Quantifying phase separation at the nanoscale by dual-color fluorescence cross-correlation spectroscopy (dcFCCS)

Liquid–liquid phase separation (LLPS) causes the formation of membraneless condensates, which play important roles in diverse cellular processes. Currently, optical microscopy is the most commonly used method to visualize micron-scale phase-separated condensates. Because the optical spatial resolution is restricted by the diffraction limit (~200 nm), dynamic formation processes from individual biomolecules to micron-scale condensates are still mostly unknown. Herein, we provide a detailed protocol applying dual-color fluorescence cross-correlation spectroscopy (dcFCCS) to detect and quantify condensates at the nanoscale, including their size, growth rate, molecular stoichiometry, and the binding affinity of client molecules within condensates. We expect that the quantitative dcFCCS method can be widely applied to investigate many other important phase separation systems.


INTRODUCTION
Biomolecules are found to form membraneless organelles in live cells through multivalent interactions, which is known as LLPS (Banani et al. 2017;Hyman et al. 2014). A well-known membraneless organelle is nucleolus, which mediates RNA processing and ribosomal biogenesis (Boisvert et al. 2007;Feric et al. 2016;Mitrea et al. 2016). Many other condensates formed by LLPS also play important roles in various biochemical processes, including cell signaling and DNA damage responses (Wu 2013;Zeng et al. 2021).
Recently, LLPS has attracted significant attention for its great importance in various cellular functions. Many studies are focused on the physical and chemical properties of condensates, mechanisms of condensates formation and the molecular basis of their functions (Alberti et al. 2019). Methods used in these studies include morphological, rheological and structural characterization of condensates . Optical microscopy, especially the confocal fluorescence microscopy, is the most commonly used method to visualize LLPS. However, it is restricted by the optical diffraction limit (~200 nm). Herein, we developed a dcFCCS method to capture condensates at the nanoscale. In addition, the dcFCCS can quantify the size, growth rate, molecular stoichiometry of condensates and the binding affinity with condensates.

DEVELOPMENT OF NANOSCALE PHASE SEPARATION QUANTIFICATION METHODS
To detect phase separation at the nanoscale, various methods have been used in previous studies. Superresolution microscopy has been applied to capture biomolecular condensates beyond the optical diffraction limit (Sydor et al. 2015). For instance, stochastic optical reconstruction microscopy (STORM), with a spatial resolution of ~30 nm, was used to observe stress granule in vivo, which revealed detailed characterization of core-shell structure of stress granules and quantified the size of cores (~200 nm in diameter) (Jain et al. 2016). In addition, transmission electron microscope was used to characterize the hydrogel formed by fused in sarcoma (FUS) protein, which is amyloid-like fibers with 500 nm in length and 30 nm in thickness (Kato et al. 2012). Correlated light and electron microscopy (CLEM) was also used to capture the ultrastructure of nucleolus (Normand et al. 2016). However, none of these techniques are able to capture the dynamic transition process from miscible individual molecules to micron-scale condensates. Here, we provided a detailed protocol of our previously published dcFCCS method (Peng et al. 2020). We believe that this protocol will help researchers to visualize and to quantify nanoscale condensates in other important LLPS systems.

APPLICATIONS AND ADVANTAGES OF THE PROTOCOL
Our developed dcFCCS method is a simple and powerful way to quantify condensates at the nanoscale. Firstly, dcFCCS is suitable for freely-diffusing molecules, complexes and condensates, whose sizes range from sub-nanometer to micrometer. Therefore, the dynamic formation process from miscible individual molecules to condensates can be captured. Secondly, dcFCCS is highly sensitive to capture heterocomplexes and condensates containing two kinds of fluorophores. Therefore, concentrations far above the physiological conditions and the addition of crowding agents, which were commonly used to induce the formation of micron-scale condensates , are not needed. Thirdly, molecular stoichiometry and binding affinity with condensates can be quantified. Lastly, for each data collection, only 5-20 μL of labeled molecules, whose concentrations range from subnmol/L to μmol/L, are needed, which is user-friendly. In our previous report, LLPS at the nanoscale formed from a model system built from yeast SmF (ySmF) variants was examined (Peng et al. 2020).

LIMITATIONS OF THE PROTOCOL
Our method has the following limitations. Firstly, biomolecules of interest including proteins and nucleic acids need to be labeled with suitable organic fluorophores or be fused with fluorescent proteins, whereas commonly used turbidity experiment can use unlabeled samples. Secondly, dcFCCS calculates crosscorrelation curves of two different fluorophores. When the formation of condensates is driven by three or more components, dcFCCS assays need to be performed and repeated with different doubly-labeling schemes. Three or four different fluorophores of different emission wavelengths can be used, only when their excitation and emission crosstalk is carefully corrected. Thirdly, dcFCCS can only capture freely-diffusing molecules and condensates. Therefore, large condensates, which precipitate, are not suitable for dcFCCS measurements. Lastly, to perform quantification analysis, size distributions of condensates cannot be too broad, so that the dcFCCS curve can be well fitted by the singlecomponent diffusion model (Peng et al. 2020). In our ySmF LLPS model system, condensates formed at the nanoscale satisfy this criterion.

OVERVIEW OF THE PROTOCOL
A common application of fluorescence correlation spectroscopy (FCS) is to quantify the dwell time of molecules of interest in the confocal detection volume, from which diffusion coefficients of molecules can be quantified (Hess et al. 2002). The rationale behind this protocol is based on the fact that the sizes of freelydiffusing molecules, complexes and condensates determine their diffusion coefficients, which can be quantified by the dcFCCS method (Schwille et al. 1997). Two fluorophores of different emission wavelengths are needed for dcFCCS assays, which not only measure the sizes of complexes and condensates containing both fluorophores but also quantify the proportions of labeled molecules participating in the condensates containing both fluorophores. Briefly, to perform dcFCCS measurements, components participating into LLPS formation are labeled. After preparation of passivated slides and calibration of dcFCCS instrument, dcFCCS measurements are performed to quantify LLPS at the nanoscale. After data analysis, the size and growth rate, the molecular stoichiometry of condensates can be quantified, as well as the binding affinity of client molecules within condensates. Note that some parts of the protocol can be modified and optimized, as described in the section "Experimental design" below.  to form condensates in the tube. 12 Mix client protein, AF488 labeled PDZ, into the PRM 14 -(SH3-KKETPV) 14 phase separation system, add the whole mixture to the coverslips and record dcFCCS curves and raw photon data for 5 min under 488 nm and 640 nm laser excitation. 13 dcFCCS curves and raw photon data are used to calculate the size, growth rate, stoichiometry of condensates formed, as well as the binding affinity of client protein within condensates. τ (A) Quantify the size of condensates. The diffusion times ( Dx ) derived from the cross-correlation curve are used to calculate hydrodynamic radii of condensates. τ (B) Quantify the growth rate of condensates. Divide the 9-min-length raw data into 1-min-length data to recalculate dcFCCS curves, from which changes of Dx and radii over time are estimated. (C) Quantify the molecular stoichiometry within condensates. Raw photon data is binned into 1ms bins to generate fluorescence trajectories. By defining the threshold as three standard deviations (SDs) above the mean, only bursts exceeding the threshold are selected to calculate intensity ratio (I AF488 /I Cy5 ), which is converted into the molecular composition (N KKETPV /N PDZ ) after correcting relative intensity and background. (D) Quantify the binding affinity of the client within condensates. Amplitudes of autocorrelation and cross-correlation curves are calculated and their ratios are used to estimate the binding constant of the client within condensates.

Sample preparation
dcFCCS is a fluorescence based method, which requires signals from two fluorophores of different wavelengths. It is necessary to choose a suitable dye with minimal crosstalk between them for dcFCCS measurements. We recommend AF488 and Cy5 (or fluorophores of similar spectra). The crosstalk of AF488 signal into the Cy5 detection channel is ~1%. However, the crosstalk of Cy3 signal into the Cy5 detection channel is 5%-6%. Proteins and nucleic acids can be labeled via different chemical procedures. Both ySmF derived proteins, KKETPV 14 and PDZ 14 , contain an engineered cysteine residue to site-specifically react with maleimide derived fluorophores. The reaction between NHS ester derived fluorophores and NH 2 group is another common way to label proteins. Fluorescent proteins fused proteins are suitable for dcFCCS measurements. Labeled short DNA and RNA can be customized synthesized.
Please pay attention to the influence of labeling on the aggregation and activity of the protein. Sometimes, excess dye or high labeling temperature induces aggregation of the protein. Therefore, size-exclusion chromatography is recommended to remove aggregated proteins before dcFCCS assays. A monomeric variant of GFP (A206K) is recommended to avoid oligomerization induced by GFP (Alberti et al. 2018). In addition, specific tags, such as Q3 tag (GQQQLG) (Lin and Ting 2006) and A1 tag (GDSLDMLEWSLM) (Zhou et al. 2007), are alternative labeling approaches to label proteins.

Passivated slides preparation
PEG-passivated slides are prepared to reduce nonspecific adsorption of biomolecules and condensates on slide surface, which decreases signals and increases background and noise. If needed, 0.1%-1% BSA or 0.02%-0.1% Tween-20 (Bi et al. 2016) can be included to further reduce non-specific adsorption. However, whether BSA and Tween-20 affect LLPS needs to be examined case-by-case. The fluorescent background contributed by the buffer is usually 10-500 Hz. If the background is higher than expected, buffer and coverslips need to be replaced by a fresh clean batch.

dcFCCS calibration
Before performing the experiment, it is necessary to calibrate the instrument using a standard fluorophore and a dual-labeled dsDNA, to estimate the excitation volumes of two lasers and their overlapped volume. The excitation volume of 488 nm laser is determined by a standard fluorophore, such as AF488, whose diffusion coefficient is known. The value of the excitation volume is an important indicator, which is usually around 1 fL. Its sudden increase indicates misalignment of the microscope, which needs to be adjusted before further measurements. Correction factor Cd 488 is used to calibrate diffusion times extracted from autocorrelation curves and cross-correlation curves. Correction factors Cr 488 and Cr 640 are the ratios of the overlapped excitation volume over the excitation volume of 488 nm laser and 640 nm laser, respectively. Usually, values of Cr 488 and Cr 640 are ~0.5, otherwise, the instrument needs to be maintained to increase overlapping between 488 nm and 640 nm lasers.

Data acquisition
Before the experiment, confirm all optical components including dichroic mirrors and the bandpass filters are suitable for selected fluorophores. Our experiment is based on a home-built confocal microscope. Commercial microscope, such as FV 1200 laser scanning confocal microscope equipped with avalanche photodiode detectors (APDs), is also able to perform dcFCCS measurements.
Quantitative interpretation of FCS results strictly depends on the geometrical shape of the confocal excitation volume from which fluctuating fluorescence signals are detected. Due to reflection index mismatch between immersion oil and an aqueous sample, the water microscope objective is recommended for quantifying concentrations of labeled species in solution. However, in this procedure, molecular stoichiometry and relative concentration ratio of labeled species are quantified without quantifying their concentrations. As a result, the confocal microscope equipped with an oil immersion objective is also suitable for such applications.
After mixing, the growth of condensates formed from AF488-KKETPV 14 and Cy5-PDZ 14 can take hours. Therefore, dcFCCS curves and raw photon data can be collected for at least 1 h for this model system. According to our own experience, the formation of nanoscale condensates is usually faster than what we expect based on the results of conventional optical microscopy. Therefore, we recommend to start data collection right after mixing all necessary components to initiate LLPS.

dcFCCS data analysis
This step is data mining. The first step is to extract amplitudes and diffusion times from correlation curves. Different models are applied under different conditions. Autocorrelation curves of AF488-KKETPV 14 and Cy5-PDZ 14 , respectively, are fit by Eq. 1, which includes three-dimensional (3D) diffusion and the triplet state of a single component.
in which A is the amplitude of the autocorrelation curve (A 488 and A 640 ), is the diffusion time of the labeled molecules, T is the triplet-state fraction and is the relaxation time of the triplet state. For the confocal volume from which fluorescence signals were collected for FCS analysis, a is the ratio of the vertical radius of the confocal volume over its horizontal radius. A is the G(0) value of the auto-correlation curves, and G(0) = 1/N with N being the average number of molecules within the confocal volume.
Cross-correlation curve (also known as dcFCCS curve) between AF488-KKETPV 14 and Cy5-PDZ 14 , is fit by 3D diffusion model of a single component, shown in Eq. 2.
τ Dx in which A x is the amplitude of the cross-correlation curve, that is the G x (0) value of the cross-correlation curve, and is the diffusion time of the dual-labeled molecules.
The fraction of AF488-KKETPV 14 forming duallabeled molecules is calculated by and the fraction of Cy5-PDZ 14 forming dual-labeled molecules is calculated by correction factor Cr 488 and Cr 640 are determined in Step 8(F). When quantifying stoichiometry, it is important to set a threshold so that bursts and background are well separated. In KKETPV 14 and PDZ 14 phase separation system, the threshold is defined as three SDs above the mean. Thresholds from two SDs above the mean to four SDs above the mean are also tested, displaying minor effects on the intensity ratio (I AF488 /I Cy5 ). Users should adjust the threshold value in their own measurements.

Data acquisition [TIMING 2-3 d]
9 After sample labeling and instrument calibration, it's time to acquire the data.

Data analysis [TIMING 1-2 d]
13 dcFCCS curves and raw photon data are used to extract various physical and chemical properties of condensates, including the size and growth rate of condensates, stoichiometry within condensates as well as the binding affinity of client molecules with condensates. τ Dx R cond (A) Quantify the size of condensates. In Steps 9-10, dcFCCS curves have been acquired. According to Eq. 2, dcFCCS curves are fitted to extract diffusion times ( ), which can be used to quantify hydrodynamic radii of heterocomplexes and condensates formed from AF488-KKETPV 14 and Cy5-PDZ 14 ( ) via Eq. 6. R Quantifying phase separation at the nanoscale by dcFCCS τ Dx τ dye here, of heterocomplexes and condensates and of AF488 have been determined in Steps 9(C)-9(D) and Step 7(F), respectively. R dye of AF488 is 0.58 nm according to published results (Heyman and Burt 2008). [? TROUBLESHOOTING] τ Dx (B) Quantify the growth rate of condensates. The 9min-length raw data is divided into nine 1-minlength data. Like Step 13(A), for each 1-minlength data, calculate and fit autocorrelation curves with Eq. 1 and fit cross-correlation curves with Eq. 2. Values of A 488 , A 640 and A x , and of dcFCCS curves for each 1-min-length data are all quantified. i. Fraction of AF488 labeled molecules participating into condensates formation is calculated via Eq. 3. ii. Fraction of Cy5 labeled molecules participating into condensates formation is calculated via Eq. 4. τ Dx iii.
indicates the size of condensates. It is also used to quantify dynamics of condensates growth over time from the changes of hydrodynamic radii calculated from 1-minlength data via Eq. 6. (C) Quantify the molecular stoichiometry within condensates. Raw photon data is binned into 1ms bins to generate fluorescence trajectories. i. To convert the intensity ratio into molecular ratio, the brightness of individual molecules needs to be determined. In Step 9(C), autocorrelation curves of AF488-KKETPV 14 and Cy5-PDZ 14 have been acquired, respectively, from which A 488 and A 640 are determined. Molecular brightness of AF488-KKETPV 14 (Q AF488 ) and Cy5-PDZ 14 (Q Cy5 ) can be estimated.
in which I 488 and I Cy5 are the fluorescence intensities collected in the AF488 and Cy5 detection channels, respectively, which are usually defined as the number of photons collected per ms. In our system, Q AF488 of AF488-KKETPV 14 is 16.8 ± 0.4 counts per ms, and Q Cy5 of Cy5-PDZ 14 is 9.2 ± 0.6 counts per ms. ii. Defining the threshold as three SDs above the mean, only bursts exceeding the threshold in both AF488 and Cy5 detection channels are selected to calculate the intensity ratio (I AF488 / I Cy5 ) after subtracting of the background. The molecular composition (N KKETPV /N PDZ ) of each burst can be estimated via Eq. 9.
plot the distribution of log(N KKETPV /N PDZ ) of all bursts and fit it with Gaussian function to determine the peak center, from which averaged molecular stoichiometry within condensates is estimated.
[CRITICAL STEP] Defining the suitable threshold is an important step to select bursts to calculate the molecular composition within condensates. In the previous study, we also tested 2 SDs above the mean and 4 SDs above the mean, which have minor effects on the intensity ratio (I AF488 /I Cy5 ). In different phase separation systems, it is necessary to adjust the threshold value to optimize the burst selection. × (D) Quantify the binding affinity of client molecules with condensates. In Steps 11-12, client AF488-PDZ is added to bind with PRM 14 -Cy5-(SH3-KKETPV) 14 condensates, and raw data is acquired. Like Step 13(A), fit autocorrelation curves and cross-correlation curves to calculate A x and A 640 . Corrected A x /A 640 indicates the proportion of client molecules (AF488-PDZ) binding with condensates. c AF488-PDZ and c KKETPV are initial concentration of AF488-PDZ and initial effective concentration of KKETPV, respectively, which are usually similar to each other.
[AF488-PDZ-KKETPV] is the concentration of AF488-PDZ bound with condensates calculated via Corrected A x /A 640 c AF488-PDZ . Then binding constant can be calculated via Eq. 10.

ANTICIPATED RESULTS
We generated two ySmF variants (KKETPV 14 and PDZ 14 ) (Zhou et al. 2020) to induce LLPS. KKETPV 14 and PDZ 14 are labeled by maleimide-derived AF488 and Cy5 fluorophores, as shown in Steps 1-5. After mixing AF488-KKETPV 14 and Cy5-PDZ 14 , dcFCCS experiments were performed to detect dual-labeled condensates whose diffusion times correlate with molecular weight, as shown in Steps 8-9 (Fig. 1A). When high concentrations of KKETPV 14 and PDZ 14 were used, diffusion time of dcFCCS curves increased (Fig. 1A). Longer incubation time leads to larger condensates and longer diffusion time (Fig. 1A). After data analysis, as shown in Step 13(A), diffusion time of dcFCCS was converted into hydrodynamic radii (Fig. 1B).
To examine the dynamics of phase separation formation, growth rates of condensates were calculated, as shown in Step 13(B). 9-min-length raw data was divided into nine 1-min-length data. Fractions of components and condensates radii were plotted over time to quantify the growth rate of condensates (Fig. 1C, 1D). To quantify the stoichiometry, as shown in Step 13(C), bursts above the background were identified and selected from 1-ms-binned fluorescent trajectory (Fig. 1E). After correcting relative intensity and background, distributions of KKETPV 14 /PDZ 14 molecular composition within each burst were fitted by Gaussian distributions to determine the molecular stoichiometry (Fig. 1F).
To quantify the binding affinity of client protein within condensates, another phase separation system was generated. It is formed from unlabeled PRM 14 and Cy5-(SH3-KKETPV) 14 , which is able to recruit AF488-PDZ. Then dcFCCS experiment was performed, like Step 12. After data acquisition, auto-correlation and crosscorrelation curves were obtained between Cy5-PRM 14 -(SH3-KKETPV) 14 condensates and AF488-PDZ to calculate the binding affinity ( Fig. 2A, 2C). As shown in Step 13(D), based on concentrations of components and corresponding participating proportions, binding affinities (K d ) between PDZ and KKETPV in the absence of phase separation and in the presence of condensates of different sizes were quantified.   • Sodium bicarbonate (Sigma-Aldrich, cat. no. 127-09-3)

Amino-silane reagent
Add 1 mL 3-aminopropyltriethoxysilane and 5 mL acetic acid into 94 mL methanol. Prepare the solution freshly every time.
[CAUTION!] Acetic acid is volatile. Handle in a fume hood.

PEGylation solution
Dissolve 60 mg mPEG2000 in 240 μL 0.1 mol/L sodium bicarbonate. Prepare fresh solution every time and add them onto coverslips within minutes.