Resolution Estimation Of Cryo-EM 3D Density Map Based On Multi-scale Spectral Analysis

Cryo-EM 3D reconstruction technology has a rapid development in biomolecule’s 3D structure study in recent years.Compared with the traditional methods,it shows excellent performance and has achieved a near atomic resolution.It attracts more and more researchers’ attention.Resolution estimation of Cryo-EM 3D density map has significant meaning.It influences the direction of calculating biomolecule’s 3D structure in iterative procedure,and also is a target of evaluating the quality of the final result of 3D reconstruction.However,the existing resolution estimation methods all have their own defects.In this paper,we propose a new resolution estimation method for Cryo-EM 3D density map based on multi-scale spectral analysis.Multi-scale spectral analysis utilizes a series of masks with different sizes to realize resolution estimation.An ideal mask is the mask that can exactly separate the biomolecule signal part and the surrounding noise part in Cryo-EM 3D density map.Thus the relationship between powers of noise inside and outside the mask can be used to calculate a spectral signal to noise ratio inside the mask.Finally a resolution can be determined based on the spectral signal to noise ratio curve.However,in real experiment situation,an ideal mask cannot be generated.So we propose to use a series of unsatisfactory masks with different sizes to calculate multi-scale spectral signal to noise ratio curves.The masks with different sizes are generated by making two size-related parameters change in a range.For every different mask,we can calculate a resolution inside the mask.Multi-scale spectral analysis algorithm puts the resolution and the corresponding parameters’ values on the same picture to obtain a resolution 3D surface.There is an obvious border line on the surface,and multi-scale spectral analysis algorithm supplies two strategies to determine the key point on the border line.The key point’s resolution is the final resolution value of the Cryo-EM 3D density map.In this paper,we propose to use multi-scale spectral analysis to calculate the Cryo-EM 3D density map’s resolution,improve the method of calculating spectral signal to noise ratio based on mask,and explore the relationship between FSC and SSNR.Through conducting experiments on 20 real datasets,we verify effectiveness of the proposed multi-scale spectral analysis algorithm for calculating resolution of the Cryo-EM 3D density map.This algorithm overcomes the traditional methods’ shortcomings and has a great performance.