Protein cryo-EM projection images have a new algorithm for three-dimensional reconstruction

Three-dimensional reconstruction is performed from multiple two-dimensional projection images of cryo-EM to obtain the three-dimensional structure of the protein. Courtesy of Lanzhou University

Protein structure analysis is the core topic of molecular biology, which is of great significance for people to understand the function of proteins, understand the pathogenesis of diseases, and carry out drug design and disease treatment. In recent years, cryo-EM technology has made breakthroughs in the determination of the structure of biological macromolecules, although the AlphaFold developed by DeepMind can already predict the three-dimensional structure of proteins from protein sequences, but its accuracy needs to be improved, and its results can only be used as prediction results.

Recently, Lu Yonggang, a professor at the School of Information Science and Engineering of Lanzhou University, collaborated with Zhu Li, associate professor of the School of Life Sciences of Lanzhou University, and He Jing, a professor in the Department of Computer Science of Ou Daoming University, to propose a three-dimensional protein reconstruction algorithm based on spherical embedding, which helps to reconstruct a more accurate protein three-dimensional structure from cryo-EM images. The relevant results were published online in Communication Biology under the title of “Three-dimensional Reconstruction of Cryo-EM Projection Images Based on Two Spherical Embeddings”.

Single particle analysis is the mainstream technique for determining protein structure by cryo-EM. After using cryo-EM to obtain a large number of two-dimensional projection images of the same protein molecule, the technology uses a three-dimensional reconstruction algorithm to calculate the three-dimensional structure of the protein. Among them, the core problem of protein three-dimensional reconstruction is to estimate the projection direction of each projected image, which is essentially a non-convex optimization problem. Most of the existing algorithms are based on template matching, or parameter estimation algorithms based on expectation maximization, which are easily affected by the initial parameter selection, easy to fall into the local extreme, and may reconstruct the wrong protein structure.

In order to improve the reliability of the three-dimensional reconstruction results, Lu Yonggang’s research group made full use of the total consistency constraints of the entire projection image in terms of projection direction and equivalence line in this research work, and obtained the projection direction estimation that satisfies the consistency constraint of the whole projection image in three-dimensional space through two spherical embeddings, and then calculated the three-dimensional structure of the protein. This method is characterized by the lack of initial templates, the mining constraints from within the data as much as possible, and the dependence on initialization is small, thus improving the reliability and accuracy of the reconstruction results. In addition, Lu Yonggang’s research group also proposed a new projection direction representation method, using two mutually perpendicular vectors (the normal vector of the projected image and the X axis of its own coordinates) to represent the projection direction, and discussed the equivalence of this representation and the commonly used Euler angle representation.

In the experimental work of the paper, the research team used a simulated data set and two sets of real data sets to evaluate the algorithm. By comparing with several common algorithms (Synchronization, LUD, EMAN 2.1 and RELION-2), the effectiveness of the proposed algorithm is verified. The simulated data were generated by computer simulation projections of protein structures corresponding to E. coli 70S ribosomes. The real data used cryo-EM images of the Plasmodium falciparum 80S ribosome dataset (EMPIAR-10028) downloaded from the EPIAR database, and cryo-EM images of the Hedgehog receptor patch with the nanoantibody antibody TI23 complex (EMPIAR-10328).

Experimental results show that the spherical embedding algorithm proposed in this paper can more accurately estimate the projection direction, and in the case of high noise (such as SNR=0.1 or 0.2, etc.), the algorithm can greatly reduce the error of projection angle estimation. The results of the three-dimensional reconstruction also prove that the algorithm has certain advantages when reconstructing on different noise levels and different numbers of projection images, and the resulting reconstruction has a higher resolution and is closer to the real structure. (Source: China Science Daily Wen Caifei Faisa)

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