Statistical spatial analysis for cryo-electron tomography

•Cryo-electron tomography (cryo-ET) is uniquely suited to precisely localize macromolecular complexes within their cellular compartments.•Point Pattern Analysis (PPA) functions are adapted to quantitatively describe macromolecular organization in situ.•We provide a software for calculation of PPA functions that implements the numerical corrections required to handle irregular 3D shapes such as molecular complexes and cellular compartments, and that can process large datasets.•Applications of our software are expected to provide a spatial characterization of macromolecular crowding, as well as liquid and lipid phase separation. [Display omitted] 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.