## Abstract

We present a fluorescence correlation spectroscopy setup based on a software correlator. The setup can process autocorrelation curves in real-time at countrate as high as 8MHz, with time resolution of 1µs. It uses the F2Cor autocorrelation algorithm, a low cost counting board and a desktop computer. Symmetrical normalization, which improves the signal to noise ratio of the FCS curve for large values of the lag-time, is adapted to the F2Cor algorithm. A new acquisition mode, which we call *oscilloscope-mode,* is presented. It takes advantage of the flexibility F2Cor, and proves to be very useful for optical setup adjustment. As an application of this setup, we performed FCS measurements on a reference tetramethylrhodamine solution at high concentration, up to 2.5µM, which extend to the micromolar range the concentration applicable in FCS, using a conventional optical setup. At such high countrates the FCS curves need to be corrected for dead-time of the photo-detector, which was done successfully.

© 2013 Optical Society of America

## 1. Introduction

Fluorescence correlation spectroscopy (FCS) is a well established technique [1–3], which is used to measure local concentration, mobility and interactions of fluorescent species in solution. The calculation of the autocorrelation function of the fluorescence signal can be performed using either a hardware correlator [4] or a software correlator [5–9]. Software correlators give more flexibility and the cost is reduced. On the other hand, hardware correlators can calculate and display autocorrelations trace in real-time even at high fluorescence countrate.

The multiple-tau correlation technique has been regularly used in hardware correlators [4, 10]. It consists on calculating the autocorrelation function (ACF) for geometrically increasing values of the lag time over a large range. The conventional implementation uses a bin-and-multiply approach (B&M): photon data are binned and multiplied over time intervals of a fraction of the considered lag time. Compared to linear correlators, the number of operations is dramatically reduced, and one can access a high dynamics of correlation times. This approach was also implemented using a field programmable gate array (FPGA) [11]. In 2000, Eid et al developed a dedicated electronic ISA acquisition card [12], which allows full access to the photon sequence. They presented FCS results as well as photon counting histogram measurements (PCH), but didn't give details about the algorithm they used. In 2001 Magatti et al [6] presented the first multiple-tau software correlator. It used the same B&M principle as hardware correlators. Using a National Instrument PCI-6602 timer/counter board, it could process data in real-time for lag times higher than 5µs, and in batch processing for lower lag time values. In 2003 they proposed a new version [7], still using a PCI-6602, which could process data in full real-time for all values of the lag time, as low as 25ns, but for countrates lower than 30kHz. In 2006 Laurence et al [5] proposed a very flexible algorithm, with arbitrary lag time spacing and bin width. The execution speed is comparable to the B&M approach. For their measurements, they also used a PCI-6602. The calculation was performed offline. In 2009, Yang et al introduced a new algorithm which we name simple correlation histogram algorithm (SCH), the calculation time of which is independent of the time resolution. Using a PC-6602 they could process FCS curves in real-time but only up to 500Hz, because of the small buffer size of the board. However the algorithm itself, which is very simple, can process photon data at rates higher than 1MHz, depending on the maximum lag time value. Recently, we proposed a new photon correlation algorithm, named F2Cor [13], which is the fastest to date. It combines both the B&M and the SCH approach: the ACF is calculated using the SCH approach for short values of the lag time, while conventional B&M approach is used for larger values of the lag time. The optimal limit between the two modes depends on the countrate. The calculation time scales linearly with the number of photons. Using a laptop PC computer, and a single microprocessor core, it can process the ACF of photon file as fast as 0.1µs/photon. However in [13] the calculation was performed offline, using pre-recorded data files.

In this paper, we present an FCS setup which integrates the F2cor algorithm and uses the low cost PCI-6602 counting board. It can calculate in full real-time ACF at countrates as high as 8 MHz, with a 1µs resolution time, which is only limited by the data transfer rate between the acquisition board and the computer.

In a section 2 we present the experimental setup, and the way the data are acquired and processed in real-time. In section 3 we present the symmetrical normalization scheme and its adaptation to F2Cor. In section 4 we present what we call the *oscilloscope mode* FCS, which can monitor the instantaneous FCS curve as a function of the time, which is very useful to optimize the settings of the setup. In section 5 we show measurements performed on a tetramethylrhodamine reference dye solution as a function of the concentration. In particular we show that our setup, thanks to its high countrate capability, is able to perform FCS measurements in real-time, at concentration as high as 2.5µM, which to our knowledge was never attained before using a conventional optical setup. Finally we propose what might be the future developments of this technique and potential applications.

## 2. Setup

The measurements were performed on a Leica DMIRE2 SP2 confocal microscope (PIXEL facility of University of Rennes 1, France). The optical setup is represented in Fig. 1. The excitation wavelength was 561nm, the power of which is adjusted using an acousto-optic beam splitter (AOBS). The laser light is focused into the sample using a 1.2NA water immersion x60 objective (UPLSAPO60XW/1.20/WD:0.28mm, Olympus). The fluorescence signal is detected in the descanned mode, using the so-called X1 port of the scanning head, with a 570-625 nm band-pass interference filter. The fluorescence is focused onto the core of a multimode optical fiber and detected by a single photon avalanche photodiode (SPAD) (SPCM-AQR-12-FC, Perkin-Elmer), which generates TTL photo-pulses.

Figure 2 represents the diagram of the acquisition chain. The SPAD is connected to a low cost general purpose PCI counter/timer board (NI-PCI6602, National Instruments). To acquire and process the data we use an ordinary desktop PC (AMD Phenom 2, 4GB RAM, windows XP). Both the PCI6602 and Eid's card [12] can acquire the photons following either the photon mode (PM) or the time mode (TM). In PM the board records the arrival time of each photon and send it to the host computer. In TM, which is the acquisition mode we use, a counter counts the number of photo-pulses during each integration time, which is defined by an internally generated clock. More precisely, the PCI-6602 has eight counters, and two of them are used in our application. Counter 0 is used to generate the internal reference frequency, while Counter 1 counts the number of photo-pulses arriving at its source terminal between two consecutive gate rising edges. The TTL output of the SPAD is connected to the source of Counter 1, while the internally generated clock is connected to the gate of Counter 1. The maximum clock frequency is limited by the transfer rate between the counter board and the host computer. We use a binning time of$\Delta {t}_{0}=1\mu s$ (a sustained throughput frequency as high as 1 MHz can be obtained by reducing the number of interrupts the counter board will generate [14]). The data are continuously read by the host computer, with no loss of photons, even at very high count rate, except for those lost due to the dead-time of the SPAD.

While the time resolution in the PM mode is limited by the internal timebase of the acquisition board, in TM the time resolution is the binning time Δ*t*_{0}, which is limited by the DMA transfer rate between the acquisition board and the host computer. In FCS, when only considering motion of molecules and not faster processes such as triplet kinetics or chemical reaction kinetics, a time resolution of 1µs is quite enough (as we will see in the results section, the typical correlation time of a small dye in water using a high N.A. objective is about 30-40µs). In addition the portion of the FCS curve in the microsecond range is generally affected by the after-pulse effect so that this part of the curve is often discarded [15]. Thus in most applications a 1µs time resolution is not a limiting factor.

The master program is written in LabVIEW language (LabVIEW 2010, NIDAQ-mx). It is responsible for data acquisition and user interaction. Figure 3 (Media 1) shows the real-time FCS curve display at high countrate, and the subsequent fitting of the curve. LabVIEW is advantageous for fast prototyping and its dataflow principle makes parallel programming very simple. In our case two tasks need to be accomplished in parallel, namely the raw photon data acquisition, and the ACF calculation. More precisely, in a “while” loop, a first task is responsible for loading a photon record of 10ms while a second task processes the ACF of the previous photon record, the curve display of which is updated every 100ms. Note that continuously acquiring the data uses almost 100% of one microprocessor core, but still the three others remain available (we use a 4 core CPU).

As the F2cor algorithm works in the so-called photon mode (PM), it requires photon arrival times. The TM raw photon data have first to be converted online into photon arrival times, which is straightforward: If, for example, there are 12 photons occurring in a particular 1µs interval at time t = 123678 µs, the number “12” is converted into a sequence of 12 numbers, all of which are 123678. The value of *K*, which is the level of the lag time from which F2Cor uses the B&M scheme [13], must be set manually by the user before starting the measurement.

## 3. Symmetrical normalization

We upgraded F2Cor to implement the so-called symmetrical normalization scheme [16], which provides a better signal-to-noise ratio for large values of the lag time.

Before presenting the symmetrical normalization, we need to introduce some of the variables and quantities used by the F2Cor algorithm: We precise for which lag time series the autocorrelation is performed [Eq. (1)], how the fluorescence signal is represented depending on the level of the correlator [Eq. (2)]. As F2Cor is a two stage correlator, we present the unnormalized ACF provided by the B&M higher stage [Eq. (3)] and by the SCH lower stage [Eq. (4)]. How these results are calculated is explained in [13]. In Eq. (5) we give the general definition of the normalized ACF. Then we introduce the symmetrical normalization, the definition of which is given in Eq. (6) for a linear correlator. Finally we apply this definition to the two stages of the F2Cor correlator [Eq. (7-10)].

The result provided by F2Cor follows the multiple-tau scheme. More precisely, the correlator is linear by level, and the time resolution is lowered by a factor of two from one level to the next.

The ACF is calculated for the following lag times in $\Delta {t}_{0}$units:

*k*is the level of the lag time$\tau ={2}^{k}l$.

Let $I\left(n\right)$ be the raw fluorescence signal that is the number of photons detected for $n\Delta {t}_{0}\le t<\left(n+1\right)\Delta {t}_{0}$.

Let *L* be the photon record length in $\Delta {t}_{0}$ unit. $0\le t<L\Delta {t}_{0}$.

We denote ${I}_{k,m}$ the binned fluorescence signal at level *k* that is the number of photons for.

*K*the level of the lag time from which F2Cor uses the B&M scheme.

For$k\ge K$:

For shorter values of the lag time F2Cor uses the SCH scheme:

Compared to${G}_{B\&M}\left(\tau \right)$, ${\overline{I\left(n\right)I\left(n+\tau \right)}|}_{Tr}={G}_{Tr}\left(\tau \right)/\left({2}^{k}\left(L-\tau \right)\right)$ is an improved estimator of $\u3008I\left(n\right)I\left(n+\tau \right)\u3009$.

The normalized ACF is defined by:

*k*is a linear correlator. The symmetrically normalized ACF estimator is then [17]:

## 4. Oscilloscope mode FCS

Since our correlator is a software correlator, it is flexible. We make use of this flexibility to provide a new acquisition mode, which we name *oscilloscope mode* (OM), and which is especially useful to optimize the setup. Before starting measurements, the FCS setup requires careful adjustment: alignment, correction collar, pinhole diameter using a reference dye solution. For this purpose one wishes one could continuously visualize the FCS curve while adjusting the system. This is precisely what OM allows. It calculates and displays continuously the FCS curve over a sliding time window. If the time window is too short, the FCS curve is too noisy, while a very long time makes the FCS curve display not responsive enough. In practice, the FCS curve is updated every Δ*T*_{0} = 0.1s, and the time window is Δ*T* = 2s in duration.

Repeating a correlation calculation every 0.1s over a $\Delta T=2s$ time interval would require a very high calculation time. In the following, we will show how we can calculate this OM ACF, which takes into account the symmetrical normalization, by simply using intermediate results of the full time ACF calculation, which are stored as the measurement progresses. For that purpose, first we write the expression of the symmetrically normalized OM ACF we want to calculate: As F2Cor is a two stage correlator we need to consider successively the B&M stage and the SCH stage. The expression of the symmetrically normalized OM ACF for the B&M stage is given in Eq. (11). For the SCH stage we first derivate the unnormalized OM ACF [Eq. (13)]. Then making the connection between the B&M stage and the SCH stage we derivate the final result [Eq. (15)] which uses intermediate results provided by F2Cor [Eq. (14)].

In the B&M mode the symmetrically normalized ACF at time $L\Delta {t}_{0}$averaged over a Δ*T* time window is defined as:

From Eq. (4) we find

During the normal full length FCS calculation, every Δ*T*_{0}, the following intermediate results are stored:

Figure 5 (Media 2) shows the user interface operating in real-time in OM. In particular a display shows the time trace of the molecular brightness, calculated as the product of the countrate and the average of the first few points of the ACF. While continuously monitoring the ACF curve and the brightness one can very rapidly optimize the setup, by changing the z-position of the objective, the correction collar and the confocal pinhole diameter. Optimization criteria are maximum brightness and smallest detection volume (highest ACF amplitude). In the case of a water immersion objective the z-position is not critical. When using an oil immersion objective, the laser focalization is no more diffraction limited when moving far away from the interface between the coverslip and the dye solution. In this latter case the z-position is important. Without OM, measuring and displaying a signal every 0.1s would result in a very noisy correlation curve so that the user would not easily see the effect of the adjustment on the correlation curve. In opposite, in OM, any sudden adjustment change will have an effect on the next curve update, while keeping an acceptable signal-to-noise ratio thanks to the 2s time window. Media 2 shows the real-time effect of the settings on the ACF curve and on the brightness.

## 5. Measurements on a reference dye

We wanted to evaluate the performance of our system at high countrate resulting from a high concentration reference dye solution.

First we measured the ACF on a reference dye solution of 5-Carboxytetramethylrhodamine (TMR) (reference dye sampler kit R-14782, Invitrogen), in the micromolar concentration range. Figure 5 shows the results we got for concentration ranging from 0.5 to 2.5µM. The excitation wavelength was 561nm, the power at the sample was 4.0µW, and the collection time was 60s. For an easier comparison, we display $C\times G$ the product of the concentration and ACF.

Ideally all curves should superimpose. However we see that the higher the concentration, the lower the amplitude of $C\times G$. At high countrate, dead-time ${t}_{dd}$of the SPAD, which is the time after each detected photon during which the SPAD won't be able to detect another photon, is not negligible. To the first order, the ACF is modified as follow [18]:

Thus, to the first order, the dead-time will only increase the apparent number of molecules that is why the measured correlation time is constant as a function of the concentration [inset of Fig. 6].

Figure 7 represents the countrate as a function of the concentration. For a negligible dead-time, the curve would be linear.

The relation between the expected countrate $\u3008n\u3009$and the measured one $\u3008m\u3009$ is [19]:

In our reference dye solution the expected countrate is proportional to the concentration $\u3008n\u3009=\alpha C$, so that ${t}_{dd}$ can be simply measured by fitting the curve of Fig. 7 by the following equation:We found*t*= 36ns. Using Eq. (16) we were able to correct the dead-time effect. The result is presented in Fig. 8, where we see that all curves superimpose. We see however that at 2.5µM the curve slightly departs from the average. This is because the validity condition of the correction $2{t}_{dd}\u3008n\u3009/\Delta {t}_{0}<<1$ is not well fulfilled anymore (1/2

_{dd}*t*= 14MHz).

_{dd}## 6. Discussion and prospects

To perform FCS measurements in the micromolar range using a setup which cannot operate at high countrate, one would need to reduce the excitation power by a factor we call *R*. This reduced excitation power has several consequences. First the individual brightness of the molecules will be reduced by a factor *R*. The signal-to-noise of the FCS curve depends quadratically on the brightness so that to maintain the same signal-noise-ratio, one would need to increase the measurement time by a factor *R*^{2}. Our system operates satisfactorily up to 8MHz. To get the same result on a system operating at 1MHz, one would need to increase the measurement time by a factor 64. For example, the acquisition time for the measurements of Fig. 8 was 60s for each curve. The measurement time would then need to be increased to more than one hour in the case of a system operating up to 1MHz. Another consequence of the reduced molecular brightness is that the autocorrelation curve will be more affected by the after-pulse effect. Indeed, if we performed FCS on a solution of fluorescent beads, the after-pulse effect would not be seen on the ACF curve because fluorescent beads are very bright particles. In opposite, if we performed FCS on an extremely highly concentrated solution (in the millimolar range) at very low excitation power, we would only see on the ACF curve the effect of the after-pulse and that of the instability of the instrument. To avoid the after-pulse effect a correction using a calibration process would be necessary, or the cross-correlation between two detectors would have to be performed, which would further increase the measurement time.

In terms of applications, performing FCS measurements at high concentration could be useful to analyze reactions with weak affinity. In the case of living cells, the concentration of proteins can also be high. FCS measurements in the micromolar range have been performed using nanoapertures milled in a metallic film [20], the effect of which is to reduce dramatically the observation volume. The advantage of our method is that we don't need coverslips with metallic coating, and in the case of measurements in living cell, the measurement could be performed at any point in the cell. The drawback is that because of the dead-time effect, the FCS curves need to be corrected. One might expect in the future SPAD will be available with shorter dead-time. Alternatively, one may use a multichannel photodetector, so that the countrate of each channel is much below saturation. Incidentally, using a dispersion prism one may this way perform spectrally resolved FCS. Ultimately the concentration range will be limited by the instability of the system (mechanical instability, laser fluctuation) [15], but as shown in section 5, our current limit is due to the dead-time of the SPAD and to the limit of validity of our correction process.

In this paper, the oscilloscope mode we have introduced was used simply as a convenient mode for adjusting the system. Its use could be extended to implement *time-resolved* FCS. In the case of a non-stationary system, such as living cells, the concentration/mobility of the protein of interest may evolve as a function of time. Time-resolved FCS would then be able to continuously measure the concentration/mobility fluctuations as the system evolves. The FCS curve at a given time necessarily results from the averaging over a certain time window. The shorter the time window is, the better the time resolution is, but the lower the number of photon is. The signal-to-noise ratio of the FCS curve is essentially dependant on the brightness of the molecule (the ratio of the countrate and number of molecules in the observation volume). If the brightness of the molecules is high, the capability of performing real-time ACF measurement at high countrate is essential, if one want to work even at moderate concentration. In this respect F2Cor is advantageous. To have a high brightness, the choice of the dye is naturally very important, as well as a very high photon collection efficiency. One can also increase the excitation power, with two limiting factors: first the photobleaching, and possibly a saturation of the dye due to the triplet state. Photobleaching affects the correlation function, the apparent diffusion time of which is shortened. Besides, as biological cells have a limited volume compared to that of the excitation volume, photobleaching may deplete the stock of fluorescent molecules in the case long acquisitions. One way to reduce the negative effects of the photobleaching could be the use of scanning FCS (SFCS) [21]. SFCS will reduce the distortion of the correlation curve and in addition, if the photobleaching is mediated by the triplet state, SFCS can reduce the photobleaching itself. In the case of very long acquisitions in living cells one might then combine SFCS and time-resolved FCS.

In this paper we used the PCI-6602 to construct an FCS setup at reduced cost, operating continuously in real-time at high countrate, with a time resolution of 1µs. However, our LabVIEW software, which integrate the F2Cor library, could easily be adapted to other single photon counting acquisition modules from various manufacturers (Beck&Hickl, Picoquant, Hamamatsu), which have better time resolution. All LabVIEW VIs as well as the F2Cor DLL library can be obtained by contacting the author.

## 7. Conclusion

We presented an FCS setup that can perform online ACF calculation at very high countrate, up to 8MHz, with minimum hardware. This high countrate capability results from the use of the counting board in the time mode, and from the use of F2Cor, a very fast software correlator. We have shown that henceforth real-time measurements in the micromolar range can be performed on a conventional optical setup, which should be useful for low affinity molecular interactions studies as well as measurements in living cells. In addition, this high countrate capability combined with the flexibility of the software approach opens up the way to time-resolved FCS, which will be useful to study non-stationary systems.

## Acknowledgments

This work was supported by Région Bretagne, Rennes Métropole, Conseil Général d’Ille-et-Villaine and by European Regional Development Fund.

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