Bayesian inference of multi-point macromolecular architecture mixtures at nanometre resolution

Gaussian spot fitting methods have significantly extended the spatial range where fluorescent microscopy can be used, with recent techniques approaching nanometre (nm) resolutions. However, small inter-fluorophore distances are systematically over-estimated for typical molecular scales. This bias can be corrected computationally, but current algorithms are limited to correcting distances between pairs of fluorophores. Here we present a flexible Bayesian computational approach that infers the distances and angles between multiple fluorophores and has several advantages over these previous methods. Specifically it improves confidence intervals for small lengths, estimates measurement errors of each fluorophore individually and infers the correlations between polygon lengths. The latter is essential for determining the full multi-fluorophore 3D architecture. We further developed the algorithm to infer the mixture composition of a heterogeneous population of multiple polygon states. We use our algorithm to analyse the 3D architecture of the human kinetochore, a macro-molecular complex that is essential for high fidelity chromosome segregation during cell division. Using triple fluorophore image data we unravel the mixture of kinetochore states during human mitosis, inferring the conformation of microtubule attached and unattached kinetochores and their proportions across mitosis. We demonstrate that the attachment conformation correlates with intersister tension and sister alignment to the metaphase plate.Author summary: Light microscopy is an exceptionally powerful tool for observing and measuring biological structures and dynamics. However, spatial resolution is limited by the wavelength of the utilised light, 400–700 nanometres in the visible spectrum, traditional imaging being limited to essentially the wavelength itself. This is because point source objects appear under the microscope as a spot with dimensions the order of the wavelength. For sufficiently well spaced point source like objects spot fitting can be used. The spot centres can be localised with nanometre accuracy, and thus the distance between centres of spots in different colours can in turn be determined with nanometre spatial resolution. By labelling different parts of a molecular structure in different colours, the structure can be mapped in 3D with high spatial resolution. However, these distances are in fact systematically over estimated because of spot centre measurement error. We present an algorithm that corrects this overestimation for multi-fluorophore images, inferring the full geometry of the labelled structure, giving greater accuracy over previous methods, particularly for small distances. We also present an algorithm that can unravel mixtures of different conformational (geometric) states. We demonstrate our algorithm on the kinetochore macro-molecular complex and its change in structure during cell division.