Optimizing Voronoi-based quantifications for reaching interactive analysis of 3D localizations in the million range.

Area of Science:

• Cell Biology
• Biophysics
• Microscopy

Background:

• Single-molecule localization microscopy (SMLM) offers nanoscale spatial resolution for studying molecular organization and dynamics.
• Voronoi-based methods are effective for 2D SMLM data analysis, but 3D implementations are computationally intensive.
• Existing 3D Voronoi diagram generation methods are too slow for large datasets.

Purpose of the Study:

• To develop a fast algorithm for generating 3D Voronoi diagrams from SMLM data.
• To make Voronoi-based analysis methods, like SR-Tesseler, accessible for 3D SMLM datasets.
• To optimize Voronoi-based clustering methods by approximating computationally expensive simulations.

Main Methods:

• Developed a hybrid CPU-GPU algorithm (Voro3D) for rapid 3D Voronoi diagram generation.
• Applied Voro3D to datasets with millions of localizations, achieving generation times in minutes.
• Approximated Monte-Carlo simulations in ClusterVisu using a customized gamma probability distribution function.

Main Results:

• Voro3D generates 3D Voronoi diagrams from millions of localizations in minutes, a significant speed improvement.
• This enables the use of Voronoi-based analysis tools for large-scale 3D SMLM datasets.
• The gamma distribution function accurately approximates costly Monte-Carlo simulations for clustering analysis.

Conclusions:

• The Voro3D algorithm dramatically accelerates 3D Voronoi diagram generation for SMLM data.
• This advancement democratizes advanced 3D spatial analysis for cell biologists.
• Optimized clustering analysis in SMLM through efficient approximation of simulations.