Lacunarity method for subcellular microscopic analysis


A study published in the journal cells provides a quantitative gap-based analysis method to assess nanoscale cell structure and homogeneity of target molecules in single-molecule localization microscopy. The proposed method provides accurate and rapid information on the subcellular structure of biological samples.

Study: Application of lacunarity for quantification of single molecule localization microscopy images. Image Credit: pinkeyes/

Limitations of Conventional Light Microscopes

Conventional microscopes have a resolution of 200 nanometers. The diffraction of light limits their spatial resolution. Below this spatial resolution, images become blurred and cellular structures cannot be distinguished. This implies that conventional microscopy cannot detect most subcellular structures and molecular complexes.

Single-molecule localization microscopy: a high-resolution fluorescence microscopy technique

Various high-resolution microscopy techniques have been developed to overcome the shortcomings of conventional microscopes, such as stimulated emission depletion microscopy (STED), structured illumination microscopy (SIM), and single molecule localization microscopy ( SMLM).

SMLM techniques are more accurate than other microscopy techniques in determining the locations of single-emission fluorophores. These powerful microscopy techniques use the blinking of fluorescent molecules to accurately detect their position below the diffraction limit at the tens of nanometer scale.

Some of the most commonly used SMLM techniques in biology are light-activated localization microscopy (PALM), direct stochastic optical reconstruction microscopy (dSTORM), and ground state depletion microscopy (GSDM).

Quantitative analysis of SMLM

Quantification of SMLM images and datasets has attracted a lot of attention. However, its unique 3D data format requires new evaluation algorithms, merit functions and visualization techniques.

Various techniques have been suggested to quantify the density and underlying structure of target molecules in SMLM.

Cluster analysis techniques

SMLM images are generated by location dots indicating the positions of individual fluorophores bound to target molecules, such as proteins. Clustering is a common configuration of these proteins.

Cluster analysis techniques such as Voronoi tessellation and DBSCAN are frequently used when cluster composition, area, and size can be directly assessed from raw location data.

However, these techniques rely on predetermined parameters and their operations can be computationally demanding.

Gap analysis

Gap analysis is a proven multi-scale method in materials science. It was mainly used in fractal analysis to differentiate between fractals of different structures but of the same dimensions.

Lacunarity can identify patterns at multiple scales in a flexible and systematic way. This makes it a viable tool for defining the structure of subcellular systems unraveled by SMLM.

Using the Lacunarity Algorithm for Quantitative Analysis of SMLM Datasets

A lacunarity calculation algorithm was developed using the gliding-box technique. TestSTORM, a dSTORM simulation software, has developed test data in which target molecules have been organized into various groups of nanofocuses to replicate real samples.

A modified disk pattern generator randomly distributed epitopes in a circular area at a specified orientation and density and generated 8,000 images for the simulated data. The samples were not derived and a Gaussian point spread function was applied.

The rainSTORM reconstruction program performed a 2D multi-Gaussian analysis to capture each blink event.

The size of the clusters, the number of clusters in the region of interest, the distance between adjacent clusters, the size of the nanofoci, the density of the nanofoci, the localization density in a cubic micron volume and the number of localizations per nanofoci were evaluated five times at different values.

Important Study Findings

Processing SMLM data has always been a computational challenge due to the size of the datasets. However, the proposed lacunarity algorithm can quantitatively assess homogeneity and subcellular structures in SMLM data.

The lacunarity algorithm can provide accurate information about the structure of SMLM data faster than cluster analysis. Therefore, lacunarity data can be analyzed and used to quantitatively determine the structured localization of SMLM data using computed and simulated datasets. In addition, the visualization technique makes it possible to instantly assess the relative homogeneity of the image.

Convenient scope

DNA double-strand break (DSB) is a harmful lesion that must be repaired as quickly and efficiently as possible to minimize chromosome loss and translocation.

DNA repair proteins form foci around the DSB to carry out the repair processes. The size of the foci is on the order of 100 nanometers, which makes high-resolution SMLM essential for understanding the DNA repair process.

The proposed method demonstrates that DSB-inducing chemicals and radiation increase the frequency of DSBs and lead to the formation of larger repair foci.


The lacunarity algorithm uses a single value to describe the structure of a sample of a particular size. This implies that distinct mechanisms can have a significant effect on lacunarity.

In the experiment, the lacunarity curve responded similarly to an increase in the number or size of clusters. Therefore, lacunarity data cannot be interpreted without preliminary computational and simulation analysis.


Kovács, BBH, Varga, D., Sebők, D., Majoros, H., Polanek, R., Pankotai, T., Hideghéty, K., Kukovecz, Á., & Erdélyi, M. (2022). Application of lacunarity for quantification of single molecule localization microscopy images. cells.

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