Luminescent-reaction-enabled super-resolution imaging

Reaction-enabled imaging is based on specifically designed luminescence chemistry, which can be tailored for different applications (Fig. 1a). Specifically, ECL is triggered and controlled by electrochemical reactions, imparting high surface sensitivity, which inherently facilitates imaging of objects near the electrode. CL relies on the reactant diffusion in solution, enabling homogeneous excitation throughout the imaging volume. BL makes use of enzymatic reactions to produce catalytic luminescence in living organisms, providing excellent biocompatibility for live-cell imaging. Despite these advantages, so far, the reaction-based luminescence suffers from low photon output, usually requiring prolonged exposure times by tens of seconds to accumulate a single image^10,11, which inevitably overlooks the spatiotemporal information. As a result, unlike established super-resolution fluorescence microscopy, achieving super resolution using reaction-enabled luminescence remains challenging.

From a fundamental perspective, the reaction-based luminescence is a highly dynamic process, intrinsically initiated by individual reactions. To achieve super-resolution imaging, we propose to experimentally monitor these reaction-based luminescence processes in an image sequence through a spatiotemporal isolation strategy. This enables the extraction of distinct reaction-driven photon statistics for super-resolution reconstruction using a tailored workflow (Fig. 1b, Extended Data Fig. 1 and Supplementary Video 1). Spatiotemporal recordings uncover unique luminescence profiles of zero-light excitation background, high signal-to-noise ratio and high-contrast fluctuations between the emitting reaction sites and the dark background (Extended Data Fig. 2 and Supplementary Figs. 1 and 2). Accordingly, we performed spatiotemporal cross-correlation analysis on sequences of photon events excluding pixels dominated by overlapping emitters and narrowing the point spread function (PSF) width, drawing on recent fluctuation-based super-resolution fluorescence methods^12,13,14. To further mitigate discontinuities from ECL heterogeneity, we introduced a spatial entropy map before the correlation analysis, quantifying the local information content and refining the correlation cumulant. Finally, a subsequent deconvolution was applied to sharpen the spatial resolution and the image contrast under low-photon-budget conditions (Extended Data Fig. 3).

To validate this workflow, we implemented simulated data to confirm that reaction-driven photon statistics can provide effective fluctuations for resolution enhancement, which shows genuine reconstruction of the ground-truth structures (Extended Data Fig. 4). Further, we introduced Fourier ring correlation (FRC) resolution¹⁵, resolution-scaled error (RSE) and resolution-scaled Pearson coefficient (RSP) metrics¹⁶ for step-by-step evaluations (Extended Data Fig. 3). These results indicate that RIED reconstruction effectively improves image resolution while introducing limited artefacts. Moreover, as RIED is tailored to reaction-based luminescence processes, it demonstrates improved reconstruction performance compared with conventional super-resolution methods^12,13,14,17 originally developed for fluorescence sequences (Extended Data Fig. 5). Overall, our optimized pipeline yields the reaction-driven super-resolution images, as exemplified in Fig. 1c.

We first evaluated the performance of RIED in ECL imaging. In conventional ECL imaging, efforts to improve the performance of ECL-based cell imaging have focused on increasing the photon emission by engineering amplified probe systems or extending the imaging time¹⁸. Nevertheless, these strategies entail limitations in effective labelling and imaging resolution. As such, conventional ECL microscopy only provides extracellular, whole-cell or obscure subcellular information^19,20. So far, efficient ECL imaging of intracellular organelles has not been demonstrated, imposing a fundamental barrier to super-resolution imaging (Supplementary Note 1).

To address this issue, we developed a high-efficiency ECL cell imaging system (Fig. 2a). Ru(bpy)₃²⁺ molecules were anchored to the antibody as the luminescent probe, which exhibits excellent binding specificity and can efficiently label cellular structures with high coverage by means of immunolabelling. Bis(2-hydroxyethyl)amino-tris(hydroxymethyl)methane (Bis-tris), a known co-reactant in ECL^21,22, was chosen here to replace commonly used tripropylamine (TPrA) for ECL cell imaging. We found that Bis-tris improved the ECL cell imaging brightness by about 1,000-fold under optimized imaging conditions (Fig. 2b,c and Supplementary Fig. 3), allowing imaging of microtubules²³. This improvement is attributed to the intrinsic long lifetime and the extended diffusion distance of Bis-tris radical²², which increases the probability of its encountering and reacting with Ru(bpy)₃²⁺-labelled organelles.

With this profoundly enhanced ECL performance, microtubule filaments can be clearly visualized even under 20-ms exposure time (Supplementary Video 2). Implementation of RIED in ECL further allows visualization of intracellular organelle structures at the sub-diffraction scale. For cross-validation, we compared the reconstructed RIED results with the fluctuation-based fluorescence super-resolution imaging using autocorrelation with two-step deconvolution (SACD)¹² because both methods can target the same microtubules and their corresponding images exhibit a high consistency (Fig. 2d,e). Imaging of other targets, such as mitochondria and integrins, further demonstrates the applicability of RIED-ECL for intracellular imaging (Supplementary Fig. 4). A quantitative FRC resolution evaluation reveals a substantial improvement in the spatial resolution of ECL, reaching 97 nm (ref. ²⁴) (Fig. 2f). The peak-to-peak separation of the intertwining microtubule filaments suggests that the resolving power of RIED is comparable with that of fluorescence SACD (Fig. 2g). Although improving spatial resolution typically requires prolonged imaging time, RIED can efficiently use individual ECL photons to generate a super-resolution image from just 100 raw frames at 20-ms exposure time (Fig. 2h). The imaging quality is confirmed by the structure similarity index measure (SSIM > 0.9) (Fig. 2i) and FRC analysis (<110 nm) (Fig. 2j), demonstrating high spatiotemporal resolution in ECL imaging (Supplementary Figs. 5–7 and Methods). We noted that, in some RIED-ECL images, microtubules seem discontinuous. This feature was also observed in the corresponding summed raw ECL data and fluorescence super-resolution images (Extended Data Fig. 6), which probably reflect the underlying probe distributions associated with the chemical fixation²⁵ and the characteristics of the electrochemical excitation (Supplementary Fig. 8 and Supplementary Note 2).

So far, 3D ECL microscopy remains a technical challenge, mainly because of the difficulty in regulating the excitation depth. In our experiments, we observed that the ECL emission depth increases with increasing voltage, reflecting enhanced generation of reactive radicals (Bis-tris^•). Nevertheless, higher voltages also accelerate radical consumption and quenching, which can reduce the effective ECL signals. Accordingly, we used stepped voltage application, using a lower voltage (1.0 V) to image regions near the electrode surface and gradually increasing the voltage to 1.8 V to access deeper layers (Extended Data Fig. 7). By synchronizing voltage control with imaging focal plane changes (Methods, Supplementary Fig. 9 and Supplementary Note 3), a 3D-RIED image was built that clearly distinguishes the cytoskeleton network in all dimensions (Fig. 2k, Extended Data Fig. 7 and Supplementary Video 3). Notably, microtubules spaced by 235 nm in the axial distance and 116 nm in the lateral plane can be resolved with 3D-RIED (Fig. 2l,m and Supplementary Fig. 9), comparable with the 3D fluorescence super-resolution imaging¹².

An extra benefit from the high spatiotemporal resolution of RIED is high-throughput imaging. Microtubules on a large scale (0.53 × 0.53 mm²) area with 3 × 3 fields of view (FOVs) (Fig. 2n and Supplementary Fig. 10) were imaged (Supplementary Video 4) with a mean rolling Fourier ring correlation (rFRC) resolution²⁴ of 153 nm (Fig. 2o,p). Together, we demonstrated the first high spatiotemporal, 3D and high-throughput super-resolution cell imaging using RIED-ECL.

Because the reaction is triggered at the electrode surface¹⁰ and no excitation light is introduced, ECL inherently offers high surface sensitivity (Supplementary Note 4). RIED-ECL allows for the distinct observation of microtubule filaments near the electrode (Fig. 3a), as further evidenced by curvature analysis (Fig. 3b). We analysed the curvature and orientation of microtubule filaments across different mitotic phases (Extended Data Fig. 8). Notably, at the same mitosis stage, the RIED results exhibit smaller curvature values and reveal more concentrated orientation distributions compared with the fluorescence super-resolution results. This difference can be attributed to the high surface sensitivity of ECL, which mainly accounts for more linear microtubules near the surface.

Owing to its high sensitivity, ECL has been an established tool in ultrasensitive bioassay⁷. Building on this strength, the super-resolution ECL implementation further enables ultrasensitive single-cell biomarker imaging. We evaluated the sensitivity of RIED-ECL, defined as the detection threshold for imaging a biomarker, carcinoembryonic antigen (CEA), and compared it with results from fluorescence SACD (Fig. 3c,d and Supplementary Fig. 11). Despite the lower efficiency of ECL, quantitative analysis reveals an eightfold reduction in the detection threshold for investigating CEA using RIED-ECL than fluorescence SACD (Fig. 3e), aided by the elimination of autofluorescence in ECL. These results highlight the superior sensitivity of RIED-ECL and its ability to provide complementary insights to fluorescence super-resolution microscopy.

Given the basic principle of RIED, this chemical microscopy concept is universally applicable to other reaction-based luminescence imaging systems, including CL and BL—a subtype of CL occurring in live organisms. CL and BL only require standard biochemistry for intracellular imaging, obviating the need for electrochemical set-up in ECL (Fig. 4a). Different from conventional optical microscopy relying on light for illumination, RIED manipulates the imaging characteristics by tuning luminescence chemistry, allowing direct adaptations to diverse applications.

For the RIED-CL demonstration, we used a bioluminescence resonance energy transfer (BRET)-based enzyme catalysis system, green-enhanced nano-lantern (GeNL)²⁶, in which NanoLuc luciferase acts as the donor, mNeonGreen fluorescent protein functions as the acceptor and fluorofurimazine (FFz) serves as the substrate for imaging mitochondria in fixed COS-7 cells. Taking advantage of the uniform volume excitation in CL, RIED-CL realizes 3D mapping of the mitochondrial distribution with a step-scanning configuration (Fig. 4b and Methods), achieving lateral and axial resolutions of 102 nm and 221 nm, respectively (Fig. 4c–e and Supplementary Fig. 12). The reconstructed results were further confirmed by correlated imaging with the fluorescence SACD (Fig. 4d,e and Extended Data Fig. 9).

After benchmarking RIED-CL in fixed cells, we then transformed the same enzyme-based luminescence chemistry into live cells for BL demonstration. Using BL in live COS-7 cells, we explored the broad applicability of RIED for imaging a variety of intracellular organelles, including microfilaments (Fig. 4f), endoplasmic reticulum (Fig. 4g) and microtubules (Fig. 4h). Their reconstructed results are comparable with the fluorescence super-resolution images. Notably, RIED-BL achieves a spatial resolution of 117 nm, far surpassing conventional diffraction-limited BL imaging (Supplementary Fig. 13), demonstrating the versatility of RIED for super-resolution BL imaging.

Notably, by eliminating laser-induced phototoxicity and photobleaching, BL offers excellent biocompatibility, facilitating continuous super-resolution imaging of live cells while supporting cellular viability over extended periods under the reaction imaging conditions (Supplementary Figs. 14 and 15 and Supplementary Note 5). We compared RIED-BL with a live-cell super-resolution fluorescence technique—structured illumination microscopy (SIM)¹⁷. Under continuous laser illumination, SIM rapidly shows severe photobleaching for live-cell imaging within 18 min (Methods). On the other hand, RIED-BL maintains a stable luminescence state over the same period and even lasts for hours (Fig. 4i). Moreover, BL prevents photodamage, preserving the imaging area of mitochondria, whereas fluorescence imaging exhibits a marked loss of detectable structures over time (Fig. 4j). Taking advantage of this intrinsic stability, RIED-BL permits continuous ultralong-term live-cell imaging for 41 h, with a stable luminescence intensity and imaging contrast (Fig. 4k,l and Supplementary Video 5). Collectively, the extension to CL and BL emphasizes luminescent-reaction-enabled super-resolution microscopy as a light-excitation-free imaging modality offering chemistry-designed 3D capacity and long-term live-cell compatibility.

Next we applied RIED-BL for long-term observation of live-cell dynamics, enabling direct observation of fission and fusion of individual mitochondria (Extended Data Fig. 10) and their network dynamics. At an imaging resolution of 104 nm, we continuously monitored mitochondrial motions in live COS-7 cells (Fig. 5a, Supplementary Fig. 16 and Supplementary Video 5). Within a 55 × 55-µm² FOV, individual mitochondria were quantitatively analysed to obtain their mean velocity, diameter and counts over time (Fig. 5b). The analysis reveals faster movement near the cell periphery and slower motion in the perinuclear region, with velocity fluctuations in an hourly timescale at the perinuclear zone (Fig. 5a). We also found that, during the continuous observation, the number of mitochondria decreases after about 25 h, whereas the mean diameter begins to increase (Fig. 5b), probably reflecting the hallmarks of the apoptotic process²⁷.

Mitochondrial transfer is increasingly recognized as an important mechanism in intercellular communication, cellular repair and tumour microenvironment modulation^28,29. Using techniques such as flow cytometry, electron microscopy and fluorescence imaging^30,31,32, three transfer pathways, including tunnelling nanotubes, extracellular vesicles and free release/capture, have been identified³³. However, resolving the transfer dynamics at the single-mitochondrion level remains elusive. Here we tracked individual mitochondrial trajectories using RIED-BL. This enabled the continuous, ultralong-term super-resolution observation of mitochondrial behaviour beyond the constraints of conventional imaging windows (Fig. 5c and Supplementary Video 6). Our analyses reveal two distinct transfer modes: the direct motion and the indirect motion (Fig. 5d,e and Supplementary Fig. 17). The direct motion is characterized by relatively straight trajectories (Fig. 5f) and higher, more uniform velocities with average diffusion exponent of mean square displacement, MSD(α), of 1.34 (Methods). By contrast, the indirect mode exhibits a multiphase process, including initial steady movement, transient stalling and subsequent directed motion towards the recipient cell, accompanied by more variable trajectories (Fig. 5g) and heterogeneous velocities with average MSD(α) of 0.96. These observations offer a quantitative, whole-process view of mitochondrial transfer dynamics at the single-organelle level in live cells.

In summary, we have presented a chemistry-enabled imaging methodology, RIED, which achieves 3D super-resolution ECL, CL and BL intracellular imaging, matching the resolution of state-of-the-art live-cell fluorescence super-resolution microscopy while providing unique chemical-excitation-defined advantages.

Across the diverse classes of super-resolution fluorescence microscopy, there exists a fundamental trade-off in their spatiotemporal resolution, excitation depth, FOV, imaging duration and phototoxicity—a critical constraint for live-cell imaging³⁴ (Supplementary Table 1). On one hand, ultrahigh-resolution fluorescence techniques^{35,36,37,38,39} offer sub-nanometre localization precision but are typically limited in imaging speed or FOV, making them suitable for resolving local molecular organizations. On the other hand, live-cell fluorescence methods^12,13,14,17 enable rapid, low-phototoxicity super-resolution imaging over large FOVs but are often limited to moderate spatial resolution. Distinct from these fluorescent methods, RIED relies on reaction excitation and benefits from an intrinsic zero-light excitation background regime for high sensitivity, which shows a balanced spatial/temporal resolution, a large FOV and an ultralong-term continuous live-cell observation merit.

Looking forward, reaction-enabled super-resolution microscopy marks a transition from optically controlled excitation physics to reaction-tailored luminescence chemistry, enabling the design of new imaging opportunities. As the image contrast in reaction-enabled microscopy is driven by chemical reactivity, this chemical microscopy intrinsically visualizes the activity of the molecule rather than just molecular positions (Supplementary Fig. 18). Future coupling of this unique mechanism to native biochemical reactions may provide a further activity view into functional imaging analysis. Therefore, we anticipate that the development of RIED will highlight a chemistry-based super-resolution imaging methodology, shining a unique, reaction-driven light on biological processes.

Labelling the cellular structures with ECL probes

Preparation of Ru(bpy)₃ ²⁺-N-hydroxysuccinimide-ester-labelled antibody

1 ml, 1 mg ml⁻¹ goat anti-rabbit immunoglobulin G (IgG) antibody (Huabio, HA1002) was dialysed (Viskase, Membra-Cel MD44) overnight at 4 °C in 3 l of 0.01 M phosphate buffer saline (PBS, pH 7.6, Sigma) and adjusted to a concentration of 2 mg ml⁻¹. Then 1 mg of Ru(bpy)₂(mcbpy-O-Su-ester)(PF₆)₂ (Aladdin, R131404) was dissolved in 50 µl dimethyl sulfoxide and added to the purified goat anti-rabbit IgG antibody immediately. The reaction mixture was incubated at 25 °C for 1 h. Subsequently, the unreacted Ru(bpy)₂(mcbpy-O-Su-ester)(PF₆)₂ was removed using dialysis (4 °C, in 3 l PBS for 6 h, with buffer replacement every 2 h). The obtained labelled antibody was diluted with PBS to a final concentration of 1 mg ml⁻¹ for use.

Cell culture and immunolabelling

The HeLa cells, COS-7 cells and MCF-7 cells (Shanghai Institute of Biochemistry and Cell Biology, Chinese Academy of Sciences) were cultured at 37 °C with 5% CO₂ in high-glucose Dulbecco’s modified Eagle’s medium (DMEM, Gibco) mixed with 10% foetal bovine serum (FBS, Gibco) and 1% penicillin-streptomycin solution (Sangon Biotech). When reaching about 90% confluency, the cells were digested by 0.25% trypsin-ethylenediaminetetraacetic acid (trypsin-EDTA, Thermo Fisher Scientific) solution for 1 min and then transferred to sterilized indium tin oxide (ITO) coverslips. After 24 h, the transferred cells were rinsed with PBS three times and immediately fixed for 30 min at room temperature with 4% paraformaldehyde (PFA, Sangon Biotech). The excess PFA was removed by washing the samples with PBS. Then the cells were permeabilized and blocked with 1% Triton X-100 (Sigma-Aldrich) mixed with 5% bovine serum albumin (BSA, Sangon Biotech) in PBS for 1 h at room temperature. After washing, the cells were stained by rabbit anti-alpha tubulin antibody (Abcam, ab52866) with a dilution of 1:100 in 5% BSA/PBS blocking buffer overnight at 4 °C. For mitochondrial imaging, the cells were stained with rabbit anti-TOMM20 antibody (Abcam, ab186735). For CEA imaging, the cells were stained with rabbit anti-carcinoembryonic antigen CEA antibody (Abcam, ab133633). For integrin imaging, the cells were stained with rabbit anti-integrin alpha 5 antibody (Abcam, ab275977) under the same conditions. The cells were then washed three times with PBS and stained with 10 µg ml⁻¹ Ru(bpy)₃²⁺-labelled goat anti-rabbit IgG antibody at 37 °C for 2 h. Finally, the cells were washed three times and imaged. Cell lines were authenticated using short tandem repeat analysis by the supplier. All cell lines were routinely tested and confirmed to be negative for mycoplasma contamination.

Labelling the cellular structures with CL and BL probes

Construction of mammalian expression vectors

CL and BL labelling of the intracellular targets was achieved by using a genetically encoded BRET probe (GeNL), which used NanoLuc luciferase as the donor and mNeonGreen fluorescent protein as the acceptor in this study. The only difference is that CL was applied to fixed cells, whereas BL was applied to live cells. The GeNL system was constructed according to the reference method²⁶. All targeted sequences used for cell transfection are listed in Supplementary Table 2.

Cell culture and transfection

HeLa, COS-7 and MCF-7 cells were transfected at approximately 70–90% confluence with 0.25 μg of plasmid DNA using Lipofectamine 3000 (Thermo Fisher Scientific). After 12 h, the medium was replaced with phenol red-free DMEM for subsequent live-cell BL imaging.

ECL imaging

ITO coverslips were prepared using the reported protocol⁶. An inverted optical microscope (IX83, Olympus) with an oil immersion 100× objective (numerical aperture (NA) = 1.45, Olympus) was used. For large FOV imaging, an oil immersion 40× objective (1.35 NA, Olympus) was used. A 488-nm laser beam (MDL-D-488-200 mW, CNI) was delivered through a single-mode fibre and a collimator (FP5-F5AP-A, LBTEK) and then coupled into the microscope for the fluorescence excitation of the Ru(bpy)₃²⁺ probe for cross-validation. The images were captured by a water-cooled (178 K) electron-multiplying charge-coupled device (EMCCD) camera (iXon Ultra 897, Andor). The ECL images were collected under an electron multiplying (EM) gain of 500 and different exposure times (20 ms, 200 ms, 500 ms, 1,000 ms, 3,000 ms).

For ECL excitation, a three-electrode electrochemical system was used with ITO, Ag/AgCl and Pt plate (10 mm × 10 mm × 0.1 mm) as the working electrode, the reference electrode and the counter electrode, respectively. 100 mM TPrA (Energy Chemical) and 100 mM Bis-tris (Energy Chemical) in 0.01 M PBS were used as the ECL imaging buffer, respectively. An electrochemical workstation (CHI 760e, CH Instruments) was used to control the applied voltage and perform cyclic voltammetry. The excitation voltage was varied between 0.9 V and 1.8 V versus Ag/AgCl. The cyclic voltammetry scan range was between 0 V and 2 V, with a scan rate of 0.1 V s⁻¹.

2D-ECL image sequence was acquired with the electrode surface as the focal plane and 3D-ECL image sequence was acquired in axial scanning mode with a scanning step of 200 nm starting from the electrode surface (0 µm) to the upper layer (1.6 µm) while synchronously increasing the applied voltage from 1 V to 1.8 V with a 0.1-V step. For large FOV imaging, the stage was shifted to each of the nine sub-FOVs (512 × 512 pixels, about 204 µm × 204 µm) with 20% overlap.

CL imaging

CL images were collected under an EM gain of 500 and an exposure time of 500 ms/1,000 ms. 10 μM FFz (Promega) in PBS buffer was used for CL excitation. NanoLuc first catalyses FFz to generate CL, which transfers to the proximity of mNeonGreen fluorescent protein for luminescence. An axial scanning stack with a 200-nm step was acquired here for 3D-CL imaging of mitochondria, which was subsequently concatenated into a 3D projection.

BL imaging

Live-cell imaging was conducted at 37 °C in 5% CO₂ using an inverted microscope (Ti2e, Nikon) equipped with oil immersion objectives (100×/1.42 NA, Nikon; 60×/1.49 NA, Nikon) and a live-cell workstation (STXG, Tokai Hit). A 488-nm laser beam (Oxxius, L4Cc) was introduced for the fluorescence cross-validation. The image stacks were captured by the EMCCD camera. The BL images were collected under an EM gain of 500 and exposure times of 100 ms, 500 ms or 1,000 ms. The BL imaging buffer (4 μM/6 μM/10 μM FFz prepared in phenol red-free DMEM, supplemented with 10% FBS) was refreshed at a rate of 40–250 µl min⁻¹ using a peristaltic pump (Masterflex, Ismatec Reglo ICC) during BL imaging to obtain a steady luminescence signal, while minimizing the cytotoxicity induced by substrate-generated radicals.

Cell viability evaluation

To assess the cellular impact of BL, we used an established cell physiology evaluation metric—the phototoxicity fitness time trial⁴⁰. Cell viability and physiological integrity were assessed through division time, cellular diameter, mitochondrial dynamics, membrane integrity and viability assay. A continuous 24-h bright-field observation was conducted for the cell division with 4 µM FFz in the DMEM. The division time was determined by TrackMate⁴¹ (a plugin of Fiji/ImageJ). The membrane integrity was determined by a commercial dye, propidium iodide (PI, Thermo Fisher Scientific). Dead cells with compromised membrane integrity were subsequently identified and quantified by measuring the red nuclear fluorescence signals.

RIED reconstruction

Main steps of RIED

In ECL imaging experiments, strong sampling noise interferes with the effective extraction of ECL temporal fluctuations. To mitigate this, we first applied a 2D Gaussian filtering preconditioning step to the raw ECL stack, effectively suppressing high-frequency noise beyond the passband of the imaging system. Second, Fourier interpolation was performed to upsample the ECL stack along the x–y direction, recalculating the images on a finer grid. This process ensured sufficient pixel support for the subsequent resolution enhancement. Third, a pre-deconvolution step using accelerated Richardson–Lucy (RL) deconvolution was used to reduce the sampling noise and enhance the resolution¹². These preprocessing steps ensured that the subsequent entropy-weighted correlation cumulant focuses on enhancing the resolution using the ECL temporal responses on a finer grid, without being affected by the noise or the spurious fluctuations. Finally, the post sparse deconvolution with dual constraints was executed as the last step to maximize the image quality and the spatial resolution (fulfilling a \(2\sqrt{2}\text{-fold}\) improvement in 3D resolution). The same RIED workflow was used for CL/BL unless otherwise specified.

Entropy-weighted correlation cumulant

Entropy was used to identify ECL emitters, which can be considered as the expected information content of the ECL photon events. The entropy value is higher if there are more photon events, which makes the pixel contain greater intensity variation and higher information content. By calculating the entropy value for each pixel, the ECL signals were effectively highlighted against the random sampling noise. Moreover, as entropy captures the spatial distribution of ECL emitters, the resulting entropy map provides a weighting scheme for correlation analysis, compensating for the spatiotemporal heterogeneity in the ECL emission. A sample in the ECL imaging system can be seen as a collection of individual ECL emitters (N) located at position r_k exhibiting stochastic and independent emission behaviours, which can be described as

in which h, l and w represent the PSF of the ECL imaging system, the emitter luminescence brightness and the emitter time-dependent emission events, respectively. To exploit the individual blinking characteristic of each ECL probe molecule, we calculated the correlation cumulant to deplete the pixels dominated by overlapping emitters and narrow the PSF, which can be given as

in which δR(r, t) = R(r, t) − ⟨R(r, t)⟩_t and ⟨∙⟩_t denotes the time averaging. As the emission events of individual ECL probe molecules are independent and uncorrelated with those of the others, the correlation terms between different emitters (i ≠ j) vanish and only autocorrelation terms remain in the result. Then the spatiotemporal cross-correlation cumulant was calculated for interpolation pixels between the original adjacent pixels:

in which r₁ and r₂ represent the adjacent positions of original pixels and (r₁ + r₂)/2 is the geometric centre of r₁ and r₂. The cross-correlation cumulant takes advantage of the high-contrast blinking of ECL probe molecules, filtering out the pixels dominated by overlapping emitters in an effective way. When taking the second-order correlation cumulant with zero time lag, the reconstruction results in a PSF narrowing by a factor of \(\sqrt{2}\).

Notably, although the high contrast ratio induced by ECL reactions enables considerable resolution improvement, the inherent spatiotemporal heterogeneity of the ECL probe molecules tends to introduce discontinuities in the correlation reconstruction. Therefore we introduced the Shannon entropy as a weighting factor for compensation:

in which P is the intensity probability distribution of the pixel located at position r. The entropy measures the expectation of the information content to judge whether there exist ECL emitters or not. A high entropy value indicates a dense distribution of the ECL probe molecules, which provides an emitter distribution map to weight the correlation reconstruction and compensate for the spatiotemporal heterogeneity. The entropy-weighted autocorrelation is given as:

Also, the cross-entropy was calculated to measure the information content between the original adjacent pixels:

in which Q is the intensity probability distribution of the neighbouring pixel. Thus, the cross-entropy weighted cross-correlation was calculated as:

Post sparse deconvolution

In general, to achieve the optimal spatial resolution under the Nyquist sampling criterion, the PSF must cover at least a 3-pixel-square area, ensuring continuity along the lateral axes. Furthermore, ECL emission signals are blurred by the optical system and further degraded by noise during detection, making the true signal even sparser than the recorded one. Accordingly, the continuity prior and the sparsity prior are involved in RIED to constrain the final step deconvolution to reduce the artefacts and improve the resolution and, thus, the post sparse deconvolution is given as:

in which the first term represents the distance between the result of entropy-weighted correlation EC and the recovered image y, h is the PSF of the ECL imaging system, the second and third terms represent the continuity and sparsity constraints, respectively, and λ_c and λ_s denote the weight factors to balance the image continuity and the resolution improvement, respectively.

Specifically, an optional iterative wavelet analysis step was designed to remove the out-of-focus noise in CL/BL imaging. The out-of-focus luminescence emission can be estimated by iteratively extracting the lowest-frequency wavelet bands of the entropy-weighted correlation cumulant¹⁷. The reconstructed result is therefore given by:

in which IWTA is the iterative wavelet analysis for estimating out-of-focus noise from EC.

3D-RIED reconstruction

To achieve 3D super-resolution ECL reconstruction, RIED can be easily transformed into the 3D form. Specifically, the ECL imaging stacks at different depths were consecutively collected through synchronous control of the voltage and the imaging focal plane change. Then the preprocessing of Gaussian filtering, Fourier interpolation, pre-deconvolution and entropy-weighted correlation calculation was conducted on each ECL imaging stack at different depths to reduce the sampling noise and enhance the resolution in the x–y direction.

After that, the results of the entropy-weighted correlation obtained at different depths were concatenated into a 3D matrix. To match the resolution improvement and resolve more subtle details in the z-direction, the Fourier interpolation was used to axially upsample the 3D matrix to result in smaller axial size voxels. As a final step, the 3D sparse deconvolution approach was applied to the Fourier-interpolated 3D matrix to increase the spatial resolution.

High-throughput super-resolution reconstruction

For high-throughput large-FOV super-resolution ECL imaging, the RIED super-resolution reconstruction was performed for each sub-FOV with a temporal upsampling strategy. The Fourier interpolation was used to upsample the ECL raw images along the t-direction, which provided a finer time interval to describe the ECL blinking, resulting in a decrease in the temporal heterogeneity of the ECL emission (Supplementary Fig. 7). In the final step, we used the BigStitcher ImageJ plugin⁴² to stitch the super-resolution reconstruction tiles (3 × 3) to a full super-resolution image of about 0.53 × 0.53 mm². Segmentation and curvature/orientation analyses of microtubule filaments from different mitosis phases were performed using a microtubule filament retrieval computational tool SIFNE⁴³ with default parameters.

Simulation analysis of reconstruction fidelity under heterogeneous emission

To assess the potential reconstruction artefacts under low-photon and heterogeneous-emission conditions, we performed quantitative simulations in which two types of emission heterogeneity were explicitly defined. Luminescence yield heterogeneity, reflecting the spatially non-uniform photon output across the emitters, was modelled as a log-normal distribution η(x, y) ~ log-normal(µ, σ²). Blinking kinetics heterogeneity, describing spatially distributed on/off switching rates, was modelled as a beta distribution τ(x, y) ~ beta(α, β). Reference parameters for typical heterogeneity levels in different luminescence modalities were estimated from the experimental data, with representative values of σ = 0.6, α = β = 3 (ECL); σ = 0.3, α = β = 8 (CL); and σ = 0.2, α = β = 8 (BL). Four synthetic heterogeneity levels were then generated: low (σ = 0.1, α = β = 10), medium (σ = 0.3, α = β = 7), high (σ = 0.6, α = β = 4) and extremely high (σ = 0.8, α = β = 2). For each heterogeneity level, dual-line structures were simulated and reconstructed using RIED with different frame numbers (100, 200, 500 and 1,000 frames). Reconstruction fidelity was quantified using the peak signal-to-noise ratio (PSNR) and RSE against the ground truth. The results show that noticeable reconstruction deviations arise only under the combined conditions of extremely high heterogeneity and limited frame number. Under other conditions, including low-to-high heterogeneity levels with sufficient frames, the reconstructed structures remain largely consistent with the ground truth, with no evident artefact amplification. Given that experimental ECL, CL and BL systems in this work typically fall within the low-to-high heterogeneity range, these results suggest that RIED can recover structural features with good fidelity under standard experimental conditions.

Performance metrics

Spatial resolution

The FRC resolution and rFRC map²⁴ were calculated using two independent frames with identical content under the same imaging conditions. These frames were obtained by splitting the raw ECL image sequence into two subsets and reconstructing them separately.

SSIM

The SSIM⁴⁴ is defined as

in which x represents the reference image, which is the RIED reconstruction result from a 1,000-frame ECL image stack, y denotes the corresponding RIED reconstructions using ECL image stacks ranging from 20 to 800 frames, µ_x and µ_y are the averages of x and y, respectively, σ_x,y is the covariance of x and y, σ² is the variance and c₁ and c₂ are the variables used to stabilize the division with a small denominator.

PSNR

The PSNR is given by:

in which x represents the reference image, which is the RIED reconstruction result from 1,000-frame ECL images, y denotes the corresponding RIED reconstructions using ECL image stacks ranging from 20 to 800 frames, m and n denote the row and the column of the image, and MAX denotes the maximum pixel value of the image.

Error analysis

Error maps and quantitative metrics were calculated using the SQUIRREL framework¹⁶. The reconstruction image was convolved with an estimated Gaussian kernel (resolution scaling function) to generate a resolution-scaled image, followed by linear intensity rescaling to match the raw summed reference. A pixelwise absolute difference map was computed. Two global metrics were derived: the RSE (root mean square error between the resolution-scaled image and the reference) and the RSP.

Comparing super-resolution reconstruction algorithms

We compared the reconstruction performance against prevalent fluctuation-based methods on our ECL image stack, including SOFI¹³, ESI⁴⁵, eSRRF¹⁴ and SACD¹².

SOFI

For SOFI reconstruction, a Fourier interpolation operation was performed to upsample the ECL stack along the x–y direction, after which a second-order autocorrelation cumulant was calculated. For the 3,000-frame CL data, fourth-order autocorrelation cumulants were also computed.

ESI

Image labelled with ‘ESI’ was reconstructed through the ESI ImageJ plugin with ‘image in output’ as ‘1’ and ‘Order’ as ‘2’, and other options with the default parameters.

eSRRF

Image labelled with ‘eSRRF’ was obtained through the eSRRF ImageJ plugin by means of the temporal radiality average reconstruction, with ‘Magnification’ set as ‘2’, ‘Radius’ set as ‘5’ and ‘Sensitivity’ set as ‘1’, with other parameters remaining default.

SACD

A Fourier interpolation step was performed to upsample the raw ECL stack along the x–y direction (×2), obtaining a smaller pixel size without changing the image content. Then a 2D RL deconvolution was applied to each ECL image, improving the resolution while reducing the sampling noise. After that, a second-order autocorrelation cumulant was calculated. To match the pixel size of the RIED reconstruction, a Fourier interpolation was again used, resulting in a finer pixel grid and a larger pixel number (×2). Finally, a post-RL deconvolution was applied to the interpolated cumulant, further enhancing the resolution. For the 3,000-frame CL data, fourth-order autocorrelation cumulants were also calculated.

Sparse deconvolution

A modified iterative wavelet transform was performed on the fluorescence images estimating and removing the background noise from out-of-focus emissions. Next, a Fourier upsampling operation was conducted to provide pixel size support for the subsequent resolution enhancement. In the final step, a continuity–sparsity joint constraints deconvolution was applied on the background-removed and interpolated image, resulting in a resolution enhancement reconstruction with minimized artefacts and improved robustness.

Pre- and post-deconvolution for comparative methods

To enable fair comparisons with other fluctuation-based super-resolution reconstruction methods, ESI and eSRRF were also processed with pre- and post-deconvolution steps. The pre-deconvolution consists of Gaussian pre-filtering, Fourier interpolation (×2) and RL deconvolution applied to each frame. The post-deconvolution consists of a second RL deconvolution applied to the final reconstructed image. All other parameters were kept identical to the standard implementations of each method.

SIM for live-cell imaging

To demonstrate the biocompatibility and excellent imaging time of RIED, we conducted parallel live-cell fluorescence correlation experiments for mitochondrial imaging. A commercial HIS-SIM (CSR Biotech) imaging system was used here⁴⁶, which is based on an inverted fluorescence microscope (IX83, Olympus). A 488-nm laser beam (L4Cc, Oxxius), oil objective (100×/1.5 NA, Olympus) and live-cell station (H301, OKO Lab) were used for mNeonGreen fluorescent protein excitation, signal collection and live-cell incubation (maintained at 37 °C and 5% CO₂ in a humidified chamber). A scientific complementary metal–oxide–semiconductor (sCMOS; Kinetix, C15440-20UP, Hamamatsu) camera was used for recording raw data videos. During fluorescence excitation, the power of the 488-nm laser was set to 5 mW mm⁻² to minimize the photodamage to live cells. Continuous acquisition of fluorescence data was conducted under an exposure time of 100 ms. Finally, the SIM images were analysed and reconstructed by HiFi-SIM⁴⁷. The imaging duration was quantitatively defined as the point at which the fluorescence intensity and contrast declined to 30% and 50% of their initial values, respectively.

Mitochondrial tracking and analysis

Reconstructed long-term super-resolution BL image sequences of mitochondria were first median-filtered, followed by automatic threshold-based binarization to generate masks for mitochondrial recognition. The binarized data were then imported into the TrackMate plugin⁴¹ in ImageJ for automated tracking. The mask detector module was used to identify mitochondria from the predefined binary regions, allowing localization of the irregular subcellular structures. Mitochondrial linking was realized using the Simple LAP tracker. The resulting trajectories, containing temporal coordinates and instantaneous velocities, were exported for the subsequent analysis of mitochondrial counts, diameter and velocity.

For intercellular mitochondrial transfer tracking, the manual tracking mode was used. Trajectories were recorded during the full transfer process and both before and after the event could be clearly observed. Cell segmentation was performed using the Cellpose 4.0 generalist algorithm⁴⁸ and further refined by analysing the mitochondrial motion direction and origin. The extracted trajectory data, including time, position and velocity, were used for the subsequent transfer mode analysis. Mitochondrial transfer behaviour was quantified by calculating the time-dependent MSD. For each trajectory, the MSD at a time lag τ was computed using:

To minimize the statistical uncertainty owing to the reduced sampling at large time lags, the analysis was restricted to the first 25% of the total trajectory duration. To determine the diffusion mode, the anomalous diffusion exponent (α) was derived by fitting the MSD curves to a power-law model:

where D denotes the propotionality factor determining the magnitude of MSD. Linear regression was performed on the log–log-transformed data. All computational analysis and curve fitting were implemented using MATLAB.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

We have provided the full code and demo ECL/BL data to perform RIED super-resolution reconstruction in this paper. The code is also available from Zenodo (https://doi.org/10.5281/zenodo.20328840) (ref. ⁴⁹), or GitHub (https://github.com/SR-Wiki/RIEDm) (ref. ⁵⁰).

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Author notes

1. These authors contributed equally: Wenxin Zhu, Chi Zhang, Jiahui Gui

Authors and Affiliations

1. Laboratory of Experimental Physical Biology, Department of Chemistry, Zhejiang University, Hangzhou, China

   Wenxin Zhu  (朱文鑫), Chi Zhang  (张弛), Yibo Yang  (杨熠博), Yuxin Wan  (万宇欣), Xin Wang  (王鑫), Ao Guo  (郭奡), Ziqing Zhang  (张紫晴) & Jiandong Feng  (冯建东)

2. Innovation Photonics and Imaging Center, School of Instrumentation Science and Engineering, State Key Laboratory of Matter Behaviors in Space Environment, Frontier Science Center for Interaction between Space Environment and Matter, Harbin Institute of Technology, Harbin, China

   Jiahui Gui  (桂家辉), Liying Qu  (曲丽颖), Zhenqian Han  (韩镇谦) & Weisong Zhao  (赵唯淞)

3. College of Optical Science and Engineering, Zhejiang University, Hangzhou, China

   Jiandong Feng  (冯建东)

4. Institute of Fundamental and Transdisciplinary Research, Zhejiang University, Hangzhou, China

   Jiandong Feng  (冯建东)

Contributions

J.F. and W. Zhu initiated the project and developed the imaging methodology; J.G. and W. Zhao developed the super-resolution algorithm; W. Zhu, Y.Y., Y.W., A.G. and Z.Z. performed the ECL and FL experiments; C.Z., W. Zhu and Y.W. performed the BL and CL experiments; W. Zhu, J.G., C.Z., X.W., L.Q. and Z.H. analysed the data; J.F. and W. Zhao conceived and supervised the study; W. Zhu, J.G., W. Zhao and J.F. wrote the manuscript. All authors participated in the discussions and data interpretation.

Corresponding authors

Correspondence to Weisong Zhao  (赵唯淞) or Jiandong Feng  (冯建东).

Competing interests

J.F., W. Zhu, W. Zhao, J.G. and C.Z. have filed a pending patent application on the presented method (patent application number CN 202610137019.3). The other authors declare no competing interests.

Peer review information

Nature thanks David Baddeley, Johan Hofkens, Boris Louis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Reporting Summary (download PDF )

Peer Review File (download PDF )

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