The nuclear pore complex (NPC) is an intricate structure comprising multiple distinct nuclear pore proteins known as nucleoporins (Nups). It plays a crucial role in the transformation of matter and information between the nucleus and cytoplasm. With a total molecular weight of 110‒125 MDa, the NPC is hailed as the "holy grail" of structural biology. Scientists have used such techniques as electron microscopy, atomic force microscopy, and cryoelectron microscopy to collectively reveal the composition, assembly, and ultrastructure of the NPC, providing a solid structural foundation for further exploration of its functions. The diameter of the NPC is approximately 130 nm. Therefore, single-molecule localization microscopy (SMLM) with an imaging resolution of 20 nm is an ideal tool for studying the ultrastructure of NPC. However, during long-term imaging, data loss may occur because of sparse blinking, and the dynamic activities of life also lead to heterogeneity in imaging results, posing challenges for data analysis. To address these issues, corresponding image reconstruction methods must be developed. Clustering algorithms are powerful tools for quantitative extraction, classification, and analysis of SMLM data. The unique clustered distribution structure of the NPC makes clustering methods highly suitable for structural analysis of the NPC. Therefore, to compensate for the limitations of SMLM data and obtain more detailed structural information about the NPC, a processing procedure for SMLM images of the NPC was developed in this study based on clustering algorithms. It involves screening out NPC structures with a more uniform morphology, followed by subjecting these structures to high-throughput statistical analysis and reconstruction.

After PFA fixation, permeabilization with a blocking buffer, and labeling with antibodies (Nup133 and Nup98), U2OS cells were imaged by a self-built SMLM imaging system. A total of 50000 frames were captured after appropriate fields of view were selected. Through localization and drift correction processes, corresponding SMLM images were obtained. After the regions of interest were selected, the coordinate data with high localization accuracy were preserved for further analysis. First, a first round of density-based spatial clustering of applications with noise clustering (DBSCAN) analysis was used to remove background noise, identify individual NPCs, and determine the centroids of the NPCs (Fig. 3). To achieve a more accurate delineation of each Nup within every NPC in the case of retaining all signal points, a combination of the DBSCAN algorithm and hierarchical clustering was employed in the second round of delineation. In the second round of DBSCAN analysis, the algorithm was applied to identify the number of individual Nups within each NPC, and the data were further input into a hierarchical clustering algorithm for refinement of Nup localization. Subsequently, NPCs containing four to eight Nups were retained, and a second screening based on shape factors was performed to preserve NPCs with more uniform morphologies. Finally, the centroids of all remaining NPCs were aligned to obtain the complete distribution of labeled Nups in the NPCs. Using the least-squares method with NPC centroids as the center, a reconstruction of the Nup distribution with octagonal symmetry was achieved (Fig. 4). The reconstructed structure can be used to analyze the spatial characteristics of the Nup.

Nup133, as a characteristic "Y"-scaffold-shaped component protein, has received extensive attention in recent research. Through statistical analysis of multiple datasets, the first round of the DBSCAN algorithm identified 10329 NPCs (Fig. 5). Among them, 3076 NPCs containing four to eight Nup133 were present, accounting for approximately 30% of the total. By selecting based on shape factors, a final set of 558 NPCs with relatively regular shape was obtained, accounting for approximately 5% of the total (Table 1). The retained NPCs were aligned by their centroids, resulting in an overlapped NPC image. Gaussian fitting was applied to calculate the radii of all Nup133, with the peak corresponding to a horizontal coordinate of (58.4±0.1) nm. This value is very close to the Nup133 radius of (59.4±0.2) nm calculated using the particle averaging method with antibody labeling. This further demonstrates the high-precision performance of the screening and reconstruction methods used in this study. In addition, the same analysis process was applied to analyze NPCs labeled with Nup98. Compared with that of Nup133, the distribution of Nup98 located in the inner ring of the NPC is more condensed (Fig. 6). A total of 10668 NPCs were analyzed, and 1126 NPCs were ultimately retained, accounting for approximately 10% of the total (Table 1). Similarly, the remaining NPCs labeled with Nup98 were aligned by the centroids, and Gaussian fitting was applied to the overlapped Nup98, resulting in a peak corresponding to a horizontal coordinate of (39.7±0.2) nm (Fig. 6). Compared with that of Nup133, the radius of Nup98 is smaller by 18.7 nm, indicating that Nup98 is closer to the center position of the NPC than Nup133. Finally, the eightfold symmetric structure of Nup133 and Nup98 was successfully reconstructed using the rotation alignment method, which is consistent with the acknowledged model.

The present study proposes a processing workflow based on clustering methods for screening and reconstruction of SMLM images of the NPC. The workflow has three main parts: classification, screening, and reconstruction. By performing two rounds of clustering to identify the NPC and Nup components, NPCs with a uniform shape containing four to eight Nups are selected and subjected to reconstruction analysis. The NPC with an eightfold symmetric structure is successfully reconstructed using the proposed workflow. Experimental results on Nup133 and Nup98 show that the radius of Nup133 is (58.4±0.1) nm, which closely aligns with the radius determined by the particle averaging method. The radius of Nup98 is (39.7±0.2) nm, indicating that Nup98 is situated in closer proximity to the central region of the nuclear pore. The proposed method reproduces the eightfold symmetric structure of the NPC, providing accurate localization information and aiding in a deeper understanding of the composition of this important structure. This clustering-based reconstruction method can also be extended to other nuclear pore-like structures, such as centrioles and basal bodies, or other structures with isotropic symmetric features, offering important strategies and methods for deciphering complex biological structures.