Gaussian Mixture Model for Coarse-grained Modeling from XFEL

We explore the advantage of Gaussian mixture model (GMM) for interpretation of single particle diffraction patterns from X-ray free electron laser (XFEL) experiments. GMM approximates a biomolecular shape by the superposition of Gaussian distributions. As the Fourier transformation of GMM can be quickly performed, we can efficiently simulate XFEL diffraction patterns from approximated structure models. We report that the resolution that GMM can accurately reproduce is proportional to the cubic root of the number of Gaussians used in the modeling. This behavior can be attributed to the correspondence between the number of adjustable parameters in GMM and the amount of sampling points in diffraction space. Furthermore, GMMs can successfully be used to perform angular assignment and to detect conformational variation. These results demonstrate that GMMs serve as useful coarse-grained models for hybrid approach in XFEL single particle experiments.