A numerical method for resolving finite mixtures of three-dimensional inter-site distance distributions measured by single-molecule localization microscopy

Abstract

Abstract The three-dimensional (3D) inter-site distance can be measured by single-molecule localization microscopy. Existing theories and analysis tools for 3D inter-site distance measurement only consider the simplest case where all measured distances are from an identical 3D Rician distribution. There are many problems where the 3D inter-site distance measurement result is made up of multiple components, for example, the measurement of intramolecular distances of deoxyribonucleic acid with multiple possible conformations. In these cases, the overall distance distributions become finite mixtures of 3D Rician distributions (or 3D Rician mixtures). Here, we provide a numerical method using the 3D Rician mixture model to resolve the finite 3D inter-site distance mixtures, which is based on the expectation–maximization algorithm. The proposed method has been tested on simulation data of finite 3D inter-site distance mixtures. The result using the Gaussian mixture model in the developed method is also discussed for comparison.