the fluorescence emitted from two focal spots was collected using two independent multimode fibers. However, this method is not amenable to increasing the number of measurement points, because of the illumination optics. In contrast, SPIM-FCS, mpFCS, and other camera-based FCS methods [16] can achieve over 1,000 measurement points. However, because of the use of an imaging sensor, either the time resolution or the photon detection sensitivity-or both-must be sacrificed, although only electron multiplying CCD (EM-CCD) has a higher quantum efficiency than the single photodetectors used for FCS, such as the photomultiplier tube (PMT) and the avalanche photodiode. In the future, the time resolution and photon detection sensitivity may reach the current performance of single photodetectors. TICS and scanning FCS, including pCFs, are image processing methods based on laser scanning microscopy (LSM). They have the advantage that the number of measurement points can be selected up to the maximum pixel number. On the other hand, the time resolution of such methods is limited to the frame rate or the pixel dwell time of the LSM images. RICS is also an image processing method using LSM images. Spatiotemporal information about the target molecule can be extracted from the auto-correlation image of the region of interest (ROI) in the original LSM image. Diffusion information can only be obtained from one ROI; therefore, the spatial resolution is decreased to the size of the ROI. Thus, most multipoint measurement methods for diffusion sacrifice the number of measurement points, spatial resolution, time resolution, and/or photon detection sensitivity. The M-TIR-FCS technique that we previously developed achieved simultaneous measurement at seven two-dimensionally distributed points; however, its measurement points were restricted to the near field of the coverslip.
The multipoint holographic FCS (MP-hFCS) system that we introduce here is an expansion of the two-beam cross-correlation method and M-TIR-FCS that overcomes the limitation of the number of measurement points. The system simultaneously measures seven points distributed in an arbitrary plane at an arbitrary depth in a living cell while maintaining the high spatial resolution and high time resolution of single-point FCS. The number of excitation beam spots can be flexibly increased using a holography technique. The fluorescence emitted from each excitation beam spot is detected by an independent PMT. Practically, the number of measurement points can be increased by increasing the number of detectors.

Experimental setup
A schematic of the MP-hFCS system is shown in Fig. 1(a). The laser beam-a 488-nm semiconductor laser (Sapphire 488-20, Coherent, USA)-is expanded and incident to a liquid crystal on a silicon spatial light modulator (SLM, SLM-X02-T, Hamamatsu Photonics KK, Japan). When a designed holographic pattern is sent to the SLM as a Digital Visual Interface signal, the SLM functions as a Fourier phase hologram that generates seven focused laser spots in the focal plane of the objective, L o (UPlanApo × 60, numerical aperture = 1.20, water immersion, Olympus, Japan). An example of the holograms generated by the gratings and lens method [17][18][19] is shown in Fig. 1(b). In the gratings and lens method, the phase holograms of optical gratings, which deflect light to an arbitrary position as 1st-order diffraction light, are superimposed. In this system, the positions of the laser spots can be adjusted only by changing the hologram without any mechanical adjustment. The phase hologram is imaged in the back focal plane of L o using a 1 × telescope consisting of L 1 and L 2 . The fluorescence spots excited by the beam-spot array are shown in Fig. 1(c). There were also undesired beam spots, 0th-order diffraction light, and 2nd-or higher-order diffraction light for each grating of hologram, outside of the field of view. Such undesired beam spots do not disturb the MP-hFCS measurement; however, they cause the loss of excitation light. The emitted fluorescence is focused on the seven optical fiber cores of a multicore fiber with a magnification of 60 × using the imaging lenses L I and L o ( Fig. 1(d)). Each aperture of the fiber core functions as a pinhole ( Fig. 1(e)), such that the fluorescence detection is equivalent to confocal detection in multiple channels. Any geometry of illuminated points can be realized via the SLM; however, the geometry of confocal detection points cannot be defined arbitrarily, because the measurement positions are defined by the positions corresponding to the fiber cores. The output signals from the PMT array are recorded with a time resolution of 1 μs by a computer through a multichannel 8-bit pulse counting board, whose sampling rate is 80 MHz, constructed using the field-programmable gate array board used in a previous M-TIR-FCS system [11]. Autocorrelation functions (ACFs) and cross-correlation functions (CCFs) among the channels are calculated using newly developed software for the multichannel calculation of ACFs/CCFs. By fitting the FCS model equations to the ACFs, the kinetics of fluorescent molecules (i.e., the diffusion times and the number of molecules) at the seven points can be determined simultaneously. The MP-hFCS system can perform multipoint FCS measurement at an arbitrary depth in three-dimensional samples because the multipoint confocal detection is realized via the holography technique and the multicore fiber. This is a significant advantage over M-TIR-FCS, where measurement can only be performed near the surface of the coverslip.

FCS measurement and analysis
In all measurements, the ACFs or CCFs in the direction of channel n to m were calculated to analyze the fluorophore dynamics, as follows: where n I and n I represent the fluorescence intensity signal of channel n and its time average, respectively. The bracket < > represents the ensemble average operation. In the case of n = m, Eq. (1) is the ACF of channel n. Equation (1) also represents the spatiotemporal CCF. When there is a flow toward channel m from n, the spatiotemporal CCF G c n,m (τ) has a peak at the traveling time to m from n.
If a fluorophore diffuses slowly, the diffusion time is long, and the decay rate of the ACF is low. A larger number of fluorescent molecules yields a lower amplitude of the ACF. Each ACF obtained by the MP-hFCS system was fitted with the theoretical ACF of FCS [21], as follows: where F triplet and τ triplet are the average fraction of triplet-state molecules and the triplet relaxation time, respectively. The fraction and the diffusion time of the i th component are expressed as F i and τ Di , respectively. N is the number of fluorescent molecules in the detection volume defined by the radius w 0 and length 2z 0 , and s is a structural parameter given by s = z 0 /w 0 . The normalized ACF is defined by The diffusion constant of the i th component can be calculated using the equation D i = w 0 2 /4τ Di . w 0 and s can be obtained via the measurement of a rhodamine 6G solution as a standard sample whose diffusion constant is 414 μm 2 /s. The detection volume V can be obtained as The molar concentration C can be estimated as

FCS measurement and analysis in cells
The forward correlation to the nucleoplasm from the cytosol G c c,n (τ) and the backward correlation G c n,c (τ) are defined as where F n and F c represent the fluctuating fluorescence intensity detected in the nucleus and the cytosol, respectively. r and r' are the positions of the measurement points in the nucleus and the cytosol, respectively. The brackets represent the time average operation. If there is molecular translocation to the nucleus from the cytosol, the forward correlation must have a peak corresponding to the traveling time between the two measurement points. Such an anisotropic component can be easily extracted by using the difference curve of these CCFs:

Transient transfection in cell culture
HeLa cells were transfected using the Optifect Transfection Reagent (Invitrogen, USA) with 0.5 μL/well green fluorescent protein (GFP) or GFP-GRα wt , according to the instructions provided by the manufacturer.

Experiments on aqueous solution
The shape of the confocal volume of the newly developed MP-hFCS system was first investigated via measurement of a rhodamine 6G water solution as a standard dye with a known diffusion coefficient (D = 414 μm 2 /s) [20]. The typical ACFs of rhodamine 6G measured by each channel are shown in Fig. 2(a). The ACFs of such a fast-diffusing dye were successfully measured because of the high time resolution of MP-hFCS, whereas it is difficult to measure such fast-diffusing dyes using other multipoint methods that sacrifice the temporal resolution. The diffusion times and structural parameters of each channel are shown in Figs. 2(b) and 2(c), respectively. All the fitted parameters are shown in Data File 1. The average diffusion time and structural parameter of the seven channels were τ D = 70.3 ± 3.5 μs and s = 4.88 ± 0.21, respectively. Using the known diffusion coefficient of rhodamine 6G, the average waist and measurement volume of the seven channels were determined as w 0 = 339 ± 9 nm and V = 1.11 ± 0.08 fL, respectively (see the "FCS measurement and analysis" section). The waist of the confocal volume, w 0 , was slightly larger than the diffraction limit (~250 nm). The fiber core (1.67 airy unit), which acted as a pinhole, has a larger diameter than airy disc. To decrease the volume, a smaller fiber core or an objective lens with a higher magnification is needed. These data indicate that the MP-hFCS system had multiple confocal volumes with relatively uniform shapes.  Table 1 presents a comparison of the diffusion coefficients and the count per molecule (CPM), which is the average fluorescence count rate (CR) per molecule, measured using MP-hFCS and a commercial FCS system (ConfoCor 2 unit built into LSM 510 Meta, ZEISS, Germany). All the fitted parameters are shown in Data File 2. The data confirm that solutions of fluorescent molecules with various diffusion coefficients could be measured via MP-hFCS and that the results were similar to those of the other well-established system. The relatively large standard deviation of the diffusion coefficients obtained via MP-hFCS likely arose from the low laser power per measurement point due to the laser spot separation. This is supported by the low CPMs obtained via MP-hFCS. The low CPM was likely caused by a factor such as the narrow transparent band of the emission filter (520-535 nm for MP-hFCS and 505-550 nm for ConfoCor2), diffraction of an unwanted order, or fluorescence crosstalk. To reduce the standard deviation of the diffusion coefficient, either the laser power or the measurement duration can be increased. Data are the mean ± standard deviation. The MP-hFCS data are the average value of seven channels, with one measurement each (n = 7). The ConfoCor 3 data are the average value of three independent measurements (n = 3).

Experiments on living cell
MP-hFCS measurements were performed on a single HeLa cell transiently expressing GFP, as shown in Fig. 3(a). Channels 1 and 7 were in the nucleolus, and the remaining channels were in the nucleoplasm. As shown in Fig. 3(b), the height of the boundary between the coverslip and the cell was defined as z = 0 μm. The upper direction was defined as the positive direction of the z-axis. MP-hFCS measurements were performed from z = −1 to 8 μm at intervals of 1 μm. The fluorescence photon CR distribution, which corresponds to the fluorescence intensity, is shown in Fig. 3(c). The CRs inside the nucleolus were lower than those inside the nucleoplasm. This result is in good agreement with a previous study [22] and might be due to the dense fibrillar component in the nucleolus. In addition, each CR distribution had single peak at z = 4 μm, which was attributed to the center plane of the cell. The normalized ACFs of channel 1 (nucleolus) and channel 4 (nucleoplasm) measured at z = 4 μm are shown in Fig. 3(d). The wild-type human glucocorticoid receptor α (GRα wt ) is a nuclear receptor localized in the cytosol in the absence of a ligand. Following the binding of a ligand such as dexamethasone (Dex), GRα wt translocates to the nucleus through the nuclear pore complex (NPC). Finally, GRα wt binds to DNA and regulates the expression of its target genes. The transition time of GRα wt through the NPC, which has remained unclear, was analyzed as one of the applications of MP-hFCS. Figures 4(a) and 4(b) show HeLa cells transiently expressing GFP and GFP-GRα wt , respectively. The measurement points (white arrows) were reduced to two in order to reduce the phototoxicity for this long-term measurement. Figures 4(c) and 4(d) show the CRs of GFP and GFP-GRα wt , respectively. For this measurement, 100 nM Dex (final concentration)-a GRα wt ligand-was added to the cell culture medium at 0 s. The CRs of the GFP in both the nucleoplasm and the cytosol remained unchanged. In contrast, following Dex treatment, the CR of the GFP-GRα wt in the cytosol decreased, and that in the nucleoplasm increased. These results confirm the nuclear translocation of GFP-GRα wt after Dex addition. The 10-s measurement was repeated 54 times. For each time course measurement, 18 measurements were concatenated, and the ACFs were calculated. Finally show the ACFs of the GFP in the cytosol and the nucleoplasm, respectively, and Figs. 4(f) and 4(h) show those of the GFP-GRα wt . In the case of the GFP, the number of fluorescent molecules (N) and the diffusion time (τ D1 ) remained unchanged in the nucleoplasm and the cytosol following Dex treatment. Whereas the N in the nucleoplasm was increased by adding Dex, the N in the cytosol decreased. In addition, the diffusion constants D 1 and D 2 in the nucleus decreased, and the fraction of the slow component increased. These results agree well with the FCS results from a previous report [23], which concluded that GFP-GRα wt was bound to the DNA inside the nucleus. The ACF in the nucleoplasm during the period of −180 to 0 s could not be calculated, because of the very small amount of GFP-GRα wt present in the nucleus prior to Dex addition. The mean diffusion constants and diffusion times of the GFP and GFP-GRα wt calculated for several different cells of the same cell line (HeLa) are shown in Data File 4.
MP-hFCS measurement also provides the spatiotemporal CCF, whereby the average transition time of each molecular flow can be obtained from the same signals used in the ACF analysis [8]. The forward correlation to the nucleoplasm from the cytosol G c c,n (τ), the backward correlation G c n,c (τ), and the difference curve G c (τ) defined by Eqs. (4) and (5) were used. If there is a molecular flow, G c (τ) should have a peak at τ corresponding to the flow rate because two measurement channels detect similar fluorescence intensity signals with a time difference according to the transition time between the two channels.
Figures 4(i) and 4(j) show the G c (τ) of the GFP and GFP-GRα wt , respectively. The G c of the GFP had no peaks, indicating that the diffusion of the GFP (27 kDa) was non-directional because molecules smaller than 40 kDa could freely pass through the NPC via free diffusion. In contrast, peaks appeared on the G c for the GFP-GRα wt (113 kDa) after the addition of Dex. This result shows that the GFP-GRα wt molecule was unidirectionally translocated to the nucleus via active transport. The peaks were at τ ≈45.1 s; therefore, the nuclear translocation of GFP-GRα wt between two measurement points took 45.1 s. If there is no membrane and GFP-GRα wt diffuses freely between the two measurement points, a peak should appear at 149.0 ms. The latter time was calculated by assuming a mean diffusion constant of 6.43 μm 2 /s for GFP-GRα wt in cytosol, using the CCFs based on the dual-focus FCS theorem [8]. Interestingly, the measured GFP-GRα wt nuclear translocation time was significantly longer (more than 300-fold) than the expected result for free diffusion. In addition, it was far longer than that observed for NLS-GFP (27 kDa) translocation via the nuclear membrane, which ranged from 1 to 40 ms [24]. This large difference in the transition time could be due to the large molecular size of GFP-GRα wt , as large molecules have difficulty passing through the holes of NPCs. These data therefore suggest that there could be a relationship among the transition time, molecular size, and energy expense.

Conclusions
We described the development of a new MP-hFCS system based on flexible wavefront control optics and confocal detection. Because of this highly flexible illumination [18], we can realize any pattern of multiple confocal detection with other multicore fibers. In this MP-hFCS system, one PMT and one counter were used for each channel while both the photon sensitivity and the time resolution were maintained. It was demonstrated that the confocal volumes of the MP-hFCS could be determined using organic fluorescent dyes; such measurement is difficult using other multipoint methods that sacrifice the time resolution. The MP-hFCS system was used in vivo to detect GFP inside a HeLa cell. The dynamics of the GFP diffusion were measured simultaneously at seven points. Introducing spatiotemporal CCF analysis to the MP-hFCS system allowed for the calculation of the transition time for nuclear transport through the nuclear membrane of Dex-bound GFP-GRα wt which was found to be approximately 45.1 s. Although this transition time was significantly shorter than expected and this issue remains to be resolved, the proposed MP-hFCS system is capable of detecting directional molecular diffusion.
We anticipate that the MP-hFCS system will be useful for revealing various properties of molecular dynamics, such as flow, translocation, and intracellular communication. We also believe that by using faster detectors with less noise [25,26], the MP-hFCS measurement can be extended to a faster correlation time for obtaining rotational diffusion coefficients that are more approximate to the molecular shape and orientation of oligomerization than current MP-hFCS system.

Disclosures
The authors declare that there are no conflicts of interest related to this article.