High photon count rate super-resolution fluorescence fluctuation spectroscopy

Probing the diffusion of molecules has become a routine measurement across the life sciences, chemistry and physics. It provides valuable insights into reaction dynamics, oligomerisation, molecular (re-)organisation or cellular heterogeneities. Fluorescence correlation spectroscopy (FCS) is one of the widely applied techniques to determine diffusion dynamics in two and three dimensions. This technique relies on the autocorrelation of intensity fluctuations but recording these fluctuations has thus far been limited by the detection electronics, which could not efficiently and accurately time-tag photons at high count rates. This has until now restricted the range of measurable dye concentrations, as well as the data quality of the FCS recordings, especially in combination with super-resolution stimulated emission depletion (STED)-FCS. Here, we investigate the applicability and reliability of (STED-)FCS at high photon count rates (average intensities of more than 1 MHz) using novel detection equipment, namely hybrid detectors and real-time gigahertz sampling of the photon streams implemented on a commercial microscope. By measuring the diffusion of fluorophores in solution and cytoplasm of live cells, as well as in model and cellular membranes, we show that accurate diffusion and concentration measurements are possible in these previously inaccessible high photon count regimes. Other advantages include greater flexibility of experiments with biological samples with very highly variable intensity (e.g. due to a wide range of expression levels of fluorescent proteins), much shorter acquisition time, and improved data quality. This approach also pronouncedly increased the robustness of challenging live cell STED-FCS measurements of nanoscale diffusion dynamics.


Introduction
Fluorescence correlation spectroscopy (FCS) has, since its introduction almost 50 years ago, become a widely applied technique to study diffusion dynamics in synthetic and biological applications [1][2][3] . It has greatly contributed to the understanding of molecular diffusion in model systems and living cells, both in 2D (in vitro models or cellular membranes) and in 3D (solution or cellular cytoplasm and nucleus) environments [4][5][6][7][8] . Notably, it has offered fundamental insights into the dynamic organisation of living systems at the molecular level, e.g. by characterising the transient, dynamic, yet structured nature of the organisation of fluid membranes 5,9 .
FCS provides a plethora of information about molecular dynamics. The diffusion rates and local concentrations of fluorescent molecules can be determined directly from the autocorrelation functions 1,10,11 . The spatial variability can be further evaluated by laser-scanning [12][13][14] and imagingbased variants of FCS [15][16][17][18] . Further, molecular interactions can be probed either directly, e.g. binding of molecules detected by cross-correlation (FCCS) 19 , or indirectly via variations of the apparent diffusion coefficient at different length scales, measured by spot-variation FCS 20 providing information on diffusion modes as in single particle tracking 21 . Finally, the combination of FCS with superresolution stimulated emission depletion (STED) microscopy allows direct observation of nanoscale diffusion dynamics, shedding new light on molecular organisation below the diffraction limit 22 .
All these invaluable details are extracted from intensity fluctuations due to the transit of fluorescent molecules through the observation spot of the microscope. As the fluctuations (i.e. bursts in the fluorescence intensity trace) are most obvious for sparsely labelled samples, FCS is often considered a single molecule technique, and has thus been shown multiple times to perform accurately in the range of pico-and nanomolar concentrations 2 . These concentrations, though, can be far from physiological levels present in living systems, where molecular abundance can be much higher (e.g. average concentration of a protein in eukaryotic yeast cells is estimated to be around 1 µM 23 ).
Nevertheless, it has been theoretically predicted and experimentally verified that FCS can perform 4 similarly and can generate accurate results also for much larger concentrations (>100 nM) 24 . In this regime, the main factors for signal quality of FCS, often described by the signal-to-noise ratio (SNR), are the acquisition time (T), and the number of detected photons per molecule (i.e. molecular brightness, B, which depends on the absorption cross section and quantum yield of the dye, the power of the excitation laser, and the detection efficiency of the measurement setup): SNR  B  T 1/2 (see for example 11,[25][26][27][28]. For the most efficient and reliable detection of fluorescence fluctuations, sensitive single-photoncounting detectors are typically used, often coupled to fast electronics that enable accurate recording of photon arrival times thus also allowing additional photon filtering in post-processing 29 . One of the main drawbacks of this instrumentation, however, has been its rather long dead time after each photon detection (>100 ns) 30 , limiting photon count rates to a maximum of 1 MHz. This has posed a severe limitation to the accuracy and flexibility in FCS experiments at high fluorophore concentrations, which are however unavoidable for many applications -for example when measuring binding dynamics of low affinity, or diffusion dynamics and concentrations of cellular proteins at different expression levels. Several approaches have been developed to enable FCS measurements even in such cases: labelling of only a fraction of the molecules, reduction of the simultaneously visible fluorophores via fluorescence photoswitching 31,32 , splitting-up of the signal onto several detectors such as on custom-built detector banks 33 , or reduction of the effective observation volume 34,35 using for example small sample containers 36 , near-field structures 37,38 , plasmonic near-field optics 39-41 , or super-resolution STED microscopy 5,42 . Unfortunately, all of these techniques introduce more complexity and possible bias, for example due to required controls to check whether the fraction of labelled or photoswitched molecules truly reflect the entire population, influence on the sample and fluorescent molecules by surface or small volume effects, setup complexity, or perplexing photophysics of the fluorescent label.

5
Here, we demonstrate the straightforward realisation of FCS measurements at high photon count rates on a commercially available microscope, using novel photon counting instrumentation. By measuring the diffusion of fluorescent dyes in solutions, artificial and cell membranes, we explore performance, capabilities, accuracy, applicability and limitations of confocal FCS and STED-FCS experiments at photon count rates of up to 20-30 MHz per detection channel, revealing great potential for FCS experiments at high count rates. As examples, we show the independence of cytosolic protein diffusion on cellular expression levels and the application of high count rates to STED-FCS measuring the diffusion behaviour of lipids in cellular plasma membranes.

Non-saturated photon detection at high dye concentrations and laser excitation powers
We first tested the advanced photon counting instrumentation, implemented on a confocal and STEDcapable microscope, by recording fluorescence fluctuation data from a single dye (Atto655) diffusing in aqueous solution at different concentrations or excitation laser powers, resulting in different photon count rates. The photon counting instrumentation included hybrid detectors with very short dead times and fast FPGA electronics with real-time GHz sampling and pattern matching, which together with the 80 MHz pulsed fluorescence excitation allows for detection of photon count rates of tens of MHz without corrections (as described in detail in the Materials and Methods section). Figure 1A and B show fluctuations in the normalized photon count rates over time as recorded for three different dye concentrations and laser excitation powers, respectively. As expected from theory 10,25-28 , the relative fluctuations around the average count rate decrease with increasing dye concentration, but much less so with excitation laser power. Most importantly, we could follow a linear increase of photon count rate with dye concentration and laser excitation power ( Figure 1C Figure 1D) were to be expected due to dye photobleaching and saturation of excited state population and consequently fluorescence emission (i.e. not due to detector saturation, compare Figure 1C at same count rate levels), while slight saturation effects at very high dye concentrations may result from photon re-absorption and dye self-quenching, as indicated previously 33,43 . In due consideration of acquisition count rate being the limiting factor in conventional equipment, we present the rest of the data as a function of this parameter.

FCS noise levels at different count rates
The ability to record photon time traces at high count rates consequently allowed us to acquire FCS data for Atto655 up to 1 µM high dye concentrations and excitation laser powers up to 40 µW (≈ 30 kW/cm²). The autocorrelation curves for these unconventional conditions show similar decays as for low dye concentrations and laser powers (Figure 2A  An interesting feature of the FCS data recorded at different dye concentrations or excitation laser powers, i.e. photon count rates, are the different noise levels and resulting data quality. From theory 11,24,26 , the noise in FCS data should linearly decrease with excitation laser power and be independent of dye concentration. The latter has for example been experimentally verified for dye concentrations of up to around 100 nM 24 . Consequently, we set out to investigate noise levels for FCS data recorded at the large dynamic range of dye concentrations and laser powers, which became accessible using the new equipment. This provides us with a single value for the data quality of each measurement. Conveniently, this measure roughly corresponded to the relative standard deviation of the values of average transit times determined from fitting of the data (Figure SI 2, the nRMSD relates closely to the measurement error). In accordance with the theoretical predictions 11,24,26 , the nRMSD was only weakly affected by varying concentration ( Figure 2E), but could be greatly improved by increased excitation laser power ( Figure 2F). The excitation laser power directly increases the dyes' excited state population and thus fluorescence emission rate and the average detected count rate per single dye (molecular brightness), which is the reason for the improvements in noise levels. Under comparable measurement conditions, the nRMSD is therefore also a direct indicator of the molecular brightness of the investigated dye (inset in Figure 2E and Figure SI 3). Deteriorated noise levels, i.e. higher nRMSD values, were again observed at dye concentrations around 1 µM, but were much less pronounced at the highest excitation laser powers above 20-40 µW, despite detected saturation of photon count rates ( Figure   1D) and deviations of values of the transit times and correlation amplitudes ( Figure 2D) as highlighted above.

FCS noise levels at different acquisition times
Predicted from theory and to a certain extent verified experimentally 11,24,26 , the noise in FCS data should decrease with the square root of the acquisition time. We could well reproduce this dependence for different dye concentrations and excitation laser powers ( Figure 2G and H; again, the same issues as outlined above caused deviations at high dye concentrations and excitation laser powers). This data establishes unique possibilities of adapting to experimental conditions. Due to the absence of saturation effects in photon count rates in the 5-500 nM concentration range, the possibility of increasing the laser power and detecting correspondingly higher photon count rates does not only increase the data quality (i.e. lower nRMSD values), but alternatively allows for a significant reduction (up to two orders of magnitude) in the acquisition time required for generating similar data quality ( Figure 2G and H, Figure SI 2).  These data indicate that within the tested range the mobility of GFP is independent of expression level. In addition, the quality of the FCS data as quantified by the nRMSD values was maintained over the range of tested expression levels ( Figure 3D), as predicted from the behaviour of the organic dye in solution (compare Figure 1). Only in the regime beyond 10 MHz (in our case corresponding to concentrations around 1 µM), we observed notable signal deterioration.

STED-FCS of lipid dyes in model membranes
The and thus detected photon count levels ( Figure 4A, schematics). Large observation spots at the confocal recordings entail already high count rates and high values of N at rather low dye concentrations, while the smaller observation spots at the STED microscopy recordings require relatively large dye concentrations to reach photon count rates and values of N that are high enough for allowing reasonably low acquisition times (it has also been shown theoretically that too low count rates or concentrations lead to noisy and inaccurate FCS data 11,24,26 ). This has limited the range of useful dye concentrations in STED-FCS measurements using conventional detection electronics.   Note that we here measured the diffusion in the apical membrane of HeLa cells, i.e. 5-10 m above the microscope coverslip ( Figure 5A), rather than in the basal membrane as before 44 . This avoids potential biasing effects by the coverslip surface. Yet, penetration through the aqueous cellular environment over such a distance causes spherical aberrations when employing a traditional oilimmersion STED microscope objective (due to the refractive index mismatch between water and oil) 45

Conclusions
We systematically evaluated the reduction in error and bias of FCS measurements recorded at high photon count rates, as enabled by novel detection electronics integrated into a turn-key microscope.
We were able to record highly accurate FCS data with detected photon count rates of up to about 10 MHz, i.e. dye concentrations up to 1 M. This improved performance introduces huge flexibility for performing FCS experiments to measure diffusion or concentration, previously impossible due to limitations in the detection electronics (allowing e.g. only recordings of photon count rates of up to 0.8-1 MHz). This now enables: 1) FCS measurements at high dye concentrations for e.g. low-affinity binding assays, 2) the recording of fluctuation data with reduced acquisition times by increasing the excitation power to higher count rates, 3) performing live-cell experiments in a wide range of expression levels of fluorescently tagged proteins, and 4) optimization of the data quality of STED-FCS recordings over a wide range of observation spot sizes by increasing dye concentration and/or excitation laser power. Using these features we could for example show that cytosolic diffusion of GFP was independent of expression level in live HeLa cells, and that the fluorescent lipid analogue was diffusing freely in the apical membrane similarly as reported before for the basal membrane 44 Improved detection instrumentation as the one presented here are becoming increasingly available and will be further optimized, pushing the ease of use of FCS or related measurements, such as fluorescence cross correlation spectroscopy (FCCS) 49 , fluorescence lifetime correlation spectroscopy (FLCS) 50 , number and brightness (N&B) analysis 51 , or line-and raster-scanning correlation spectroscopy (RICS) 12,52 . In combination with high-throughput methods this could enable the systematic evaluation of overexpression of fluorescent proteins 53 , tracking of dynamically changing diffusion properties, or other previously unattainable applications.

Preparation of Supported Lipid Bilayers (SLBs)
SLBs were prepared by spin coating as described previously 54

19
The transfections of GFP-SNAP, cytoplasmic GFP, obtained from Dr. Katharina Reglinski, were performed with Turbofect (ThermoFisher) according to the manufacturer's protocol.

Preparation of Giant Plasma Membrane Vesicles (GPMVs)
GPMVs were prepared as described previously 54,55 . In brief, HeLa cells were cultured as described All FCS experiments were performed using the hybrid detectors (HyD-SMDs), featuring very short dead times, and FALCON electronics allowing acquisition of TCSPC data at photon count rates of up to 80 Mcps per detection channel without the necessity for corrections. This implementation is based on sampling the signal from the pulsed laser and detectors using fast FPGA electronics and applying pattern matching to the resulting bitstreams, producing as output the photon arrival times with a resolution of 97 ps and deadtime <1.5 ns, at GHz sampling rates.
Measurement times ranged as indicated from 10 to 60 seconds. Only for the lifetime measurements we used 40 MHz pulsing of the white light laser for excitation.

Data analysis
Correlation, time trace cropping, gating and fitting was performed using the built-in routines in LAS-X (Leica Microsystems). Time gates were applied as appropriate; most importantly in STED-FCS to remove confocal contributions (see Figure SI 7). Fitted curves, intensity traces and fitting parameters were exported to Excel (Microsoft) for further analysis. Solution and cytoplasmic GFP data were fitted with a free 3D diffusion model (including offset and triplet as appropriate: triplet time GFP 40 µs, Atto655 none 57 , Abberior STAR Red 5 µs). SLB, GPMV and cell membrane data were fitted with a 2D diffusion model (including offset and triplet time for Abberior STAR Red-PEG-Chol: 5 µs).
For concentration estimation we assume a confocal volume of 1 fL. Given that the amplitude relates to the inverse number of particles, concentrations can be estimated 10 .

21
As a measure of data quality and curve smoothness, nRMSD values were calculated by taking the rootmean-square difference between the measured FCS curve and its fit up to the transit time, and normalised to the fitted amplitude. For STED-FCS experiments the diffusion coefficient was calculated as described before 22 using the following formula: