Methods for Characterizing the Material Properties of Biomolecular Condensates

Abstract

Biomolecular condensates are membrane-less sub-cellular compartments that perform a plethora of important functions in signaling and storage. The material properties of biomolecular condensates such as viscosity, surface tension, viscoelasticity, and macromolecular diffusion play important roles in regulating their biological functions. Aberrations in these properties have been implicated in various neurodegenerative disorders and certain types of cancer. Unraveling the molecular driving forces that control the fluid structure and dynamics of biomolecular condensates across different length- and time-scales necessitates the application of innovative biophysical methodologies. In this chapter, we discuss major experimental techniques that are widely used to study the material states and dynamics of biomolecular condensates as well as their practical and conceptual limitations. We end this chapter with a discussion on more advanced tools that are currently emerging to address the complex fluid dynamics of these condensates.

1. Introduction

Biomolecular condensates are liquid-like bodies harboring multiple protein and RNA molecules and are believed to form via liquid-liquid phase separation (Alberti, 2017a; Banani, Lee, Hyman, & Rosen, 2017; Forman-Kay, Kriwacki, & Seydoux, 2018; Hyman, Weber, & Jülicher, 2014; Mitrea & Kriwacki, 2016). The molecular components of a biomolecular condensate can be categorized as either scaffolds or clients (Banani et al., 2016; Ditlev, Case, & Rosen, 2018). Scaffolds are multivalent proteins/RNA/DNA that are necessary to form a biomolecular condensate, their absence directly results in the disappearance of such condensates in the cell. Clients are molecules that localize within biomolecular condensates due to preferable interactions with the scaffolds but may not directly contribute to their formation/stabilization. The fluid properties of a condensate in vivo are determined by inspecting whether these condensates undergo coalescence, display jetting or dripping behavior, and exchange molecules with the surrounding environment. Furthermore, the liquid state of a condensate can be assessed by characterizing the diffusion of constituent components within the condensates’ internal microenvironment (Brangwynne et al., 2009; Feric et al., 2016; Nott et al., 2015).

It is becoming increasingly clear that the fluid properties of biomolecular condensates are intricately connected to the sequence composition and structure of the scaffolding biopolymers (Alshareedah et al., 2019; Boeynaems et al., 2019; Guillén-Boixet et al., 2020; Wang et al., 2018; Zhou et al., 2019). Furthermore, environmental factors such as macromolecular crowding, salt concentration, and pH have been shown to substantially influence the material properties of these condensates (Alberti, 2017b; Guillén-Boixet et al., 2020; Kaur et al., 2019). These molecular and environmental cues are essential to the physiological regulation of a condensate’s biological function. Alterations in the fluidity and hence the internal dynamics of a condensate by means of gelation and/or aggregation have been implicated in many neurodegenerative disorders (Aguzzi & Altmeyer, 2016; Alberti & Hyman, 2016; Forman-Kay et al., 2018; Gitler, Dhillon, & Shorter, 2017; King, Gitler, & Shorter, 2012; Ramaswami, Taylor, & Parker, 2013; Shin & Brangwynne, 2017). Therefore, understanding the molecular rules governing the material properties of biomolecular condensates is indispensable for mitigating their pathological deterioration at the onset of disease.

The majority of the current techniques used to assess the dynamics of biomolecular condensates involve the application of fluorescence microscopy. Recently, optical tweezers have been utilized to manipulate biomolecular condensates and infer some key mechanical properties (Alshareedah et al., 2019; Kaur et al., 2019; Patel et al., 2015; Wang et al., 2018). Here, we present a detailed account of the current methods to probe the physical properties of biomolecular condensates (see Table 1). Our description will focus on conceptual and procedural details of applying these techniques and not on the instrumental aspect, since almost all of these experiments can be done utilizing available commercial instruments without any special requirements.

Table 1.

Summary of the experimental techniques discussed in this chapter.

Technique	Measured quantity
Active droplet coalescence	Viscosity:Surface tension
Fluorescence recovery after photobleaching (FRAP)	Macromolecular diffusion
Single Particle Tracking (SPT)	Condensate viscosity
Active microrheology	Surface tension Viscosity Viscous and elastic moduli

2. Measuring mesoscale physical properties of liquid droplets using optical trap-induced droplet coalescence: Concepts

One of the hallmarks of liquid droplets is the ability to coalesce and relax to different shapes in response to the governing forces. This is due to the flexibility of the liquid surface and the relatively weak and reversible binding between the molecules constituting the liquid. The formation of protein/RNA condensates by liquid-liquid phase separation is usually manifested in the form of spherical liquid droplets that are enriched in these biomolecules (Brangwynne, Tompa, & Pappu, 2015). These condensates assume spherical geometry (in the absence of an external field) to minimize their surface energy (Berthier & Brakke, 2012; Rowlinson & Widom, 2013). Any deformation from the spherical shape of a droplet is thermodynamically unfavorable due to the creation of pressure gradients on either side of the surface (Leal, 2007). However, such deformities may be stable in the presence of external forces such as shear flow or adhesion to a solid surface (Berthier & Brakke, 2012). The relaxation of a deformed droplet into the equilibrium spherical shape occurs on a time scale that is dictated by the interfacial tension and viscosity of the droplet (Leal, 2007). Specifically, the interfacial tension is the driving force for the relaxation process while the viscosity opposes such a process via a drag/friction force. Simply put, a droplet with high surface tension and low viscosity will have a short relaxation time (fast relaxation) while a droplet with low surface tension and high viscosity will have a long relaxation time (slow relaxation) (Leal, 2007). The method presented here utilizes the event of droplet coalescence to extract the characteristic time-scale of relaxation. When two droplets come in contact with each other, a capillary bridge forms between them, joining the droplets together into a single body of liquid that has an ellipsoidal shape (Paulsen, Carmigniani, Kannan, Burton, & Nagel, 2014). The relaxation of this deformed liquid drop back to a spherical shape can be monitored in real time. Conventionally, the parameter used to quantify the relaxation process is the aspect ratio of the droplet (Brangwynne, Mitchison, & Hyman, 2011; Eggers, Lister, & Stone, 1999; Elbaum-Garfinkle et al., 2015; Jeon et al., 2018). The aspect ratio is defined as the ratio between the lengths of the orthogonal semi-major axes of the deformed droplet. During coalescence, the aspect ratio relaxes from an initial value of 2 to a final value of 1 given that the two droplets are identical in size (Fig. 1). In a mathematical form, the aspect ratio (A) can be written as

$$A=1+(A_0-1)e^{-\frac{t}{\tau }}$$ (2.1)

Where τ is the characteristic time of relaxation. In the case of a Newtonian liquid, where there is a linear relationship between stress and strain, we can relate the relaxation time τ to the viscosity η and surface tension γ as

$$\tau =l\left(\frac{\eta }{\gamma }\right)\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }$$ (2.2)

Where l is the average diameter of the two droplets (Brangwynne et al., 2011). It is clear from equation 2.2 that the relaxation time also depends on the size of the coalescing droplets. This calls for normalization with respect to the droplet size in order to extract the mesoscale fluid properties of the condensate. For Newtonian liquids, plotting the relaxation time against the average diameter of the coalescing droplets should yield a linear relation with a slope of η/γ. The quantity η/γ is also called the inverse capillary velocity (Brangwynne et al., 2011). Droplets that have viscoelastic properties may not display a simple relaxation process. This is due to the relaxation process being accompanied by an increase in the elastic energy of the fluid due to compression, which hinders the relaxation process leading to arrested coalescence (Pawar, Caggioni, Hartel, & Spicer, 2012). In other words, for predominantly elastic condensates, the relaxation process is expected to take an indefinitely long time with no visible change (Dahiya, Caggioni, & Spicer, 2016). Accordingly, this assay is advantageous for judging the condensate material property since it displays a clearly distinct behavior for viscous and viscoelastic condensates.

Fig. 1.

Probing droplet coalescence using aspect ratio analysis.

Conventionally, analyzing droplet coalescence events is done using video microscopy (Brangwynne et al., 2009; Brangwynne et al., 2011; Elbaum-Garfinkle et al., 2015; Jeon et al., 2018). A sample containing protein/RNA condensates is deposited on a non-adhesive glass surface and imaged for a long period. Passive fusion events occur when droplets within proximity of each other touch and undergo coalescence. Image analysis is then used to extract and monitor the aspect ratio of the deformed droplet as a function of time (Fig. 1). Although widely used, this method suffers from some technical and practical issues:

1. Droplet coalescence is opposed by the friction between the condensate and the glass surface, which may alter the characteristic relaxation time.

2. The sample requires a high number density of droplets to efficiently detect a statistically significant number of fusion events since these events are stochastically driven.

3. For droplets with low viscosity and/or high surface tension, the fusion processes are fast (typically in millisecond time scale) which poses a limitation on the detection capabilities of the instrument used and may require the use of expensive imaging devices (for higher time resolution).

4. The initial shape of the two coalescing droplets is not usually a perfect ellipsoid and fitting errors may reduce the quality of the data.

To overcome such limitations, a series of recent studies have used optical tweezers to analyze the coalescence of droplets (Alshareedah et al., 2019; Kaur et al., 2019; Patel et al., 2015; Wang et al., 2018). In these experiments, two droplets are optically trapped in two different highly focused laser beams. The optical trapping is possible due to the refractive index mismatch between the interior of the droplet and the external dilute phase. Trapped droplets are then brought into contact to initiate coalescence. The laser signal from the optical trap is able to detect the relaxation process and is used to extract the characteristic relaxation time. In what follows, we will describe the concept of this method as well as its application on biomolecular condensates in vitro.

The ability of an optical trap to detect the relaxation of a deformed droplet stems from the time-dependent deflection of the trapping laser through the droplet. When two optically trapped droplets undergo fusion, the intermediate state of the fusion process constitutes a deformed droplet and the final state is a spherical droplet shifted from the center of the optical trap (Fig. 2a). To illustrate the concept of detection, we consider the deflection of a single ray of light passing through the droplet at the deformed and relaxed states. Due to the change in the droplet shape from deformed to relaxed, the curvature of the droplet surface increases, which leads to variation in the angle of incidence of the ray from small to large, respectively (Fig. 2b). Thus, the deflection of the ray by the condensate is enhanced at the relaxed state. A similar principle can be applied to the optical trap (constituting millions of rays) to understand how the deflection of the trap varies during the condensate shape relaxation. As the shape of the droplet relaxes to a sphere, the angle of incidence, and hence the deflection of the laser, relax to a steady-state value (Fig. 2c). The advantages of measuring the relaxation time via optical tweezer-controlled fusion are listed below:

Fig. 2.

Optical trap-induced droplet coalescence as a method to measure the relaxation time (a) a schematic diagram showing that the fusion process is induced by two optical traps. (b) a schematic ray diagram showing how the laser deflection (x) of the optical trap varies with droplet shape due to the change in the angle of incidence θ. (c) A representative laser signal from Trap-1 as a function of time during the relaxation process.

1. Droplets are suspended in solution and hence there are no spurious friction effects as those caused by surface adhesion in the case of passive fusion (Jeon et al., 2018).

2. Optical traps (with sampling rate > 70k Hz) usually offer higher time resolution than video cameras [~10² fps for CCD-based cameras and 10³ fps for SPAD detectors (Shen et al., 2017)], thereby allowing the detection of very fast fusion events with sub-millisecond relaxation time.

3. The sample does not require a high density of droplets since one can actively trap droplets and induce fusion events. This offers a key practical advantage over passive fusion assays as it allows a feasible collection of a large number of fusion events for statistical purposes.

3. Measuring mesoscale physical properties of liquid droplets using optical trap-induced droplet coalescence: Methods

Definition

Measuring the characteristic relaxation time of protein/RNA droplets using optical tweezer-induced coalescence

Rationale

Fusion-relaxation time is a measure of the inverse capillary velocity (or the ratio of viscosity/surface tension; equation 2.2). Conventionally, the passive fusion of condensates that occurs stochastically is imaged with a video camera and analyzed in terms of the condensate aspect ratio. Here, we describe a protocol to measure the fusion-relaxation time using optical tweezers to provide higher time resolution, eliminate surface adhesion effects, and ensure practicality in collecting statistically large data sets using 1 μl sample volume.

Materials, equipment, and reagents

Dual-trap optical tweezers (1064 nm laser/1–10 mW power), coupled with a bright-field or confocal microscope, a sample containing phase-separated protein/RNA mixture, 1 mm thick glass slide, microscope coverslips, double-sided tape, Tween 20 or Pluronic F-127, Ethanol (190–200 proof).

Note: The experimental data discussed here were collected using a dual-trap optical tweezer operating at a 78 kHz sampling frequency. However, a similar analysis could also be done with any sampling frequency as long as the fusion rate is considerably slower than the sampling rate (Jahnel, Behrndt, Jannasch, Schäffer, & Grill, 2011; Patel et al., 2015).

Protocols

1. Put two strips of double-sided tape on a microscope glass slide as shown in Figure 3.

2. Add 1–1.5 μl of the droplet-containing sample between the two sheets of double-sided tape.

3. Place the coverslip on top of the sample and press firmly to “sandwich” the sample between the glass slide and coverslip. If the sample touches the sides of the double-sided tape, reduce the volume of the sample and ensure that it is placed at the center of the chamber.

4. Load the sample onto the optical trap-microscope system.

5. Turn on the traps at minimum power. If the droplets have a lower dielectric constant than the surrounding medium, they will be attracted to the trap. Make sure to keep the trapped droplets away from the surface at the lower and upper edges of the sample, to avoid surface adhesion.

6. Slowly increase the power of the trapping laser until droplets are not visibly fluctuating around the center of each trap (around 5–15 % of the total trap power of ~10 mW split equally between two traps, excluding the power lost in the optics). However, avoid trapping droplets with too much power (20–100% of the total trap power of ~10 mW, excluding the power lost in the optics), which may heat the droplets and change their material properties or cause a visible droplet “boiling”.

7. Once you have two trapped condensates, take an image of the two droplet system (confocal or bright-field). This image will be used to measure the diameter of each of the fusing droplets (see Figure 4).

8. Set Trap-1 to move at a constant velocity towards trap-2. Once the fusion starts, you will see a clear change in the laser signal followed by an exponential relaxation phase (see Fig. 5a for an example). Allow sufficient time for the fusion-relaxation process to be completed.

9. Once the fusion is completed, save the detected laser signal from Trap-1 for further analysis. Release the relaxed droplet from the traps by using the shutter or simply switching the traps off.

10. Repeat steps 1–9 at different locations within the sample to collect the desired number of fusion events. Fusion events should be collected with droplets of varying sizes. Varying the size of the trapped droplets can be easily achieved by allowing the traps to collect more droplets before initiating fusion. It is also advisable to keep the fusing droplets similar in size for each fusion. This allows for more accurate analysis (see analysis section).

Fig. 3.

Sample holder preparation for optical trap-induced coalescence experiment.

Fig. 4.

Bright-field images of two optically trapped protein condensates as they are driven to undergo coalescence. Trap-1 velocity was set at 40 nm/sec. Scale bar represents 5 μm.

Fig. 5.

(a) Raw laser signal recorded from fusing two optically trapped droplets. (b) Trimming the laser signal to selectively extract the fusion-relaxation signal (the exponential phase). The green double-sided arrow shows a reasonable trim. The red double-sided arrow shows an unrecommended trim since most of the points lie in the linear part of the signal and may result in a biased fit. (c) The trimmed signal in (b) is re-plotted. (d) The final laser signal functional form is a combination of an exponential relaxation process and a linear process.

Precursor techniques

Coating glass slides and coverslips

1. Prepare a 20% (vol/vol) solution of Tween20 or 1% (wt/vol) solution of Pluronic F-127.

2. (optional) Clean the microscope glass slides and coverslips with 70% ethanol. You may sonicate glass slides and coverslips for 15 minutes for efficient cleaning.

3. Dry the residual ethanol under nitrogen.

4. Immerse the glass slides in the coating solution and leave them as such for 30 minutes.

5. Rinse the glass slides and coverslips with milliQ water for 8–10 times to remove excess coating solution.

6. Dry the glass-slides in a vacuum chamber or a heated oven at 40–50 °C overnight.

7. Dry coated glass slides and coverslips can be wrapped in lens paper and stored at room temperature for later use.

Safety considerations and standards

Follow the standard safety guidelines when dealing with optical traps. This includes wearing appropriate PPE as required by the manufacturer’s safety guidelines.

Analysis and statistics

The analysis for this technique involves three steps: (i) extracting the relaxation time of each fusion event by fitting the laser signal with a relaxation model, (ii) plotting the relaxation time as a function of droplet size, and (iii) fitting the relaxation time vs. droplet size data to extract the inverse capillary velocity. These steps are described in detail below.

A typical fusion relaxation laser signal is shown in Figure 5a. The data can be trimmed to effectively analyze only the relaxation process (Fig. 5b & c). Care should be taken not to include an excessive amount of data points at the linear regime where the relaxation process is completed, since this will bias the fit towards the linear part. The trimmed data should have a time span that is approximately twice the time taken for the signal to reach the lowest value (see Fig. 5b). The trimmed data is then normalized to facilitate the fitting process. The normalized laser signal (S) is fitted with the following function

$$S\left(t\right)=a{e}^{-\frac{t}{\tau }}+bt+d$$ (3.1)

Where a, τ ,b and d are fitting parameters. The fusion process is expected to exhibit an exponential relaxation trend which is accounted for by the first term in equation 3.1. If we consider the case of an infinitely slow trap, then the signal will predominantly show a relaxation trend (Fig. 5d). The second term is linear in time and is added to account for the signal coming from the movement of the trap across the droplet. The signal for an infinitely fast fusion will only display the signal coming from the trap movement (Fig. 5d). Combining these two terms gives a functional form that effectively describes the signal coming from a fusion-relaxation experiment (Fig. 5a &d). The linearity in time in the signal coming from the trap requires that throughout the fusion process, the trap must remain in the linear regime (the displacement of the particle from the center of the trap is linear with the laser signal). This implies an additional consideration for conducting these experiments, i.e., the velocity of the moving trap should be close to the velocity of fusion to ensure that the trap remains in the linear regime throughout the fusion relaxation process. Failure to do that may result in erroneous fusion curves and/or the loss of the signal coming from the first trap due to the droplet being completely drawn out of the trap.

Once the fitting is done (Fig. 6a), the size of the fusing droplets (before fusion) should be determined using image analysis. Although confocal images are preferred for more accurate determination, bright-field images can also be used. The size determination of the fusing droplets can be done manually using Fiji-ImageJ software (Rueden et al., 2017) or through the use of programming scripts such as Python or Matlab. For the manual case, Fiji-ImageJ software is used to measure the diameters of the fusing droplets as follows: using the “measure tool”, a line is drawn across the center of the droplet which has its endpoints on the periphery of the droplet and the droplet diameter is recorded. This measurement is repeated for several lines on the same droplet and their average is taken as the droplet diameter. Similarly, the diameter of the second droplet is measured. Finally, the average diameter of the two droplets is recorded and used for subsequent analysis. A more accurate and perhaps a practical way is the use of coding scripts to measure the diameter of the droplets. This can be done using the function regionprops() in Matlab or the function skimage.measure.regionprops() in python (skimage python library is required). These scripts fit the droplets in the image with ellipsoids (Fig. 6b). An example of a Matlab script to detect the droplet diameter is given below:

Fig. 6.

(a) Fitting (red curve) of the laser signal (black curve) to extract the characteristic time of the relaxation process. (b) Image processing of the two droplets under investigation to extract their average diameter. The fluorescence micrograph is converted to a binary image by applying a threshold and the droplets are fitted with ellipses to extract the diameters (see the provided Matlab script).

%Read Image

a = imread(‘Fluorescence_RG_pU.png’);

%Convert to a binary image by applying a threshold

bw = a > 100;

%show binary image

imshow(bw);

saveas(gcf,’Binary Image.png’);

% find regions and save the center and major axes length

props = regionprops(‘Table’,bw,’Centroid’,’MajorAxisLength’,’MinorAxisLength’);

%calculate diameters of each circle by averaging the major axis length

%(this should give you an array of two with diameters in pixels

diameters = mean([props.MajorAxisLength props.MinorAxisLength],2);

pixelsize= 0.1 %micron

display(diameters*pixelsize)

%for visualization

centers = props.Centroid;

radii = diameters/2;

hold on

viscircles(centers,radii);

hold off

saveas(gcf,’Droplet Fit.png’)

The presented analysis is repeated for multiple fusion events with varying droplet diameters. Plotting the relaxation time against the average diameter of the fusing droplets for each fusion event gives a linear relation (Fig. 7) for purely viscous droplets. The slope of the linear fit gives the scaled relaxation time which is equal to the inverse capillary velocity η/γ (viscosity to surface tension ratio) for the condensates under investigation (Ceballos, McDonald, & Elbaum-Garfinkle, 2018; Elbaum-Garfinkle et al., 2015; Feric et al., 2016).

Fig. 7.

The relaxation time scales linearly with droplet size, with a slope equal to inverse capillary velocity η/γ (Alshareedah et al. unpublished).

$$\mathit{\text{slope}}=\frac{\tau }{l}=\frac{\eta }{\gamma }$$ (3.2)

It is important to only consider fusion events for which the fitting procedure yields a good fit. Any irregularities in the fusion-relaxation signal should be excluded unless they are consistently appearing for all trapping powers and all velocities. One important consideration to note is that the linear relation between the fusion-relaxation time and the droplet diameter is a property of purely viscous droplets. This method is useful for relative comparison between droplets in different conditions (as in protein/nucleic acid sequence variations, mixture composition variation, varied buffer conditions, pH, molecular crowding, etc.). However, it should be understood that standing alone, this method only gives the ratio between viscosity and surface tension and does not provide any direct information on either quantity.

Related techniques

Passive fusion analysis using video microscopy is an alternative method for determining the inverse capillary velocity. This method consists of imaging fusion events that occur on the surface of the glass slide and conducting droplet aspect ratio analysis to extract the fusion relaxation time. A description of this method can be found elsewhere (Brangwynne et al., 2011; Ceballos et al., 2018).

Pros and cons

Pros	Cons
Eliminating surface adhesion effects that are present when analyzing fusion events on a glass surface using video microscopy. Allows for rapid and efficient data collection of multiple fusion events for statistical analysis. Does not require fluorescence labeling of molecules.	Does not provide information on either viscosity or surface tension but only the ratio between the two quantities. The method is quantitative for liquid droplets but binary for solid-like droplets (can only reveal if a droplet is solid-like or not).

Troubleshooting & Optimization

Problem	Solution
Droplet is lost from the trap during fusion.	This might indicate that the fusion process is much faster than the velocity of the moving trap. Increasing the velocity of the moving trap should resolve the issue. Alternatively, repeating this assay with larger or smaller droplets may resolve this issue.
Droplet leaps from trap-1 to trap-2 during fusion.	Increase the power of the trapping laser. Increase the velocity of the moving trap.
Laser signal from the optical trap is noisy.	This is an indication that the trapping power is too low. Increasing the power of the trapping laser should eliminate this problem.
Droplets are falling to the glass surface rapidly, impeding the chance to collect a large number of fusion events.	This can be overcome in two ways: Increasing the thickness of the sample chamber by using two layers of double-sided tape instead of one. This creates a deeper channel with a lower surface area on the glass slide-sample interface. The use of hydrophobic coatings such as SigmaCote or Silane may resolve this issue. These types of coatings prevent certain droplets from sticking to the surface and hence can be easily picked up by the optical traps.
Sample is drying too fast which impedes the collection of large numbers of fusion events	Seal the sample chamber open ends with coverslip sealant. Avoid using excessive amounts of the sealant as it may touch the microscope objective.
Data is not reliably reproducible	Make sure the conditions such as trapping laser power, the temperature of the sample, and the velocity of the moving trap are as consistent as possible across samples. Also, make sure the measurements are taken within a consistent time span as sample drying/aging may alter the material properties of the condensates.

Summary

The use of optical tweezers to measure the fusion-relaxation time and inverse capillary velocity of biomolecular condensates in vitro has been demonstrated as a powerful tool to assess their material properties. Optical traps provide higher time resolution of the process and allow for practical and efficient collection of large numbers of fusion events, a feature that is absent in methods that use video microscopy to extract these physical quantities.

4. Determining nanoscale biomolecular diffusion within liquid droplets using fluorescence recovery after photobleaching (FRAP)

Fluorescence recovery after photobleaching (FRAP) is a widely used technique to probe the diffusivity of fluorescently tagged protein/RNA molecules within biomolecular condensates in vitro and in vivo (Banerjee, Milin, Moosa, Onuchic, & Deniz, 2017; Elbaum-Garfinkle et al., 2015; Feric et al., 2016; Jain et al., 2016; Kroschwald et al., 2015; Li et al., 2012; Molliex et al., 2015). The concept of FRAP is based on monitoring the exchange rate of labeled molecules between a region of interest and the surrounding environment, which is subsequently used to quantify their diffusivity dynamics. To achieve this, a region of interest (ROI) within the droplet is irreversibly photo-bleached through a high power laser excitation. Bleaching is the result of photochemical damage of the fluorescence probes such that it permanently loses its ability to fluoresce (Kubitscheck & Peters, 2013). This results in the ROI having a significantly lower fluorescence (or zero) intensity as compared to the surrounding regions (Fig. 8a). The recovery of fluorescence intensity in the bleached region is then monitored as a function of time. If the labeled species undergoes fast diffusion, the rate of exchange between the bleached region and the surrounding area would be high and the resultant recovery time would be short. Conversely, the recovery time for a molecular species with slow diffusivity dynamics would be long.

Fig. 8.

(a) Diagram illustrating the concept of a FRAP experiment. Each green dot represents a single fluorescently-labeled molecule. (b) FRAP recovery curve showing full recovery. The dashed line indicates the recovery half time. (c) FRAP recovery curve showing partial recovery. The red dashed double-sided arrow indicates the recovered intensity [fraction of mobile phase is 50% in (c) and 100 % in (b)]. The blue dashed double-sided arrow indicates the bleaching depth.

The information that can be extracted from FRAP depends on two parameters, the recovery half time and the fraction of mobile phase. The recovery half time is defined as the time taken for the bleached region to recover half of its final intensity, which provides insights into how fast the labeled molecules are diffusing (Fig. 8b). The fraction of mobile phase is estimated by the ratio of the recovered fluorescence intensity of the bleached spot to the bleaching depth (Fig. 8c). If the labeled species is completely mobile (as in the case of a purely viscous liquid), the fraction of mobile phase is expected to be ~100% (Fig. 8b). If the labeled species has two populations, mobile and immobile, the fraction of mobile phase is typically much less than 100%, which is classically interpreted as apparent viscoelasticity (Fig. 8c). Ideally, apparent diffusion coefficients can be extracted from FRAP curves by fitting the recovery time trace with an appropriate diffusion model, however, FRAP is more readily used only to qualitatively access the mobility of the molecules under investigation.

Many studies have utilized FRAP to measure the diffusivity of molecules within biomolecular condensates using purified in vitro systems and in cells (Alshareedah et al., 2019; Banerjee et al., 2017; Elbaum-Garfinkle et al., 2015; Feric et al., 2016; Jain et al., 2016; Kaur et al., 2019; Kroschwald et al., 2015; Li et al., 2012; Molliex et al., 2015; Onuchic, Milin, Alshareedah, Deniz, & Banerjee, 2019; Patel et al., 2015; N. O. Taylor, Wei, Stone, & Brangwynne, 2019; Wang et al., 2018). While the implementation of the experiment and analysis is fairly straight forward, the interpretation of FRAP results has proven tricky and often needs careful considerations on a case-by-case basis. For example, the FRAP recovery rate is sensitively dependent on the molecular identity of the labeled species in the case of heterotypic condensates harboring multiple molecular species (Boeynaems et al., 2019; Chalupníková et al., 2008; Weidtkamp-Peters et al., 2008). In the same biomolecular condensate, FRAP measurements on one component might reveal liquid-like behavior (complete recovery), while the same analysis on another component might reveal viscoelastic behavior (partial recovery) (Chalupníková et al., 2008; Weidtkamp-Peters et al., 2008). This variation of FRAP results with the probe molecules for heterotypic condensates is interpreted as a result of differential intermolecular interactions and spatial heterogeneities within the droplet. This differential FRAP behavior can be rationalized in light of a scaffold-client model. As noted earlier, scaffolds are biopolymers that feature multivalent binding domains. Clients, on the other hand, do not require multivalency and can partition within a condensate through monovalent scaffold-binding modules (Banani et al., 2017). Therefore, scaffold-client interaction can be more transient than scaffold-scaffold interactions. Consequently, scaffolds are expected to have intrinsically slower mobility than the clients since a scaffold makes substantially more and possibly stronger intermolecular contacts compared to a client (Alberti, 2017b; Banani et al., 2016). Apart from such component-specific diffusivity dynamics, a recent study has shown that the extracted diffusion coefficients are highly dependent on the dimensionality of the diffusion model used to fit the data as well as the boundary conditions, with large variance occurring between different models (N. O. Taylor et al., 2019). Therefore, it is important to take additional considerations into account when interpreting FRAP results for biomolecular condensates. Nevertheless, FRAP remains widely used since it is a simple, accessible, and convenient technique that can be done to get a qualitative idea on the diffusivity of molecules within a condensate. More importantly, FRAP is one of the few techniques for probing condensate dynamics that can be performed in vivo (Brangwynne et al., 2009; Feric et al., 2016; Jain et al., 2016). Moreover, FRAP experiments are conveniently done in a confocal fluorescence microscope, which is widely accessible.

5. Determining diffusion dynamics within liquid droplets using fluorescence recovery after photobleaching: Methods

Definition

Measuring the molecular diffusivity of a fluorescently tagged molecule by monitoring the fluorescence recovery after photobleaching (FRAP).

Rationale

FRAP experiments provide a simple way to make a preliminary judgment on whether a condensate is a liquid or solid. It is also one of the few experiments on molecular diffusivity that can be done in vivo for biomolecular condensates.

Materials, equipment, and reagents

Confocal fluorescence microscope, a sample containing phase-separated protein/RNA droplets with desired fluorescently labeled species, 1.0 mm thick glass slide or microscope coverslips, tween-20 or Pluronic F-127, Ethanol (190–200 proof)

Protocols

1. Place the condensate sample containing fluorescently labeled species on a tween-coated microscope glass slide/coverslip. A 5 μl sample is sufficient for ≥ 30 minutes of imaging provided the sample is kept covered to prevent evaporation/drying.

2. Load the sample onto the microscope stage.

3. Take a fluorescence image of the sample at the glass surface to make sure that the labeled molecules are positively partitioning into the droplets and that the fluorescent intensity is appropriate (no detector saturation is observed). Adjust the laser power and/or detection settings to ensure the proper level of sample brightness is well within the detectors’ dynamic range.

4. Focus the confocal volume on a region where you can see at least two droplets stationary on the glass slide surface.

5. Set the bleaching spot at the center of one of the droplets, make sure that the size of the bleaching spot is significantly smaller than the size of the droplet [at least three times smaller (N. O. Taylor et al., 2019)]. This is to improve the accuracy of the analysis and minimize interfacial resistance effects (see the analysis section for more details).

6. Start the bleaching experiment by shining the excitation laser with maximum intensity for 1–2 seconds. You can set the parameters of the bleaching experiment using the software of your microscope or a customized automation script, if available.

7. Image the two droplets after bleaching for a fixed time interval. If the recovery is slow, it is advisable to increase the time interval between consecutive frames to minimize photofading effects (see analysis section for details). Keep imaging until the intensity of the bleached region reaches a plateau.

8. Repeat steps 4–7 for multiple droplets to ensure the statistical significance of the results. Notice that the recovery time depends on the size of the bleaching region (see the analysis section for details), hence it is advisable to keep the bleaching region to droplet diameter ratio similar throughout the experiment (if possible). This will allow for online monitoring of the consistency of the data.

Precursor techniques

Coating glass slides and coverslips

1. Prepare a 20% (vol/vol) solution of Tween20 or 1% (wt/vol) solution of Pluronic F-127.

2. (optional) Clean the microscope glass slides and coverslips with 70% ethanol. You may sonicate glass slides and coverslips for 15 minutes for efficient cleaning.

3. Dry the residual ethanol under nitrogen.

4. Immerse the glass slides in the coating solution and leave them as such for 30 minutes.

5. Rinse the glass slides and coverslips with milliQ water for 8–10 times to remove excess coating solution.

6. Dry the glass-slides in a vacuum chamber or a heated oven at 40–50 °C overnight.

7. Dry coated glass slides and coverslips can be wrapped in lens paper and stored at room temperature for later use.

Notes

1. Make sure that the labeled species is added to the sample before forming the condensates. This is important to eliminate interfacial resistance effects and ensure good partitioning of the labeled molecule within the droplet.

2. Depending on the detector sensitivity of the microscope, the optimal probe concentration may vary. A probe is defined as a site-specifically labeled protein/RNA (or DNA) molecule. Such site-specific labeling protocols are thoroughly reviewed in the literature and will not be discussed here (Banerjee & Deniz, 2014). Usually, probe concentrations that we use in our laboratory range between 300 nM to ~ 1μM. The brightness of the fluorescent dye may also be a factor in optimizing the concentration of the fluorescent probe. It is not advisable to utilize ~ 100% of the labeled protein in the sample since labeling may alter the biomolecular properties and hence may change the behavior of condensates. A ratio of the labeled species to unlabeled species of ~ 1% or less is typically found to be a good practice in our experiments. However, this consideration generally excludes proteins containing an exogenous fluorescence protein tag, such as a GFP-tag.

Safety considerations and standards

Follow the standard safety guidelines when dealing with biological samples including wearing appropriate PPE.

Analysis and statistics

To analyze FRAP experiments, one needs to carefully consider the experimental conditions in order to choose a suitable model. Here, we will demonstrate the analysis using a two-dimensional diffusion model with infinite boundary conditions (Kaur et al., 2019; N. O. Taylor et al., 2019). The prerequisites for this analysis is that the bleached spot radius is smaller than that of the droplet by a factor of 3 or more. Furthermore, the laser used for bleaching has a Gaussian profile. These are necessary to ensure that the interface has a reduced effect on the recovery (since it is far from the bleached spot). Another issue that needs attention when analyzing FRAP data is photofading. Photofading can be described as progressive decay in the fluorescence intensity of the whole imaging area during the FRAP experiment due to non-specific bleaching. This usually occurs due to repeated excitations of fluorescent molecules over a long duration of time. To correct for photofading, a reference droplet that is not bleached or altered but included within the imaging area is recorded and analyzed (Fig. 9a). The decrease in intensity of the reference droplet is assumed to be due to photofading, and hence, can be used to correct for the photofading effect for the bleached droplet. Typically, the intensity time trace of the reference droplet shows a linear decrease with time (Fig. 9b & d) due to photofading. Below, we will show two FRAP curves to illustrate important details in this analysis.

Fig. 9.

(a) confocal images of a protein-RNA droplet before bleaching, after bleaching, and at a full recovery. The yellow circle indicates the bleaching spot; the cyan circle indicates a reference region in an unbleached droplet. (b-c) Intensity time traces of the reference droplet (red) and the bleached droplet (black) before correction (b) and after correction (c). (d&e) Same as (b&c) but for a sample with strong photofading effects.

To correct for photofading effect, we calculate a correction factor C from the intensity time-trace of the reference droplet. For each time point t, the correction factor is calculated as

$$C\left(t\right)=\frac{R\left(0\right)}{R\left(t\right)}$$ (5.1)

Where R(t) is the fluorescence intensity of the reference droplet at time t. The corrected FRAP curves are then calculated using

$$I_{\mathit{\text{correct}}}\left(t\right)=C\left(t\right)*I\left(t\right)$$ (5.2)

Where I(t) is the raw intensity signal coming from the bleached region at time t. The corrected FRAP curves are shown in Figure 9c&e. Once FRAP curves are corrected, they can be normalized with respect to the bleaching depth using the following equation:

$$I_{\mathit{\text{noramlized}}}\left(t\right)=\frac{I_{\mathit{\text{correct}}}\left(t\right)-\text{min}\left(I_{\mathit{\text{correct}}}\right)}{I_{\mathit{\text{correct}}}\left(0\right)-\text{min}\left(I_{\mathit{\text{correct}}}\right)}$$ (5.3)

This normalization makes it easier to extract the relevant quantities from the FRAP curve (see Fig. 10). Notice that I_correct(0) is the value of intensity before bleaching starts (usually we take few frames before bleaching in order to quantify the bleaching depth and the normalization). Fitting FRAP curves to extract the recovery half time requires the use of the appropriate fitting function. Several functions have been suggested in the literature (Axelrod, Koppel, Schlessinger, Elson, & Webb, 1976; Braeckmans, Peeters, Sanders, De Smedt, & Demeester, 2003; Day, Kraft, Kang, & Kenworthy, 2012; Kang, Day, Kenworthy, & DiBenedetto, 2012; Mazza et al., 2008; Soumpasis, 1983; Sprague, Pego, Stavreva, & McNally, 2004), with each corresponds a specific set of conditions that depend on the experimental conditions such as laser profile, the relative size of the bleached droplet, the size and shape of the bleached region, the dimensionality of the diffusion process, the existence of reaction processes (via binding and unbinding events) that couple with free diffusion (Kang & Kenworthy, 2008; N. O. Taylor et al., 2019), etc. We will solely focus here on fitting the FRAP recovery time trace and extract the recovery half-time and the fraction of the mobile phase (Fig. 8). Here, we will use two independent cases (see Fig. 9b&d) to illustrate how one fitting function may work for some systems but not others. For the FRAP curve in case 1, we find that a single exponential function is sufficient for fitting the data (Fig. 10a)

$$I\left(t\right)=a\left(1-\text{exp}\left(-\frac{t}{\tau }\right)\right)$$ (5.4)

Where a,τ are fitting parameters and τ_1/2 = τ In 2. In case 2, the exponential function does not give a good fit while the function (Day et al., 2012)

$$I\left(t\right)=\frac{a+b\left(\frac{t}{{\tau }_{1/2}}\right)\mathrm{ }}{1+\frac{t}{{\tau }_{1/2}}}$$ (5.5)

fits the data significantly better (Fig. 10b). Here, a,b,τ_1/2 are fitting parameters.

Fig. 10.

(a) FRAP data fitting for case 1, Figure 9c using equations 5.4 (red) and 5.5 (green). (b) FRAP data fitting for case 2, Figure 9e using equations 5.4 (red) and 5.5 (green).

These examples serve to illustrate that the choice of fitting function is important for the final values of the apparent diffusion coefficient (to be estimated using the τ_1/2 obtained from fitting). The values of the fitting parameters for each of these cases are shown in Table 2.

Table 2.

Extracted recovery half-time and the R² (Coefficient of determination) for the two cases (Fig. 10 a&b) as fitted by models 1 & 2 (equations 5.4 (red) and 5.5).

Model 1				Model 2
Case 1		Case 2		Case 1		Case 2
τ1/2	R2 (COD)	τ1/2	R2 (COD)	τ1/2	R2 (COD)	τ1/2	R2 (COD)
35.9 ± 0.5 s	0.98072	10.1 ± 0.2 s	0.97102	49 ± 2 s	0.96991	6.8 ± 0.2 s	0.9829

To extract the diffusion coefficient, one needs to estimate the area of the bleached spot. Qualitatively speaking, the diffusion coefficient is proportional to the area of the bleaching spot divided by the characteristic time (Kang et al., 2012)

$$D\mathrm{ }~\frac{R^2}{{\tau }_{1/2}}$$ (5.6)

Where R is the radius of the bleaching spot. Due to the Gaussian shape of the laser as well as the diffusion process within the bleached region, the post-bleaching intensity profile across the bleached region assumes a Gaussian shape. The active diffusion processes into the bleached region during the bleaching period results in differences between the predetermined bleaching region (set by the software of the microscope) and the effective bleaching area. To account for this discrepancy between predetermined and effective bleaching areas, we define two radii, R_n and R_e, identifying the predetermined and effective bleaching spots, respectively. R_n is taken from the experimental parameter used or can be determined using Fiji-ImageJ software (provided the software exports the predetermined regions to Fiji-ImageJ). R_e can be measured by fitting the intensity profile across the bleached area immediately after bleaching with a Gaussian function (Fig. 11 a&b). An example of a function that has been used to fit the post-bleaching profile is (Kang et al., 2012)

$$F\left(x\right)=a-a_{1}exp\left(-\frac{{\left(x-b\right)}^2}{R_e^2}\right)$$ (5.7)

Where a,a₁,b,R_e are fitting parameters. The parameter that gives the effective width of the Gaussian function and hence the effective diameter of the bleaching spot is R_e. One can also perform two-dimensional fitting by considering the surface plot of intensity in the XY plane (Fig. 11c). And then fitting it using the function (Day et al., 2012)

$$F\left(x,y\right)=a\text{exp}\left(-\mathit{\text{Kexp}}\left(-2\mathrm{ }\frac{{(x-b)}^2+{(y-c)}^2}{R_e^2}\right)\right)$$ (5.8)

Where a,b,c,K,R_e are fitting parameters.

Fig. 11.

(a) Fluorescence image of a protein-RNA droplet immediately after bleaching. (b) Intensity profile along the yellow dashed line in (a) fitted to a Gaussian function (equation 5.7). Residuals are shown. (c) 2D surface plot for the raw intensity values as a function of position (left). The surface fit of the data is generated using equation 5.8.

Finally, the diffusion coefficient can now be calculated using the following modified formula (Kang et al., 2012)

$$D_{\mathit{\text{apparent}}}=\frac{R_n^2+R_e^2}{8{\tau }_{1/2}}$$ (5.9)

The presented analysis to extract diffusion coefficients from FRAP is one of the most widely used but not unique. In fact, the literature on FRAP analysis is plentiful with different models that can be used to fit the data and extract diffusion coefficients. A recent study has summarized some of the models that have been used for liquid-liquid phase separation in biology (N. O. Taylor et al., 2019). One of the important conclusions was that the FRAP model has to be chosen according to the shape and relative size of the effective bleaching spot with respect to the droplet size. One of the common problems in FRAP is that many systems form condensates that are small in size (~ 1 um). This makes it inevitable for the bleaching region to have a comparable size to the droplet, which results in both finite boundary conditions and the interfacial resistance to contribute to the resulting FRAP recovery profile. For such cases, a theoretical model has been developed which requires complementing FRAP with Fluorescence Correlation Spectroscopy (FCS) to extract the diffusion coefficient (N. O. Taylor et al., 2019). Furthermore, the choice of the labeled molecule has been shown to affect FRAP results drastically, to the point where one molecular species displays liquid-like behavior and other molecular species display solid-like behavior (Boeynaems et al., 2019; Weidtkamp-Peters et al., 2008). These drastic differences between molecules within the same condensate challenges the simplistic views of classical material characterization ideas such as viscosity and diffusion. Overall, for FRAP analysis to be reliable, we recommend the following:

1. The FRAP model should be chosen based on the experimental conditions regarding the relative size and shape of the effective bleaching region.

2. The chosen model should be used consistently throughout the study.

3. The extracted values of diffusion coefficients should only be interpreted relatively and not to be claimed as absolute values.

4. A statistically large data set (i.e. collecting multiple FRAP events for the same sample) can improve the reliability of the results.

5. FRAP should not be the only method used to determine the physical property of the condensates. Complementary techniques are discussed throughout the chapter.

6. Performing FRAP with each component is warranted for heterotypic multi-component condensates.

Related techniques

Fluorescence correlation spectroscopy (FCS) and Single and multiple particle tracking.

Pros and cons

Pros	Cons
Ease of implementation in vitro and in cell culture models. Does not require specialized equipment. Can be a useful tool for initial and preliminary characterization of biomolecular condensates.	Does not report on the material state of the condensate but only the diffusion dynamics of the labeled molecules. Highly sensitive to the experimental conditions, instrumentation, and parameters such as the area of the bleached region. Highly sensitive to the diffusion model being used to fit the data Highly sensitive to the identity of the probe molecule.

Troubleshooting & Optimization

Problem	Solution
Bleaching of the droplet does not occur.	This problem indicates that the recovery is too fast such that the droplet is already fully recovered by the time the first post-bleaching frame is imaged. In that case, reducing the bleaching time may resolve the issue. Also, make sure the detectors are not saturated due to a high concentration of the fluorescent probe.
Bleaching profile is not Gaussian.	This can sometimes be a result of excessive bleaching that leads to a post-bleach profile that is closer to a square well rather than a Gaussian. The following suggestions may resolve this issue: Decreasing the intensity of the bleaching laser. Decreasing the pixel time (dwell time) of the bleaching laser. Decreasing the size of the bleaching spot.
Sample is photofading at a fast rate.	Increase the time duration between consecutive post-bleaching frames. Decrease the intensity of the excitation laser. Increase the fluorescent probe concentration in the sample.

Summary

FRAP is a quick and simple method to get an idea of the diffusivity dynamics of fluorescently tagged molecules in a biomolecular condensate. However, care should be taken when conducting the experiment and choosing the fitting model. It is recommended that FRAP is complemented with other techniques to provide an orthogonal verification of the material state of the biomolecular condensates.

6. Single particle tracking (SPT)

Particle tracking is a classical technique for measuring the viscous properties of liquids. Several studies have used particle tracking techniques to measure the viscosity of biomolecular condensates (Elbaum-Garfinkle et al., 2015; Feric et al., 2016; Jawerth et al., 2018; N. Taylor et al., 2016; Zhang et al., 2015). The experiment is done by tracking an exogenous spherical particle diffusing inside a biomolecular condensate (Fig. 12a). The tracking is usually done through video microscopy, by imaging the motion of the particle over a set duration of time. The imaging series is then analyzed using particle tracking software or custom-built programs that implement a tracking algorithm (Feric & Brangwynne, 2013; Zhang et al., 2015). The output of the particle tracking experiment gives the location of the particle as a function of time (the trajectory, Fig. 12b), from which the mean square displacement (MSD) can be calculated and plotted for a set of lag times τ (Fig. 12c).

Fig. 12.

(a) A schematic diagram and a bright-field image showing a microsphere is trapped inside a protein droplet. (b) A representative trajectory of a microsphere in a particle tracking experiment. (c) Mean square displacement (MSD) calculated for the trajectory in (b). Red: MSD data; Black: a line with a slope equal to 1.

The relation between the mean square displacement MSD and the lag time τ is given by

$$MSD\left(\tau \right)=\mathrm{ }<r^2>\left(\tau \right)=4D{\tau }^{\alpha }$$ (6.1)

Where D is the diffusion coefficient of the bead and α is the diffusive exponent. For classical Brownian motion in a purely viscous fluid, the value of α is equal to unity. The viscosity η of the condensate can be determined using the Stokes-Einstein equation ($\eta =\frac{k_{B}T}{6\pi DR}$ ), where R is the radius of the bead. Furthermore, the MSD functional relation with the lag time τ provides useful information on the type of motion the bead is exhibiting inside the condensate. This can be done by inspecting the value of the diffusivity exponent α, which is different from unity for anomalous diffusion. The value of α is also used to distinguish between sub-diffusion (0<α<1) and superdiffusion (α>1) (Metzler, Jeon, Cherstvy, & Barkai, 2014).

Particle tracking is a useful and reliable technique for measuring the viscosity of the condensate. One of the possible issues regarding the implementation of particle tracking in protein condensates is non-specific interactions between the tracer particle and the molecules within the condensate. To resolve this, the beads used for particle tracking are coated with passive/inert polymers such as poly(ethylene glycol) (PEG), which can prevent such non-specific interactions. The coating procedure utilizes well established techniques such as carboxylate-amine or biotin-streptavidin coupling chemistry (Elbaum-Garfinkle et al., 2015; Feric & Brangwynne, 2013; Feric et al., 2016). One of the advantages of the SPT method is the fact that it is a label-free approach for probing condensate dynamics. While the tracer particle may be fluorescently tagged, the biopolymers constituting the condensates need not be fluorescently labeled. Furthermore, SPT can be used to trace nanoparticles and individual molecules in living cells using advanced labeling techniques and super-resolution microscopy. This makes SPT an important tool for studying single-molecule dynamics in vivo (Hansen et al., 2018; Shen et al., 2017). Finally, combining particle tracking methods to obtain the condensate viscosity with coalescence assays to measure the inverse capillary velocity allows for the inference of the surface tension of the condensate (equation 2.2) (Feric et al., 2016).

Single particle tracking: Methods

Definition

Measuring the mean square displacement of a tracer microsphere within a biomolecular condensate and detecting the condensate’s apparent viscosity.

Rationale

Particle tracking is a simple method of estimating the viscosity of a condensate. It does not require special instrumental setup or fluorescent labeling.

Materials, equipment, and reagents

Confocal/epifluorescence/bright-field microscope, a sample containing phase-separated protein/RNA mixture, Carboxylate functionalized polystyrene microspheres (typically 20–500 nm in diameter, passivated with PEG), Tween20/Pluronic F127 coated microscope cover glass.

Protocol

1. Prepare the sample by adding the passivated polystyrene beads to the buffer followed by the addition of the protein/RNA to form the condensates. The condensates must be formed in a buffer that already contains passivated polystyrene beads (in order to encapsulate the beads within droplets). Bead concentration should be adjusted to have few beads within each droplet (ideally, 1–2 beads per droplet).

2. Load the sample onto the microscope and make sure that the beads are exhibiting Brownian motion.

3. Focus the microscope on a droplet that is stationary on the surface of the glass slide and contains one or two beads and collect a movie of the bead motion inside the droplet. For single particle tracking, one bead inside a droplet is ideal so that the motion of the bead can be traced over a larger area without interference from other particles in the field of view, even though some algorithms can detect multiple particles simultaneously (Crocker & Grier, 1996). Also, make sure that the bead being imaged is not close to the droplet interface as the latter will constrain the bead motion and give inaccurate results.

4. Repeat step 3 for a statistically significant number of trials. It is advisable to track different beads in different droplets in each of the trials.

Precursor techniques

The coating of microscope glass chambers is described in section 2. Bead passivation is a standard procedure and has been described elsewhere (Elbaum-Garfinkle et al., 2015; Feric & Brangwynne, 2013; Feric et al., 2016).

Analysis and statistics

The outcome of the particle tracking experiment is a movie capturing the bead movement inside a droplet. The analysis constitutes tracking this particle and measuring its position as a function of time. This can be done using custom-made tracking programs or commercially available tracking software. Here, we used Fiji-ImageJ software along with the TrackMate plugin to track the bead’s movement inside a droplet. Once tracking is completed, the output constitutes the XY coordinates of the particle as a function of time. The particle trajectory can then be plotted as shown in Figure 12b. The calculation of mean square displacement <r²> for a lag time τ from a trajectory of a total time T can be done by considering the mathematical definition of the MSD

$$〈r^2〉\left(\tau \right)=\mathrm{ }{〈{\left|r\left(t_0+\tau \right)-r\left(t_0\right)\right|}^2〉}_{t_0}$$ (6.2)

Where the brackets denote averaging over all time initial time points t₀ (for multiple particle tracking, the averaging is done over time and particles (Feric & Brangwynne, 2013)). The values of τ are multiples of the time resolution of the trajectory. A plot of the MSD as a function of the lag time τ is shown in Figure 12c. For a Newtonian fluid droplet in equilibrium without internal directional flow, the MSD functional dependence on τ follows Brownian dynamics and can be expressed as

$$\mathit{\text{MSD}}=\mathrm{ }〈r^2〉\left(\tau \right)=4D{\tau }^{\alpha }$$ (6.3)

Where D is the diffusion coefficient and α is the diffusive exponent. Fitting the data in Figure 12c with this equation yields a diffusion coefficient of D = 0.012 ± 0.009 μm²/s and a diffusivity exponent α = 0.85 (Fig. 13). This means that the motion is possibly sub-diffusive (α<1). We note that this analysis should be repeated for multiple trajectories to get accurate information on the condensates under study. Furthermore, to estimate the errors in MSD calculation, the particles can be fixed on the sample surface and imaged for a duration of time. The same analysis of MSD will give the MSD noise signal, any value of MSD larger than that noise is expected to occur due to the actual motion of the particle (Feric & Brangwynne, 2013). The viscosity can be calculated by assuming Brownian dynamics and using the Stokes-Einstein equation

$$\eta =\frac{k_{B}T}{6\pi aD}$$ (6.4)

Where a is the size of the particle and T is temperature. Using the obtained value of the diffusion coefficient, the viscosity is calculated by equation 6.4 to be η = 0.18Pa.s. The particle tracking experiment could be repeated with beads of different sizes to verify the scaling of the diffusion coefficient D with the particle diameter a (Elbaum-Garfinkle et al., 2015; Feric & Brangwynne, 2013).

Fig. 13.

MSD data extracted from the trajectory in Figure 12. Red: MSD data. Black: a fitting model using equation 6.3.

Pros and cons

Pros	Cons
Provides unbiased information on the viscosity of a condensate. Does not require fluorescence labeling of the biomolecules under study.	Sensitive to the quality of passivation, especially when using surface-modified beads since they may interact with the proteins/RNAs in the condensate. Impractical to apply if the system forms condensates of relatively small size (droplet size comparable to bead size).

Troubleshooting & Optimization

Problem	Solution
Beads do not stay in the focal plane of the microscope for a long time and diffuse in the z-direction. This limits the ability to follow the motion of the bead for a sufficient time.	Increase the hydrophilicity of the surface by modifying the coating procedure to enhance droplet wetting on the glass slide surface. This would provide lesser volume in the z-direction and enable longer tracking.
Beads are constrained in the droplet and are not showing diffusion motion.	This problem indicates two possibilities: (a) biomolecules are forming a network within the droplet with mesh size less than the bead diameter, and/or (b) the bead is interacting with biomolecules and changing the droplet properties. Improving the passivation and decreasing the bead diameter may help to resolve the issue.

Summary

Particle tracking is a classical experimental technique to measure the apparent viscosity of biomolecular condensates. It constitutes the imaging of a bead diffusing inside a condensate for a finite duration of time. The bead is tracked and quantities such as the MSD, diffusion coefficient, and apparent viscosity are extracted from the particle trajectory. When complementing particle tracking with droplet fusion assays, one can estimate both viscosity and surface tension of a biomolecular condensate.

7. Advanced methods

Measuring Frequency-dependent viscoelasticity and surface tension using dual optical traps

Many cellular condensates exhibit properties of a complex viscoelastic fluid rather than purely viscous liquid. Jawerth et al. recently reported a new method of using optical traps to measure the viscoelastic properties of protein droplets (Jawerth et al., 2018). This method involves trapping a droplet between two tracer particles and applying controlled oscillatory stresses to the condensate (Fig. 14a&b). By monitoring the response of the system, the authors demonstrated that the droplet viscoelastic properties, as well as interfacial tension, could be measured. In brief, droplets are formed in a buffer containing microspheres (similar to SPT assay described above). The resulting droplets will contain microspheres immersed within. Two optical traps are then used to trap two beads and then place them on a radial distance from the center of a suspended droplet, thereby slightly stretching the droplet. In this configuration, the beads can now act as handles to apply stress on the droplet. The traps are then set to oscillate at fixed frequencies and the corresponding forces from the optical traps are recorded (see Figure 14c).

Fig. 14.

(a) A diagram showing a trapped droplet between two optically trapped microspheres. (b) Driving Trap-1 to undergo oscillation applies stress on the condensate due to repetitive stretching. (c) Simulated data of Trap position, the force from Trap-1 (F₁), the force from Trap-2 (F₂) as a function of time during the oscillatory stress.

From the forces on the optical traps, one can calculate the frequency-dependent spring constant of the system using the relation

$${\chi }_{sys}^{*}\left(\omega \right)=({\tilde{F}}_1\mathrm{ }-{\tilde{F}}_2\mathrm{ })/2{\tilde{x}}_{sys}$$ (7.1)

Where ${\tilde{F}}_1$ is the force measured by trap-1,${\tilde{F}}_2$ is the force measured by trap-2, ${\tilde{x}}_{sys}$is the distance between the two traps (all as a function of frequency). One can derive the spring constant of the droplet from the relation

$${\chi }_{\mathit{\text{drop}}}^{*}\left(\omega \right)=\frac{{\chi }_{sys}^{*}\left(4k_1{k}_2+i\zeta \omega \left[k_1+k_2\right]\right)}{2k_1\left(2k_2+i\zeta \omega \right)-4{\chi }_{sys}^{*}(k_1+k_2+i\zeta \omega )}$$ (7.2)

Where k_1,2 is the trap stiffness of trap 1,2. ζ is the drag coefficient of the surrounding medium (can be calculated using ζ= 6πη_mediumR_droplet). At the low-frequency regime, corresponding to the slow oscillations, the spring constant of the droplet is dominated by surface tension. The surface tension can be calculated from

$$\gamma \mathrm{ }\approx \frac{{\chi }^{\mathrm{\text{'}}}\left(\omega \right)}{1.25+4.36{\theta }_0^2}$$ (7.3)

Where θ₀=r_bead/R_droplet. This relation is valid for θ₀≪1. The complex modulus is then calculated by subtracting the surface tension effects from the droplet spring constant (Jawerth et al., 2018)

$$G^{*}\left(\omega \right)=\frac{[{\chi }_{\mathit{\text{drop}}}^{*}\left(\omega \right)-\left(1.75+6.31{\theta }_0^2\right)\gamma ]}{R_{\mathit{\text{droplet}}}\left(0.58+3.42{\theta }_0^2\right)}=G^{\mathrm{\text{'}}}\left(\omega \right)+i\mathrm{ }G\mathrm{\text{'}}\mathrm{\text{'}}\left(\omega \right)$$ (7.4)

The complex modulus G* provides a rich description of the mechanical properties of materials. First, it allows the quantification of the elastic (G’) and viscous (G”) response of the material, thereby allowing for a precise elucidation of viscoelasticity (Rubinstein & Colby, 2003). For a purely viscous condensate, G” dominates, whereas for an elastic condensate, G’ dominates. Furthermore, quantities such as viscosity and terminal relaxation time can be extracted from the material’s complex modulus. For example, a Newtonian liquid has a complex modulus of the form $G^{*}\left(\omega \right)=i\eta \omega$, where η is the liquid viscosity (Rubinstein & Colby, 2003). In such a case, the droplet spring constant will have both real and imaginary parts (χ_droplet=χ′+iχ″). The real part is independent of frequency and quantifies the contribution of the surface tension (see Figure 15). Notwithstanding the limitation of implementing such a procedure that requires the formation of large droplets (~10–20 um), and ensuring that the microsphere’s refractive index is higher than that of the droplets (to ensure the feasibility of trapping a microsphere within a condensate), the method provides unique and novel insights into the viscoelastic properties as well as the surface tension of biomolecular condensates.

Fig. 15.

Representative diagram for the frequency-dependent spring constant of a Newtonian fluid droplet. The real part of the spring constant (black) contains information on the surface tension of the droplet and the imaginary part of the spring constant (red) gives information on the viscosity.

8. Conclusion

Here, we discussed the common experimental methods to determine the fluid properties of a biomolecular condensate. Optical trap-induced coalescence provides information on the droplet dynamics at the mesoscale level. FRAP provides information on the molecular diffusivity in the nanoscale regime. Single particle tracking experiments can measure the apparent viscosity of a condensate. Combining MSD and fusion assays on the same sample enables the measurement of the interfacial tension by inference (Elbaum-Garfinkle et al., 2015; Feric et al., 2016). Combining FRAP and coalescence assays provides a multiscale picture of how condensate material properties may vary with length-scales (Alshareedah et al., 2019; Kaur et al., 2019). One major advantage of FRAP is that it could be utilized to study cellular condensates in vivo. However, it should be stressed that these techniques do not provide an absolute measure of the condensate material properties, rather they provide simple tools to measure the relative changes in droplet material properties at different conditions. Advanced methods such as active microrheology using optical tweezers may provide critical and much-needed tools to measure the viscoelastic properties of biomolecular condensates.