Article https://doi.org/10.1038/s41467-025-60709-1
Structural Repetition Detector for multi-
scale quantitative mapping of molecularcomplexes through microscopy
Afonso Mendes1,2,3, Bruno M. Saraiva1,2,3, Guillaume Jacquemet4,5,6,7,
João I. Mamede8, Christophe Leterrier9& Ricardo Henriques1,3,10
From molecules to organelles, cells exhib it recurring structural motifs across
multiple scales. Understanding these s tructures provides insights into their
functional roles. While super-resolut ion microscopy can visualise such pat-
terns, manual detection in large dataset si sc h a l l e n g i n ga n db i a s e d .W ep r e s e n t
the Structural Repetition Detector (SR eD), an unsupervised computational
framework that identi fies repetitive biological st ructures by exploiting local
texture repetition. SReD formulates structure detection as a similarity-
matching problem between local image reg ions. It detects recurring patterns
without prior knowledge or constra ints on the imaging modality. We
demonstrate SReD ’s capabilities on various fluorescence microscopy images.
Quantitative analyses of diffe rent datasets highlight SReD ’s utility: estimating
the periodicity of spectrin rings i n neurons, detecting Human Immunode fi-
ciency Virus type-1 viral assembly, a nd evaluating microtubule dynamics
modulated by End-binding protein 3. Our open-source plugin for ImageJ or FIJI
enables unbiased analysis of repetitive structures across imaging modalities indiverse biological contexts.
Biological systems exhibit structural repetition across multiple
scales, from biomolecules to supramolecular assemblies and cel-lular structures
1. Understanding these patterns is crucial for iden-
tifying their functional signi ficance and underlying biological
processes2. Microscopy techniques offer molecular-level resolu-
tion but manually detecting repetitive motifs in large datasets isimpractical, biased, and expertise-dependent
3. To address these
limitations, machine learning, particularly deep convolutionalneural networks (CNNs), has been employed to detect and segmentbiological structures automatically
4. However, CNNs require
extensive labelled training data, inheriting biases5.P r e v i o u smethods enable unbiased registration but need point data, limiting
their applicability6,7. We present the Structural Repetition Detector
(SReD), an unsupervised framework to identify repetitive biologi-
cal structures by exploring local texture redundancy. SReD for-
mulates structure detection as similarity matching between localimage regions, allowing pattern detection without prior knowledgeor microscopy modality constraints. We demonstrate SReD ’s cap-
abilities on fluorescence microscopy images of diverse cell types
and structures, including microtubule networks, nuclear envelope,pores, and virus particles (Fig. 1). SReD generates Structural
Repetition Scores (SRSs) highlighting regions with repetitiveReceived: 30 September 2024
Accepted: 3 June 2025
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1Optical Cell Biology group, Instituto Gulbenkian de Ciência, Oeiras, Portugal.2Gulbenkian Institute for Molecular Medicine, Oeiras, Portugal.3Instituto de
Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal.4Turku Bioimaging, University of Turku and Åbo Akademi
University, Turku, Finland.5Faculty of Science and Engineering, Cell Biology, Åbo Akademi University, Turku, Finland.6InFLAMES Research Flagship Center,
Åbo Akademi University, Turku, Finland.7Turku Bioscience Centre, University of Turku and Åbo Akademi University, Turku, Finland.8Department of Microbial
Pathogens and Immunity, Rush University Medical Center, Chicago, IL, USA.9Aix Marseille Université, CNRS, INP UMR7051, NeuroCyto, Marseille, France.
10UCL Laboratory for Molecular Cell Biology, University College London, London, United Kingdom. e-mail: christophe.leterrier@univ-amu.fr ;
r.henriques@itqb.unl.pt
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textures. Users can provide arti ficial blocks or extract them from
the data for repetition analysis. An unbiased sampling schememaps global repetition by testing every possible image block as a
reference (Supplementary Note 1). We showcase SReD ’s utility
through three datasets: 1) spectrin rings in neuronal axons, accu-rately estimating ring periodicity and pinpointing periodic pat-terns, 2) Human Immunode ficiency Virus (HIV) Gag assembly,
mapping viral structures without structural priors, and 3) dynamicEnd-Binding Protein 3 (EB3) and microtubule structures, assessing
structural displacement and stability over time. Our open-sourceImageJ/FIJI
8,9plugin enables versatile, unbiased analysis of redun-
dancy in microscopy images. SReD advances computational
microscopy by providing a generalised framework for detectingrepetitive structures without labelled training data or single-molecule localisation input, facilitating the quantitative study ofstructural motifs across scales in diverse imaging datasets.
(a)1-to-All: Simulated
repetition
(c)All-to-All: Single Scale
(d)All-to-All: Multiscale(b)1-to-All: Empirical repetitionInputInput Repetition mapReference blocks
Repetition mapReference blocks
1.0
Relative repetition0.01.0 1.0Scale1.0
0.0 0.0 0.01-to-All
Change reference blockAll-to-All
Test blocks
Reference blockInput
Depth/Time
SReD maps structural repetition against individual
blocks (1-to-all) or all possible blocks (all-to-all)
Fig. 1 | Applications of the Structural Repetition Detector (SReD) algorithm in
fluorescence microscopy. a Detection of Structural Repetition Using Simulated
Blocks: Microtubules imaged with STORM analysed for repetitive patterns using
simulated structural blocks. The analysis was performed using SReD ’s‘block
repetition ’mode, which features a ‘1-to-all ’matching scheme where a reference
block is compared with all the remaining image blocks. A rotation-variant corre-lation metric (Pearson ’s correlation coef ficient) was used to account for structure
orientation. Coloured regions in the repetition map correspond to repetitions of
same-coloured blocks above. Scale bar: 2 µm.bDetection of Structural Repetition
Using Empirical Blocks: HeLa cell nuclei stained with DAPI used to detect repetitivestructural patterns using manually extracted empirical reference blocks. The ana-
lysis was performed in a similar manner as shown in ( a) but the reference blocks are
extracted directly from the input data. Coloured regions in the repetition mapcorrespond to repetitions of same-coloured blocks in the previous subpanel. Scale
bar: 30 µm.cGlobal Repetition Detection: Jurkat cell expressing inducible HIV Gag-EGFP fusion protein analysed using global repetition detection and a rotation-
invariant metric ( ‘absolute difference of standard deviations ’). The analysis was
performed using SReD ’s‘global repetition ’mode, which features an ‘all-to-all ’
matching scheme where all image blocks are compared with all the remaining
image blocks. The repetition map reveals structures not easily detectable in inputimage and their relative frequency. Scale bar: 5 µm.dMultiscale Global Repetition:
Xenopus laevis nuclear pores imaged with STORM analysed using different-sized
receptive fields to detect structural repetition at various scales. The analysis was
performed using SReD ’s‘global repetition ’mode, where each iteration used a dif-
ferent block-to-image size ratio. The repetition map identi fies repeated structures
from single nucleoporins (orange) to nucleoporin clusters (blue) and nuclear pore
units (magenta). A rotation-invariant correlation metric was used to analyse
structures irrespective of their orientation. Scale bar: 120 nm. Centre panel: Sim-plified SReD algorithm work flow, illustrating key steps from input preprocessing to
repetition map generation.Article https://doi.org/10.1038/s41467-025-60709-1
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Results
Implementation, theoretical foundation and core functionality
SReD is an open-source ImageJ and Fiji8,9plugin that leverages
graphics-processing unit (GPU) acceleration to identify repetitive pat-
terns in microscopy images. The algorithm ’sw o r k flow, outlined in Fig. 1
(centre panel), begins with the application of the GeneralisedAnscombe Transform (GAT) to stabilise noise variance (SupplementaryNote 1)
10This step addresses the noise in microscopy images, which
often exhibit Poisson and Gaussian noise. The GAT nonlinearly remapspixel values to produce an image with near-Gaussian noise and stabi-lised variance, preserving local contrast and overall image statistics.This stabilisation is essential for robust downstream processing, miti-gating violations of normality, homoscedasticity, and outlier assump-tions that can compromise correlation metrics. Following noisestabilisation, SReD generates a relevance mask to exclude regions
lacking substantive structural in formation, based on local texture
prominence quanti fied by variance (Supplementary Note 1; Supple-
mentary Fig. 1). The rationale is that structural elements presentthemselves as regional image textures with non-zero variance. There-fore, areas devoid of structure will exhibit minimal texture. Due to theubiquitous presence of noise, we calculate a threshold at which imagetexture is minimal by estimating the average noise variance
11.T h e final
relevance threshold is de fined by multiplying the estimated average
n o i s ev a r i a n c eb ya na d j u s t a b l ec o n s t a n t ,w i t ht h ed e f a u l ts e ta t0 .T h i sproduces a binary mask outlining areas with suf ficient structural con-
tent. The analysis proceeds using reference blocks, either simulated or
sampled from the image (i.e., empirical). These blocks are matched
against the input using correlation metrics to generate repetition maps(Supplementary Note 1). Our algorithm leverages a custom samplingscheme in which a reference block is compared with all possible testblocks in the image. The scheme can be ‘1-to-all ’or ‘all-to-all ’,
depending on the application. The first requires a user-provided
reference block, while the latter provides unbiased structure detection.The comparisons between blocks consist of calculating correlationmetrics. The correlation metrics can be rotation-variant (e.g., Pearson ’s
correlation coef ficient) or -invariant (e.g., absolute difference of stan-
dard deviations (ADSD))(Supplementary Note 1). In both cases, the
blocks ’dimensions are prede fined by the user to match a speci fic scale.
A repetition map is calculated for each ‘1-to-all ’comparison, where each
pixel is assigned a score (named Structural Repetition Score, or SRS),which re flects the similarity between the local neighbourhood centred
at that position and the reference block. Finally, the repetition map isnormalised to its range. The SRS is given by Eq. 1.
SRS X
i,Yj/C16/C17
=Corr Xi,Yj/C16/C17
/C1Rel Yj/C16/C17
ð1Þ
where Xi=x1,x2,...,xn/C8/C9
and Yj=y1,y2,...,yn/C8/C9
are the reference
and test blocks with size n(in pixels) centred at pixel positions iand j,
and
Rel Yj/C16/C17
=0,if Var Yj ðÞ≤Var
1,if Var Yj ðÞ>Var(
ð2Þ
the binary ‘relevance ’label of the test block is calculated as in Eq. 2,
where Varis the average noise variance of the input image. To analyse
local textures and calculate a single value for each, the reference andtest blocks require a de fined centre. Therefore, the blocks ’dimensions
need to be odd, and as a result, i=[ (r
h,H−rh]a n d j=[rw,W−rw], where
rwand rhare the blocks ’width and height radii, and Wand Hare the
input image ’s width and height. In the block repetition mode, the input
image is probed for repetitions of a single reference block using the ‘1-
to-all ’sampling scheme. This generates a repetition map re flecting the
likelihood of the reference pattern occurring at that each location. Inthe global repetition mode, SReD enables unbiased structure analysis
by using the entire universe of image blocks as a reference ( ‘all-to-all ’
sampling scheme). Each reference block generates a repetition mapthat is averaged, and the average value is plotted at the coordinates
corresponding to the centre of the reference block. The average uses
an exponential weight function based on the distance between thestandard deviations of the blocks in each comparison, which enhancesstructural details. Therefore, the global repetition scores represent therelative repetition of a local texture across the image. Mathematically,the global SRS is calculated as in Eq. 3.
GSRS X
i,Yj/C16/C17
=P
jCorr Xi,Yj/C16/C17
/C1WXi,Yj/C16/C17
/C1Rel Yj/C16/C17
N/C1P
jWXi,Yj/C16/C17 ð3Þ
where Nis the size of the input image (excluding borders with length
equal to the XY radii of the blocks). The exponential weight function is
defined in Eq. 4.
WXi,Yj/C16/C17
=e/C0σXi/C0σYj/C12/C12/C12/C12/C12/C122
Varð4Þ
Here, in Eq. 4.,σXiandσYjare the standard deviations of the reference and
test blocks. The resulting repetition maps highlight regions likely tocontain structural repetitions. Non-linear mapping can be applied toenhance the contrast between different SRSs within the repetition maps,facilitating visual in terpretation and subse quent analysis. In our
experience, we have found that applying a power transformation tothe SRSs often yields the most effect ive enhancement. This transforma-
tion involves raising each SRS value to a speci fice x p o n e n t .T h ec h o i c eo f
exponent plays a crucial role in determining the degree of contrastenhancement. In this study, we explored a range of exponents between10 and 10,000. Typically, we initiate the analysis with an exponent of 10and iteratively adjust it based on the visual assessment of the resulting
repetition map. For datasets with sub tle structural rep etitions or low
signal-to-noise ratios, higher exponents may be necessary to amplify thedifferences between SRSs and reveal hidden patterns. Conversely, fordatasets with prominen t structural repetitions, lower exponents may
suffice to achieve adequate contrast enhancement without introducing
excessive noise ampli fication. The optimal exponent ultimately depends
on the speci fic characteristics of the data and the desired level of visual
clarity. By carefully selecting the exponent, users can tailor the contrastenhancement to their needs, facilitating the identi fication and inter-
pretation of repetitive patterns in diverse microscopy images.
General applications of SReD
To demonstrate SReD ’s versatility across diverse biological contexts,
we conducted a comprehensive analysis of various microscopy data-sets (Fig. 1; Supplementary Note 2). We first examined a Stochastic
Optical Reconstruction Microscopy (STORM) image reconstruction ofa cell with labelled microtubules
12using the Pearson ’s correlation
coefficient as a rotation-variant correlation metric. This approach
effectively mapped microtubules at various orientations and crossings(Fig. 1a; Supplementary Fig. 2). We further illustrate SReD ’sv e r s a t i l i t y
by detecting nuclear envelopes in DAPI-stained cells
13following the
same approach but using empirical reference blocks extracted directlyfrom the input image. Here, SReD dis tinguished different morpholo-
gical states potentially related to cell division or stress (Fig. 1b; Sup-
plementary Fig. 3; Supplementary Note 2). SReD also enablescharacterisation of structures without user-provided references. Weexemplify this functionality by analysing an image of a Jurkat cellexpressing an HIV Gag-EGFP construct, which induces the production
of virus-like particles (VLPs) (Fig. 1c; Supplementary Fig. 4). In this
mode, SReD mapped every structure in the image and assigned scoresArticle https://doi.org/10.1038/s41467-025-60709-1
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based on their relative repetition. A rotation-invariant correlation
metric (ADSD) was used to analyse structures irrespective of theirorientation. As expected, the top score was given to the most repeatedelement, the diffuse EGFP signal, with viral structures exhibiting lower
frequencies. Localisation of round viral structures via local extrema
calculation revealed that the repetition map provided a superiorplatform for extrema detection compared to direct analysis of the rawimages (Supplementary Fig. 4). The algorithm ’s multiscale analysis
capability is achieved by adjusting the ratio of block-to-image dimen-sions. Larger ratios capture larger structures, while smaller ratioscapture finer details. For computational ef ficiency, it is preferable to
modulate scale by downscaling the input rather than enlarging blocks,although combining both approaches often preserves structural detailbest. We demonstrate this multiscale analysis by examining nuclearpore complexes in STORM image reconstructions with labelled gp210
proteins
14also using the ADSD metric. SReD successfully mapped
structures across different scales, discerning single nucleoporins,nucleoporin clusters, and entire nuclear pores (Fig. 1d; Supplementary
Fig. 5). SReD ’s utilisation of image reconstructions and intensity-based
analysis ensures broad applicability across all types of microscopydata. We demonstrate this versatility by detecting and classifying HIVviral particles in transmission electron microscopy (TEM) data,achieving a 90% concordance compared to a CNN-based approach
15
(Supplementary Note 3; Supplementary Fig. 6; SupplementaryMovie 1). Furthermore, SReD enabled the detection and quantitativedescription of HIV assembly platforms using STORM data, allowing for
an assessment of how actin-debranching drug CK666 in fluences the
stability of these platforms (Supplementary Note 4; SupplementaryFig. 7). A comparative analysis of SReD ’s capabilities against other
methodologies in the same domain is presented in SupplementaryTable 1.
1-to-all case example: detectio n of spectrin ring periodicity
in axons
We used SReD ’s block repetition mode to map and quantify the
membrane-associated periodic scaffold (MPS) architecture in neuro-nal axons automatically and without bias (Fig. 2). The MPS, composed
of actin, spectrin, and associated proteins, forms a crucial structural
component of neuronal axons
16,17Super-resolution microscopy has
shown that the MPS consists of ring-like structures spaced 180 –190 nm
apart, with alternating actin/adducin and spectrin rings orthogonal tothe axon ’sl o n ga x i s
18Mapping this nanoscale organisation across
entire neuron samples has been challenging due to the need formanual region selection, potentially introducing bias. We analyseddatasets from Vassilopoulos et al.
19. comparing neurons treated with
DMSO (control) or swinholide A (SWIN, an actin-disrupting drug).Using SReD with the rotation-sensitive Pearson ’s correlation coef fi-
cient metric, we developed an automated work flow to determine axon
orientations by probing skeletonised neuron images with simulated
lines at varying angles (Supplementary Note 5; Supplementary Fig. 8).This enabled consistent alignment of axon segments for downstreamanalysis. We optimised parameters for simulated ring blocks to matchobserved ring patterns in control data, yielding an inter-ring spacing of192 nm, consistent with previous studies (Supplementary Fig. 9)
18,19
SReD-generated repetition maps highlighting regions of high local
similarity across neuron samples, allowing automatic extraction andquanti fication of MPS organisation without manual region selection
(Fig. 2b; Supplementary Fig. 10). We measured an average spacing of
178 nm under control conditions using autocorrelation functions ofthe automatically extracted periodic regions (Fig. 2c; Supplementary
Fig. 11d). In agreement with Vassilopoulos et al.
19. repetition maps
showed that swinholide A treatment disrupted MPS structure, withreduced pattern prominence and frequency compared to controls(Fig. 2b, c). We used correlation metrics that minimise information loss
while being aware of potential imprinting. Nonlinear mapping (e.g.,power functions) of the output data effectively distinguishes real
patterns from imprinted ones (Supplementary Figs. 2d, e, 11c). Ourmethod accounts for neuron thickness variability and provides theaverage distance between patterns for additional biological insights.
SReD ’s local repetition scores quanti fied the fraction of structures with
MPS patterns, revealing a 39% reduction in axons with detectableperiodic scaffolds after swinholide A treatment ( P< 0.001, Fig. 2d).
SReD ’sm a p si d e n t i fied drug-affected regions with con fidence values,
offering a detailed platform for analysing structural dysregulation(Fig. 2c). SReD also showed higher statistical sensitivity, detecting a
12% reduction in pattern prominence post-treatment (P < 0.05) pre-viously unreported (Supplementary Fig. 11e). To test SReD ’sn o i s e
robustness, we conducted a sensitivity analysis with images at varyingsignal-to-noise ratios (SNRs) (Supplementary Fig. 12). SReD con-sistently detected ring structure s even at low SNRs near 1, where pat-
terns were visually indiscernible. SReD-generated maps outperformed
direct STORM reconstructions in autocorrelation analysis, reliablyidentifying an average inter-ring spacing of 192 nm across all SNRs,demonstrating the algorithm ’s robustness in detecting structural
periodicity despite signi ficant noise. We assessed SReD ’ss p e c i ficity
and robustness to pattern deformations by applying stretch defor-mations to test images (Supplementary Fig. 13). As the stretch factorincreased, the average SRS decreased, indicating pattern disruption.However, SReD remained speci fic to the original pattern within the
expected interval. Even at higher stretch factors, non-speci fic patterns
were quantitatively discernible and re flected the intrinsic properties of
the test data. This robustness is valuable for analysing periodic struc-
tures in diverse biological contexts, where deviations from ideal pat-terns are common due to sample preparation artefacts, imaging noise,or biological variability.
All-to-all 3D case example: detecting HIV Gag assembly in 3D
The establishment of a viral infection is the product of complex host-pathogen interactions, comprising an evolutionary ‘tug-of-war ’
where cells evolve protective mechanisms whilst viruses evolve tocircumvent them. Viruses typically hijack cellular transcription andtranslation machinery to produce viral progeny required for viral
replication
20Therefore, viral assembly represents a critical platform
for host-pathogen interactions that signi ficantly impact infection
outcomes. The HIV gag gene encodes the Gag polypeptide pre-
cursor, which is cleaved into several key structural components. Thispolypeptide aggregates at the membrane of infected cells andinduces the budding of membranous viral particles
20Expression of
Gag alone is suf ficient to induce the formation of non-infectious
virus-like particles (VLPs)21,22To map viral structures in an unbiased
manner, we examined an image of a Jurkat cell expressing an indu-cible HIV Gag-EGFP construct using SReD with the rotation-invariantADSD metric (Fig. 3a, b). The 3D data comprised 2D images acquired
with a 0.5 µm offset in the Z-axis, which enabled using SReD ’s3 D
mode. To evaluate the algorithm ’s accuracy, we generated a popu-
lation of simulated diffraction-limited particles with randomly dis-tributed intensities across the image ’s dynamic range, which served
as a reference with a known ground-truth. The ImageJ/Fiji
8,9‘3D
Maxima Finder ’plugin, which computes local maxima in 3D space,
was used to calculate 3D local maxima corresponding to active viralassembly sites from both the input image and the repetition map(Fig. 3c). Remarkably, SReD enabled the detection of 96% of the
simulated particles, compared to only 32% in the input image,demonstrating the algorithm ’s superior accuracy over direct analysis
of input images (Fig. 3d). Visual inspection of the detected EGFP
intensity signal vs. the SRS for the same pixel location revealed that
high-SRS regions corresponded to input regions with a wide range ofintensity values. We observed that most structures of interest wereallocated to the sample fraction above an arbitrary threshold of SRS0.8, whilst the fraction below this threshold contained mostlyArticle https://doi.org/10.1038/s41467-025-60709-1
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background signal and some reference particles (Fig. 3e). Given that
autofluorescence often corrupts microscopy analyses, we evaluated
the algorithm ’s performance in the presence of synthetic non-
speci fic structures (Supplementary Note 6). The repetition maps
produced by SReD consistently provided a superior platform fordetecting simulated reference particles and viral structures across
conditions (Supplementary Fig. 14). This analysis demonstrates
SReD ’s robust capability to map biological structures, such as
assembling viral particles. The algorithm ’s high sensitivity and spe-
cificity, even in the presence of non-speci fic structures, highlight its
potential for studying dynamic cellular processes like viral assembly,where the ability to accurately detect and characterise structures
amidst variable backgrounds is showcased.
All-to-all live-cell case example: Assessment of the microtubule
network ’s stability along time
The multidimensional capabilities of SReD can be extended to analyse
structural dynamics over time, providing insights into structural sta-
bility. We demonstrate this application using time-lapse imaging ofRPE1 cells stably expressing EB3 fused to GFP (Fig. 4a). EB3 binds to the
plus ends of microtubules, appearing as comet-like structures thattravel along the cytoplasm when visualised under fluorescence
Optimize reference blockCalculate neuronal
segment angles180º
Map rotation-sensitive
block repetition
Quantitative analysisa b
cd
CTRL
Structural Repetition ScoreSWIN1.0
0.0STORM
Repetition MapRepetition MapHigh order Angles Low order
STORM
Fig. 2 | Automated detection and quanti fication of spectrin ring periodicity in
neuronal axons. a SReD-based analysis pipeline. Calculate neuronal segment
angles: SReD is used to determine axon orientations by detecting repetitions of
reference blocks containing lines at different orientations in ‘skeletonized ’axons.
Optimise reference block: An optimised reference block resembling a periodic ringpattern block is generated by designing test blocks with different combinations of
inter-ring spacing and ring height and using SReD to determine the degree of
repetition of each test block in several test input images. Autocorrelation functionsare calculated for each repetition map, and the first harmonics ’amplitudes are used
as a measure of how well each test block fits the test data ’s periodic patterns. The
set of parameter values with the highest average amplitude is chosen. Map rotation-
sensitive block repetition: Block repetition analysis is used to find repetitions of the
optimized block at various orientations. Quantitative analysis: The repetition mapsare analysed by calculating autocorrelation functions and determining the average
inter-ring spacing and pattern prominence from the autocorrelations ’firstharmonics ’positions and amplitudes. All repetition analyses performed using the
Pearson ’s correlation coef ficient metric. bControl (CTRL) dataset image: STORM
localization density (grey) overlaid with SReD repetition maps (magenta). Insets:
(i)’Angles ’- axon skeletons colour-coded by orientation; (ii) ’High order ’- repetition
map calculated using a 9-ring reference block; (iii) ’Low order ’—repetition map
calculated using a 3-ring reference block. Scale bar: 5 µm.cRepetition maps com-
paring CTRL and swinholide A-treated (SWIN) groups. SWIN-treated samples show
reduced periodic structures. Scale bar: 1 µm.dQuanti fication of axon segments
with ring patterns. Box plots show a signi ficant reduction in pattern-containing
segments in SWIN vs. CTRL ( n= 6 per group, mean ± SEM; CTRL: 0.694 ± 0.008,
SWIN: 0.421 ± 0.007; p< 0.001, two-sided unpaired t-test). Box plot elements are
represented as such: center line as the median (50th percentile); box limits as upper(75th) and lower (25th) quartiles; whiskers indicate minimum and maximum values.Source data are provided as a Source Data file.Article https://doi.org/10.1038/s41467-025-60709-1
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microscopy23We used SReD with the rotation-insensitive ADSD metric
to generate a global repetition map by treating time as the thirddimension in our analysis, using a time-lapse sequence of ~2 min(Fig. 4b). To quantify structural changes, we calculated the Normalised
Root Mean Squared Error (NRMSE) between the first and last frames of
the time-lapse for both the input im ages and the repetition maps. The
NRMSE of the input images re flected the spatial displacement of
dynamic structures, yielding a relatively low value. In contrast, theNRMSE calculated from the repetition maps was higher, indicatinggreater sensitivity to structural changes over time (Fig. 4c). SReD
effectively mapped the spatial distribution of EB3 comet activity over
time. By quantifying the repetitiveness of structures, it assigned scores
to different regions, highlighting areas with high EB3 comet presenceand their trajectories. The NRMSE maps further emphasised this dis-tinction, revealing elevated values along comet paths, indicative oftheir dynamic nature. In contrast, the Microtubule Organizing Center(MTOC) demonstrated notably lower NRMSE, suggesting its greater
stability compared to the more mobile EB3 comets (Fig. 4d). The time
interval used in the analysis captures the slower dynamics of EB3comets in this context. While individual comet tracking is not theprimary focus of this method, the approach effectively reveals thespatiotemporal stability of structures, where instability often resultsfrom displacement, visually manifesting as comet trajectories. Tofurther validate our approach, we performed the analysis withincreased temporal resolution. We compared SReD ’sr e s u l t sw i t h
conventional time projections of the input data, revealing advantagesof our method. Unlike time projections, which typically integrate local
intensities across time, SReD calculates local correlations of images
across time, providing relative repetition scores that indicate howmuch the texture at each location changes relative to all other textures.This approach offers two signi ficant bene fits: (i) it provides a more
nuanced measure of structural stability over time, and (ii) it is less
a
b cd
eSReDzy
xInputImage reconstruction Local maxima
Intensity profileAccuracyCalculate 3D all-to-all repetition Find 3D local maxima
Input
Test blocksNext reference block Reference block
1 0
Global repetition20 1.5
Z-position (µm) SRSInput SReDEGFP intensity detection match (%)
0
0100
0
1 0.81EGFP
Reference
SRS<0.8 SRS>=0.8
EGFP
Reference
Fig. 3 | Detecting HIV virus-like particles in 3D. a Analysis pipeline schematic. The
algorithm uses 3D reference blocks for rotation-invariant structural ( ‘absolute dif-
ference of standard deviations metric) repetition analysis, locating viral structures
via 3D local maxima detection from the input image and repetition map.
bZ-projections of the input image (top) and repetition map (bottom), highlighting
viral-like particles ( ‘EGFP ’) and simulated reference particles ( ‘Reference ’). The
‘Reference ’particles were designed as diffraction-limited particles with randomly
distributed intensities across the input ’s dynamic range and serve as a reference
with a known ground-truth to evaluate the algorithm ’sa c c u r a c y . cLocal maximaplots showing detected structures in the input image (top) and repetition map
(bottom), with increased sensitivity in the repetition map. dAccuracy plot com-
paring arti ficially-added reference particle detection: input image (32%) vs. repe-
tition map (96%). eIntensity pro file graph of EGFP signal (green) and structural
repetition score (SRS, magenta), with a threshold at SRS 0.8 (dashed red line). Insetshows pixels below (left) and above (right) the threshold, indicating high-SRSstructures. Scale bars: 5 µm (main images), 1 µm (inset). Source data for ( c–e)a r e
provided as a Source Data file.Article https://doi.org/10.1038/s41467-025-60709-1
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susceptible to noise and intensity inconsistencies across time points
(Supplementary Note 7; Supplementary Fig. 15). In this type of com-
bined spatial and temporal analysis, instead of producing a time series,
SReD ’s output is a single map that shows the local stability of the
timelapse over a speci fic time interval. This representation offers a
comprehensive view of structural dynamics that is not easily achievedusing traditional methods such as k ymographs. While kymographs areuseful for tracking individual structures over time, SReD provides a
broader perspective on the overall stability and dynamics of sub-
cellular structures across the entire field of view.
Discussion
In neuronal axons, SReD enabled automated, unbiased mapping of the
membrane-associated periodic scaffold (MPS), revealing nuanced
t = 0 sec t = 105 secInputt = 0 sec t = 105 sec NRMSESReDbc
daCalculate 2D+time all-to-all repetition
t0tnNRMSE
Input
Time
Test blocksNext reference blockAnalyse structural stability
Reference block
1 0
Global repetition0.5 0
NRMSEEB3-GFP
SReD
NRMSE = 0.08NRMSE = 0.03
NRMSEError
Input SReD0.08 0.03 0Article https://doi.org/10.1038/s41467-025-60709-1
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changes in pattern frequency and prominence following pharmaco-
logical perturbation. While previous studies by Vassilopoulos et al.19.
reported a 40% reduction in overall MPS prominence after treatmentwith swinholide A, SReD ’s analysis provides a more detailed char-
acterisation of the phenotype. By first distinguishing between regions
with and without periodic patterns, and then analysing only the
pattern-present areas, SReD detected a 12% reduction in pattern pro-minence and a 32% reduction in pattern frequency. This re fined ana-
lysis not only corroborates the previously reported overall effect butalso decomposes it into two distinct components, offering deeperinsights into the nature of the structural changes. This analysis show-cased how SReD offers a distinct approach for studying periodicstructures compared to other methods, such as that described byBarabas et al.
24. For example, while both methods rely on prior esti-
mation of axon orientations to facilitate ring pattern detection, theydiffer in their implementation. Barabas et al.
24. employ the Hough
transform algorithm25to determine the orientation of axon edges,
while SReD employs skeletonization and compares skeletons againstreference blocks containing lines at different angles. In de fining peri-
odic patterns, Barabas et al.
24. analytically model the periodic ring
structure with an equation that characterizes its features. This equa-tion is then used alongside Pearson correlation to identify regionscontaining the pattern. In contrast, SReD de fines periodicity using
image-based reference patterns, enabling comparisons based onactual structural representations rather than mathematical abstrac-tions. This approach potentially makes SReD more adaptable fordetecting irregular or complex motifs that are dif ficult to describe
analytically. Thus, while Barabas et al.
24. analytical approach may be
advantageous for scenarios requiring precise mathematical descrip-tions of periodicity, SReD ’s image-based framework offers greater
flexibility for extending its application to diverse structural patterns.
These differences underscore th e complementary nature of the two
methods, with each suited to speci fic research goals and datasets.
Our results demonstrate SReD ’s versatility and analytical power
across diverse biological contexts. For HIV Gag assembly, SReDachieved sensitive detection without relying on structural priors, sig-nificantly outperforming direct analysis of input images. This cap-
ability is particularly valuable in studying dynamic cellular processes
like viral assembly, where the ability to accurately detect and char-
acterise structures amidst variable backgrounds is crucial. In live-cellimaging of microtubule dynamics, SReD ’s multidimensional cap-
abilities allowed for quantitative assessment of structural stabilityacross space and time. This analysis provided insights into the differ-ential dynamics of EB3 comets and the microtubule organising centre,demonstrating SReD ’s potential for studying complex, time-
dependent cellular processes.
A key advantage of SReD is its ability to detect and characterise
structures without the need for extensive labelled training data orsingle-molecule localisation input. This feature is particularly useful forexploratory analysis of complex biological systems where the under-
lying structural patterns may not be fully known a priori. The frame-
work ’sflexibility in accommodating different reference blocks, from
simulated idealised structures to patches extracted from the image,enhances its utility across diverse experimental scenarios. Importantly,this strength also introduces a dependence on pre-processing stepsand the choice of the reference block, which can signi ficantly in fluence
the output. Careful optimization of these factors is essential to ensurereliable and interpretable results. Another crucial feature is SReD ’s
robustness to noise and pattern deformations, as demonstrated in oursensitivity analyses. This resilience enables reliable structure detection
and quanti fication even in challenging imaging conditions, expanding
the range of biological questions that can be addressed throughquantitative image analysis. The algorithm ’s multiscale mapping cap-
abilities provide a unique perspective on hierarchical structural orga-nisation, as exempli fied by our analysis of nuclear pore complexes at
different spatial scales. While SReD offers signi ficant advantages, it is
important to acknowledge its limitations. The algorithm ’sp e r f o r -
mance can be in fluenced by the choice of reference blocks, requiring
their optimisation. Additionally, while SReD reduces the need formanual region selection, some level of results curation may still benecessary, particularly in complex or heterogeneous samples. Fur-
thermore, SReD utilises correlation metrics, each offering distinct
advantages and limitations. For example, metrics such as the Pearsoncorrelation coef ficient and the Structural Similarity Index Measure
(SSIM) produce satisfactory results but exhibit sensitivity to rotationalvariations. Conversely, metrics that demonstrate rotational invariance,such as the absolute difference of standard deviations, do not posesscomparable sensitivity for detecting structural nuances. Finally, thealgorithm ’s computational complexity warrants attention. Consider a
2D image with dimensions n
1×n2pixels and a block of size k1×k2
pixels. Each pairwise comparison between the block and an image
region requires O(k1k2) operations. The total number of such over-
lapping image regions is ( n1−k1+1 ) (n2−k2+ 1). Consequently, the ‘1-
to-all ’scheme (block repetition) entails a computational complexity of
O((n1−k1+1 ) (n2−k2+1 )k1k2). When the image dimensions signi ficantly
exceed the block size ( n1≫k1andn2≫k2), this simpli fies to O(n1n2k1k2).
In the ‘all-to-all ’scheme (global repetition), the computational com-
plexity scales quadratically with the image size and linearly with theblock size, resulting in O(n
2
1n2
2k1k2). SReD mitigates this computa-
tional burden by harnessing GPU acceleration and pre-calculatingbackground regions that do not warrant analysis.
Future developments of SReD could focus on further automat-
ing the reference block selection process, potentially incorporating
machine learning approaches to optimise block parameters based on
image characteristics. Integration with other computational tools,such as deep learning-based segmentation algorithms, could alsoenhance SReD ’s capabilities for more comprehensive structural
analysis pipelines. To address the trade-off between rotational sen-sitivity and structural detail detection, future work could enhancethe SReD pipeline by incorporating rotation-aware analysis. Thiscould involve systematically rotating reference blocks whenemploying rotation-sensitive metrics, enabling SReD to retain thehigh structural sensitivity of metrics like the Pearson ’s correlation or
SSIM while mitigating their rotational limitations. Although thisapproach is explored in the present study, further optimization
could re fine the pipeline by automating processes such as image
transformations. This automation would not only improve ef ficiency
but also reduce user intervention and potential variability, broad-ening SReD ’s applicability across diverse biological contexts with
varying structural orientations.Fig. 4 | Assessment of the microtubule network ’s stability along time
using SReD. a Analysis pipeline schematic. Global repetition analysis used time as
the third dimension on a timelapse sequence of RPE1 cells expressing EB3-GFP over105 s (35 frames) ( ‘absolute difference of standard deviations ’metric). The first
frame served as the control. Normalised Root Mean Squared Error (NRMSE)
quanti fied structural differences between time points. bOverlay of input images
(green) and temporal global repetition maps (magenta) at t= 0 (left) and t= 105 s
(right). The first frame ’s repetition map highlights EB3 comets, while the entiretime-lapse map shows comet trajectories and repetition over time. cBar graph of
average NRMSE between input images and repetition maps. A higher error in the
repetition maps (0.08) vs. control images (0.03) indicates greater sensitivity tostructural changes. Source data are provided as a Source Data file.dNRMSE maps
of input images (top row) and repetition maps (bottom row), showing structural
stability over time. High NRMSE values (warmer colours) in EB3 trajectories indicate
lower stability, while lower values (cooler colours) in the Microtubule OrganisingCentre (MTOC) indicate higher stability. Scale bars: 10 µm.Article https://doi.org/10.1038/s41467-025-60709-1
Nature Communications |         (2025) 16:5767 8
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Methods
Optimisation of block parameters for ring pattern detection
A collection of 248 testing blocks incorporating various combinations
of inter-ring spacing and ring height was generated. This process was
automated using a custom ImageJ8macro. To create input images, five
representative segments from the distal axons within each datasetwere randomly selected, comprised of six neurons per treatment.These regions were then rotated to align with the horizontal axis toguarantee consistency across subsequent calculations. Then, SReDwas used to generate repetition maps for every test block, and theirautocorrelation functions were calculated. The relative amplitude ofthe autocorrelations ’first harmonic was used to assess how effectively
each block captured the underlying periodic pattern. The set of blockparameter values that maximised the first harmonics ’relative ampli-
tude was systematically identi fied. The optimised set of parameter
values served as a reliable representation of the periodic pattern within
the dataset. The optimisation was performed separately for eachdataset analysed in this study.
Detection of reference and virus-like particles using Global
Repetition
An image volume containing 3D simulated reference particles was
generated using a custom Python script. The reference particles wereadded to the input volume by addition. Global Repetition maps werecalculated using a block size of 5 × 5 × 5 pixels and a relevance constantof 0. Then, the repetition maps were non-linearly mapped using a
power transformation with an exponent of 10000. 3D maxima were
calculated using the ImageJ
8‘3D Maxima Finder ’plugin, which com-
putes local maxima in 3D space using a flooding-based approach, with
an XY and Z radius of 5 pixels and a minimum threshold of 0.1. Thecomparison of coordinates between the 3D maxima calculated and thereference particles was performed using a custom Python script.
Cell culture
Jurkat cells were cultured in RPMI 1640 (Gibco) supplemented with10% fetal bovine serum (FBS), 2 mM L-glutamine and 50 µg/mL genta-
mycin. HEK293T and RPE1-EB3-GFP cells were cultured in DMEM sup-
plemented with 10% fetal bovine serum (FBS), 2 mM L-glutamine and
50µg/mL gentamycin. Cell lines were cultured at 37 °C and 5% CO
2.
DNA plasmids and cell lines
The RPE1-EB3-GFP cell line was kindly provided by Dr. Mónica
Bettencourt-Dias. A plasmid expressing HIV Gag with an internal EGFPtag was generated using the NEB HiFi Assembly Kit (New England Bio-
labs). A lentiviral back bone containing a tetracyc line-inducible promoter
and a gene encoding rtTA was prepared by digesting the pCW57.1plasmid (Addgene #41393) with 5 µg/mL restriction enzymes BamHI and
NheI (New England Biolabs) according to the manufacturer ’s instruc-
tions for 1 h at 37 °C. The digestion product was separated using 1%
agarose gel electrophoresis (AGE) and the 7.6 ˜kb band was puri fied
using the GFX PCR & Gel Band Puri fication Kit (Sigma-Aldrich) according
to the manufacturer ’s instructions. Then, three DNA fragments were
generated by polymerase chain-reaction (PCR) using Q5 High-FidelityDNA Polymerase (New England Biolabs). The fir s tf r a g m e n t( 4 4 5 b p ) ,
encoding the HIV-1 Matrix protein f ollowed by an HIV-1 protease clea-
vage site (MA-PCS), was generated using Optigag-mNeonGreen-IN
26as a
template and primers 5′-tcagatcgcctggagaattgggccaccatgggtgcgcga3 ′
(Fw)+5′-ccatacgcgtctggacaatggggtagttttgactgacc-3 ′(Rv).T h es e c o n d
fragment (751 bp), encoding EGFP ,w a sg e n e r a t e du s i n gH I V - ( i ) G F P
ΔEnv21as a template and primers 5′-ccattgtccagacgcgtatggtgagcaag-3 ′
(Fw)+5′-tagttttgacttctagacttgtacagctcgtc-3 ′(Rv).T h et h i r df r a g m e n t
(1.2 kb), encoding a PCS and the HIV-1 Capsid, Nucleocapsid and p6proteins (PCS-CA-NC-p6), was generated using Optigag-mNeonGreen-IN
26as a template and primers 5′-caagtctagaagtcaaaactaccccattgtc-3 ′
(Fw)+5′-aaaggcgcaaccccaaccccgtc attgtgacgaggggtctgaac-3 ′(Rv).T h ethree fragments were puri fied using DNA puri fication columns and their
molecular size was con firmed by AGE. The HiFi Assembly reaction was
performed using 50 ng of digested ve ctor and equimolar amounts of the
three fragments and incubated at 50 °C for 1 h. The reaction product was
diluted 1:4 in dH20, and 2 µL of the dilution was transformed into che-
mically competent STABL4 bacteria ( Thermo Fisher). The bacteria were
plated in LB-agar supplemented with 100 µg/mL ampicillin and incu-
bated overnight at 37 °C. Several colonies were picked and inoculatedinto liquid LB containing ampicillin at 100 µg/mL. The plasmid DNA from
these colonies was extr acted using the GenElute Plasmid Miniprep Kit
(Sigma-Aldrich) and was con firmed by digestion with restriction enzyme
XbaI followed by AGE (2.3 kb and 7.5 kb fragments). A positive colonywas then sequenced using Sanger sequencing (Genewiz) and primers 5′-
cgtcgccgtccagctcgacca3 ′,5′-ccattgtccagacgcgtatggtgagcaag-3 ′and 5′
aaaggcgcaaccccaaccccgtc attgtgacgaggggtctgaac-3 ′.T h i sp r o c e s sy i e l d e d
the lentiviral plasmid TetOn-Opti gag(i)EGFP, where a human codon-
optimised gaggene contains a PCS- flanked EGFP-encoding gene. Len-
tivirus packaging TetOn-Optigag- (i)EGFP were produced to transduce
Jurkat cells. To do this, HEK293T cells were cultured in 6-well plates until∼80% of con fluence, transfected using 300 µL/well of transfection mix-
ture (DMEM, 3 µg of TetOn-Optigag-(i)EGFP, 1.5 µgo fp s P A X 2( A d d g e n e
#12260), 1.5 µg of CMV-VSV.G (NIAID) and 12 µLo fl i n e a rp o l y -
ethyleneimine MW-25,000 ( final concentration of 5 µg/µL)(Sigma-
Aldrich)) and incubated overnight for 8 h. Then, the culture medium wasreplaced with complete DMEM, followed by a 24-h incubation. The virus-rich supernatant was collected and filtered with 0.22 µms y r i n g e filters.
Jurkat cells (2 mL at 1 × 10
6cells/mL) were inoculated with 300 µLo f
virus-rich supernatant and Polybrene (10 µg/mL), followed by a 3-day
incubation. Antibioti c selection of transduced cells was performed by
replacing the culture medium with complete RPMI containing pur-omycin at 2 µg/mL and incubating for 3 days, at which point an ‘empty
virus ’control sample had no live cells remaining. The cells were incu-
bated with doxycycline at 1 µg/mL for 24 h to induce expression and
single cells were isolated using Fluorescence-assisted Cell Sorting(FACS). The EGFP-positive population was divided into three subsetsaccording to their relative signal intensity ( ‘Low ’,‘Medium ’and ‘High ’)
and single cells were plated into 96-well plates. The cultures were
expanded for 15 days, and the resulting cell lines were validated using
fluorescence microscopy and Western blotting. A clonal line of the
‘Medium ’subset was used for this study.
Sample preparation and acquisition of microscopy data
HILO imaging of HIV virus-like particle assembly in activated
Jurkat cells . Activation surfaces were prepared based on the protocol
in ref. 27To do this, Lab-Tek 8-well chambers (Thermo Fisher) were
cleaned with 100% isopropanol for 10 min and followed by threewashing steps with dH
20. Then, 200 µL of a mouse anti-CD3 antibody
diluted in PBS at a final concentration of 1 µg/mL was added to the wells
and incubated overnight at 4 °C. The wells were carefully washed twice
with PBS to remove unbound antibodies. Jurkat cells expressingTetOn-Optigag-(i)EGFP were incubated with 1 µMo fd o x y c y c l i n e
(Sigma-Aldrich) for 24 h. Then, 50,000 cells were added to each welland allowed to adhere and stabilise for 1 h. Imaging was done in aNanoimager (ONI) using the 488 nm laser at 10% and channel 0 (two-band dichroic: 498 –551 nm and 576 –620 nm). The HILO angle was
optimised manually, and images were acquired at 100 ms exposure.Pixel size: 117 nm. The anti-CD3 antibody was produced at the FlowCytometry & Antibodies Unit of Instituto Gulbenkian de Ciência,Oeiras, Portugal.
3D imaging of HIV virus-like particle assembly in activated
Jurkat cells . Jurkat cells expressing TetOn-Optigag-(i)EGFP were
centrifuged at 200 × gfor 5 min and resuspended in complete
RPMI containing 0.5 µM of doxycycline to induce Gag expression.
Glass coverslips (1.5 mm thick, round, 18 mm diameter) wereArticle https://doi.org/10.1038/s41467-025-60709-1
Nature Communications |         (2025) 16:5767 9
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washed with isopropanol for 10 min followed by three washes
with dH 20. The coverslips were coated with Poly-L-Lysine (PLL,
Sigma Aldrich) at 0.1% and incubated for 15 min at room tem-perature, followed by three washing steps with dH
20. The PLL-
coated coverslips were dried, mounted in an Atto fluor chamber
(Thermo Fisher) and fixed on the microscope ’ss t a g e .T h e
microscope ’s enclosure (Okolabs) was heated at 37 °C and a
manual gas mixer (Okolabs) was used to supply 5% CO 2.T h ec e l l s
were seeded in the pre-treated coverslips and allowed to settle inthe microscope enclosure for 30 min. Imaging was performed onan inverted microscope ECLIPSE Ti2-E (Nikon Instruments)equipped with a Fusion BT (Hamamatsu Photonics K.K., C14440-20UP) and a Plan Apo λ100× (NA 1.45) Oil objective. The sample
was illuminated with LED light at 515 nm (CoolLED pe800) andacquisition was done at 75 ms exposure with an active Nikon
Perfect Focus system and the NIS-Elements AR 5.30.05 software
(Nikon Instruments). Volumes were captured by acquiring framesat different depths (z-step size: 0.5 µm). Image deconvolution
was performed using a custom Python script based on theRichardson-Lucy method
28,29as described in refs. 30,31.
Imaging EB3-GFP comets in RPE1 cells . RPE1-EB3-GFP cells (50000
per well) were seeded into Lab-Tek 8-well glass chambers (ThermoFisher) and allowed to adhere for 24 h. Wide field imaging was per-
formed in a Nanoimager (ONI) using the 488 nm laser at 10% andchannel 0 (two-band dichroic: 498 –551 nm and 576 –620 nm). Images
were acquired at 75 ms exposure for 2 min. Pixel size: 117 nm.
Assessment of the microtubule network ’s stability along time
using SReD . Subsets of the original time lapse were created by keeping
images belonging to the time frames of interest. Global repetitionmaps were generated from the temporal subsets using an XY block sizeof 7 × 7 pixels, a Z block size equal to the number of images in eachsubset, and a relevance constant of 0. The repetition maps were non-linearly mapped using a power transformation with an exponent of1000. NRMSE maps were calculated using the ‘scikit-image ’library
(v0.22.0, accessible at https://scikit-image.org/docs/stable/api/
skimage.metrics.html ).
Statistics and reproducibility
No statistical method was used to predetermine sample size. No data
were excluded from the analyses. The experiments were not rando-mized. The Investigators were not blinded to allocation duringexperiments and outcome assessment.
Reporting summary
Further information on research design is available in the NaturePortfolio Reporting Summary linked to this article.
Data availability
The data obtained in this study is available at https://doi.org/10.5281/
zenodo.13764726 and https://doi.org/10.6019/S-BIAD1620 under CC
BY 4.0 license. The STORM data containing cells with labelled micro-t u b u l e si sa v a i l a b l ea t https://doi.org/10.5281/zenodo.5534351
12The
widefield microscopy data containing DAPI-stained nuclei is available
athttps://doi.org/10.5281/zenodo.323247813The STORM data con-
taining nuclear pores with labelled gp210 is available at https://www.
embl.de/download/ries/excitation_intensities/Nup96-BG-AF647_250kWcm2_57_2.zip
14. Source data are provided with this paper.
Code availability
The SReD algorithm, along with all custom scripts used in this manu-script are available at http://github.com/HenriquesLab/SReD (release
v1.0). All source code is under an MIT License.References
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Acknowledgements
A.M. thanks Simão Coelho and Estibaliz Gómez-de-Mariscal for their
feedback during the formulation of the algorithm and its demonstrationin biological studies. A.M. and R .H. acknowledge the support of the
Gulbenkian Foundation (Fundação C alouste Gulbenkian), the European
Research Council (ERC) under the European Union ’s Horizon 2020
research and innovation programme (grant agreement No. 101001332)(to R.H.) and funding from the European Union through the HorizonEurope program (AI4LIFE project with grant agreement 101057970-AI4LIFE and RTSuperES project with grant agreement 101099654-RTSuperES to R.H.). Funded by the European Union. Views and opinions
expressed are, however, those of the authors only and do not necessarily
reflect those of the European Union. Neither the European Union nor the
granting authority can be held responsible for them. This work was alsosupported by a European Molecular Biology Organization (EMBO)
installation grant (EMBO-2020-IG-4734 to R.H.), a Chan ZuckerbergInitiative Visual Proteomics Grant (vpi-0000000044 with https://doi.
org/10.37921/743590vtudfp to R.H.) and a Chan Zuckerberg Initiative
Essential Open Source Software for Science (EOSS6-0000000260).This study was also supported by the Research Council of Finland(338537 to G.J.), the Sigrid Juselius Foundation (to G.J.), the CancerSociety of Finland (Syöpäjärjestöt; to G.J.), the Solutions for Health
strategic funding to Åbo Akademi University (to G.J.), the InFLAMES
Flagship Programme of the Academy of Finland (decision numbers:337530, 337531, 357910 and 357911). This research was also supportedby the National Institutes of Health (NIH) with grants K22AI140963,K61DA058348 and subcontract R01AI50998 (to J.I.M). C.L.acknowledges funding from the Agence National de la Recherche (ANR-
20-CE13-0024 ‘ASHA ’,A N R - 2 1 - C E 4 2 - 0 0 1 5 - 0 1 ‘5D-SURE ’). C.L. acknowl-
edges the INP NCIS imaging facility and Nikon Center of Excellence forNeuro-NanoImaging for service an d expertise, with funding from
Excellence Initiative of Aix-Marseille University, A*MIDEX, a French
‘Investissements d ’Avenir ’program (AMX-19-IET-002) through the Mar-
seille Imaging and NeuroMarseille Institute.
Author contributions
A.M. and R.H. conceived the study in its initial form; A.M. and R.H.developed the SReD framework with code contributions from B.M.S.;B.M.S., G.J., J.I.M. and C.L. provided samples, data, critical feedback,testing and guidance; A.M. performed experiments and analysis; G.J.,J.I.M., C.L. and R.H. acquired funding; C.L., R.H. supervised the work; A.Mand R.H. wrote the manuscript with input from all authors.
Competing interests
The authors declare no competing interests.
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