Super-resolution Mapping and Quantification of Molecular Diffusion via Single-molecule Displacement/Diffusivity Mapping (SMdM)

CONSPECTUS:

Diffusion both underlies vital physicochemical and biological processes and provides a valuable window into molecular states and interactions. However, it remains a challenge to map molecular diffusion at subcellular and sub-micrometer scales. Whereas single-particle tracking of fluorescent molecules provides a path to quantify motion at the nanoscale, its typical pursuit of long trajectories limits wide-field mapping to the slow diffusion of bound molecules.

Single-molecule displacement/diffusivity mapping (SMdM) rises to the challenge. Rather than following each fluorescent molecule longitudinally as it randomly visits potentially heterogeneous environments, SMdM flips the question to ask, for every location (e.g., a 100×100 nm² spatial bin) in a wide field, how different single molecules of identical nature move locally. This location-centered strategy is naturally effective for the spatial mapping of diffusivity. Moreover, by focusing on local motion, each molecule only needs to be detected for its transient displacement within a fixed short time window to achieve local statistics. This task is fulfilled for fast-diffusing molecules using a tandem excitation scheme in which a pair of closely timed stroboscopic excitation pulses are applied across two tandem frames, so that wide-field single-molecule images are recorded at a pulse-defined ≲1-ms separation unlimited by the camera framerate. With fitting models robust against mismatched molecules and diffusion anisotropy, SMdM thus successfully achieves super-resolution D mapping for fluorescently labeled molecules of contrasting sizes and properties in diverse cellular and in vitro systems.

For intracellular protein diffusion, SMdM uncovers nanoscale diffusion heterogeneities in the mammalian cytoplasm and nucleus, and further elucidates their origins from the macromolecular crowding effects of cytoskeletal and chromatin ultrastructures, respectively, through correlated single-molecule localization microscopy (SMLM). Across diverse compartments of the mammalian cell, including the cytoplasm, the nucleus, the endoplasmic reticulum (ER) lumen, and the mitochondrial matrix, SMdM further unveils a striking charge effect in which the diffusion of positively charged proteins is biasedly impeded. For cellular membranes, the integration of SMdM with fluorogenic probes enables diffusivity fine-mapping, which in combination with spectrally resolved SMLM (SR-SMLM), elucidates nanoscale diffusional heterogeneities of different origins. For biomolecular condensates, another synergy of SMdM and SR-SMLM uncovers the gradual formation of diffusion-suppressed, hydrophobic amyloid nanoaggregates at the surface of FUS (fused in sarcoma) protein condensates during aging. Beyond spatial mapping, the mass accumulation of single-molecule displacements in SMdM further affords a valuable means to quantifying D with exceptional precision. This advantage is harnessed to show no enhanced diffusion of enzymes in reactions, to uncover ubiquitous net charge-driven protein-protein interaction in solution, and to show with strategically manipulated cytoplasmic extracts, that molecular interaction in the crowded cell is defined by an overwhelmingly negatively charged macromolecular environment with dense meshworks, echoing our parallel results in the mammalian cell.

Together, by uniquely enabling super-resolution mapping and high-precision quantification of molecular diffusion across diverse systems, SMdM opens a new door to reveal fascinating spatiotemporal heterogeneities in the living cell and beyond.

Graphical Abstract

1. Background

Molecular diffusion and transport underly vital physical, chemical, and biological processes. Molecules must meet before reactions can occur, and proteins need to reach their targeted locations to function. Conversely, understanding the diffusion patterns of a molecule provides a valuable window into its state, interactions, and surrounding environments.^5–14

However, it remains a challenge to map diffusion at subcellular and sub-micrometer scales. Traditional fluorescence microscopy approaches based on photobleaching/photoactivation^5,15,16 and fluorescence correlation spectroscopy (FCS)^7–9,12 offer limited fidelity, resolution, and mapping capabilities, even though recent efforts integrating imaging FCS with super-resolution microscopy point to new possibilities.^17,18 Single-particle/single-molecule tracking (SPT)^13,14,19 provides a path to quantify molecular motion at the nanoscale. The recent integration of wide-field SPT with photoactivation and fluorophore exchange, common strategies in single-molecule localization microscopy (SMLM)²⁰, further permits high-density sampling and super-resolution mapping.^11,21 However, as the starting point of SPT is often to acquire long trajectories so that sufficient statistics are attained for each molecule to allow diffusion properties to be extracted individually, wide-field SPT is often limited to the slow (~1 µm²/s) diffusion of molecules bound to lipid membranes, chromosomes, or the small volume of bacteria. As an unbound protein in the mammalian cell readily diffuses out of the ~±400 nm focal range of high-numerical-aperture objective lenses within the typical 10 ms frame time of single-molecule cameras,¹ tracking appears infeasible for even just two frames.

2. SMdM: Concept, approach, and analysis

Single-molecule displacement/diffusivity mapping (SMdM) rose to the challenge.¹ Rather than try to follow each fluorescent molecule over many frames as it randomly visits different, potentially heterogeneous locations, SMdM flips the question to ask, for every location (e.g., a 100×100 nm² spatial bin) in the field of view, how different single molecules of identical nature move locally. This location-centered strategy is naturally effective for mapping diffusivity, assuming a stable spatial pattern exists for diffusivity as for (cellular) structures. Moreover, by focusing on local motion, one would only need to detect the transient displacement of each molecule within a fixed short time window to achieve local statistics.

To capture transient displacements d for fast-diffusing fluorescent molecules, we devised a tandem excitation scheme in which a pair of closely timed stroboscopic excitation pulses are applied across two tandem frames, so that the wide-field images recorded in the two frames are separated by the short (≲1 ms) time separation Δt between the paired pulses, rather than the frame time (Figure 1a).¹ Repeating this scheme ~10⁴ times thus records the transient motion of millions of single molecules over time. It is further worth noting that the short separation Δt between the paired excitation pulses leaves ample illumination-off time between the anti-paired pulses (gray in Figure 1a), during which different molecules diffuse into and out of the view. SMdM thus works well with common, non-photoactivated fluorophores (e.g., Figure 2a)¹ relying on diffusional fluorophore exchange to overcome photobleaching, although photoactivatable fluorophores are still preferred for in-cell experiments to control the count of emitting molecules in the view.

Figure 1.

The SMdM approach. (a) Capturing the transient displacements d of single molecules in the wide field far beyond the camera framerate by applying a pair of closely timed stroboscopic excitation pulses across two tandem frames, so that the two recorded images capture molecular motion over the short (≲1 ms) time separation Δt between the paired pulses. (b) The tandem excitation scheme is repeated ~10⁴ times, and the accumulated single-molecule displacements are spatially binned, e.g., with a 100 nm grid. Displacements in each bin are individually fitted to a diffusion model to assess the local diffusion coefficient D. (c) The resultant D value of each bin is assigned a color to render a super-resolution map. Adapted from¹. Copyright 2020, the authors.

Figure 2.

SMdM fitting models. (a,b) Distributions of SMdM-measured 1-ms single-molecule displacements of mEmerald fluorescent protein for the same region in a cell, recorded at contrasting densities of ~0.06 (a) and ~0.4 (b) molecules/μm²/frame. Blue curves: fits to our diffusion model, with resultant D and uncertainties marked. Panels (a,b) are from¹. Copyright 2020, the authors. (c) Distributions of simulated SMdM displacements with 0%, 10%, and 25% background molecules. (d) Relative uncertainty of D from fitting the simulated data to our model, as a function of displacement counts and background levels. Panels (c,d) are from²⁵. Copyright 2022 American Chemical Society. (e) Two-dimensional plot of single-molecule displacement vectors at Δt = 9.1 ms for BDP-TMR-alkyne at an ER tubule [arrows in (h,i)]. A principal direction θ of 48° is evaluated with an anisotropy α of 0.61. (f,g) 1D distributions after projecting the displacements along (f) and perpendicular (g) to θ. Blue curve in (f): fit to a 1D diffusion model, yielding D = 2.7 µm²/s. (h) Color map presenting the local θ (hue) and α (color saturation), obtained by analyzing the single-molecule displacement vectors in each 100×100 nm² spatial bin. (i) pSMdM D map based on 1D diffusion fits along local θ. Panels (e-i) are from². Copyright 2020 American Chemical Society.

For data analysis, single molecules are first localized in every frame as in SMLM.²⁰ For every localization in even frames, a matching localization is searched for in its preceding odd frame within a cutoff radius (e.g., 800 nm for intracellular protein diffusion), and the displacement between the paired localizations is calculated and recorded. The accumulated single-molecule displacements, all corresponding to transient molecular motion in Δt, are then spatially binned, e.g., with a 100 nm grid, so that the displacements gathered in each bin are separately fitted to a diffusion model (below) to assess local diffusion coefficient D (Figure 1b). Color-plotting the resultant D for each bin thus yields a wide-field super-resolution map of local diffusivity (Figure 1c).

The gridding step above left each spatial bin with hundreds of single-molecule displacements under a fixed Δt. While single-step displacement analysis has been used to estimate D in SPT,^22–24 given the likely higher molecular densities and frequent probe exchanges in SMdM, we modified the fitting model to add a background term to tolerate mismatched molecules, i.e., those randomly diffuse into the view during Δt.¹ In displacement distributions, this term translates to a linearly increasing tail, as validated with both experimental and simulated data (Figure 2a–c). For the experimental data, we showed that our fitting model worked robustly for data collected at contrasting single-molecule densities, yielding consistent D locally (Figure 2a,b) and for the entire D map.¹ For simulations, we compared fitting results at different counts of single-molecule displacements N (Figure 2d).²⁵ We thus found that under zero background, the relative uncertainty of D is ~1/√N, so 10% and 1% uncertainties are achieved with 100 and 10,000 displacements, respectively. Higher backgrounds require 200-300 displacements to achieve ~10% uncertainties.

The accumulated single-molecule displacements may also be treated as vectors for anisotropy analysis.² Figure 2e plots the single-molecule displacement vectors for BDP-TMR-alkyne diffusing at an endoplasmic reticulum (ER) tubule. An anisotropic distribution is noted, as molecular motion is unrestrained along the tubule but confined in the width direction. From the angular distribution of the displacement vectors, a principal direction θ of 48° is evaluated with an anisotropy α of 0.61. Projecting the displacements along and perpendicular to θ gives contrasting distributions: the former is fitted to a one-dimensional (1D) diffusion model to extract D (Figure 2f), whereas the latter is confined by the tubule width (Figure 2g). Applying the same analysis to every gridded spatial bin yields a super-resolution map of local θ and α, showing well-defined diffusion preferences along ER tubules (Figure 2h). Projecting the single-molecule displacements in each bin along its local θ direction next enables their individual fitting to the 1D diffusion model to extract D. The resultant principal-direction SMdM (pSMdM) D maps (Figure 2i) thus overcome geometric complications to unveil faster diffusion in the ER membrane over the plasma membrane, consistent with the expected lower lipid packing order of the former.

3. Mapping diffusion in the cytoplasm

SMdM was initially developed to map the fast diffusion of unbound proteins in the mammalian cytoplasm.¹ Figure 3a presents results with a popular photoswitchable fluorescent protein (FP) mEos3.2,²⁶ whose 29 kDa molecular weight coincides with the medium size of human proteins.²⁷ At a grid size of 100×100 nm², SMdM under 1-ms pulse separation Δt showed that while vast regions in the mammalian cell had D~25 µm²/s, as expected,^5,27 nanoscale linear features exhibited lower D down to ~10 µm²/s (Figure 3a), with moderate intracellular and cell-to-cell variations noted. Correlated SMLM of phalloidin-labeled actin²⁸ showed a good correlation of local slowdowns with actin bundles (Figure 3b), thus unveiling the importance of cytoskeletal crowding in modulating cytoplasmic diffusion.

Figure 3.

SMdM of diffusion in the cytoplasm. (a) SMdM D map of mEos3.2 FP in a live PtK2 cell. (b) SMLM image of phalloidin-labeled actin for the same region after fixation. (c) SMdM D map of the 560 Da dye Cy3B in an A549 cell. (d) Local distributions of 400-µs single-molecule displacements for regions pointed to by the black and white arrows in (c), respectively, and fits to our diffusion model with resultant D and uncertainties marked. (e) SMdM D maps of CF640R-tagged cyclic adenosine monophosphate in an A549 cell. (f) SMdM D maps of mEos3.2 species of −14, −7, 0, +7, and +14 net charges in live PtK2 cells, plotted on the same D scale as (a). (g) Mean D values for the above proteins in different subcellular environments. Error bars: standard deviations between individual cells. Panels (a,b,f,g) are from¹. Copyright 2020, the authors. Panels (c-e) are from²⁹. Copyright 2023 American Chemical Society.

SMdM further identified the protein net charge as a key determinant of intracellular diffusion. Intriguingly, as sequence-modified mEos3.2 FPs were expressed in the mammalian cell, the negatively charged variants diffused similarly as neutral, whereas variants carrying positive net charges exhibited drastically reduced diffusivities (Figure 3f,g). Echoing other recent microscopy and NMR studies generally showing slower intracellular diffusion for positively charged proteins,^30–34 these results point to a negatively charged macromolecular environment in the cell^1,35 that biasedly suppresses the diffusion of positively charged proteins, which we explore further below with SMdM for intraorganellar and in vitro systems.

SMdM also addressed the challenge of small (≲1 kDa) solutes.²⁹ By reducing the tandem-pulse separation Δt to 400 µs and exploiting suitable intracellular delivery methods,^36,37 SMdM resolved their very fast (>200 µm²/s) diffusion in the mammalian cell while noting sub-micrometer foci of trapped diffusion (Figure 3c,d). Importantly, for diverse dyes (e.g., Figure 3c) and dye-tagged nucleotides (e.g., Figure 3e), SMdM showed a dominance of fast-diffusion regions where D reached 60-70% of that in water, commensurate with the slightly higher mammalian cytoplasm viscosity over water³⁸ and suggesting no further impediment by macromolecular crowding. These results lifted a paradoxical D limit in which previous, spatially unresolved data suggest alarmingly low (~25% of in water) intracellular diffusivity for small solutes.^6,27,39

In collaborative studies, SMdM examined protein diffusion in the bacterial cytoplasm, showing D scaling with the protein-complex mass.⁴⁰ In another work, SMdM analyzed the intracellular dynamics of CRISPR-Csm-labeled RNA, visualizing contrasting motion modes of NOTCH2 mRNA upon puromycin treatment.⁴¹

4. Mapping intraorganellar and cytoskeletal diffusion

Our initial SMdM study also mapped the diffusion of mEos3.2 FP in the nucleus,¹ visualizing D~20 µm²/s for the fastest regions and drastically reduced D at the nucleolus (Figure 4a). Outside the nucleolus, correlative SMLM using a DNA stain next showed that regions devoid of DNA and high in DNA density respectively correlated with fast and slow patterns of local D (Figure 4b), thus signifying the role of chromatin ultrastructure in modulating nuclear diffusion. The SMdM-resolved coexistence of chromatin-modulated fast and slow diffusion domains in the nucleus may be functionally important, as envisioned by the chromosome-territory–interchromatin-compartment model.⁴⁴

Figure 4.

SMdM of intraorganellar and cytoskeletal diffusion. (a) SMdM D map of mEos3.2 for the nuclear region of a live PtK2 cell. (b) Overlay of (a) with SMLM image of DNA (white). Asterisk: nucleolus. Red/orange arrows: local regions of fast/slow diffusion. Panels (a,b) are from¹. Copyright 2020, the authors. (c) pSMdM D maps of Dendra2 FPs of varied net charges diffusing in the ER lumen of live COS-7 cells. (d) SMdM-determined D values for differently charged Dendra2 FPs in the ER lumen (blue) and mitochondrial matrix (orange) of live COS-7 cells. Error bars: standard deviations between individual cells. Panels (c,d) are from⁴². Copyright 2023 American Chemical Society. (e,f) SMdM D map of vimentin-mEos3.2 expressed in a living COS-7 cell, after hypotonicity-induced disassembly (e) and within 5 min of reverting to the isotonic medium (f). Panels (e,f) are from⁴³. Available under a CC-BY 4.0 license.

Unexpectedly, as we added a nuclear localization sequence (NLS) to mEos3.2 to achieve nuclear specificity, SMdM detected substantial D drops to <4 µm²/s.¹ Seeing possible contributions from the +15 net charge of the NLS, we examined mEos3.2 variants of different net charges, and uncovered drastic D reduction for positively, but not negatively, charged variants in both the cytoplasm and the nucleus (Figure 3f,g).

To understand the prevalence of this intriguing charge effect, we directed charged-varied FPs into the ER lumen and mitochondrial matrix of mammalian cells using signal/transit peptides.⁴² By resolving D at the nanoscale, SMdM again unveiled biased diffusion suppression for positively charged proteins in both organelles (Figure 4c,d). Analysis of existing mass-spectrometry results^45,46 showed most proteins in both organelles and the mammalian cytoplasm as negatively charged,^1,42 with the ER protein PPIB being a salient exception. Notably, SMdM of the +6-charged wild-type PPIB showed significantly lower intra-ER D than a neutral mutant.⁴² Together, our SMdM results point to generally negatively charged macromolecular environments across different compartments of the eukaryotic cell, in which positively charged proteins incur promiscuous interactions and diffusion suppression, a notion we examine further below with in vitro systems.

In another study, we employed SMdM to characterize the dynamic disassembly-assembly of the vimentin cytoskeleton in living cells.⁴³ As hypotonic stress disintegrated the vimentin cytoskeleton, SMdM reported drastic increases in vimentin-mEos3.2 diffusivity from ~1.5 µm²/s to ~6–8 µm²/s (Figure 4e), suggesting that the vimentin cytoskeleton was disassembled into oligomers of ~10 proteins. Yet, after osmotic recovery, the SMdM-determined D quickly collapsed back to <2 μm²/s as vimentin precipitously reassembled into short fibers throughout the cell (Figure 4f).

5. Mapping diffusion in cellular membranes and integration with SR-SMLM

SMdM also offers advantages for mapping diffusion in cellular membranes.² Whereas PAINT (points accumulation for imaging in nanoscale topography)⁴⁷ provides a powerful SMLM strategy to resolve lipid-membrane morphologies through the reversible binding of fluorogenic probes to the lipid phase, the short probe-membrane resident time (~10 ms)⁴⁸ challenges SPT. SMdM obviates the need for continuous trajectories and integrates seamlessly with PAINT: the stroboscopic illumination efficiently captures transient in-membrane displacements as fluorogenic molecules dynamically enter and leave the membrane to enable high-density sampling and thus fine mapping.

Given the relatively low D in membranes, we either relaxed the pulse separation Δt to 2.5 ms or excited at the middle of every frame for Δt = 9.1 ms.² SMdM yielded similar D under both conditions; the latter allowed single-molecule displacements to be extracted between consecutive frames at the expense of larger displacement values. After accounting for geometric factors (Figure 2h,i above), SMdM determined in mammalian cells a decreasing D order for the ER membrane, the plasma membrane (PM), and nanodomains in the PM induced by cholera toxin B (arrows in Figure 5a,b).² This trend matches an increasing packing order of lipid membranes, which we previously visualized through spectrally resolved SMLM (SR-SMLM)^50,51 as emission blueshifts⁵² with the solvatochromic dye Nile Red.⁵³

Figure 5.

SMdM of membrane diffusion. (a) SMdM diffusivity map of BDP-TMR-alkyne in the membrane of a COS-7 cell treated with fluorescently labeled cholera toxin B (CTB). (b) Fluorescence image of CTB for the same field of view. (c,d) Concurrently acquired super-resolution maps of cellular membranes using Nile Red, for D via pSMdM (c) and for chemical polarity via SR-SMLM (d). (e) Fluorescence image of GRAMD2a-GFP, a marker for ER-PM contacts. (f) Averaged single-molecule spectra at ER-PM contacts vs. adjacent ER regions and the PM. Panels (a-f) are from². Copyright 2020 American Chemical Society. (g) Distributions of 9-ms single-molecule displacements in live-cell PMs for Nile Red (left) and the fluorogenic dimer BTF-2 (right), with fits and resultant D marked. (h) Three-dimensional SMLM vertical cross-sections of the two dyes at the PM. (i) Corresponding scattering in depth (Z) for flat regions, with standard deviations marked. Panels (g-i) are from⁴⁹. Copyright 2022 American Chemical Society.

Locally reduced diffusivity was also noted at the nanoscale for ER-PM contacts (arrows in Figure 5c,e). Comparison of concurrently acquired Nile-Red SMdM and SR-SMLM data, however, showed indistinguishable emission spectra at these slowdown sites versus adjacent ER regions (Figure 5d,f). This result suggests that the abundance of trans-ER-membrane proteins at the contact sites impedes local membrane diffusion through macromolecular crowding^54–57 without altering the lipid packing order.

In another collaborative study,⁴⁹ SMdM characterized the diffusion of fluorogenic dimers in cell membranes, showing drastically reduced D over typical membrane dyes (Figure 5g). The reduced D, and consequently subdued motion blur, substantially improved three-dimensional SMLM (Figure 5h,i), for which the common astigmatism approach⁵⁸ relies on the accurate determination of single-molecule image shapes.

6. Uncovering nanoscale heterogeneities in biomolecular condensates

Another recent synergy of SMdM and SR-SMLM uncovered nanoscale heterogeneities in biomolecular condensates.³ Microdroplet-like biomolecular condensates formed through liquid-liquid phase separation have emerged as an important research field over the past decade.^59–61 SMdM with the 560 Da dye Cy3B showed that in model condensates formed by the RNA-binding protein FUS, the fastest diffusing regions only reached D ~10 µm²/s (Figure 6a). Such substantially suppressed D, ~3% of that in water, suggests a highly crowded local environment that may be functionally significant for the condensates to act as interaction sites for biomolecules.^59–62 A closer examination of the SMdM D maps noted nanoscale domains at the condensate surface where D was further drastically reduced to ~0.5 µm²/s (insets in Figure 6a), and such diffusion-suppressed nanodomains gradually increased their surface coverage over aging (Figure 6a).

Figure 6.

Integration of SMdM and SR-SMLM uncovers nanoscale heterogeneities in FUS condensates. (a) SMdM D maps of Cy3B for FUS condensates aged for different days. (b) Nile Red SR-SMLM of FUS condensates, colored by local single-molecule emission wavelength. (c) Averaged spectra at the surface nanodomains (blue) and the interior (green). (d) CRANAD-2 SMLM of FUS condensates. (e) Correlated CRANAD-2 SMLM (left) and Cy3B SMdM D map [right; same D color scale as (a)] for a 3-day-old FUS condensate. (f) Similar to (e) but for another condensate subjected to mechanical shear from 20 times of pipetting. (g) Model: Accumulation of amyloid aggregates at the condensate surface during aging. Insets in (a,b,d): Zoom-ins highlighting surface nanodomains. Reproduced from³. Copyright 2023 American Chemical Society.

Meanwhile, SR-SMLM with Nile Red unveiled analogous nanodomains at the condensate surface as enhanced signal and blue-shifted spectra (Figure 6b,c), indicating locally lowered chemical polarity. To identify these hydrophobic and diffusion-suppressed nanodomains, we performed SMLM with CRANAD-2, a fluorogenic probe selective for amyloid fibrils.^63,64 Remarkably, CRANAD-2 highlighted analogous nanostructures at the condensate surface (Figure 6d). Correlative CRANAD-2 SMLM and Cy3B SMdM of the same condensates next showed good correspondences between the CRANAD-2 marked and diffusion-suppressed surface nanodomains, for both aged condensates (Figure 6e) and condensates in which amyloid formation was mechanically promoted (Figure 6f).

Together, the integration of SMdM, SR-SMLM, and amyloid-specific SMLM elucidated a model in which nanoscale amyloid fibrils, of locally reduced motility and chemical polarity, aggregate and expand at the condensate surface over aging (Figure 6g). These valuable insights into nanoscale heterogeneities in physicochemical parameters and protein states challenge general assumptions in which single-component condensate microdroplets are treated as homogeneous phases.

7. Quantifying diffusion in the solution phase

While SMdM was originally developed for intracellular D mapping, the mass-accumulated single-molecule displacements in the wide field can also be pooled to achieve large statistics and thus high-precision D quantification in solution. By detecting 10s of single-molecule displacements in each paired frames and running at 110 fps, >10⁴ displacements may be accumulated in 10 s, sufficient to achieve <1% D uncertainty (Figure 2d).

Experimentally, beyond estimating uncertainties from displacement fitting (e.g., Figure 2a,b) and comparing results from repeated measurements of the same sample, the precision and sensitivity of SMdM for D quantification were further validated through correctly resolving D changes in response to altered medium viscosities, e.g., phosphate-buffered saline (PBS) containing varying glycerol amounts (Figure 7a,b). Moreover, as we applied SMdM to diverse proteins in buffers, good size trends were observed in agreement with the empirical Young-Carroad-Bell model⁶⁵ without using any fitting/adjusting parameters (Figure 7c and Figure 9b below). Interestingly, SMdM-determined D values for small (≲1 kDa) solutes also largely followed the Young-Carroad-Bell model (Figure 7d).²⁹ Fundamentally, this fixed scaling of D versus molecular weight M as M^−1/3 may be rationalized by the similar mass densities of typical proteins and organic compounds. Practically, the excellent, near-predictive D-M relationship suggests that the high D precision achieved by SMdM may be harnessed as a quantification tool to probe molecular size, state, and environments over wide ranges.

Figure 7.

SMdM in solution: validation and size trends. (a) Distributions of SMdM-measured 600-μs single-molecule displacements for Cy3B-labeled catalase diffusing in PBS containing 0%, 5%, 10%, and 15% glycerol. (b) Resultant D vs. glycerol percentage (data points; squares and circles for two batches of samples on different days) compared to that predicted by the medium viscosity (dash line). 95% confidence intervals are comparable to the symbol sizes. (c) SMdM-measured D of proteins of varying sizes in buffers. Dashed line: values expected by the Young-Carroad-Bell model. Panels (a-c) are from²⁵. Copyright 2022 American Chemical Society. (d) SMdM-measured D of small solutes (colored) vs. proteins (black), plotted on a logarithmic scale vs. molecular weight. Dashed line: the Young-Carroad-Bell model. Reproduced from²⁹. Copyright 2023 American Chemical Society.

Figure 9.

SMdM elucidates complex environments. (a) Schematic: cytoplasmic extract from Xenopus eggs. (b) SMdM-determined D of 15 proteins in PBS (hollow symbols) and in the extract (filled symbols). Red, blue, and light-blue symbols: Negatively, positively, and weakly positively charged proteins. Curves: Expected D in PBS from the Young-Carroad-Bell model (solid) and its half-values (dashed). (c) Color symbols: Relative in-extract D over in-PBS values, as a function of added NaCl, for positively charged HEWL-Cy3B (blue) and negatively charged BCA-CF647 (red). Black diamonds (right y-axis): Ratio between the two datasets. Error bars: Sample standard deviation between results from two or three measurements at each data point. (d,e) SMdM D maps of HEWL-Cy3B in extract samples 3 h after ribonuclease treatment (d) or immediately after adding 1 mg/mL polylysine (e). Panels (a-e) are from⁷⁸. Available under a CC-BY 4.0 license. (f) SMdM-determined D of the 0.6 kDa Cy3B and 67 kDa BSA in expandable hydrogels relative to in PBS, at varied expansion factors (bottom x-axis) and hence polymer contents (top x-axis). Reproduced from⁷⁹. Copyright 2023 American Chemical Society.

The high D precision was employed to address whether enzyme diffusion speeds up in catalytic reactions, for which contradicting results have been reported,^66–71 some attributed to artifacts in traditional D measurements.^68,70 SMdM offered a unique single-molecule examination of this system in the free aqueous solution, and detected no enhanced diffusion, both in terms of single-molecule displacement distributions (Figure 8a) and resultant D values with ~±1% precisions at 95% confidence intervals (Figure 8b), for the catalytic reactions of four highly contested enzymes.²⁵

Figure 8.

SMdM of solution-phase systems. (a) Distributions of SMdM-measured 600-μs single-molecule displacements for Cy3B-labeled catalase diffusing in PBS with H₂O₂ added at 0, 1, 5, and 50 mM. Inset: photo showing bubbles from the reaction. (b) Resultant D at the different substrate concentrations. Error bars: 95% confidence intervals from SMdM fitting. Panels (a,b) are from²⁵. Copyright 2022 American Chemical Society. (c) SMdM-determined D values for 200 pM Cy3B-labeled HEWL in pH = 7.3 buffers of varied ionic strengths, as a function of added BSA. (d) Effective diffuser diameters (2× Stokes radii) of proteins of varying net charges (z) in pH = 7.3 buffers of 2 mM ionic strength as a function of added BSA, as converted from SMdM-determined D values. Inset model: A positively charged diffuser drags along a shell of negatively charged BSA interactors. Panels (c,d) are from⁴. Copyright 2024 American Chemical Society.

SMdM also helped recapitulate and elucidate net charge-driven protein interactions in solution.⁴ Here, SMdM provided precise D quantification in the limit of low (~100 pM) diffuser concentrations, thus avoiding potential coacervate/aggerate formation between oppositely charged proteins.^72–74 With a system as simple as hen-egg-white lysozyme (HEWL) being the positively charged diffuser and bovine serum albumin (BSA) being the negatively charged interactor, SMdM detected ionic-strength-dependent diffusion suppression at ppm interactor levels (Figure 8c), while also showing unvaried diffusivities when same-charge interactors were added. Additional experiments confirmed that this diffusion suppression was determined by the protein net charge states, as probed by varying the solution pH or chemically modifying the proteins, and was ubiquitous across different diffuser-interactor pairs. By converting the measured diffusivities to effective diffuser diameters, SMdM further showed that with BSA addition, diverse positively charged diffusers quickly grew and stabilized to similar final sizes of ~20 nm (Figure 8d), ~3× the BSA diameter. This result suggests that in the limit of excess negatively charged interactors, a positively charged diffuser effectively drags along one monolayer of interactors (Figure 8d inset). As the mammalian intracellular environment is dominated by negatively charged macromolecules^1,35,42, the ubiquitous net charge-driven protein-protein interaction elucidated by SMdM provides an intuitive and refined model for the mechanism underlying the above-discussed SMdM-observed diffusion suppression of positively charged proteins in the cell.

8. Elucidating complex molecular environments

While the in-solution measurements above provide a clean system to study protein interaction, they are overly simplistic. In the other limit, our characterizations of protein interaction in cells were limited by what molecular species can be introduced/labeled and heterogeneity due to intracellular structures and cell-to-cell variations. Cytoplasmic extracts from Xenopus eggs^75–77 (Figure 9a) offer a homogenized, near-native cytoplasm model that can be closely examined and strategically manipulated.

In collaboration with Prof. Rebecca Heald, we employed SMdM to quantify how proteins of diverse sizes and charges diffuse in Xenopus egg extracts.⁷⁸ Notably, whereas negatively charged proteins consistently exhibited diffusivities 40-50% of their in-PBS values (which followed the Young-Carroad-Bell model), positively charged proteins diffused substantially slower at ~10-20% of their in-PBS diffusivities (Figure 9b). Adding salt to the extract progressively alleviated this excessive diffusion suppression (Figure 9c), signifying electrostatic interactions within a predominately negatively charged macromolecular environment.

To dissect the contribution of RNA, an abundant negatively charged component, to this environment, we treated extracts with ribonuclease. Unexpectedly, SMdM visualized the gradual formation of micrometer-sized low-diffusivity domains (Figure 9d). This result is attributed to the vast (>1 mg/mL) liberation of positively charged ribosomal proteins upon RNA degradation, which presumably aggregate with the abundant negatively charged macromolecules in the cytoplasm. Indeed, adding 1 mg/mL positively charged proteins to the extract caused similar aggregation (Figure 9e), whereas ribonuclease treatments of ribosome-depleted extracts did not. These results highlight the importance of maintaining RNA integrity in neutralizing positively charged ribosomal proteins to prevent cytoplasmic aggregation.

To next explain why negatively charged proteins exhibited an invariant 40-50% scaling of D independent of size, we noticed that actin polymerization is inhibited in typical extract preparations.^75–77 The size-dependent suppression of molecular diffusion depends on the actin cytoskeleton.⁸⁰ Using expandable hydrogels as a controllably tuned system, SMdM showed that size-dependent diffusion suppression requires sufficiently dense meshworks (Figure 9f).⁷⁹ Consequently, restoring or enhancing actin polymerization in the extract progressively suppressed the diffusion of larger proteins,⁷⁸ recapitulating behaviors observed in cells. Together, our results indicate that molecular interaction in the crowded cell is defined by an overwhelmingly negatively charged macromolecular environment with dense meshworks.

9. Conclusion and outlook

By focusing on the local statistics of single-molecule displacements, SMdM eliminates the need for continuous molecular trajectories, thus providing an efficient framework to map diffusion at the super-resolution level. With the introduction of a frame-synchronized excitation scheme to capture transient single-molecule displacements across tandem frames in the wide field, SMdM further readily accesses fast dynamics as molecules stochastically diffuse in and out of the field of view. SMdM thus achieves super-resolution D mapping, from unbound proteins and small solutes to fluorogenic probes, for diverse systems. These experiments unveil a wealth of nanoscale spatial heterogeneities in diffusivity in the mammalian cell and beyond, while further elucidating their origins due to macromolecular crowding, charge interactions, lipid packing order, and amyloid fibril formation. Besides spatial mapping, the mass accumulation of single-molecule displacements in SMdM also affords a valuable means to quantifying D with outstanding precision. This advantage is harnessed to show no enhanced diffusion of enzymes in reactions and to establish how net charge and molecular size impact diffusion in solution, extracted cytoplasm, and expandable hydrogels, echoing our parallel results in the mammalian cell. While our experiments have focused on biological samples, the potential applications of SMdM to material and chemical systems, as previously demonstrated extensively with SPT,¹⁴ present additional opportunities. Meanwhile, while in this Account we have focused on results from our lab, we look forward to the gradual adoption of SMdM by other researchers,^40,81,82 for which the frame-synchronized stroboscopic illumination stands as a potential hardware barrier.

Looking forward, while the signature tandem excitation scheme of SMdM effectively overcomes the camera framerate to detect transient molecular motion, each molecule is only assessed for a single displacement, and D is statistically estimated from many molecules assuming normal diffusion. Future efforts may overcome this limitation and record single-molecule motion over a few time points to further improve quantification and elucidate possible anomalous diffusion. Concurrent multicolor/multichannel detection may provide part of the solution, which on its own may also be valuable and thus should be further explored for detecting the interactions between different molecular species. Meanwhile, whereas our current data analysis starts by localizing single molecules to determine displacements across paired frames so that they are fitted to predefined parametric models based on normal diffusion, rising machine-learning approaches^83–86 may more efficiently extract diffusivity and other parameters from the single-molecule raw data.

In a broader picture, SMdM adds to the growing family of multidimensional and functional super-resolution microscopy methods uniquely enabled by the mass accumulation of single-molecule spectroscopy.^87,88 As we have already demonstrated the powerful integration and correlative use of SMdM with SMLM and SR-SMLM, future integration with other methods, as well as the likely emergence of other novel approaches related to the concepts brought about by SMdM, present exciting perspectives.

Biographies

Wan Li obtained her bachelor’s and master’s degrees from Tsinghua University and her Ph.D. degree from Cornell University. She joined Xu Lab in 2015 and is currently a Research Scientist.

Ke Xu is an associate professor of Chemistry at UC Berkeley. He received his B.S. from Tsinghua University and Ph.D. from Caltech, and performed postdoctoral research at Harvard University. He is a physical chemist who develops single-molecule and super-resolution microscopy tools to interrogate biological, chemical, and materials systems at the nanoscale with extraordinary resolution, sensitivity, and functionality.