Surface-Tethering Enhances Precision in Measuring Diffusion Within 3D Protein Condensates

Abstract

Biomolecular condensates, or membraneless organelles, play pivotal roles in cellular organization by compartmentalizing biochemical reactions and regulating diverse processes such as RNA metabolism, signal transduction, and stress response. Super-resolved imaging and single molecule tracking are essential for probing the internal dynamics of these condensates, yet the intrinsic Brownian motion of the entire condensate in vitro could interfere with diffusion measurements, confounding the interpretation of molecular mobility. Here we systematically assess and address this challenge with both experiments and simulations, using in vitro reconstituted condensates as simplified models of endogenous cellular assemblies. We show that tethering effectively suppresses the global translational and rotational Brownian motions of the entire condensate, eliminating inherent motion interference while preserving their spherical morphology. Quantitative analysis reveals that untethered condensates systematically overestimate molecular diffusion coefficients and step sizes, particularly for slowly diffusing structured mRNAs, while rapidly diffusing unstructured RNAs are unaffected due to temporal scale separation. Comparative evaluation of tethering strategies demonstrates tunable control over condensate stability and internal dynamics, with implications for optimizing experimental design. Finally, combining with simulations that sweep through the whole physiological parameter space, we provide a practical guideline for judging whether tethering is necessary in an experiment based on condensate size, diffusion type, and diffusion coefficient of the biomolecule of interest. Our findings establish surface tethering as a valuable and robust approach for accurate quantification of intra-condensate molecular dynamics, providing a methodological framework for future studies of membraneless organelles.

Graphical Abstract

Introduction

Biomolecular condensates, also known as membraneless organelles, have emerged as fundamental organizers of cellular biochemistry [1,2], orchestrating the spatial and temporal distribution of proteins, RNAs, and other macromolecules without the need for membrane boundaries [3–5]. These dynamic assemblies form through diverse phase separation mechanisms—including complex coacervation, percolation, gelation, and multi-component transitions [6–8]—enabling the compartmentalization of biochemical reactions and the control of cellular processes, including RNA metabolism, signal transduction, stress response, and genome organization [4,9–11]. Notable examples include nucleoli, stress granules, P-bodies [12], Cajal bodies [13], and germ granules, each contributing to critical aspects of gene expression, ribonucleoprotein complex assembly [14], and cellular adaptation to environmental cues [2].

To probe the internal organization and molecular dynamics within condensates, super-resolved position determination and single molecule diffusion measurements have become indispensable tools [15–20]. Techniques such as single molecule tracking (SMT) and super-resolution fluorescence microscopy allow researchers to quantify the mobility, interactions, and spatial distribution of individual molecules within the dense and heterogeneous environment of condensates. These approaches provide critical insights into the physical properties and functional mechanisms governing condensate behavior and are often performed in vitro.

However, a significant and often underappreciated challenge in these in vitro studies arises from the intrinsic Brownian motion of condensates in vitro. As discrete microscopic entities, biomolecular condensates exhibit translational and rotational movements driven by thermal fluctuations when placed on untreated or inadequately passivated surfaces [21–23]. These whole-droplet motions arise from the same physical principles governing the Brownian motion of any suspended particle in a viscous medium. Intrinsic condensate motions have the potential to interfere with diffusion measurements, possibly leading to systematic over- or underestimation of molecular mobility and confounding the interpretation of single molecule trajectories. In vitro studies have yet to address that poorly immobilized condensates can compromise the accuracy of diffusion data analysis, particularly if nanometer spatial resolution and millisecond temporal resolution are desired, where whole-condensate movements can be mistaken for intra-condensate molecular diffusion.

Fused in Sarcoma (FUS) protein has become a widely used model for studying biomolecular condensates due to its robust phase-separation behavior and its direct pathological relevance [24–27]. FUS is an RNA-binding protein implicated in the formation of stress granules and other nuclear and cytoplasmic condensates [28]. Mutations and aberrant phase behavior of FUS are linked to neurodegenerative disorders such as amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD), where abnormal condensate dynamics and aggregation contribute to disease progression [25,27]. Thus, accurate measurement of molecular diffusion and organization within FUS condensates is critical for understanding both fundamental biophysical principles and disease mechanisms.

In this study, we address the challenge of condensate motion interference by developing and systematically evaluating three surface-tethering strategies—using biotinylated DNA, protein, or antibody tethers—to immobilize FUS condensates on passivated glass surfaces. Our findings reveal that controlled surface passivation and tethering are critical for maintaining the spherical morphology [29] and structural stability of FUS protein condensates. We employ single molecule tracking and diffusion analysis to quantify the impact of tethering on both condensate stability and the precision of intra-condensate diffusion measurements. Our results demonstrate that surface tethering effectively suppresses whole-condensate Brownian motion and minimizes motion‐induced interference, while maintaining condensate sphericity. By constraining center-of-mass translation and rotation, tethering creates a stable inertial frame in which inherent molecular motions can be probed without convolution by bulk droplet movements. We further show that the usefulness of tethering depends on the timescale of molecular diffusion relative to condensate motion, with implications for experimental design and data interpretation. By providing a robust methodological framework, our work enables more accurate and reproducible investigations into the molecular dynamics of membraneless organelles, advancing our understanding of their roles in cellular organization, regulation, and disease. Collectively, our results establish surface tethering as a valuable and tunable approach for the precise quantification of intra-condensate molecular dynamics, enabling interrogation of a defined region of the complex condensate material‐state without reliance on bulk droplet motion correction.

Results

Surface passivation and tethering governs morphology and stability of FUS protein condensates

Recently, evidence has emerged supporting a critical impact of surface treatment and tethering strategies on the morphology and behavior of biomolecular condensates [29,30]. To further test this notion, we used confocal microscopy to image condensates across multiple z-slices and assess their three-dimensional shape under various surface treatment conditions. On untreated bare glass surfaces, condensates exhibited substantial wetting interactions, spreading flatly and losing their roundness with a mean circularity (measured in two dimensions) of 0.69 ± 0.02 and a notably low object count of n = 120 (Figure 1a,b). In contrast, methylated PEG (henceforth simply “PEG”)-treated surfaces effectively restored physiologically relevant spherical morphology, significantly improving circularity to 0.78 ± 0.01 (n_objects = 450), confirming the efficacy of PEG in preventing deleterious surface wetting interactions.

Figure 1 |. Surface modification and tethering strategies control biomolecular condensate morphology and stability.

a | Confocal microscopy images showing the effects of different surface treatments on condensate morphology. Top row: schematic illustrations of surface functionalization-bare glass, PEG, DNA tether, protein tether, and antibody tether. Middle row: xz cross-sectional views reveal that condensates on bare glass exhibit extensive wetting and spreading, while PEGylation restores spherical morphology by preventing surface interactions. DNA, protein, and antibody tethers further stabilize condensates, maintaining roundness with slight deviations from perfect sphericity. Bottom row: corresponding xy images of condensate populations for each condition. b | Distributions of condensate circularity corresponding to identifiable objects in a. c | Tuning condensate morphology by varying the density of DNA tethers. Left to right: decreasing the ratio of biotinylated DNA PEG to PEG from 1:10 to 1:100000 progressively improves condensate roundness and reduces spreading, with the lowest tether density (1:100000) fully recovering spherical morphology and reducing condensate size. Schematics below illustrate the relative density of DNA tethers for each condition. Scale bar: 5 μm. d | Distributions of condensate circularity corresponding to identifiable objects in c. n = number of identified objects.

Next, while our PEG passivation successfully recovered spherical condensate morphology, random Brownian whole-condensate motion emerged as a challenge due to the particle-like Brownian motions of condensates [31,32] (Figure S1). To address this impediment to accurate intra-condensate measurements, three biotinylated tethering strategies were evaluated: DNA containing FUS binding sites, FUS protein, and anti-FUS antibody (Figure 1a).

All three tethering approaches successfully maintained condensate roundness while reducing Brownian motion. Notably, the anti-FUS antibody tethering achieved the highest mean circularity (0.80 ± 0.01, n_objects = 437), representing a modest but measurable improvement over untethered PEG-treated surfaces. Biotin-FUS protein tethering yielded intermediate circularity values (0.74 ± 0.01, n_objects = 334), while DNA tethering produced slightly lower circularity (0.72 ± 0.01, n_objects = 231) compared to untethered PEG controls (Figure 1b). To systematically investigate the relationship between tethering density and condensate morphology, DNA tethering densities were tested by varying the proportion of biotin-PEG molecules relative to unmodified PEG molecules from 1:10 to 1:100,000 (Figure 1c,d).

Here, ‘tethering density’ denotes the molar ratio of biotin–PEG–tether to unmodified PEG on the passivated surface. At a 1:10 tether-to-PEG ratio, surface binding is excessive, and condensates spread, reducing mean circularity to 0.60 ± 0.05 (n_objects = 23) (Figure 1c,d). At intermediate densities (1:100), mean circularity peaks at 0.74 ± 0.01 (n_objects = 203). Further reductions in tether frequency (1:1,000 and 1:10,000) yield similar mean circularities of 0.72 ± 0.01 and 0.70 ± 0.02, respectively. Although the 1:100,000 density—where only ~1 in 100,000 PEG molecules carry a tether—has a lower mean circularity (0.66 ± 0.01, n_objects = 316), it produces the highest fraction of condensates with circularity > 0.8 (Figure 1d). This occurs because mean circularity is sensitive to a small subpopulation of poorly tethered, non‐spherical condensates, whereas the frequency analysis highlights the predominant behavior of correctly tethered droplets. Thus, an intermediate tethering density (1:100–1:1,000) maximizes both mean and modal circularity, balancing adequate immobilization with minimal surface spreading.

Interestingly, while mean circularity peaked at the 1:100 ratio, analysis of the circularity distribution revealed that the 1:100,000 ratio produced the highest frequency of highly circular condensates (circularity > 0.8), suggesting that optimal tethering conditions depend on the specific experimental requirements for condensate shape uniformity versus mean circularity (Figure 1d).

This tunable tethering system demonstrates that both tether type and density can be optimized to balance condensate sphericity and motility reduction for specific experimental applications. Our quantitative analysis reveals that surface modification strategies must be carefully calibrated to achieve reproducible imaging conditions while preserving the spherical morphology of biomolecular condensates as indicated by their circularity.

Tethering eliminates rotational coherence and reduces overall movement fluctuations within condensates

To investigate the impact of tethering on Brownian dynamics of individual condensates, we developed an experimental approach to quantitatively assess thermal-induced motions using fluorescent microsphere tracers. Recent theoretical work has demonstrated that Brownian motion of droplets at submicron scales involves the complex interplay of intermolecular diffusion, surface tension, and thermal composition noise [33]. Our protein condensate system models a biomolecular phase separation environment where such Brownian dynamics principles apply.

Based on the optimized DNA tether density achieved with a 1:1000 biotin-PEG to PEG ratio, we employed 200 nm fluorescent microspheres as internal tracers in FUS condensates due to their optimal balance of brightness for reliable frame-to-frame localization and sufficiently slow diffusion kinetics relative to condensate motion. Imaging parameters were carefully optimized: at 20 ms intervals, microsphere movement remained within static localization error limits, while 100 ms intervals allowed detectable displacement beyond the frame-to-frame detection threshold. Time-lapse imaging over 100 frames at 100 ms intervals provided sufficient temporal resolution to capture Brownian dynamics while maintaining spatial precision for individual particle tracking.

Qualitative analysis of the resulting microsphere trajectories revealed markedly different movement patterns between tethered and untethered conditions (Figure S1). In untethered condensates, microspheres exhibited highly coordinated displacement patterns, with trajectories color-coded by frame number demonstrating collective directional shifts characteristic of whole-condensate Brownian motion (Figure S1a). This coordinated motion reflects the stochastic dynamics of the entire condensate as a microscopic particle undergoing thermal-driven Brownian motion in solution.

In stark contrast, tethered condensates showed microsphere trajectories appeared incoherent and randomized, lacking the collective directional patterns observed in untethered conditions (Figure S1b). This transition from coherent whole-condensate motion to localized microsphere diffusion indicates that going from untethered to surface-tethered effectively suppresses the thermal Brownian dynamics of the condensate as a discrete droplet suspended in solution, while preserving local diffusive processes within the condensate interior. We note, however, that while the coherent internal tracer trajectories in untethered droplets are consistent with combined translational and rotational Brownian motion of the condensate, our current measurements cannot unambiguously distinguish angular preference caused by confinement inside condensate versus rotational constraints directly imposed by interfacial anisotropy at condensate surface; direct quantification of angular fluctuations will require follow-up experiments using polarized‐light scattering or anisotropic probes targeted to the condensate interface.

A quantitative analysis of angular displacement patterns revealed dramatic differences in rotational dynamics between tethered and untethered condensates (Figure 2a). Tracking the frame-to-frame fluctuations of microsphere localization revealed a dramatic increase in fluctuations for the untethered condition (Figure 2b). Further, by analyzing the angular displacement of microspheres relative to the condensate center, we calculated a maximum rotational amplitude of 72.95° ± 5.55° for the untethered condition (Figure 2b). These extensive rotational movements of ~73° in 10 seconds were largely eliminated in the tethered condition, where maximum angular displacement was reduced to 5.98° ± 3.04° over the same timeframe (Figure 2b). Comparing this metric for all condensates, we calculated a substantially higher angular variance for the untethered condition (16.36° ± 2.35°) compared to tethered condensates (2.04° ± 0.70°; p = 0.0010, paired t-test), reflecting large-amplitude rotational movements.

Figure 2 |. Untethered condensates display increased fluctuations and rotational coherence compared to tethered condensates.

a | representative condensate for untethered and tethered conditions. Colored trajectories show microsphere positions across 100 frames (10 seconds), with colors indicating frame number according to the scale bar below. b | Frame-to-frame localization fluctuations and angle-of-rotation for the given condensates in (a) untethered (blue) and tethered (orange). c | Ensemble frame-to-frame localization fluctuations for all condensates in each condition. Each solid dot represents one condensate, while each bordered dot represents all condensates within one biological replicate. Statistics test is performed among biological replicates. Same below. d | Scatter plot of phase space area as a function of angular velocity-acceleration correlations. e | Scatter plot of velocity autocorrelation for beads within a condensate, for all condensates in each condition. At least three biological replicates are presented in each plot, which includes 320 untethered condensates and 183 tethered ones. Statistics annotation: Mann-Whitney U, ns: 0.05 < p <= 1, *: 0.01 < p <= 0.05, **: 0.001 < p <= 0.01, ***: 0.0001 < p.

Ensemble localization fluctuation analysis demonstrated that untethered condensates exhibited maximum translational fluctuations of 391.60 ± 128.44 nm and average fluctuations of 146.61 ± 50.24 nm per frame (Figures 2c, S5a). In stark contrast, tethered condensates showed substantially reduced translational fluctuations with maximum values of 68.17 ± 16.14 nm and average fluctuations of only 22.36 ± 4.84 nm per frame, representing a five-fold reduction in maximum fluctuation amplitude and a six-fold decrease in average fluctuation magnitude (Figures 2c, S5a).

Phase space area analysis provided quantitative evidence for the constrained dynamics observed in tethered condensates. Untethered condensates occupied significantly larger regions of velocity-acceleration phase space (60.62 ± 6.60 rad²/s³) compared to tethered condensates (11.61 ± 3.14 rad²/s³; Figure 2d). This greater than five-fold reduction in accessible phase space area demonstrates that tethering fundamentally restricts the range of translational motions available to a condensate. Velocity autocorrelation analysis, which quantifies the persistence of rotational motion, showed similar dramatic differences. Untethered condensates exhibited autocorrelation values of 1.94 ± 0.41 compared to 0.35 ± 0.14 in tethered condensates, indicating that rotational motions in untethered condensates are highly persistent and coordinated over time (Figure 2e). These trends hold consistent across the 100 ms and 20 ms imaging frequencies (Figure S2). We note that our single molecule tracking measurements represent 2D projections of inherently 3D molecular motions within spherical condensates. While this may affect absolute diffusion parameters, the relative comparisons between tethered and untethered conditions are valid, and the critical finding that tethering eliminates motion interference is independent of this geometric constraint.

Tethering eliminates condensate motion interference to enable precise diffusion measurements of mRNA guest molecules

To comprehensively assess how surface tethering affects the measurement of biologically relevant molecular dynamics, we tracked in vitro transcribed and fluorescently labeled FL mRNA within both tethered and untethered condensates. We imaged at 200 ms time resolution, the same time scale at which we observed condensate Brownian dynamics, to capture the slow diffusion of single AlexaFluor 647-labeled firefly luciferase (FL) mRNA guest molecules. This approach allowed direct comparison of diffusion measurements for a typical structured RNA, which exhibits more complex intra-condensate behavior than the inert microsphere tracer used in our earlier experiments.

Localization fluctuation analysis confirmed that tethering significantly reduces measurement variability for biomolecular tracking. Untethered condensates exhibited maximum fluctuations of 262.03 ± 19.10 nm and average fluctuations of 110.97 ± 11.02 nm per frame, compared to tethered condensates that showed reduced maximum fluctuations of 167.28 ± 15.55 nm and average fluctuations of 60.43 ± 6.71 nm (p = 0.0116 for maximum; p = 0.0089 for average; Figures 3a, S6a). This reduction in localization variability demonstrates that tethering provides a more stable experimental platform for accurate single molecule measurements by minimizing interference from whole-condensate Brownian motion.

Figure 3 |. Tethering preserves intra-condensate diffusion dynamics while reducing condensate motion interference.

a | Beeswarm plot of ensemble frame-to-frame localization fluctuations of FL mRNA molecules in condensates per each condition; untethered (blue) and tethered (orange). Each solid dot represents one condensate, while each bordered dot represents all condensates within one biological replicate. Statistics test is performed among biological replicates. Same below. b | Beeswarm plot of phase space area as a function of angular velocity-acceleration correlations and beeswarm plot of velocity autocorrelation. At least three biological replicates are presented in each plot, which includes 403 untethered condensates and 493 tethered ones. Statistics annotation: Paired t-test, ns: 0.05 < p <= 1 or Cliff’s $\left|\mathrm{\delta }\right|<0.147$, *: 0.01 < p <= 0.05, **: 0.001 < p <= 0.01, ***: 0.0001 < p. c | Line plots of ensemble-averaged MSD (μm²) for RNA molecules in tethered and untethered condensates as a function of lag time (τ, seconds). Shaded regions represent the standard error of the mean. d | Histogram distributions of mean step sizes (nm) per trajectory. e | Histogram distributions of log-transformed apparent diffusion coefficients (log₁₀D_app, μm²/s). f | Beeswarm plot of ensemble frame-to-frame localization fluctuations of poly(U)₁₀₀₀ RNA molecules in condensates per each condition; untethered (blue) and tethered (orange). g | Beeswarm plot of phase space area as a function of angular velocity-acceleration correlations and beeswarm plot of velocity autocorrelation. At least three biological replicates are presented in each plot, which includes 3,469 untethered condensates and 2,645 tethered ones. Statistics annotation: Paired t-test, ns: 0.05 < p <= 1, *: 0.01 < p <= 0.05, **: 0.001 < p <= 0.01, ***: 0.0001 < p. h | Line plots of ensemble-averaged MSD (μm²) for RNA molecules in tethered and untethered condensates as a function of lag time (τ, seconds). Shaded regions represent the standard error of the mean. i | Histogram distributions of mean step sizes (nm) per trajectory. j | Histogram distributions of log-transformed apparent diffusion coefficients (log₁₀D_app, μm²/s).

Angular and velocity-based analyses revealed no statistically significant differences between tethered and untethered conditions for FL mRNA motion, including phase space area and velocity autocorrelation (both p > 0.2; Figure 3b). This contrasts with the large kinematic differences observed in microsphere tracking, suggesting that for FL mRNA, the effects of whole-condensate motion on these parameters are subtler and may be partially masked by the molecule’s own motion and more variable trajectories.

FL mRNA in tethered condensates showed consistently lower mean squared displacement across all time lags (Figure 3c). Step size analysis revealed the impact of condensate motion on apparent molecular displacement measurements. FL mRNA molecules in untethered condensates displayed significantly larger mean step sizes (106.13 ± 3.20 nm, n = 270) compared to tethered condensates (66.36 ± 2.10 nm, n = 368; Figure 3d). This difference directly translates to overestimation of molecular mobility when condensate motion is not controlled.

Analysis of the apparent diffusion constant (D_app) and anomalous diffusion component (α) revealed that tethering preserves the fundamental diffusion characteristics of mRNA within condensates. The α values were similar between conditions, with tethered condensates showing 0.80 ± 0.01 (n = 352) compared to 0.75 ± 0.02 (n = 278) in untethered condensates (Figure S3). These values, close to α = 1, confirm that mRNA diffusion within condensates remains predominantly Brownian regardless of tethering status, indicating that surface immobilization preserves the inherent properties essential for intra-condensate molecular diffusion. Apparent diffusion coefficient analysis quantified the magnitude of this measurement convolution. In untethered condensates, the mean log₁₀(D_app) was −2.15 ± 0.04 log₁₀(μm²/s) (n = 378), compared to −2.42 ± 0.03 log₁₀(μm²/s) in tethered condensates (n = 476; Figure 3e). This difference represents approximately a 1.9-fold overestimation of diffusion coefficients when condensate Brownian motion is not eliminated, demonstrating how failure to account for whole-condensate movement can significantly confound single molecule diffusion measurements. Similar concerns would also apply to bulk measurements such as fluorescence recovery after photobleaching (FRAP), another widely used method for assessing molecular dynamics within condensates. In localized FRAP experiments where a small region within a condensate is photobleached, whole-condensate translation or rotation could cause the bleached region to move out of the observation field or allow bleached material to appear in the analysis area, inadvertently altering recovery kinetics and leading to erroneous diffusion coefficient estimates.

Tethering is not necessary for measuring fast diffusion of unstructured RNA molecules

We next asked whether tethering condensates has a similar impact on the quantitative analysis of the diffusive behavior of unstructured, fluorescently labeled Poly(U)₁₀₀₀ RNA molecules compared to structured RNA. Imaging at a tenfold higher temporal resolution (20 ms) than for FL mRNA was necessary to capture their rapid diffusion. This allowed us to probe the timescales over which whole‑condensate motion might interfere with molecular tracking.

Frame-to-frame localization fluctuation analysis revealed similar behavior between tethered and untethered condensates containing guest Poly(U)₁₀₀₀ RNA molecules. Average fluctuations were virtually identical between conditions, with tethered condensates showing 204.43 ± 1.09 nm and untethered condensates exhibiting 206.42 ± 0.94 nm (Figure 3f). Despite statistical significance for average fluctuations, the effect magnitude was negligible. These results suggest that individual Poly(U)₁₀₀₀ molecules retain equivalent short-timescale mobility regardless of any overlaid condensate Brownian dynamics.

Comprehensive angular dynamics analysis confirmed the absence of significant differences between tethered and untethered conditions for Poly(U)₁₀₀₀ RNA tracking. Phase space area analysis and velocity autocorrelation revealed minimal differences (both p > 0.1; Figure 3g), with both distributions highly clustered and exploring limited phase space compared to the microsphere tracers and structured mRNA molecules analyzed in our previous experiments.

Analysis of molecular diffusion parameters demonstrated that tethering provides no measurement advantage for unstructured RNA molecules. MSD-$\tau$ plot residuals overlapped even at larger time lags, with untethered condensates displaying lower average values at larger time lags (Figure 3h). Mean step sizes were essentially identical between conditions (204.76 ± 0.93 nm for tethered, n = 1,947; 205.66 ± 0.76 nm for untethered, n = 2,587), with overlapping distributions (Figure 3i). The anomalous diffusion component (α) remained close to Brownian behavior in both conditions (0.86 ± 0.01 tethered versus 0.84 ± 0.01 untethered), confirming that the fundamental diffusion characteristics of unstructured RNA are preserved regardless of condensate stabilization status (Figure S3). Log-transformed apparent diffusion coefficients showed similarly negligible differences (−0.32 ± 0.01 log₁₀(μm²/s) tethered versus −0.33 ± 0.01 log₁₀(μm²/s) untethered; Figure 3j).

The minimal impact of tethering on Poly(U)₁₀₀₀ RNA measurements can be explained by the temporal scale separation between molecular diffusion and condensate Brownian dynamics. The frame-to-frame diffusion timescale of unstructured Poly(U)₁₀₀₀ RNA molecules (10–20 ms) is approximately one order of magnitude faster than the characteristic timescales of whole-condensate Brownian motion observed in previous experiments (100–200 ms). This temporal separation means that rapid RNA diffusion effectively dominates over the slower condensate rotation, rendering tethering unnecessary for accurate measurement of intrinsic molecular dynamics.

Different tethering strategies offer tunable control over condensate stability and dynamics

To determine the optimal tethering approach for different experimental applications, we systematically compared our three distinct tethering methods—DNA containing FUS binding sites (n = 2,100), biotin-FUS protein (n = 3,221), and anti-FUS antibody (n = 2,779),—against untethered controls (n = 415) using FL mRNA as a representative structured molecule with complex diffusion behavior. Imaging at 20 ms resolution allowed capture of all relevant diffusion states. We evaluated the relative effectiveness of each approach in suppressing Brownian condensate dynamics while preserving signature molecular diffusion characteristics.

Frame-to-frame localization fluctuation analysis revealed that all three tethering methods provide comparable stabilization effectiveness. Comparing each method revealed that anti-FUS antibody tethering (72.50 ± 3.29 nm avg), biotin-FUS protein tethering (73.10 ± 3.17 nm avg), and DNA tethering (77.12 ± 4.03 nm avg) display fluctuations with similar distributions and with no significant differences (Figure 4a). Notably, these fluctuations are a marked increase from the untethered condition (54.68 ± 2.92 nm avg; Figure S4) affirming our earlier observation that the slowly diffusing structured mRNA is fluctuating on the same time scale as whole-condensate motions.

Figure 4 |.

a | Beeswarm plot of ensemble frame-to-frame localization fluctuations of FL mRNA molecules in condensates per each condition; antibody tethered (blue), protein tethered (yellow), and DNA tethered (red). Each solid dot represents one condensate, while each bordered dot represents all condensates within one biological replicate. Statistics test is performed among biological replicates. Same below. Statistics annotation: Paired t-test, ns: 0.05 < p <= 1, *: 0.01 < p <= 0.05, **: 0.001 < p <= 0.01, ***: 0.0001 < p. b | Beeswarm plot of phase space area as a function of angular velocity-acceleration correlations and beeswarm plot of velocity autocorrelation. At least three biological replicates are presented in each plot, which includes 2,779 antibody-tethered condensates, 3,221 FUS protein-tethered condensates, and 2,100 DNA-tethered condensates. c | Line plots of ensemble-averaged MSD (μm²) for RNA molecules in tethered condensates as a function of lag time (τ, seconds). Shaded regions represent the standard error of the mean. d | Histogram distributions of mean step sizes (nm) per trajectory. e | Histogram distributions of log-transformed apparent diffusion coefficients (log₁₀D_app, μm²/s).

Indeed, angular dynamics analysis demonstrated that all three tethering strategies effectively eliminate the large-scale Brownian motions observed in untethered condensates. Phase space area analysis showed dramatic reductions from untethered values (50.78 ± 4.71 rad²/s³) to all three tethered conditions: anti-FUS antibody (24.91 ± 0.89 rad²/s³), biotin-FUS protein (23.67 ± 1.08 rad²/s³), and DNA (27.54 ± 2.43 rad²/s³; Figure 4b). All tethered–untethered comparisons showed significant differences (p ≤ 0.04) but no significant differences between tethering methods, confirming that all approaches successfully suppress condensate Brownian dynamics. Similarly, negligible effect sizes were found for the velocity autocorrelation analysis between tethering methods (p > 0.2, Figure S4).

Despite equivalent condensate stabilization, tethering methods exhibited subtle, but measurable differences in molecular diffusion parameters. Notably, the MSD-$\tau$ relationship for the DNA tether condition showed consistently larger values across all time lags while antibody and protein tether overlapped entirely, and the untethered condition showed consistently lower values across all time lags (Figure 4c). Step size analysis also revealed systematic differences between approaches, with untethered condensates showing artificially reduced step sizes (46.8 ± 1.9 nm) due to whole-condensate motion interference masking true molecular displacement (Figure 4d). Among tethered conditions, anti-FUS antibody tethering produced the smallest step sizes (66.6 ± 0.9 nm), while protein (70.6 ± 0.9 nm) and DNA (71.6 ± 1.1 nm) tethering showed progressively larger values (Figure 4d).

The anomalous diffusion component (α) showed minimal variation between tethering methods (antibody: 0.61 ± 0.01, protein: 0.61 ± 0.01, DNA: 0.62 ± 0.01), all substantially higher than untethered controls (0.53 ± 0.02), confirming that tethering preserves normal diffusion characteristics while eliminating motion interference (Figure S4). Accordingly, apparent diffusion coefficient analysis revealed a consistent trend across tethering methods. Untethered condensates yielded artificially low apparent diffusion coefficients (−2.45 ± 0.04 log₁₀(μm²/s)) due to measurement convolution from Brownian motion. DNA tethering produced the highest apparent diffusion coefficients (−1.77 ± 0.02 log₁₀(μm²/s)), followed by protein tethering (−1.81 ± 0.01 log₁₀(μm²/s)) and antibody tethering (−1.86 ± 0.02 log₁₀(μm²/s); Figure 4e).

The observed subtle differences in molecular diffusion parameters between tethering methods suggest distinct biophysical interactions at the condensate-surface interface. DNA tethering, which showed the highest apparent diffusion coefficients and largest step sizes, may create a more permissive internal environment for RNA diffusion through specific protein-nucleic acid interactions that slightly reduce local condensate viscoelasticity, that is, make it behave more fluid-like. Conversely, antibody tethering, which produced more constrained diffusion parameters, may introduce additional steric hindrance or alter condensate internal organization through protein-protein interactions. Importantly, these tethering effects could potentially influence internal condensate dynamics beyond simple motion suppression, particularly in smaller condensates where the surface-to-volume ratio is high.

Necessity of tethering depends on condensate size and diffusion properties of the tracked molecules

To systematically assess the necessity of tethering for intra-condensate SMT beyond the conditions experimentally tested so far, we used Monte Carlo simulations to profile the deviation of SMT readouts in untethered versus tethered condensates across a broader parameter space (Figure 5). We generated SMT trajectories molecules with ground-truth diffusion metrics, including different diffusion coefficient (D) and anomalous coefficient (α) (Figure 5a). We added Brownian rotation of the condensate to molecular trajectories at each step of the simulation, based on rotational speed calculated from size (R) of the condensate, where molecules are at room temperature (T) with a viscosity (η) representing a typical protein solution. Finally, we extracted apparent diffusion coefficient (D_app) and anomalous coefficient (α_app) from simulated trajectories using the same MSD-τ fitting method as above. To determine the effect of tethering, we performed pairs of tethered and untethered (without and with Brownian rotation added) simulations for each condition side-by-side to assess the impact of the lack of tethering on SMT metrics.

Figure 5 |. Simulations reveal parameter-dependent bias in intra-condensate SMT measurements due to lack of tethering.

a | Schematic of the simulation workflow and parameters used for generating and analyzing SMT trajectories. b-c | Representative trajectories and distributions of D_app and α_app for a typically confined, slow-diffusing mRNA in a small (b) or large (c) condensate. d | Distributions of D_app and α_app for a typically free, fast-diffusing mRNA in an either small or large condensate, matching the size in b-c. e-f | Heatmaps showing the systematic bias introduced by the lack of tethering on D_app and α_app across physiological ranges of condensate size (0.3 – 5 μm) and ground-truth D (0.001 – 1 μm²/s) for free-diffusing (e) or confined (f) molecules. Color scale represents the ratio of apparent metrics measured in untethered versus tethered simulations: red indicates overestimation, blue indicates underestimation.

We first exemplified the impact of the lack of tethering on the intra-condensate SMT with typical biomolecules such as the confined, slow-diffusing mRNA and the free, fast-diffusing protein molecules (Figure 5b–d) [30]. For confined, slow-diffusing molecules such as mRNAs within small condensates, the lack of tethering caused noticeable additional displacements in trajectories, resulting in overestimation of both D_app and α_app (Figure 5b). Notably, the distributions of D_app and α_app under the tethered condition were centered around the ground-truth D and α, confirming that our simulation system faithfully recapitulates the expected diffusion behavior of molecules (Figure 5b). The slight deviation from ground-truth D in the D_app distribution is a known systematic error introduced by MSD-τ fitting [34], rather than the simulation itself. In contrast, the same confined, slow-diffusing molecules in larger condensates will not be affected, whether tethered or not (Figure 5c). Therefore, SMT metrics extracted from confined, slow-diffusing molecules are overestimated in small condensates but not in large condensates. For free, fast-diffusing molecules such as proteins, the distributions of D_app and α_app remain unchanged upon the lack of tethering, whether in small or large condensates (Figure 5d). This suggests that SMT measurements of free, fast-diffusing molecules are not biased by the lack of tethering. Taken together, simulation data on four biologically relevant diffusion scenarios showed that only confined, slow-diffusing molecules in small condensates are biased by the lack of tethering in the tracking experiments.

To test if this principle is generally true, we next performed a broader parameter sweep using our simulation in physiological ranges of condensate size (0.3 – 5 μm) and ground-truth D (0.001 – 1 μm²/s) and compared the distribution of D_app and α_app under tethered versus untethered conditions (Figure 5e–f). The ratio between the same apparent SMT metric extracted from untethered over tethered conditions is plotted as a heatmap, where darker color indicates a stronger bias introduced by the lack of tethering (Figure 5e–f). For free-diffusing molecules (α=1), the slower the molecules are and the smaller the condensate they are in, the more overestimated their D_app becomes (Figure 5e), suggesting that our observations under a couple combinations of parameters hold true in a broader parameter space. Interestingly, the estimation of α_app in free-diffusing molecules is never affected by the lack of tethering, whether they diffuse slowly or rapidly (Figure 5e). This means the assignment of anomalous diffusion type will never be wrong for real free-diffusing molecules, regardless of tethering condition or diffusion rate. For confined molecules (α=0.5), the same conclusions remain for the D_app but not α_app, where α_app would be overestimated for slow-diffusing confined molecules in small condensates (Figure 5f). An overestimated α_app for confined molecules (α<1) can lead to a misassignment as free-diffusing molecules (α=1). Therefore, true confined molecules may be missed if appropriate tethering is not in place when the molecules diffuse slowly and are in a small condensate.

Our experimental measurements provide direct quantitative validation of the simulation predictions for ~1 μm condensates. For confined, slow-diffusing FL mRNA molecules, we observed a 1.6-fold overestimation in step size measurements when condensates were untethered compared to tethered (106.13 ± 3.20 nm vs 66.36 ± 2.10 nm), representing a systematic error of 60%. This substantial bias precisely matches the simulation predictions shown in Figure 5b for confined molecules (α = 0.5) in small condensates, where the heatmap indicates strong overestimation (darker red coloring) in the low-D, small-condensate regime. Additionally, for fast-diffusing Poly(U)₁₀₀₀ RNA molecules, the untethered/tethered step size ratio was 1.00 (205.66 ± 0.76 nm vs 204.76 ± 0.93 nm), indicating negligible bias, which perfectly aligns with simulation predictions for free-diffusing molecules (α = 1.0) shown in Figure 5d. Accordingly, apparent diffusion coefficients showed minimal differences (10^−0.33 vs 10^−0.32 μm²/s; ratio = 0.98), and anomalous diffusion coefficients remained virtually unchanged (α = 0.84 vs 0.86; ratio = 0.98). These experimental ratios fall directly within the light-colored regions of the simulation heatmaps (Figure 5e–f), confirming that fast-diffusing molecules are unaffected by condensate Brownian motion.

In summary, our simulation sweeping a broad parameter space validates our prior conclusion that the measurement of slow but not fast intra-condensate diffusion requires proper tethering. Moreover, it reveals two new principles for determining whether tethering is necessary for intra-condensate SMT: (1) For condensates larger than 2 μm in diameter, tethering generally does not affect the estimation of D_app or α_app (Figure 5e–f), because the Brownian rotation of condensates becomes negligible relative to the physiological D and α range for biomolecules; (2) Tethering is essential for the correct identification of confined diffusion in small condensates. Confined, slow-diffusing molecules such as mRNA [30] will be misassigned as free-diffusing molecules when the condensates are not properly tethered.

Discussion

The results presented herein establish that surface tethering is a powerful and valuable strategy for eliminating interference arising from condensate Brownian dynamics in single molecule diffusion measurements. By immobilizing condensates on passivated surfaces, we provide a stable reference frame that enables accurate quantification of intra-condensate molecular mobility, especially for large, structured mRNAs that diffuse slowly, revealing the true dynamic behavior of guest RNAs (and proteins) within phase-separated assemblies. Notably, laser-induced heating during imaging could potentially exacerbate Brownian motion interference in untethered condensates, as elevated temperatures have been shown to increase protein molecular mobility and reduce condensate viscosity [35]. This suggests that tethering may be particularly beneficial for experiments requiring high laser powers or prolonged imaging periods, where photothermal effects could further amplify the motion interference we observe.

Our systematic comparison of three tethering strategies—DNA, protein, and antibody—demonstrates that all three approaches successfully suppress both translational and rotational condensate motion, as evidenced by dramatic reductions in localization fluctuations, angular displacement, and accessible phase space area (Figures 2, 3, 4). These findings directly address a longstanding phenomenon in the literature: untethered condensates, as discrete droplets suspended in solution, undergo stochastic movements [31,33,36–40] that can be misinterpreted in SMT measurements as reduced or enhanced molecular diffusion (Figure 3). While our study demonstrates the usefulness of tethering for accurate in vitro measurements, it is important to consider that many endogenous condensates such as P-bodies [41] or hyperosmotic phase separation condensates [42] are not permanently anchored and thus would exhibit similar motion interference that could affect single molecule measurements. Our results provide direct experimental evidence that such interference is prevalent in untethered systems and must be controlled for rigorous biophysical analysis.

Our comparative analysis of tethering methods further reveals that the choice of tether can subtly influence internal molecular mobility. DNA tethers facilitate enhanced RNA mobility, potentially due to specific protein-nucleic acid interactions that alter local viscoelastic properties [14,43,44], while antibody tethers slightly restrict molecular movement, possibly through steric effects or altered condensate organization (Figure 4). These findings underscore the importance of optimizing tethering conditions to balance condensate stability, preservation of inherent diffusion dynamics, and compatibility with the biological question at hand.

Importantly, our experiments and simulations demonstrate that the impact of tethering is context dependent (Figure 3, 4) and leads to the following practical guideline: (1) Appropriate tethering is essential only for slow-diffusing, confined molecules in small condensates, as neglecting tethering under these conditions leads to significant overestimation of diffusion parameters and potential misclassification of diffusion modes; (2) For fast-diffusing or unconfined molecules and for condensates larger than 2 μm, tethering is generally unnecessary. Thus, the necessity of condensate stabilization should be evaluated based on the dynamical properties of the molecules and the size of the condensates under investigation, providing a robust framework for the design and interpretation of intra-condensate SMT experiments.

The implications of this work extend beyond methodological rigor. In vivo, many membraneless organelles are anchored to cytoskeletal elements [45,46], chromatin [9,47], or membrane surfaces [20,48], restricting their motion and enabling precise spatial regulation of biochemical processes. Our tethering approach provides an in vitro platform that mimics this confinement, facilitating the study of molecular exchange, internal reorganization, and response to perturbations under controlled conditions. We also acknowledge that recent work shows that self-propelled motion can drive motility-induced phase separation, strengthen phase separation, and generate interfacial free‐energy anisotropy [49,50], while droplet asphericity serves as a hallmark of viscoelasticity in passive condensates [51]. We emphasize that surface tethering is agnostic to these mechanistic details and by immobilizing condensates against both translation and rotation, it decouples global Brownian motions from local diffusion and exchange dynamics, enabling precise measurements of intra-condensate mobility under controlled conditions.

Finally, we discovered a marked, ~2 orders of magnitude increase―from D_app = −2.42 ± 0.03 μm²/s to D_app = −0.32 ± 0.01 log₁₀(μm²/s)―in mean apparent diffusion constant from the structured, ~1,500 nt firefly luciferase mRNA to the unstructured Poly(U)₁₀₀₀, ~1,000 nt in length. This difference stands in stark contrast to the ~24% increase in D_app expected for the smaller Poly(U)₁₀₀₀ RNA based on its ~1.5× lower molecular mass, assuming random coil structures. This finding suggests that the intrinsic secondary structure of an mRNA may play a role in slowing down diffusion, possibly due to its capacity to establish the extensive intermolecular base pairing proposed to play a role in the formation of RNA-protein condensates [52,53].

In summary, our study provides a robust framework for the quantitative analysis of molecular diffusion dynamics within biomolecular condensates. By eliminating motion interference through tunable surface tethering, we enable more accurate and reproducible investigations into the physical principles and biological functions of membraneless organelles.

Materials & Methods

Method #1 Protein and RNA Purification and Labeling

FUS protein was purified using two complementary methods, both yielding tag-free protein functionally equivalent for the purpose of our experiments.

Method 1 - MBP-FUS fusion purification: MBP-FUS fusion protein was expressed in E. coli BL21(DE3) cells transformed with the MBP-FUS_FL_WT was a gift from Nicolas Fawzi (Addgene plasmid # 98651) [54]. A single colony was inoculated into 2 mL LB medium containing 100 μg/mL ampicillin and grown overnight at 37°C with shaking (160 rpm). This pre-culture was diluted 1:20 into 50 mL fresh LB-ampicillin and incubated under identical conditions to ensure robust cell viability. The entire pre-culture was then transferred into 1 L of LB-ampicillin (final volume 800 mL) and grown at 37°C until reaching mid-log phase (OD₆₀₀ = 0.6–0.8). To enhance soluble protein production, cultures were cooled to 16°C (pre-chilled shaker) before induction with 0.5 mM IPTG. Expression proceeded overnight at 16°C with shaking (160 rpm), a temperature regime optimized to balance protein yield and solubility. Cells were harvested by centrifugation (6,500 × g, 7 min, 4°C), washed with 0.5× PBS, and stored at −80°C. Expression efficiency was confirmed via SDS-PAGE by comparing pre- and post-induction samples, with successful MBP-FUS production indicated by a dominant band at the expected molecular weight (~98 kDa; Figure S5). The MBP-FUS fusion protein was purified using sequential affinity chromatography. First, amylose resin affinity chromatography captured the maltose-binding protein (MBP) tag, with optimal fractions selected for further processing. The eluate was then applied to a HisTrap HP column pre-equilibrated with MBP-HisWash buffer (500 mM imidazole), and fractions containing the His-tagged fusion protein were collected. To remove imidazole, the pooled fractions were concentrated via three parallel ultrafiltration columns (10 kDa MWCO), each diluted with 15 mL of imidazole-free MBP-Normal Wash buffer and re-concentrated. This diafiltration process was repeated twice, reducing imidazole concentration 100-fold to <5 mM. The final MBP-FUS product (6 mL) had an absorbance (A₂₈₀) of 1.3, corresponding to a concentration of 0.92 mg/mL (9.4 μM) using an extinction coefficient of 139,720 M⁻¹cm⁻¹. For tag removal, the fusion protein was treated with TEV protease (Millipore Sigma), yielding cleaved MBP and untagged FUS (Figure S5).

Method 2 - Tag-free FUS with β-cyclodextrin: Full-length human FUS was expressed in E. coli BL21(DE3) using pET-hFUS [24,55] (a gift from the Ishihama group) and culture was grown to OD₆₀₀=1.0 at 37°C and induced with 1 mM isopropyl β-D-1-thiogalactopyranoside (IPTG). After 6 h of growth at 37°C, cells were harvested by centrifugation and purified following an established protocol [24,30,55] via sequential ion-exchange chromatography (Cytiva HiTrap Q, Capto S, SP HP columns) under denaturing conditions (6 M urea). Refolding was performed in a β-cyclodextrin (BCD) containing buffer to prevent aggregation, with a two-step dialysis process (CAPSO/arginine buffer followed by HEPES/NaCl/BCD buffer). Purity was confirmed by SDS-PAGE (Figure S5). AlexaFluor 488 NHS Ester (Click Chemistry Tools) was used to label FUS (20:1 dye:protein ratio) post-refolding, followed by buffer exchange to remove unbound dye. Labeling efficiency was quantified via absorbance (NanoDrop).

AlexaFluor 647-labeled firefly luciferase (FL) mRNA was synthesized using an established protocol [56,57] by in vitro transcription (T7 promoter), followed by enzymatic capping (NEB), sequential polyadenylation with 2’-azido-dATP (Jena Biosciences) and rATP [56,57], and click-chemistry conjugation to sDIBO-alkyne dye (Thermo Fisher) (Figure S6). Similarly, polyuridylic acid (poly(U)) potassium salt (Sigma-Aldrich) underwent gel purification of the ~1000 nt fraction, followed by an initial incorporation of 2’-azido-2’-dATP (Jena Biosciences) followed by polyuridylation with poly(U) polymerase (NEB), employing rUTP [56,57]. Finally, the same click-chemistry reaction with Alexa Flour 647 sDIBO alkyne (Thermo Fisher) was conducted to produce fluorophore-conjugated poly(U) RNA. Free dye was removed from both RNAs by multiple rounds of washing of the ethanol-precipitated purified RNA pellet, which was confirmed by denaturing PAGE (Figure S6).

Surface Treatment

Glass coverslips were functionalized with (3-Aminopropyl)triethoxysilane (Sigma-Aldrich), mPEG-SVA (NEB), and biotin-PEG-SVA (NEB; 10,000:1 ratio unless specified otherwise), followed by DST treatment [58,59]. Surface treatment was completed by using a PEG-biotin:streptavidin:tether-biotin system (tether: DNA FUS binding site, FUS protein, or anti-FUS antibody) we developed. Biotinylated DNA FUS binding site (5’-/5Bioag/TCCCCGT(6x)-3’, IDT) was selected as a tether due to established interactions with FUS [60]. The biotinylation of protein and antibody tethers was achieved by reacting purified FUS protein or antibody (BioLegend) with Biotin-NHS ester (Sigma-Aldrich) in dimethylformamide, achieving a 1:5 molar ratio of protein-to-biotin. The reaction mixture was maintained at pH 8.5 to optimize NHS-ester reactivity and incubated for 1 hour in the dark to prevent photodegradation. Unconjugated biotin was removed through two cycles of centrifugal filtration using 10 kDa Amicon Ultra filters (Sigma-Aldrich) at 4,000 × g (swinging bucket rotor), with buffer exchange to physiological pH 7.4 during resuspension. The purified biotinylated FUS was aliquoted into 10 μL volumes and stored at −80°C.

Condensate Assembly

A phase separation buffer with a working concentration of 20 mM tris(hydroxymethyl)aminomethane (Tris)-HCl, pH 7.5, 100 mM NaCl, 2 mM DTT, and 1 mM MgCl2 was prepared and filtered with a 0.22 μm syringe filter (Millipore Sigma) for all experiments, which was adapted from prior phase separation studies of FUS [26,30,61–63]. Condensation was triggered by thoroughly mixing the full-length tag-free FUS at a final concentration of 10 μM (FL mRNA tracking experiments only), or MBP FUS at a final concentration of 7.5 μM (2 μM TEV used to cleave MBP), with the phase separation buffer, an oxygen scavenging system (OSS), and a specified fluorescently labeled species (microspheres, FL mRNA, or Poly(U)₁₀₀₀ RNA). The time from assembly to data acquisition was kept under 30 minutes.

For condensate SMT experiments, samples were prepared with 10 nM AlexaFluor 488-labeled FUS and 50 pM of various fluorescent species in phase separation buffer. An OSS consisting of glucose, glucose oxidase, and catalase was employed for single molecule tracking of RNAs. For imaging of FL mRNA in condensates at 200 ms time resolution, 10% (w/v) Dextran T-500 was added to modulate the timescale separation between molecular diffusion and whole-condensate motion. The 10-fold longer exposure time (200 ms vs 20 ms) reduces the temporal separation between slow mRNA diffusion (~1–10 s timescales) and condensate Brownian motion (~100–200 ms timescales). Dextran T500 was used to selectively dampen condensate motion without significantly altering internal molecular dynamics [64], restoring favorable scale separation for accurate single-molecule tracking.

Confocal Scanning Microscopy and Circularity Analysis

Z-stack imaging (Figure 1) utilized an Alba5 confocal microscope with AlexaFluor 488 dye to visualize 3D shape and glass slide location. performed with an Alba5 time-resolved laser-scanning confocal microscope (ISS, Inc) with a pulsed supercontinuum broadband laser excitation source (Fianium WhiteLase SC-400–8-PP), avalanche photodiode (APD) detectors, and a Beckr-Hickl SPC-830 TCSPC module with a 531/40nm filter. 488 nm excitation was selected using acousto-optic tunable filters and ~5uW average power was selected. Condensates tethered on the glass surface were found under regular scanning confocal imaging mode, and whole FOV were imaged in the x-y plane with slices taken every 20 nm starting below or at the glass surface and imaging until the focus plane was well above the condensates, ~40 slices. These images were subjected to downstream processing and analysis. First, the raw images were deconvolved using default settings in AutoQuant software. The deconvolved images were then loading into ImageJ and thresholded before converting to binary images. The binary image was eroded to ensure edges were accurately displayed (Figure S7). The circularity of objects identified in the final images was calculated and plotted using a homemade python script.

HILO Microscopy

Sample wells were fabricated using half-cut PCR tubes (Sigma-Aldrich) epoxy-bonded (Ellsworth Adhesives) to glass slides. For the +tether conditions only, 1 mg/mL streptavidin interface with 1 μM biotinylated FUS, anti-FUS, or DNA tethers established surface immobilization to minimize translational/rotational interference. After adding FUS condensates, mineral oil was layered to prevent evaporation. Imaging was performed on an Oxford Nanoimager S with a 100× 1.4 NA oil immersion super apochromatic objective, 405, 473, 532, 640 nm lasers with appropriate dual-band emission filters, and a Hamamatsu sCMOS Orca flash 4 V3 camera, using highly inclined and laminated optical sheet (HILO) microscopy [65] (52° laser angle) at 24 °C with 117 nm pixel size [66]. Intra-condensate SMT was achieved using the red (640 nm, ~30 mW) channel. Imaging parameters were tailored to each sample type: 200 nm fluorescent beads were imaged at 100 ms exposure for main figures (Figure 2) and at 20 ms for supplementary data; FL RNA was imaged at both 100 ms and 20 ms, and these data were further down-sampled to 200 ms for diffusion analysis (Figure 3); poly(U)₁₀₀₀ RNA was imaged at 20 ms (Figure 4); and, for the comparison of different tethering methods, FL RNA was imaged at 20 ms (Figure 4). This approach enabled direct comparison of molecular dynamics across different samples and experimental conditions while ensuring appropriate temporal resolution for diffusion analysis.

Single Molecule Tracking Fluctuation, Rotation, and Diffusion Analysis

Filtered videos were subjected to single molecule tracking analysis using TrackMate, where spots were detected with a Laplacian of Gaussian (LoG) detector (object diameter: 4 pixels, 468 nm; quality threshold ≥15, determined by the peak of false-positive spot quality values). Trajectories were extracted using the Linear Assignment Problem (LAP) algorithm with a maximum linking distance of 4 pixels and no gap closing. Exported trajectories were analyzed using custom Python scripts for fluctuation, rotation, and diffusion profiling.

The $\alpha$ value was calculated by fitting the (MSD)-lag time ($\tau$) curve on a log-log scale using the relation,

$$log\left(MSD\right)=\alpha log\left(\tau \right)+log\left(2nD\right)$$

where $n$ is the dimension of tracking ($n=2$ in our case) and $D$ is the diffusion coefficient. For optimal fitting [67], half the trajectory length was used unless the trajectory was shorter than 5 steps, in which case a minimum of 4 MSD-$\tau$ points were required. Trajectories with R² < 0.7 or with extremely small α values were excluded from further analysis.

Diffusion analysis generated distributions of mean step size, anomalous component ($\alpha$), and apparent diffusion coefficient ($D_{app}$). Mean step size was calculated for all trajectories, while α components were determined only for trajectories with a mean step size >=30nm. The $D_{app}$ and localization error were calculated for non-confined trajectories by fitting MSD-$\tau$ curve to the following formula, which is optimized for least-square fit of MSD [67,68]:

$$MSD=2nD\tau +2{\sigma }^2-4DR\tau$$

where $\sigma$ is the localization error and $R$ is the motion blur coefficient ($R=1/6$ for continuous imaging). For ensemble MSD-$\tau$ analysis, tracks were filtered to include only those with a minimum length of 10 frames and sufficient mobility (${{\mathit{l}\mathit{o}\mathit{g}}_{\mathbf{10}}D}_{app}$ above the static error threshold and displacement ≥0.2 μm).

Localization fluctuation analysis was performed by calculating the stepwise displacement ($∆\mathit{r}$) for each trajectory, extracting the average fluctuation per track. Hundreds of individual condensates were tracked per condition in each experiment to capture biological variability in condensate behavior (with n referring to the number of trajectories collected from condensates under each condition). For statistical comparisons, however, these per‑condensate values were first averaged within each independent experimental replicate (where N refers to the number of experimental replicates), and the resulting means were used as the basis for hypothesis testing. This approach ensures that statistical significance reflects experimental reproducibility rather than the large number of tracked particles. Comparisons across experimental conditions were performed using paired or unpaired t-tests, as appropriate.

Rotation analysis was conducted by calculating the angle between the position vector of each tracked molecule (relative to the condensate center) and its initial position vector, yielding a time series of rotation angles for each trajectory (Fig 3b). Trajectories were further analyzed to extract angular velocity $\omega =\frac{∆\theta }{∆t}$ and acceleration $\alpha =\frac{\omega }{{(∆t)}^2}$.

The angular velocity autocorrelation and velocity-acceleration correlation was calculated from the following equations.

$$velocityautocorrelation:g\left(t\right)=〈v\left(t\right)·v(t+\tau )〉$$

$$velocity-accelerationcorrelation:g\left(t\right)=〈v\left(t\right)·a(t+\tau )〉$$

This correlation was plotted as a function of phase space for each data point in a condition to produce a useful phase space beeswarm plot. The phase space distribution is particularly revealing because it captures the fundamental dynamical differences between tethered and untethered biomolecular condensates. This plot effectively transforms time-series rotation data into a representation that characterizes the underlying physical behavior of the system. The plot displays two key metrics for each tracked microsphere: (1) Velocity-Acceleration Correlation (x-axis) measures how angular velocity changes relate to angular acceleration. Negative values indicate damped or restrained motion (like a pendulum), while positive values suggest driven or self-reinforcing motion. (2) Phase Space Area (y-axis) quantifies the “territory” explored by the microspheres in velocity-acceleration space. Larger values indicate greater freedom of movement and more complex rotational dynamics.

Localization fluctuations, phase space area, and velocity autocorrelation were all plotted as beeswarm superplots following best practices in the field [69]. All analyses were implemented in homemade Python scripts.

Monte Carlo Simulations of Single Molecule Trajectories in tethered and untethered condensates

The simulation framework models projected 2D single molecule trajectories within spherical biomolecular condensates, using parameters and update logic designed to closely mimic SMT experiments. Each simulation is defined by a condensate diameter sampled from 0.3 to 5 μm and a molecular diffusion coefficient (D) sampled logarithmically from 0.001 to 10 μm²/s. The anomalous diffusion exponent (α) is set to either 1.0 (normal diffusion) or 0.5 (subdiffusive), representing key physical regimes observed in biological condensates.

To ensure efficient and uniform sampling of the (log10D, diameter) parameter space, we use Sobol low-discrepancy sampling with 200 sample points. For each parameter combination, 1000 molecules are initialized at random positions within a square region encompassing the condensate.

Molecular motion is simulated as 2D fractional Brownian motion (FBM), generated using the Python fbm package (Davies-Harte method) [70], with the specified D and α. The simulation is performed at a time step of 50 ms for 20 steps, matching typical SMT experimental conditions.

To model the effect of thermally driven rotational dynamics of the condensate, we implemented stochastic rotation at each time step. The mathematical expectation of the angular frequency for rotational diffusion is set using the Stokes-Einstein relation for a sphere:

$$\mathit{\omega }=\frac{{\mathit{k}}_{\mathit{B}}\mathit{T}}{\mathbf{4}\mathit{\pi }\mathit{\eta }{\mathit{r}}^{\mathbf{3}}}$$

where ${\mathit{k}}_{\mathit{B}}$ is Boltzmann’s constant, $\mathit{T}$ is temperature set to room temperature 298 K, $\mathit{\eta }$ is the viscosity of the surrounding medium (fixed at 5 mPa·s, representing protein solution at around 10 mg/ml concentration), and $r$ is the condensate radius in meters. At each time step, the positions of all molecules within the same condensate are rotated by a small random angle, drawn from a normal distribution with variance determined by $\mathit{\omega }$ and the time step, and scaled by the molecule’s distance from the condensate center. This rotation is applied perpendicular to the position vector, mimicking the effect of stochastic rotational diffusion of the entire droplet.

The simulation updates molecule positions at discrete time intervals (20 steps, each 50 ms), combining FBM increments and rotational displacements. The framework allows toggling rotational dynamics on or off to generate both control and experimental datasets. All simulations are performed under conditions reflecting typical SMT experiments. The resulting molecular trajectories are output for downstream analysis of apparent diffusion coefficients and anomalous exponents.

All simulation code, including parameter sweeps and Sobol sampling, is implemented in Python using numpy, fbm, and scipy libraries.

Appendix A: Supplemental Material

The following are the supplementary material to this article.

Data & Code Availability Statement

Data is available at…. Python scripts to process data are available at: https://github.com/walterlab-um/condensate-tether-compare-in-vitro