A human mature erythrocyte membrane skeleton is a triangular lattice network composed of various proteins under the membrane, which is essential for the maintenance of cell morphology, deformation, movement, and metabolism. The unique ultrastructural arrangement of the erythrocyte membrane skeleton is fascinating and has attracted many scientists to develop new technologies for imaging and analysis. Emerging single-molecule localization super-resolution microscopy (SMLM) has demonstrated significant capability in resolving the nanoscale ultrastructure of the erythrocyte membrane skeleton; however, the improvement of resolution has put forward high requirements for imaging analysis methods. A Vorono? diagram is a geometric analysis method that divides points in space into different regions to describe their spatial distribution. It is widely used in space exploration, materials science, machine learning, and other research fields. In recent years, this method has been prominently utilized in SMLM data extraction and analysis, mainly in the clustering and colocalization analysis of “point cluster”-shaped images. Taking advantage of the Vorono? method particularly in SMLM image analysis, we aim to apply this method to extract the distribution information of erythrocyte membrane skeleton protein SMLM images, to more quantitatively and accurately reveal skeletal organization characteristics.

SMLM super-resolution images of erythrocyte membranes and skeletal proteins were obtained using a self-built SMLM imaging system. Actin was stained with fluorescently labeled phalloidin (Alexa 647-phalloidin). CD59, N terminus of β-spectrin, tropomodulin (TMOD), and ankyrin were labeled with specific antibodies. After SMLM imaging, regions of interest in the SMLM images were selected for analysis, and the corresponding point-cloud image was drawn according to the positioning coordinates. The centroid of each point cluster was subsequently acquired using DBCAN clustering analysis, and the image boundary was determined based on the maximum and minimum values of all centroid coordinates. The obtained centroids were used as seed points for Vorono? tessellation, and the vertex coordinates of the Vorono? polygon generated by each seed point were obtained using the voronoin function in MATLAB. Area A of the Vorono? polygon was calculated using the polyarea function in MATLAB. All areas A were divided by the average area〈A〉to obtain a histogram of the area distribution (Fig. 1). Finally, the area distribution of the Vorono? polygon was fitted with the γ function, which could be used to describe the spatial distribution characteristics of the “point cluster”-shaped SMLM images of erythrocyte membrane and skeleton proteins.

First, Vorono? analysis was performed for CD59, an erythrocyte membrane protein with high lateral mobility. The x-axis corresponding to the peak of the γ distribution profile (x_peak) of CD59 was 0.78 (Fig. 2), which was slightly larger than the x_peak of the simulated points with a random distribution (Fig. 3). Considering the radius of the point-spread function in the SMLM imaging system, each simulated point was adjusted to a disk with a certain radius (set to 15 nm) for analysis. It was identified that the x_peak derived from the γ distribution of the normalized area increased with point density, while fluctuating between 0.78 and 0.8 in the density range of 60~100 μm^-2, which was consistent with the CD59 Vorono? analysis result, indicating a random distribution of CD59 (Fig. 3). Furthermore, the x_peak values of the membrane skeleton proteins localized at the nodes of the skeleton triangular lattice network of the erythrocyte membrane, including actin, the N terminus of β-spectrin, and tropomyosin, were all 0.86, while the x_peak value of ankyrin was 0.84, indicating that these skeleton membrane proteins were distributed relatively uniformly, whereas the distribution of ankyrin was more random than that of other skeleton proteins (Fig. 4). To investigate the effects of deletion and disturbance of an erythrocyte triangular lattice skeleton on Vorono? analysis results, a Vorono? tessellation of simulated points was conducted with a density considerable to that of actin (approximately 80 μm^-2 measured by SMLM imaging) using a custom-written MATLAB routine. After generating simulated points with an 80 nm interval periodic triangular lattice distribution, random disturbances of varying degrees (0-0.5) relative to the lattice length were applied to the locations of all points, and some points were randomly removed such that the density was identical to that of actin (Fig. 6). The variation trend of x_peak was explored under different disturbance rates, and the results showed that x_peak was 0.86 when the disturbance rate was 0.15 (i.e., the skeleton disturbance was approximately 15%), which was consistent with experimental results, indicating that there was a disturbance of approximately 15% relative to the lattice length in the human erythrocyte triangle lattice skeleton (Fig. 6).

In this study, a solution based on a Vorono? diagram was proposed for the analysis of SMLM super-resolution images of the erythrocyte membrane skeleton. According to the SMLM images “point cluster” feature of membrane and skeleton proteins, we extracted the centroids of point clusters for Vorono? polygon tessellation, and introduced parameters including the x-axis coordinate x_peak corresponding to the peak value of Vorono? polygon area γ distribution curve, the variation coefficient C_v of the Vorono? polygon, and the peak value of the nearest distance for quantitative analysis and characterization of the spatial distribution of erythrocyte membrane and skeleton proteins. The results demonstrated that the accepted mobile membrane protein CD59 was randomly distributed on the cell membrane. Skeleton proteins that were considered to be localized at the triangular lattice nodes, such as actin, the N terminus of β-spectrin, and TMOD, showed a relatively uniform distribution with a disturbance rate of approximately 0.15, whereas the distribution of ankyrins on the spectrin skeleton was slightly less uniform than that on the lattice node. These results demonstrated the validity of the Vorono? method in evaluating the distribution characteristics of erythrocyte membrane skeleton proteins, and the method can be extended to extract and analyze information for other “point cluster”-shaped SMLM images. Finally, the Vorono? analysis strategy is beneficial for understanding accurate spatial distribution characteristics of membrane skeleton proteins and provides novel insights and methods for in-depth information extraction from SMLM super-resolution data.