人红细胞膜骨架超分辨图像的Voronoï分析

Voronoï Analysis for Super⁃Resolution Image of Human Erythrocyte Membrane Skeleton

成熟人红细胞膜骨架是由膜下多种蛋白组成的三角晶格网状结构,在维持红细胞形态、变形性、运动和代谢等功能方面扮演着重要角色。单分子定位超分辨成像(SMLM)技术在解析骨架超微结构方面展现出了强大的能力,但分辨率的提升对成像分析手段提出了更高要求。作为一种常用的空间分析方法,Voronoï分割在SMLM图像聚类分析中已被广泛应用。笔者利用自主搭建的SMLM超分辨成像系统获得红细胞膜蛋白和骨架蛋白的超分辨点簇图像,对点簇质心进行Voronoï分割,并对Voronoï多边形面积分布进行伽马函数拟合,发现自由膜蛋白CD59的伽马分布峰值对应的x轴坐标x_(peak)为0.78。结合模拟结果,验证了自由膜蛋白CD59呈随机分布。进一步,肌动蛋白、血影蛋白N端和原肌球蛋白的Voronoï分析结果显示它们的x_(peak)均为0.86,而锚蛋白的x_(peak)为0.84,说明骨架膜蛋白呈相对均匀的分布状态,但锚蛋白较其他骨架蛋白更具随机性。Voronoï方法可助力阐释红细胞膜骨架蛋白的空间分布特性,同时也为点簇状SMLM超分辨图像数据的深入提取提供了新思路和新方法。

Objective 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 Voronoïdiagram 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 Voronoïmethod 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.Methods 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 ofβ-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 Voronoïtessellation,and the vertex coordinates of the Voronoïpolygon generated by each seed point were obtained using the voronoin function in MATLAB.Area A of the Voronoïpolygon 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 Voronoïpolygon was fitted with theγfunction,which could be used to describe the spatial distribution characteristics of the“point cluster”-shaped SMLM images of erythrocyte membrane and skeleton proteins.Results and Discussions First,Voronoïanalysis was performed for CD59,an erythrocyte membrane protein with high lateral mobility.The x-axis corresponding to the peak of theγdistribution 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 theγdistribution of the normalized area increased with point density,while fluctuating between 0.78 and 0.8 in the density range of 60~100μm-2,which was consistent with the CD59 Voronoïanalysis 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 ofβ-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 Voronoïanalysis results,a Voronoïtessellation of simulated points was conducted with a density considerable to that of actin(approximately 80μm-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).Conclusions In this study,a solution based on a Voronoïdiagram 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 Voronoïpolygon tessellation,and introduced parameters including the x-axis coordinate x_(peak)corresponding to the peak value of Voronoïpolygon areaγdistribution curve,the variation coefficient Cv of the Voronoïpolygon,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 ofβ-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 Voronoïmethod 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 Voronoïanalysis 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.