Fluorescence Correlation Spectroscopy at Micromolar Concentrations

Article pubs.acs.org/JPCB

Fluorescence Correlation Spectroscopy at Micromolar Concentrations without Optical Nanoconfinement Ted A. Laurence,*,†,§ Sonny Ly,*,†,§ Feliza Bourguet,† Nicholas O. Fischer,† and Matthew A. Coleman†,‡ †

Lawrence Livermore National Laboratory, Livermore, California 94550, United States Department of Radiation Oncology, University of California, Davis, Sacramento, California 95817, United States

‡

ABSTRACT: Fluorescence correlation spectroscopy (FCS) is an important technique for studying biochemical interactions dynamically that may be used in vitro and in cell-based studies. It is generally claimed that FCS may only be used at nM concentrations. We show that this general consensus is incorrect and that the limitation to nM concentrations is not fundamental but due to detector limits as well as laser fluctuations. With a high count rate detector system and applying laser fluctuation corrections, we demonstrate FCS measurements up to 38 μM with the same signal-to-noise as at lower concentrations. Optical nanoconfinement approaches previously used to increase the concentration range of FCS are not necessary, and further increases above 38 μM may be expected using detectors and detector arrays with higher saturation rates and better laser fluctuation corrections. This approach greatly widens the possibilities of dynamic measurements of biochemical interactions using FCS at physiological concentrations.

I. INTRODUCTION

For a single diffusing species in a Gaussian detection volume of lateral width ω and longitudinal width l, the correlation function can be modeled using6

Fluorescence correlation spectroscopy is an important technique for the dynamic measurement of interactions between molecules in biological systems.1,2 Molecules diffusing through a small optical detection volume, defined using confocal microscopy or sometimes super-resolution microscopy,3,4 lead to fluctuations in fluorescence intensity. By calculating correlation functions from these fluctuating signals, information on concentration and diffusion rates of the molecules is obtained. The amplitude of the resulting correlation function is inversely proportional to the concentration of the fluorescent molecules, and the time scale of the correlation decay is related to diffusion rates. Binding to other molecules or structures may be detected as changes in diffusion rates. Additionally, if the binding partners are labeled with two different colors, amplitudes from cross-correlation calculations indicate binding.5 This class of methodologies has been widely used both in vitro and in cell-based studies. FCS measures dynamics using the intensity correlation g(2)(τ) of fluorescence, which is calculated according to the formula gI(2)(τ )

2

= ⟨I(t )I(t + τ )⟩/⟨I(t )⟩

© 2014 American Chemical Society

gI(2)(τ ) = 1/[N (1 + τ /τD) 1 + (ω/l)2 τ /τD ] + 1

(2)

where N is the molecular occupancy of the Gaussian detection volume (the average number of molecules in the detection volumeproportional to concentration) and τD = ω2/4D, where D is the diffusion coefficient. We use this model for the simulations below. However, most often, experimental setups do not have precisely Gaussian detection volumes, and the data are fitted sufficiently well to a simplified model that neglects the longitudinal diffusion (since l ≫ ω). We use the following model for the experimental data, which has been shown to lead to only small changes in extracted diffusion times when compared to the 3D model of eq 2:6 gI(2)(τ ) = 1/[N (1 + τ /τD)] + 1

(3)

Since the correlation amplitude decreases with increasing concentration, it is intuitive to think that the signal-to-noise on the measurement would decrease with increasing concenReceived: June 13, 2014 Revised: July 22, 2014 Published: July 24, 2014

(1) 9662

dx.doi.org/10.1021/jp505881z | J. Phys. Chem. B 2014, 118, 9662−9667

The Journal of Physical Chemistry B

Article

Figure 1. Experimental setup for measuring FCS at micromolar concentrations. (a) Emission from a confocal microscope is monitored by two APD banks of four APD photodetectors each. The schematic for APD bank 1 is shown as an expanded view. A photodiode simultaneously monitors the laser intensity. (b) A cross-correlation of the signal from the two APD banks is shown as the black line. The cross-correlation between one APD bank and the photodiode, which only contains contributions from laser intensity fluctuations, is shown in red. (c) Division of the two correlations in part b leads to corrected correlations. Three examples of measurements with 3.8 μM Alexa 488 are shown.

number of molecules is placed inside the box. Periodic boundary conditions are used, allowing a molecule that leaves Vbox to reappear at the opposite side with the same lateral position. Diffusion is simulated by a series of steps with Δt = 1 μs, during which the excitation rate is kept constant. At each step, the distance changes for (x, y, z) are determined by Gaussian pseudorandom numbers, with mean μ = 0 and standard deviation σ = (2DΔt)1/2, where D is the diffusion coefficient. Until time Δt is passed, waiting times between a series of photon detection events are generated using exponential pseudorandom numbers with a constant rate λ that depends on the excitation rate at the molecule’s position; the fluorescence lifetime is neglected, as are other photophysical effects. For this simulation, the simulation box is 180 times larger than the detection volume. D was set to 10−7 cm2/ s, leading to a diffusion time of 3.0 ms. For each simulation, 180 000 molecules were simulated for 10 s of simulation time with 1 μs time steps. b. Experimental Methods. The experimental setup and data analysis for this work are shown schematically in Figure 1. In summary, two photodetector banks with four avalanche photodiodes (APDs) each are used to increase the highest count rates available. Additionally, the laser excitation power is simultaneously monitored. All detection channels are monitored at 500 kHz detection rates. These experimental modifications allow for higher count rates and laser excitation intensity corrections. A previously built confocal fluorescence microscope with single molecule sensitivity was modified for this work.17,18 A stable 487 nm diode laser (Stradus 488, Vortran Laser) is coupled through an optical fiber and used for excitation. We have used two sets of photodetector “banks”, each consisting of

tration. However, the earliest statistical analysis of FCS indicated that the signal-to-noise of the measurement depended only on the fluorescence intensity per molecule, q (often called molecular brightness), and was independent of concentration,7 citing ref 8 as experimental validation. This would mean that there is no fundamental upper limit on the concentration range possible for use with FCS. Further calculations accounting for photon statistics and lower concentrations again found that, as the concentration increases to infinity, q remains the critical parameter and the signal-to-noise is independent of concentration.9 Statistical accuracy was calculated for modern confocal detection geometries, obtaining similar results.10 In addition, ref 10 experimentally verified the independence of the correlation function signal-to-noise on concentrations up to 200 nM, and emphasized that increasing q only helps the signal-to-noise up to the point where molecular diffusion noise dominates. Despite these longstanding indications of the possibility of using FCS at much higher concentrations, nearly all FCS publications that comment on this issue indicate that FCS may only be applied effectively at low, nM concentrations.2−4,11−15 Here, we show that this consensus is incorrect. We show, using simulations combined with experimentation, that FCS may be used at micromolar concentrations as long as the detectors can handle the high count rates and other sources of fluctuations, especially laser excitation fluctuations, are corrected.

II. EXPERIMENTAL AND SIMULATION METHODS a. Simulation Methods. Simulations for translational diffusion of molecules, photon emission, and detection were performed as in ref 16. A Gaussian detection volume with ω = 0.35 μm and l = 1.75 μm is placed at the center of a 3D simulation box with size Vbox = 3.5 × 3.5 × 17.5 μm3. A fixed 9663



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Figure 2. Simulations of diffusing fluorescent molecules in a Gaussian detection volume showing that the accuracy of FCS is constant with increasing concentration which is quantified as N, the molecular occupancy of the detection volume. (a) Example time traces for N = 0.1, N = 10, and N = 1000 are shown, normalized by dividing by the mean intensity. (b) Subtracting the mean and dividing by the standard deviation of time trace intensities from part a, the fluctuations that FCS measures are revealed. For N = 0.1, the black line visible just below 0 is for 0 photon counts, which is below the average number of photon counts. (c) The errors on fitted diffusion times and concentrations for the calculated correlations do not decrease with increasing concentration. The left axis is the diffusion time, and the right axis is the ratio of the fitted occupancy of detection volume (concentration) divided by the simulation value (from the x axis). Error bars are calculated using 30 repeated simulations. Correlations for simulated 10 s measurements of fluorescent molecules diffusing through solution are shown for (d) N = 0.1, (e) N = 10, and (f) N = 1000.

four APD detectors (PD-050-CTD, Micro-Photon-Devices), to increase the count rates available. The photon count rates from all four detectors in each bank were summed to act as one channel. Cross-correlations between several combinations of the eight channels were compared to ensure overlap of the detection volumes for all of the channels. Additionally, a photodiode (PDA-155, Thorlabs) is used to monitor the laser power. The eight channels of photon counts and laser monitor channel were acquired simultaneously using two synchronized data acquisition cards at 500 kHz (PCIe-6351, National Instruments). We used a photon counting strategy rather than photon timing to avoid saturating the data acquisition system with the high count rates. The measurements were performed on serial dilutions of a sample with 380 μM free Alexa 488 dye calibrated using a spectrophotometer. Due to the small (1−2 μL) volumes of sample micropipetted during dilutions, concentration errors of up to 20% were observed. We use a 1.4 NA oil immersion objective and a 75 μm pinhole. Our fitted molecular occupancy values indicate a detection volume of 1.8 fL. c. Data Analysis Methods. Corrections for laser excitation intensity fluctuations were performed by dividing two correlation functions. Modeling the measured signal M as the product of two independent random processes I (fluorescence) and L (laser intensity), the correlation of M is the product of the correlations of I and L: (2) gM (τ ) = gI(2)(τ )gL(2)(τ )

(2) gI(2)(τ ) = gM (τ )/gL(2)(τ )

(5)

In order to calculate the correlation functions g(2) M (τ) and from our measurements, a cross-correlation approach was used to eliminate spurious detector correlations. Crosscorrelation of the two detector banks was used to calculate g(2) M (τ). Cross-correlation of the laser monitor photodiode and one of the detector banks was used to calculate g(2) L (τ). Equation 5 was then used to obtain the corrected fluorescence correlation function, g(2) I (τ). The results of these calculations are illustrated in Figure 1b and c, where the correlation due to laser fluctuations is removed from the total correlation function by division. In another publication, a photodiode was used to correct for laser fluctuations in FCS, but the methodology for applying the correction was different and was not used in the context of high concentration FCS.19 The count rates for many of these experiments neared saturation for the APDs, up to 3 MHz per detector. Due to these high count rates, it was necessary to account for the deadtimes of the APDs in order to properly remove the laser fluctuations in calculating the correlations. The correlations are calculated using a modification of the multitau algorithm.20 The primary change is that, for each bin j, a corrected intensity Ij = nj/(tj − njΔt) is used for correlation calculations rather than the number of photon counts nj. tj is the width of the bin over which nj is acquired, and Δt is the dead time for each photodetector. This correction is applied individually to the data from each photodetector prior to summing the channels for each photodetector bank. Ensuring the linearity of the photodetectors or correcting for any nonlinearity accurately is critical for eq 5 to work well. g(2) L (τ)

(4)

so that correcting for laser fluctuations can be accomplished using the following equation: 9664



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Table 1. Fitted Values for Molecular Occupancy N (Proportional to Concentration), Diffusion Time (τD), and Fit Quality (χ2) for Various Concentrations of Alexa 488 and Two Laser Powersa 5 μW laser power

a

20 μW laser power

sample

38 μM

3.8 μM

380 nM

3.8 μM

380 nM

38 nM

N (1.8 fL volume) N τD (μs) χ2

41000 41300 ± 1300 57 ± 5 1.0

4100 4600 ± 300 60 ± 5 1.0

410 380 ± 40 54 ± 10 1.2

4100 4900 ± 100 57 ± 2 1.7

410 348 ± 4 55 ± 1 2.0

41 33.5 ± 0.5 54 ± 1 2.0

The mean and standard deviation of fits for eight measurements at 5 μW and four measurements at 20 μW of 1 min each are shown.

Figure 3. Example correlation curves for Alexa 488 at three different concentrations with a constant laser power of 5 μW: (a) 38 μM, (b) 3.8 μM, and (c) 380 nM. (d) Correlations normalized using fitted molecular occupancy have similar noise and overlap.

fitted values for N and τD are shown in Figure 2c, and examples of correlations for different values of N are shown in Figure 2d−f. The results in Figure 2 demonstrate that the errors on the fitted diffusion times and molecular occupancies (concentration) do not increase with increasing concentration, supporting the original analysis of signal-to-noise.7,9,10 The fitted values for N and τD match the simulation parameters. Both statistical analysis and simulations indicate that the signal-to-noise of FCS measurements does not decrease with increasing concentration. Why, then, have no experiments shown that it is possible to perform FCS at much higher concentrations than the nM limits frequently cited? There are two important constraints. First, in order to retain the signal-tonoise on FCS correlations, it is necessary to keep the intensity per molecule q constant. This means that, if the signal-to-noise is to remain the same, increasing the concentration by a factor

III. RESULTS AND DISCUSSION a. Simulations. In order to determine the behavior of FCS accuracy at higher concentrations, first we performed simulations of fluorescent molecules diffusing through a Gaussian detection volume with averages of 0.1, 1, 10, 100, and 1000 molecules inside the detection volume at one time. Figure 2a shows normalized time traces (divided by mean count rate) for 10 s simulations with N = 0.1, 10, and 1000. The dramatic decrease in the relative size of the fluctuations leads to the intuitive but incorrect conclusion that FCS would have low signal-to-noise at high concentrations. However, this is not the best way to visualize the fluctuations leading to FCS signals. Normalizing the time traces differently by subtracting the mean and dividing by the standard deviation (Figure 2b) reveals the fluctuations FCS measures, and shows that they do not change significantly with increasing concentration. The 9665



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Notes

of 10 increases the total detected count rate by a factor of 10. For very high concentrations, detector saturation limits the amount of signal that may be measured. If the experimentalist reduces laser excitation to avoid saturation, the signal-to-noise of the FCS measurement decreases rapidly. A second limitation arises from the fact that the relative size of the fluctuations at high concentrations is small. Although the signal-to-noise does not change for ideal experiments, other fluctuations, especially those from laser excitation variations, have correlations that can obscure the fluctuations we want to observe. Neither of these limitations is fundamental, and can be overcome with proper technological improvements and modifications. b. Experiments. We performed two series of measurements with constant laser power but varying dye concentration to demonstrate FCS at μM concentrations. By keeping the laser power constant for a series of concentrations, we demonstrate that the signal-to-noise of the correlations and values extracted from them do not vary within the measurement error. For the measurements made with 20 μW laser power, four 1 min measurements were made at each concentration shown in Table 1. For those with 5 μW, eight 1 min measurements were made at each concentration. By fitting the resulting corrected correlations to the model in eq 3, we extracted molecular occupancy N and diffusion time τD, and quantified the goodness of fit using χ2. The mean and standard deviation of the fitted values for each sample and laser power are shown in Table 1. For 5 μW laser power, we were able to go to higher concentrations (up to 38 μM) before saturation. Figure 3 shows the averaged corrected correlations for the 8 min of measurements made on free Alexa 488 fluorophore with 5 μW laser power. Figure 3d shows these correlations after normalizing them by subtracting the baseline value of 1 and dividing by the fitted molecular occupancy N. The overlap of these normalized correlations shows that the noise characteristics of the correlation curves do not change with increasing concentration. These results are also supported by the consistency of the mean and standard deviation of the fitted diffusion times and molecular occupancies in Table 1. In conclusion, FCS may be performed at arbitrarily high concentrations with the use of proper detectors and applying a correction factor. We have demonstrated FCS measurements up to 38 μM concentration with our current experimental setup, and expect further increases in possible concentrations with future improvements in detectors. We attempted measurements at 380 μM, but the laser power had to be decreased too far (400 nW) to allow for experiments in a reasonable time. Nanoconfinement or superresolution approaches to increasing the concentration range of FCS are not necessary for this purpose. Nanoconfinement is still necessary for isolation of single molecules at higher concentration 3 and for performing FCS over varying subdiffraction detection volume sizes.21 Our approach may be easily combined with those approaches and with crosscorrelation measurements. The results of this work greatly enhance the potential impact of FCS for monitoring molecular interactions both in vitro and in living cells.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52−07NA27344 within the LDRD program.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Author Contributions §

These authors contributed equally. 9666



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(20) Schatzel, K.; Drewel, M.; Stimac, S. Photon Correlation Measurements at Large Lag Times: Improving Statistical Accuracy. J. Mod. Opt. 1988, 35, 711−718. (21) Eggeling, C.; Ringemann, C.; Medda, R.; Schwarzmann, G.; Sandhoff, K.; Polyakova, S.; Belov, V. N.; Hein, B.; von Middendorff, C.; Schönle, A.; et al. Direct Observation of the Nanoscale Dynamics of Membrane Lipids in a Living Cell. Nature 2009, 457, 1159−1162.

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Fluorescence Correlation Spectroscopy at Micromolar Concentrations

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