中文摘要：

低温电镜三维重构技术近年来得到飞速发展，其在分析生物大分子复合物的结构和功能中起着重要作用。低温电镜三维重构技术主要包括电子断层三维重构技术、电子晶体学及单颗粒三维重构技术。由于无需结晶，且所能达到的分辨率较高，目前，单颗粒三维重构技术已经成为电镜三维重构领域的主流技术。在用单颗粒三维重构技术进行结构解析时，有一类特殊的研究对象，即螺旋组装体，如烟草花叶病毒（tobaccomosaicvirus，TMV）、微管和微丝（microfilament）、艾滋病病毒1型（HIV-1）衣壳蛋白等，对这类螺旋组装体的结构进行三维重构不是很容易，涉及诸多物理和数学的概念。本文重点介绍螺旋组装体的基本重构原理，包括螺旋组装体的数学描述、衍射指数的推导和物理意义、螺旋点阵和真实螺旋组装体Fourier变换间的关系，以及螺旋对称参数的测定和计算等。在此基础上，文章综述了螺旋组装体的三维重构算法，主要包括频率空间的Fourier-Bessel重构方法和实空间的迭代单颗粒重构方法。最后，文章以与细胞极性发生相关的蛋白Par-3的N端结构域Par-3NTD为实例，详细介绍了Par-3NTD螺旋组装体的实空间迭代单颗粒重构方法。

英文摘要：

The cryo-electron microscopy reconstruction technique has been developed rapidly in recent years and becoming an important approach for structural studies of macromolecular complexes, and it includes three different methods, cryo-electron tomography, electron crystallography, and single particle analysis （SPA）. Among them, the SPA technique is now becoming a powerful tool to determine near-atomic resolution structures of macromolecular complexes. However, for those biological macromolecular assemblies with helical symmetry, such as tobacco mosaic virus （TMV）, microtubules, microfilament, human immunodeficiency virus 1 capsid protein and etc., it is not easy to obtain their three dimensional structures by using SPA because there are lots of math to deal with. In this paper, the authors described the helical reconstruction technique in details, including the basic mathematical description of helical assemblies, helical diffraction and its indexing, the relationship between Fourier transform of helical points array and that of real helical assemblies, and how to determine the helical parameters. Based on the above introduction, the authors reviewed two main helical reconstruction algorithms, the Fourier-Bessel reconstruction and the iterative helical real space reconstruction （IHRSR）. At the end, they selected the helical assembly of Par-3 NTD （Par3 is a kind of protein related to cell polarity control and Par-3 NTD is its N-terminal domain） as an example to show a detailed helical reconstruction protocol using IHRSR algorithm.