Observing biological spatio-angular structures and dynamics with statistical image reconstruction and polarized...

Understanding molecular orientation and density distributions is essential for exploring biological structure and function. Polarized fluorescence microscopy (PFM) provides insights into molecular architecture but struggles to resolve three-dimensional (3D) molecular orientation distributions, particularly in densely labeled or structurally complex specimens. To address this, we introduce the efficient generalized Richardson-Lucy (eGRL) algorithm, a robust framework for reconstructing 3D molecular density and orientation (spatio-angular) distributions from PFM data. By modeling the imaging process in spatio-angular hyperspace, we propose a maximum-likelihood solution enhanced by dimensionality reduction and angular domain transformation to overcome computational challenges. eGRL improves accuracy and efficiency across different PFM implementations, enabling use on standard platforms. We utilize our methods to resolve biological spatio-angular structures and dynamics otherwise impossible to resolve, including the tangential alignment of actin filaments in U2OS cells, nanowire-guided cytoskeletal organization in NIH3T3 cells, rotational actin patterns in live HeLa protrusions, and membrane tension-induced anisotropy in live macrophages.