Statistical spatial analysis for cryo-electron tomography

TL;DR

This paper introduces PyOrg, a Python package for advanced spatial analysis of macromolecular complexes in cryo-electron tomography, accounting for irregular cellular shapes and enabling detailed organization studies.

Contribution

The authors developed and validated new first and second-order point pattern analysis functions tailored for complex 3D cellular geometries in cryo-ET data, implemented in an open-source Python package.

Findings

Second-order functions outperform first-order in characterizing particle organization.

PyOrg accurately analyzes spatial patterns in irregular 3D cellular regions.

Application to experimental data demonstrates the utility of the methods for biological insights.

Abstract

Cryo-electron tomography (cryo-ET) is uniquely suited to precisely localize macromolecular complexes in situ, that is in a close-to-native state within their cellular compartments, in three-dimensions at high resolution. Point pattern analysis (PPA) allows quantitative characterization of the spatial organization of particles. However, current implementations of PPA functions are not suitable for applications to cryo-ET data because they do not consider the real, typically irregular 3D shape of cellular compartments and molecular complexes. Here, we designed and implemented first and the second-order, uni- and bivariate PPA functions in a Python package for statistical spatial analysis of particles located in three dimensional regions of arbitrary shape, such as those encountered in cellular cryo-ET imaging (PyOrg). To validate the implemented functions, we applied them to specially designed synthetic datasets. This allowed us to find the algorithmic solutions that provide the best accuracy and computational performance, and to evaluate the precision of the implemented functions. Applications to experimental data showed that despite the higher computational demand, the use of the second-order functions is advantageous to the first-order ones, because they allow characterization of the particle organization and statistical inference over a range of distance scales, as well as the comparative analysis between experimental groups comprising multiple tomograms. Altogether, PyOrg is a versatile, precise, and efficient open-source software for reliable quantitative characterization of macromolecular organization within cellular compartments imaged in situ by cryo-ET, as well as to other 3D imaging systems where real-size particles are located within regions possessing complex geometry.