Quantitative Analysis of Cytoplasmic Viscosity in Colorectal Cancer Cells by Differential Dynamic Microscopy of Genetically Encoded Nanoparticles

Abstract

The viscosity of the cytoplasm plays a key role in regulating molecular diffusion and cellular mechanics, yet quantifying it in living cells remains technically challenging. Genetically encoded multimeric nanoparticles (GEMs) have emerged as useful probes for intracellular microrheology; however, current analyses rely on single-particle tracking, which is limited by probe density, imaging noise, and expression variability. Here, we combine GEMs with differential dynamic microscopy (DDM) to enable quantitative, noninvasive, and rapid measurement of intracellular viscosity using standard wide-field fluorescence imaging. DDM extracts particle dynamics from ensemble spatiotemporal intensity fluctuations, yielding diffusion coefficients and viscosity estimates, even in crowded or heterogeneous environments where tracking fails. Validation with fluorescent nanoparticles diffusing in water confirmed that DDM accurately reproduced theoretical viscosities across a wide range of particle sizes and concentrations. Comparison with single-particle tracking (SPT) demonstrated equivalent precision under dilute conditions and improved the performance under crowding. To showcase the potential of this approach, we applied GEM-DDM to colorectal cancer cell lines with different metastatic potentials. Cytoplasmic viscosity correlated with aggressiveness, increasing from 1.9 to 2.3 cP in poorly metastatic lines to 3.6–3.7 cP in highly metastatic lines, consistent with greater macromolecular crowding and cytoplasmic reorganization reported in aggressive cells. Together, these results establish GEM-DDM as a fast, reproducible, and accessible platform for intracellular microrheology to link the physical state of the cytoplasm to cell function and disease progression.

Viscosity is a key regulator of biological processes, from molecular reactions to whole-cell behavior. Within eukaryotic cells, the constant rearrangement of molecules between compartments depends on both passive diffusion and active transport, both of which are affected by cytoplasmic viscosity. , Changes in intracellular viscosity can therefore influence diffusion rates, reaction kinetics, and overall cellular dynamics. In red blood cells (RBCs), internal viscosity is essential for maintaining deformability and proper circulation − with elevated cytosolic viscosity driving the membrane alterations observed in sickle-cell disease. Viscoelastic properties are not solely relevant for the behavior of RBCs; they can also influence cell migration through dense extracellular environments. In cancer, where migration and invasion underpin metastatic progression, intracellular viscosity has been shown to inversely correlate with migratory capacity. −

Given its importance, a variety of strategies have been developed to probe intracellular viscosity, including fluorescent dyes such as sulforhodamine B and viscosity-sensitive molecular rotors, passive nanoparticle tracers like gold particles, and active microrheology techniques employing magnetically actuated nanowires or spin labels. , Although these techniques have provided valuable insight, they typically require invasive delivery procedures that can perturb the cellular environment.

To overcome this limitation, methods based on the expression of genetically encoded fluorescent reporters were developed, allowing for intracellular measurements without the need for probe delivery. For instance, fluctuation-based imaging techniques such as RICS and STICS extract diffusion coefficients from fluorescence intensity correlations in confocal image sequences, which can be related to local viscosity. While these approaches avoid physical manipulation of cells, they still require prior knowledge of the probe’s molecular radius and depend on confocal scanning microscopy, which limits their throughput and accessibility. More recently, Brillouin microscopy has emerged as a label-free tool for biomechanical characterization of cells. , However, widespread implementation of Brillouin microscopy has been hampered by the absence of commercially available systems and the need for a Brillouin spectrometer and confocal pinhole alignment. Together, these limitations highlight the need for noninvasive, reproducible, and easily accessible techniques to quantify intracellular viscosity in living cells.

Genetically encoded multimeric nanoparticles (GEMs) have emerged as a useful tool for intracellular microrheology. , These probes are built from self-assembling scaffold proteins fused to a fluorescent protein that form bright nanoparticles of precise and uniform dimensions of approximately 20 or 40 nm in diameter. They can be expressed directly inside cells by transient or stable transfection, avoiding complications from exogenous nanoparticles, such as inefficient cytoplasmic delivery, vesicle entrapment, or aggregation. Moreover, because of this direct expression in the cytoplasm, they assemble spontaneously in transfected cells, avoiding invasive delivery steps. Importantly, GEM expression allows long-term monitoring of the viscosity changes over time with minimal cellular stress. Their defined nanoscale architecture and size make them suitable physical tracers for characterizing intracellular dynamics. Despite these advantages, quantitative analysis of GEM dynamics has relied on single-particle tracking (SPT), which becomes error-prone in crowded or highly viscous environments where trajectories overlap. To overcome this limitation, we implemented differential dynamic microscopy (DDM) as a complementary ensemble-based image analysis strategy to retrieve viscosity values from GEM dynamics. DDM extracts dynamic information from temporal intensity fluctuations in standard wide-field image sequences, allowing robust quantification of particle motion in both crowded and dilute environments. By integrating GEMs with DDM into a unified framework, hereafter referred to as GEM-DDM, we established a noninvasive, accessible technique to measure intracellular viscosity directly from wide-field fluorescence data.

We validate GEM-DDM by benchmarking DDM-derived viscosity values against SPT measurements in vitro and apply it to a panel of colorectal cancer cell lines, revealing clear differences in cytoplasmic viscosity that correlate with metastatic potential. Beyond its technical advantages, this approach opens possibilities for long-term, minimally invasive, and high-throughput studies of intracellular mechanics in living systems, offering a practical route to explore how biophysical properties such as viscosity evolve across cell states, differentiation, and disease progression.

Differential Dynamic Microscopy for Quantitative Microrheology

To quantify particle motion and extract microrheological parameters from wide-field fluorescence image sequences, we used DDM, an image-based analysis technique that extracts dynamics from spatiotemporal intensity fluctuations − (Figure A). For each time lag τ, differential images were calculated by subtracting the image at time t from the image at time t + τ, removing static features, and suppressing background noise. The Fourier transform of each differential image was calculated, and all transforms corresponding to the same time lag (τ) were averaged to obtain a mean Fourier image for that time lag. By radially averaging the mean Fourier image, we separated the dynamics at different spatial frequencies (wave vectors, q), obtaining an intensity amplitude for each q. The intermediate scattering function (ISF) was then calculated by plotting these amplitudes as a function of the corresponding time lag (τ). The ISF describes how spatial correlations decay over time: faster or steeper saturation indicates more rapid particle dynamics on the length scale of the corresponding q-vector.

1.

Overview of the analysis workflow of DDM and its validation by comparison with single particle tracking (SPT) of nanoparticles diffusing in water. (A) The DDM-based analysis involves two steps with the conventional DDM algorithm: calculating differential images and their Fourier transform for every time lag and radial averaging to obtain the image structure function (ISF) per wavevector q. In an extension, a subset of q is selected to calculate the average mean-squared displacement of all particles by an optimization loop taking the saturation level A and baseline B of every ISF as optimizing parameters. Partially adapted from ref . (B, E) Representative snapshot of 100 nm particles diffusing in water at diluted and crowed conditions. (C, F) Traces are labeled by time point; only traces suitable for microrheology analysis (containing more than 20 data points) are shown. (D, G) Measured viscosities for all samples in both diluted and crowded conditions, comparison of DDM and SPT. Dashed black line gives the reference value of 0.932 cP for the viscosity of water at 23 °C. All scale bars are equal to 10 μm.

For the analysis of both water and cytoplasmic viscosity, we selected q-vectors in the range of 3–10 μm^–1. These values correspond to spatial scales from about 600 nm, which reflects the diffraction limit and the displacement of the fluorescent nanoparticles within the exposure time, up to roughly 6 μm, comparable to the size of small cells.

Because intracellular diffusion dynamics can be complex (anomalous, Brownian, active, or confined), one cannot predict a single diffusion model that would adequately fit all ISFs. Instead, the algorithm was extended to convert each selected ISF into a mean-squared displacement (MSD) curve. First, the saturation level (A) and background (B) were estimated for each ISF. Then, using these initial sets of parameters, each ISF was transformed into an MSD. An iterative optimization loop refined A and B to minimize the error across the set, producing a converged, robust average MSD. From the converged MSD, effective diffusion coefficients were obtained by linear fitting of the initial time lags, and viscosity was then calculated using the generalized Stokes–Einstein relation, assuming a predominantly viscous environment. In complex cellular environments where multiple diffusion regimes coexist, such as in the case of GEMs exhibiting both Brownian and directed motion, the overall MSD reflects this mixture through an anomalous profile: it may grow superlinearly before reaching a plateau, capturing not only effective diffusion and viscosity but also signatures of confinement and viscoelasticity. Although this study focused on the viscous regime, MSD analysis can, in principle, be extended to extract elastic and viscoelastic properties of the medium for more detailed microrheological characterization.

To validate the performance of our DDM algorithm and ensure accurate retrieval of diffusion coefficients and viscosities, benchmark experiments on fluorescent polystyrene nanoparticles diffusing in water were performed. Time-lapse images of fluorescent polystyrene nanoparticles with diameters of 100, 200, 500, and 1000 nm were recorded at low (<0.0005 mg of particles per mL) and high concentrations (0.01 mg of particles/mL) to evaluate the effect of crowding on DDM performance (Figure B,E).

Across all particle sizes and concentrations, DDM provided viscosity values that were in close agreement with the theoretical viscosity of water (0.932 cP at 23 °C). At low concentrations, the measured viscosities for 100, 200, 500, and 1000 nm nanoparticles were 0.98 ± 0.09, 0.93 ± 0.10, 0.97 ± 0.08, and 1.00 ± 0.19 cP, respectively. At higher concentrations, the values obtained were similar (0.97 ± 0.08, 0.97 ± 0.09, 0.96 ± 0.12, and 0.97 ± 0.06 cP for 100, 200, 500, and 1000 nm nanoparticles, respectively). These results demonstrate that DDM yields consistent results independent of particle size or sample crowding (Figure D,G). This robustness arises from the ensemble-based nature of DDM, which analyses spatiotemporal intensity fluctuations rather than individual trajectories and is therefore unaffected by particle overlap or background heterogeneity.

To benchmark these results, we compared DDM with conventional single-particle tracking (SPT). At low particle concentrations, SPT produced viscosities of 0.98 ± 0.07, 0.89 ± 0.04, 1.12 ± 0.04, and 0.84 ± 0.07 cP for 100, 200, 500, and 1000 nm nanoparticles, respectively, values that closely match both the DDM measurements and the theoretical viscosity of water (Figure D). However, at higher concentrations, the SPT performance degraded substantially, yielding less reliable viscosities of 1.30 ± 0.19, 1.15 ± 0.29, 1.28 ± 0.31, and 0.06 ± 0.15 cP for the same particle sizes (Figure G). To determine if this deviation arose from trajectory ambiguity caused by frequent particle crossings and overlapping paths, the data was reanalyzed using TARDIS, a high-density tracking algorithm capable of resolving overlapping trajectories. Although this analysis reduced the error in the calculated viscosities, significant deviations persisted at higher concentrations, particularly for smaller particles (Figure S1). To systematically evaluate the effect of particle concentration, we performed controlled simulations of diffusing particles (see Simulations of Freely Diffusing Nanoparticles, Movies S1–S5). While DDM yielded accurate viscosities across the full concentration tested, both SPT and TARDIS failed at higher concentrations (Figure S2). We attribute this breakdown to detection and localization errors that become increasingly prominent at high particle densities, as both SPT-based approaches require reliable identification of individual particles. In contrast, DDM relies on ensemble-averaged intensity fluctuations rather than single-particle localization or trajectory linking, rendering it inherently more robust under high-density conditions.

Together, these validation experiments demonstrate that DDM provides accurate and reproducible viscosity measurements across a wide range of particle concentrations (0.01 to 0.0005 w/v%). Under dilute conditions, DDM achieves the same precision as SPT, while at high densities, it remains reliable when SPT fails. This robustness stems from the ensemble-averaging nature of DDM, which ensures reproducibility even in heterogeneous or crowded systems, where single-particle detection becomes unreliable. These results establish DDM as a robust, calibration-free method for quantitative microrheology, bridging the gap between single-particle tracking and more complex correlation-based approaches such as RICS or fluorescence correlation spectroscopy.

GEM-DDM Microrheology for Cytoplasmic Viscosity

Given the robustness of DDM, we applied this method to living cells to measure the cytoplasmic viscosity using GEMs. To minimize interference from cellular autofluorescence, we developed a red-shifted GEM variant in which the original YFP was replaced with the red fluorescent protein mScarlet-I. This fluorophore was selected for its favorable spectroscopic properties and rapid maturation, providing bright and stable emission suitable for wide-field imaging. The resulting 40 nm GEM construct self-assembles into fluorescent nanoparticles following transfection and expression in cells (Figure A). Cells expressing the red GEMs were imaged on a home-built wide-field microscope with a 561 nm excitation and an EM-CCD camera at 30 Hz.

2.

Evaluation of GEM-DDM workflow to measure cell viscosity benchmarked to SPT: (A) Experimental workflow involves the expression of the GEM-mScarlet gene inside the cell after which the nanoparticles form by self-assembly, and the fluorescent cell can be imaged with conventional wide-field microscopy. Partially adapted from ref . (B) KM12SM cell with low expression level with (C) zoom showing the localized particles in frame 1. (D, E) Low expression levels lead to many spread-out trajectories. (F) Highly expressing KM12SM cell with (G) zoom showing the localized particles in frame 1; many particles are missed due to heterogeneous background. (H, I) High expression levels biased the detection to a few very confined trajectories. All scale bars are 10 μm. Figure 2 was partially created with BioRender.com.

The performance of GEM-DDM in the intracellular environment was initially evaluated by comparison with single-particle tracking SPT in individual KM12SM cells expressing GEMs at different levels (Figure B,F). In cells with low GEM expression (Figure B,C), individual particles were well resolved, which resulted in numerous, long trajectories distributed throughout the cytoplasm (Figure D,E). However, only 3 out of 24 cells yielded SPT-derived viscosities within 10% of the corresponding DDM values, indicating that SPT rapidly lost accuracy as particle density increased. Nonetheless, for this small subset, both methods yielded comparable viscosity values with 2.51 cP on average measured by SPT and 2.57 cP measured by DDM. In the other 21 cells with higher GEM expression (Figure F,G), only the brightest and most confined particles could be detected (Figure H,I), leading to an overestimation of viscosity by SPT (5.86 cP) compared with DDM (2.22 cP). To determine whether a high-density tracking algorithm could improve intracellular viscosity estimates, five cells spanning the full range of particle densities were reanalyzed using TARDIS. While TARDIS agreed with DDM in cells with low GEM expression, it failed as GEM density increased and particle localization errors became significant, leading to systematic overestimation of viscosity (Figure S3 and Movies S6–S10). We conclude that DDM outperforms localization-based methods both in vitro and in the intracellular environment.

3.

Measuring in vivo cytoplasmic cell viscosity with GEM probes and DDM-based analysis. (A) Snapshots of representative cells per cell line. All show substantial crowdedness and differences in size. (B) ISF at wavevector q = 5 μm^–1. The difference in dynamics between non/low-metastatic (KM12C, KM12SM, SW480) and highly metastatic (KM12L4a, SW620) cells becomes clear, showing a slower rise and thus dynamics for more metastatic cells. (C) Average viscosity per cell line. Plotted as geometric mean with 95% confidence interval, as all data sets showed a log-normal distribution. Number of cells = 25, 24, 27, 28, and 24 for KM12C, KM12SM, KM12L4a, SW480, and SW620, respectively. Black triangles indicate the increase in metastatic potential among cell lines. (D) Average size per cell line. Plotted as geometric mean with 95% confidence interval, as all data sets showed a log-normal distribution. Black triangles indicate the increase of metastatic potential among cell lines. All scale bars are 10 μm.

These results demonstrate that GEM-DDM provides a rapid, noninvasive, and broadly accessible approach for intracellular rheology. By analyzing fluorescence fluctuations across multiple length scales and avoiding single-particle tracking, the method remains robust in crowding and heterogeneous environments, enabling reproducible viscosity measurements with standard wide-field fluorescence microscopy. The use of a single-color, genetically encoded probe eliminates the need for particle delivery or complex optical setups, simplifying the implementation of GEM-DDM and reducing perturbation of cell physiology. Together, these advantages establish GEM-DDM as a powerful and versatile platform that lowers the experimental barrier to intracellular microrheology and opens possibilities for the systematic, high-throughput assessment of cytoplasmic viscosity in living cells.

GEM-DDM Analysis of Cytoplasmic Viscosity in Colorectal Cancer Cells

To demonstrate the applicability of GEM-DDM to physiologically relevant systems, cytoplasmic viscosity was quantified in a panel of colorectal cancer cell lines differing in metastatic potential. Figure A depicts representative fluorescence images showing dense GEMs distributions within the cytoplasm in all of the lines. This complex and crowded signal provided a suitable basis for quantitative analysis using DDM. Qualitative evaluation of the intermediate scattering functions (ISFs) extracted at a representative wavenumber of q = 5 μm^–1 revealed distinct behaviors among the cell lines (Figure B). In the poorly metastatic KM12C, KM12SM, and SW480 lines, the ISFs decayed rapidly, indicating fast decorrelation of particle positions and, thus, low cytoplasmic viscosity. Conversely, the highly metastatic KM12L4a and SW620 cells exhibited slower ISF relaxation, reflecting a reduced particle mobility and higher viscosity.

Quantitative DDM analysis confirmed these differences (Figure C). Within the KM12 family, viscosity increased with metastatic potential: 1.93 cP for KM12C (poorly metastatic), 2.22 cP for KM12SM (intermediate), and 3.72 cP for KM12L4a (highly metastatic). A similar trend was obtained for the SW family with SW480 (poorly metastatic) showing 2.35 cP and SW620 (highly metastatic) reaching 3.58 cP. To account for potential size-dependent effects on molecular crowding, we quantified projected cell area and normalized viscosity values accordingly (Figure D). If viscosity differences were solely due to variations in cell size, larger cells would be expected to exhibit a lower effective macromolecular density and reduced cytoplasmic viscosity. This correction allowed us to test whether the observed differences reflected simple size effects or intrinsic changes in the cytoplasmic properties. In the KM12 series, cell area increased with metastatic potential (239 μm² for KM12C, 323 μm² for KM12SM, 401 μm² for KM12L4a), whereas the opposite trend was observed for the SW series (SW480: 463 μm²; SW620: 265 μm²). Even after normalization for cell size (Figure S4), highly metastatic cells consistently displayed higher cytoplasmic viscosity, indicating that the observed differences cannot be explained by size-dependent crowding effects alone.

The observed correlation between cytoplasmic viscosity and metastatic potential is consistent with prior reports linking increased macromolecular crowding, cytoskeletal remodeling, and altered metabolic activity to cancer aggressiveness. −

Elevated viscosity may thus reflect a more cross-linked, densely packed cytoplasmic architecture in metastatic cells, potentially driven by enhanced cytoskeletal tension, accumulation of macromolecular complexes, or altered organelle distribution.

Together, these findings demonstrate the potential of GEM-DDM as a versatile and accessible tool for intracellular microrheology, enabling the quantitative analysis of cytoplasmic viscosity across diverse cellular and physiological contexts. In addition to quantifying viscosity, this method provides a platform for future investigations into the interplay among intracellular mechanics, metabolism, and cancer progression.

This study establishes GEM-DDM as a robust and accessible framework for quantitative intracellular microrheology. By integration of genetically encoded fluorescent nanoparticles with differential dynamic microscopy, this method overcomes the limitations of single-particle tracking and enables reproducible viscosity measurements in living cells using standard wide-field fluorescence imaging.

Beyond the methodological innovation, GEM-DDM provides a practical means to link cell mechanics with the biological state. The observed correlation between cytoplasmic viscosity and metastatic potential underscores the value of viscosity as a biophysical marker of cellular organization and function.

The versatility and noninvasive nature of GEM-DDM make it well-suited for large-scale or longitudinal studies, offering a way to explore how intracellular physical properties evolve during disease progression, therapy response, or cellular differentiation. By enabling robust and accessible intracellular microrheology, GEM-DDM lays the groundwork for a broader mechanobiological understanding of cell physiology.

Nanoparticle Sample Preparation

Polystyrene nanoparticles (ThermoFisher FluoSpheres Size Kit #1, carboxylate-modified, red fluorescent 580/605 nm, 2% solids) were used for validation experiments. Particle suspensions were diluted in Milli-Q water at either 1:1000 (low concentration) or 1:100 (high concentration) and vortexed for 5 min. A 10 μL drop was dropcasted on ozonated glass coverslips and sealed with a 120 μm thick, 9 mm diameter imaging spacer (Grace Bio-Laboratories SecureSeal) and a second ozonated coverslip.

Plasmid Cloning

The original vector pCDNA3.1-pCMV-PfV-GS-Sapphire was a gift from Liam Holt (Addgene plasmid #116933; http://n2t.net/addgene:116933; RRID: Addgene 116933), who performed an extensive characterization of the resulting GEMs. Into this backbone, we subcloned mScarlet-I and removed Sapphire through restriction enzyme cloning digestion with PacI and BsrGI.

Cell Culture and Transfection

Colorectal cancer cell lines (KM12C, KM12L4a, KM12SM, SW480, and SW620) were cultured at 37 °C under 5% CO₂ in DMEM supplemented with 10% FBS, 1% l-glutamax, and 0.1% gentamicin. KM12C and SW480 are poorly metastatic and derived from primary tumors, whereas KM12SM, KM12L4a, and SW620 are highly metastatic and derived from liver, lung, or lymph node metastases, respectively. , Cells were passaged at 80–90% confluency using trypsin-EDTA. To provide a more physiologically relevant condition, 5 × 10⁵ cells were seeded on 37 kPa polyacrylamide gels over the whole area of the 35 mm glass bottom dish (CellVis). Transfection of GEM plasmids was performed with FuGene HD (3 μL per 1000 ng of DNA in 100 μL of DMEM) directly on the gels after seeding the cells.

Hydrogel Preparation and Glass Coating

Polyacrylamide hydrogels (37 kPa) were prepared following ref with 4% w/v acrylamide, 0.17% w/v bis­(acrylamide), 0.25% w/v APS, and 0.25% v/v TEMED. This gel composition was selected for its mechanical properties and favorable optical characteristics; the refractive index was estimated using the Lorentz–Lorenz equation to be n ≈ 1.338, close to that of water (n = 1.333), thereby minimizing refractive index mismatch during imaging. Fifteen μL of these gels was cast in 35 mm glass-bottom dishes (20 mm microwells Cellvis), treated with bind-silane inside a 120 μm thick, 9 mm diameter wide imaging spacer (Grace Bio-Laboratories SecureSeal). A Sigmacote-treated coverslip was added on top to maintain gel flatness during polymerization, which was performed at 37 °C for 30 min, followed by overnight swelling at 37 °C in Milli-Q water. Hydrogels were functionalized with sulfo-SANPAH under UV light and coated with collagen for 2 h at 37 °C.

Simulations of Freely Diffusing Nanoparticles

Synthetic fluorescence microscopy movies of freely diffusing nanoparticles were generated using a custom Python simulation implemented as a Jupyter notebook and made available at https://github.com/BorisLouis/Simulation_Brownian_Nanoparticles. The simulation proceeds in three stages. First, three-dimensional Brownian motion trajectories are computed for a user-defined number of particles over a specified number of frames. At each time step Δt, particle displacements in x, y, and z are drawn independently from a Gaussian distribution with zero mean and standard deviation

$$\sigma =\sqrt{2D\mathrm{\Delta }t}$$

where the diffusion coefficient D is derived from the Stokes–Einstein relation:

$$D=\frac{k_{\mathrm{B}}T}{6\pi \eta r_{\mathrm{H}}}$$

with k _B as the Boltzmann constant, T as the absolute temperature, η as the solvent viscosity, and r _h as the hydrodynamic radius of the particle. Lateral (XY) and axial (Z) boundaries are treated as periodic, thereby maintaining a constant particle concentration throughout the movie (https://github.com/BorisLouis/Simulation_Brownian_Nanoparticles). Second, each frame is rendered by placing point-source impulses at the particle positions on a high-resolution 3D volume, which is then convolved with a model point spread function (PSF) via FFT-based convolution. The PSF is approximated as the product of a 2D Airy disk pattern in the lateral plane. Laterally computed as

$$I(r)={\left(\frac{2J_1(k\mathrm{N}\mathrm{A}r)}{k\mathrm{N}\mathrm{A}r}\right)}^2$$

where J ₁(x) is the first order solution to the Bessel function, k is the wavenumber, NA is the numerical aperture, and r is the distance of the particle to the aperture, and combined with a Gaussian envelope along the axial direction, computational approximation of a defocus-aware PSF was provided. The central image plane of the 3D volume is used and binned to match the camera pixel size. Third, realistic detector noise is introduced by drawing pixel intensities from a Poisson distribution (to model photon shot noise) followed by the addition of zero-mean Gaussian noise (to model electronic read-out noise). The final synthetic movie is saved as a 16-bit grayscale TIFF stack compatible with ImageJ/Fiji, along with the corresponding ground-truth particle trajectories, stored as CSV and pickle files for downstream analysis (https://github.com/BorisLouis/Simulation_Brownian_Nanoparticles).

Fluorescence Imaging

Samples were imaged on a custom-built widefield microscope equipped with a 561 nm laser line 48 h after transfection. A water-immersion objective (60×, Olympus, long working distance, 1.20 NA) was used to reach cells on top of the hydrogel. The pixel size was set to 107 nm per pixel. Fluorescence emission was filtered through a 532 nm long pass dichroic mirror and a 595/40 nm bandpass filter. Images were acquired on an EM-CCD camera in EM mode with adjustable gain by using 30.5 ms exposure and 500 frames per acquisition.

Single Particle Tracking (SPT) Analysis

Nanoparticle trajectories were obtained and analyzed using custom MATLAB code. , Particle candidates were identified through a Gaussian scanning approach and further localized using a phasor-based super resolution fit. Trajectories required a minimum of 50 steps, a maximum frame gap of 3, and an exclusion radius of 1500 nm. Mean-squared displacements (MSDs) were calculated for each trajectory from which diffusion coefficients and viscosities were determined, as will be discussed in the next section.

Differential Dynamic Microscopy (DDM) Analysis

DDM analysis was implemented based on ref using custom MATLAB scripts and is depicted in Figure B. Preprocessing included rough segmentation of the cell from which further cell size was calculated and bleaching correction by correcting the average intensity of the frames over time. Differential images were generated by subtracting each possible pair of frames, and each of them was then Fourier-transformed. The Fourier images were averaged per timelag and radially averaged to construct image structure functions (ISFs) for each q-vector, ranging from the diffraction limit (≈ 233 nm) to the full image size.

For MSD calculations, a subset of wavevectors (1–10 μm^–1) was selected to capture particle motion in the relevant range. The upper limit (q = 10 μm^–1) corresponds to image frequencies of ∼623 nm, accounting for the diffraction-limited particle size and movement during the exposure time of 30.5 ms. In these conditions and for a diffusing nanoparticle with diameter of 40 nm, the measurable range of diffusion coefficients that would be measurable range from approximately 0.2 to 11 μm² s^–1, corresponding to viscosities of approximately 1–50 cP. The lower limit (q = 1 μm^–1) corresponds to image frequencies of ∼6 μm, which is big enough to capture the full movement inside a cell. Each wavevector has a corresponding ISF from which baseline (B(q)) and saturation level (A(q)) are initially determined by

$$\begin{array}{l}A(q)={⟨{|\mathrm{F}\mathrm{F}\mathrm{T}(I)|}^2⟩}_q\\ B={⟨{|\mathrm{F}\mathrm{F}\mathrm{T}(I)|}^2⟩}_{q=q_{\max }}\end{array}$$

These values provide starting lists of B(q) and A(q) for the optimization procedure.

From each ISF, the mean-squared displacement (MSD) is calculated using the relation:

$$⟨\mathrm{\Delta }{r}^2(\tau )⟩=\frac{-4}{q^2}\ln (1-\frac{\mathrm{I}\mathrm{S}\mathrm{F}(q,\tau )-B(q)}{A(q)})$$

This results in a set of MSDs with some variance across the q-vectors. An optimization loop, implemented with MATLAB’s fminsearch, adjusts the A(q) and B(q) parameters to minimize the standard deviation of the MSDs. The optimization uses a maximum of 10,000 iterations and a convergence cutoff of 10^–4 on the MSD standard deviation.

Once convergence is achieved, optimized A(q) and B(q) are used to calculate a final set of MSDs, which are averaged to obtain the representative MSD of the sample.

Viscosity Calculation from MSD

From the MSD, the diffusion coefficient (D) is obtained from a linear fit of the first four points of MSD versus lag time using

$$⟨\mathrm{\Delta }{r}^2(\tau )⟩=2nD\tau$$

The cytoplasmic viscosity (η) is calculated via the Stokes–Einstein relation for spherical particles in a viscous liquid:

$$\eta =\frac{k_{\mathrm{B}}T}{6\pi r_{\mathrm{h}}D}$$

where k _B is the Boltzmann constant, T is the absolute temperature, and r _h is the particle radius.

Statistical Analysis

At least 30 cells per condition were analyzed. Outliers were detected using MATLAB’s rmoutlier function and defined as elements more than 3 standard deviations from the mean. They were removed when corresponding to blurry or unhealthy cells. Statistical significance was assessed using Welch’s ANOVA using GraphPad Prism 10 software.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/cbmi.5c00261.

• Supplementary videos: Simulation_video_n50 (S1) = simulated video of 50 nanoparticles moving through solution with viscosity of 4 cP, frametime 33 ms, Simulation_video_n200 (S2) = simulated video of 200 nanoparticles moving through solution with viscosity of 4 cP, frametime 33 ms, Simulation_video_n1000 (S3) = simulated video of 1000 nanoparticles moving through solution with viscosity of 4 cP, frametime 33 ms, Simulation_video_n5000 (S4) = simulated video of 5000 nanoparticles moving through solution with viscosity of 4 cP, frametime 33 ms, Simulation_video_n10000 (S5) = simulated video of 10000 nanoparticles moving through solution with viscosity of 4 cP, frametime 33 ms, KM12C_cell1_rawvid (S6) = raw data of a representative KM12C cell with diffusing nanoparticles (real time), KM12L4a_cell2_rawvid (S7) = raw data of a representative KM12L4a cell with diffusing nanoparticles (real time), SW620_cell3_rawvid (S8) = raw data of a representative SW620 cell with diffusing nanoparticles (real time); SW480_cell4_rawvid (S9) = raw data of a representative SW480 cell with diffusing nanoparticles (real time), KM12SM_cell5_rawvid (S10) = raw data of a representative KM12SM cell with diffusing nanoparticles (real time) (ZIP)

• Video S11: representative movie of 100 nm diameter polystyrene nanoparticles moving through water at low nanoparticle density (AVI)

• Video S12: representative movie of 100 nm diameter polystyrene nanoparticles moving through water at high nanoparticle density (AVI)

• Figure S1: TARDIS analysis on diffusing nanoparticles; Figure S2: Comparison of SPT, TARDIS, and DDM on diffusing nanoparticles in different concentrations; Figure S3: Comparison of SPT, TARDIS, and DDM on diffusing GEMs in cells at different levels of crowdiness; Figure S4: Average viscosity per colorectal cell line, divided by area (PDF)

The authors declare no competing financial interest.