中国激光, 2023, 50 (15): 1507104, 网络出版: 2023-08-08   

人红细胞膜骨架超分辨图像的Voronoï分析 下载: 505次

Voronoï Analysis for Super‑Resolution Image of Human Erythrocyte Membrane Skeleton
杨建宇 1胡芬 1,*侯梦迪 1董浩 1陈靖 1潘雷霆 1,2,3,4,**
作者单位
1 弱光非线性光子学教育部重点实验室,南开大学物理科学学院,泰达应用物理研究院,天津 300071
2 药物化学生物学国家重点实验室,南开大学生命科学学院,细胞应答交叉科学中心,天津 300071
3 南开大学深圳研究院,广东 深圳 518083
4 极端光学协同创新中心,山西大学,山西 太原 030006
摘要
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,Vorono?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Vorono?分割,并对Vorono?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xpeak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Vorono?分析结果显示它们的xpeak均为0.86,而锚蛋白的xpeak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。Vorono?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。
Abstract
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 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.

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 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.

Results and Discussions

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 (xpeak) of CD59 was 0.78 (Fig. 2), which was slightly larger than the xpeak 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 xpeak 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 xpeak 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 xpeak 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 xpeak was explored under different disturbance rates, and the results showed that xpeak 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 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 xpeak corresponding to the peak value of Vorono? polygon area γ distribution curve, the variation coefficient Cv 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.

1 引言

人成熟红细胞结构简单,无细胞核和其他细胞器,仅有一层细胞膜以及依附于膜的细胞骨架网状结构,内部填充着血红蛋白。其具有独特的双凹圆盘状形态,具有极强的变形性和较高的强度1-2。区别于有核细胞由细胞骨架和膜骨架共同维持细胞的形状和运动,红细胞只有膜骨架承担此功能,因此研究红细胞膜骨架的结构和分布特性对于了解其功能至关重要。红细胞膜骨架由多种蛋白组成,呈经典的三角晶格纤维网状结构3-4。蛋白免疫印迹、流式细胞术等传统生物学方法可在多细胞水平上探究骨架蛋白组分表达,但其在单细胞纳微时空信息获取方面仍存不足5-6。受限于衍射极限,常规的显微成像难以对红细胞膜骨架的精细结构进行有效观察与解析,亟待新方法、新技术出现,以进一步揭示其中的奥妙7

近年来,研究人员利用各种先进的成像技术,如冷冻电镜技术8-9、原子力显微镜技术10-11、超分辨光学显微镜技术12-13,以及多种技术的联用14,不断地揭示红细胞膜骨架的新信息,其中新兴的超分辨光学成像技术在解析红细胞膜骨架的纳米尺度空间分布方面展现出了强大的能力15-16。如:Pan等12运用单分子定位超分辨成像(SMLM)技术在近生理条件下对人红细胞骨架的结构特性进行了研究,结合最近距离分析、二维自相关和互相关分析,证明了骨架核心组分——血影蛋白的生理长度约为80 nm,澄清了近40年来关于其生理长度的疑问。Hou等13发展了膨胀显微镜(U-ExM)结合SMLM的超分辨成像技术——U-ExSMLM,该技术达到了约6 nm的分子分辨率水平,揭示了血影蛋白骨架在红细胞凹区和边缘区分布的不对称性,为理解红细胞独特的双凹圆饼形态及形状记忆现象提供了分子水平的成像解释。然而,尽管SMLM超分辨成像可对红细胞膜骨架蛋白进行无/低损、可视、高精度检测,但获得的点簇状图像与电镜获得的纤维网状图像17-18有很大差别,难以直观地揭示膜骨架的空间排布特性。因此,对SMLM图像进行深层挖掘、提取非常关键,而这需要发展新的数据分析方法来准确、定量地描述点簇图像的分布特性。

Voronoï图是一种将空间内的点划分为不同区域以描述点在空间中分布情况的几何分析方法19,已被广泛地应用于空间探测、材料科学、机器学习等领域20-23。近年来,该方法在SMLM图像的数据提取和分析中表现突出,主要用于点簇图像的聚类和共定位分析24-26。2015年,Levet等27提出了SR-Tesseler聚类分析方法,利用Voronoï图分割SMLM图像,有效提取SMLM图像的点簇信息。类似的利用Voronoï图进行SMLM图像分割的聚类分析程序还有ClusterVisu28,这些程序在SMLM成像分析中被广泛应用。如:Su等29成功地对细胞核内的复制斑进行了SMLM成像,并使用SR-Tesseler分割出细胞核内单个复制斑的形貌,实现了对复制斑形态和分布的描述。Han等30使用SMLM对小鼠神经元胞体中的βIII-Spectrin进行成像,随后使用ClusterVisu对其进行识别,并以此为基础绘制了晶格网络结构。2019年,Levet等31在SR-Tesseler的基础上又开发出了共定位分析方法Coloc-Tesseler,该方法将两个通道的SMLM图像转化为Voronoï图后,根据重叠Voronoï多边形的归一化密度计算共定位程度。Tania等32对Hela细胞线粒体内膜、外膜以及ATAD3A蛋白进行了SMLM成像,并使用Coloc-Tesseler证明了线粒体膜与ATAD3A蛋白的共定位关系。

鉴于Voronoï方法在图像分析尤其是SMLM图像分析中所展现出的潜力和优势,笔者先通过聚类分析提取红细胞膜蛋白及膜骨架蛋白SMLM图像中点簇的质心,然后在此基础上对质心进行Voronoï分割,对面积分布进行伽马函数拟合和定量分析,并结合理论建模分析阐释红细胞膜骨架的分布特性。

2 原理与方法

2.1 红细胞膜蛋白的SMLM成像

首先需要获得近生理条件下红细胞膜蛋白的SMLM图像。红细胞制样方法与本课题组之前的工作一致12:取健康志愿者5 μL指尖血,将其加入到红细胞保存液中进行稀释,随后将细胞贴附于多聚赖氨酸处理过的玻璃基底。红细胞肌动蛋白(actin)使用荧光标记的鬼笔环肽(Alexa 647-phalloidin)进行染色,CD59、β-血影蛋白N端(N terminus of β-Spectrin)、原肌球蛋白(tropomodulin,TMOD)和锚蛋白(ankyrin)分别使用特异性抗体进行标记。

随后,利用自主搭建的横/纵向分辨率为25/50 nm的SMLM超分辨成像系统分别对上述蛋白进行成像。该系统主要包括全电动倒置荧光显微镜(Nikon,Ti-E)、405 nm和647 nm激光器以及EMCCD(Andor,DU-897)。具体步骤为:以较低的激光强度照射细胞,寻找到合适的成像视野后,将激光功率切换至约2 kW/cm2,使该视野范围内的荧光分子发生随机“闪烁”,实现相邻点之间交替稀疏发光。每个成像视野拍摄约50000帧图片,采集期间适当加入低强度紫外光,以提高荧光闪烁能力。对每一帧图片中的点扩散函数进行高斯拟合,以获得单分子质心的横向和轴向坐标,再将所有的坐标点整合到一起,并进行漂移校正,最终得到重构的SMLM图像2533

2.2 Voronoï图分析方法

构建Voronoï图的过程如下:对于给定的一组点集,点集中的每个点都被Voronoï图视为“种子点”34。以种子点为中心,将其与其他种子点作最近距离分析,找到最邻近的种子点后绘制这两点距离的垂直平分线,将所有边界线相连,得到Voronoï图27

构建好的Voronoï图有3个特点:1)每个Voronoï多边形内只有一个种子点;2)每个Voronoï多边形空间内的任意位置到其多边形内种子点的距离最近;3)Voronoï多边形边上的点到相邻两个多边形内种子点的距离相等。

可根据Voronoï图中多边形的面积、边数以及相邻种子点间距等信息定量地获得空间内点集的分布情况34-36。其中,Voronoï多边形的面积较为直观地表达了空间内点集的聚集程度。根据Voronoï分割原理,局部点密度较高区域构建的Voronoï多边形面积较小;局部点密度较低区域构建的Voronoï多边形面积较大。利用这一特征提取高密度Voronoï多边形种子点的方法已被应用于SMLM图像的聚类分析27-32。对于点簇状分布的SMLM图像,还可以根据Voronoï多边形面积定量给出区域内点集的空间分布模式。具体操作如下:首先选取要分析的SMLM图像区域,根据定位坐标绘制点云图像,随后通过结合多次DBSCAN算法和层次聚类算法的点簇识别方法获取每个点簇的质心37,再基于所有质心坐标中的最大值和最小值获得图像边界。以获得的质心作为种子点进行Voronoï分割,通过MATLAB中的voronoin函数即可获得每个种子点所生成的Voronoï多边形的顶点坐标。在生成Voronoï图过程中,位于最边缘的种子点的边界交汇处可能会伸向无限远的位置,这些边界点生成的Voronoï多边形面积会导致后续的面积分布统计出现异常。为了消除边界效应,将生成超出边界的Voronoï单元的坐标顶点去除。最后,通过MATLAB中的polyarea函数获取剩余Voronoï多边形的面积A。将所有面积A除以平均面积〈A〉,获得面积分布柱状图,如图1所示。随机分布点集的Voronoï面积分布满足双参数伽马分布35,即

图 1. SMLM图像的Voronoï分析流程图

Fig. 1. Flow chart of Voronoï analysis for SMLM image

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y=baΓaxa-1exp-bx

式中:Γ(a)为伽马函数;a为伽马分布的形状参数;b为伽马分布的尺度参数伽马分布的均值μ=a/b,方差σ2=a/b2。通过该分布即可对SMLM图像中点簇的空间分布特性进行描述。

根据Voronoï分割的原理,越是均匀分布的点,其分割后的面积越趋近于相等,即归一化后面积的伽马分布的峰值越趋近于1。

另外,还可以使用Voronoï多边形的变异系数Cv描述点簇的Voronoï多边形的规则程度,变异系数的计算公式38

Cv=inAi-A2nA

式中:Ai为提取出的第i个Voronoï多边形的面积;〈A〉为Voronoï多边形的平均面积;n为提取到的Voronoï多边形的总数。变异系数Cv是Voronoï多边形面积标准差与面积平均值的比。若点分布得均匀,分割后的Voronoï多边形面积趋近于相同,则Cv越趋近于0;若点呈簇状分布,而位于簇内点的Voronoï多边形面积越小,位于簇外点的Voronoï多边形面积越大,则Cv越趋近于1;若点呈随机分布,则Cv越趋近于0.5。通过Voronoï分析得到的伽马分布信息和Cv均可描述目标点的空间分布情况,但Cv无法针对SMLM成像的特征实现对应的调整,因此得到的数值可能与实际情况存在一定偏差,而基于Voronoï多边形分析的伽马分布则可以很方便地根据SMLM的成像特征对三角晶格骨架的模拟效果进行修正。

2.3 最近距离分析

最近距离分析又称为“最近邻分析”39,该方法的步骤是:遍历计算每个点与其最邻近点之间的距离,将得到的距离进行统计并绘制直方图,得到空间内点与点之间最近距离的分布。最近距离分布的峰值代表区域内点与点之间最近距离出现次数最多的情况。目前该方法已被用于分析红细胞晶格骨架的分布特征12

3 结果与讨论

3.1 人红细胞自由膜蛋白SMLM图像的Voronoï分析

首先对人红细胞中公认的可自由移动的膜蛋白CD5940进行SMLM超分辨成像,如图2(a)所示。普通免疫荧光图像难以分辨细节[如图2(b)所示],无法对其空间分布特性进行分析,而SMLM图像可以清晰地显示出CD59在红细胞膜上以点簇状分布。随后利用聚类分析获得点簇的质心,并计算出其密度约为80 μm-²。再对点簇质心进行Voronoï分割,提取分割出Voronoï多边形面积,然后计算CD59点簇的Voronoï多边形的变异系数Cv,结果显示Cv=0.45。

图 2. CD59分布的Voronoï图分析。(a)CD59的SMLM图像和CD59点簇质心的Voronoï分割;(b)CD59的普通荧光成像图片;(c)CD59点簇Voronoï多边形面积的伽马分布;(d)CD59点簇的最近距离分析

Fig. 2. Distribution analysis of CD59 by Voronoï diagram. (a) SMLM image of erythrocyte CD59 and Voronoï tessellation of the mass center of CD59 clusters; (b) corresponding conventional fluorescence image of CD59; (c) γ distribution of Voronoï polygon area of CD59 clusters; (d) nearest distance analysis of CD59 clusters

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接下来对CD59点簇的Voronoï多边形面积分布进行归一化及伽马函数拟合。这里得到的CD59的伽马分布峰值对应的x轴坐标xpeak为0.78,如图2(c)所示。此外,笔者还对CD59点簇质心之间的最近距离进行了统计,得到其最近距离峰值为50 nm,如图2(d)所示。

3.2 不同分布特性模拟点集的Voronoï分析

为阐明由Voronoï图得到的xpeak数值所表征的点集分布特性,笔者通过编写MATLAB程序对不同密度的随机和三角晶格点集分布数据进行Voronoï图构建,获得了不同分布模拟点集的xpeak值,并探究了该数值与点密度之间的关系,如图3所示。

图 3. 不同分布特性点集的模拟和Voronoï图分析。(a)随机分布的理想点集;(b)半径为15 nm的圆盘状随机分布点集(互斥分布点集);(c)三角晶格分布的理想点集;(d)(e)点密度对随机分布模拟点集Voronoï图伽马分布拟合损失函数和xpeak的影响

Fig. 3. Simulation and Voronoï analysis of the points with different distributions. (a) Ideal points with random distribution; (b) points adjusted to disks with a certain radius (set to 15 nm), defining as exclusive distribution; (c) points with triangular lattice distribution; (d)(e) effects of point density on the loss function of γ distribution fitting and xpeak value derived from Voronoï diagram for random and exclusive distributions

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随机分布的理想质点的Voronoï多边形分割区域被归一化以满足伽马分布,该分布的xpeak为0.72,该值与点密度无关,如图3(a)、(e)所示。对真实SMLM点簇数据进行聚类分析时发现现有的聚类方法无法提取SMLM分辨率极限以下的两个点簇,因此提取后的点簇质心必然存在一定的互斥关系。为了模拟真实点簇的分布,考虑到SMLM图像上点簇的大小,需要将随机分布的质点修正为具有一定半径的圆盘(半径设置为15 nm),其归一化面积的伽马分布峰值对应的x轴坐标xpeak在60~100 μm-²密度范围内在0.78~0.8之间浮动,如图3(b)、(e)所示。本文使用损失函数来测试伽马分布拟合的效果。损失函数为

floss=inyi^-yin

式中:yi为Voronoï多边形面积分布柱状图对应的实际值;yi^为相同x坐标下伽马分布对应的拟合值;n为伽马分布直方图组数。结果显示伽马分布在两种情况下均表现出不错的拟合效果,损失函数在10-4量级,如图3(d)所示。三角晶格分布点的Voronoï多边形分割区域大小相同,因此其归一化面积恒为1,该数值同样与点密度无关,如图3(c)所示。由模拟结果可知,CD59分子的xpeak为0.78,如图2(c)所示,与图3(b)所示的模拟的随机分布值极为相似,说明CD59随机分布在红细胞膜上。

3.3 Voronoï分析揭示红细胞膜骨架蛋白分布差异

笔者又对肌动蛋白、β-血影蛋白N端、原肌球蛋白和锚蛋白等4种具有代表性的红细胞膜骨架蛋白进行了类似的Voronoï分析,如图4所示。先通过聚类分析提取4种蛋白SMLM图像中点簇的质心,得到4种蛋白的密度分别约为80、100、70、100 μm-²,随后对点簇质心进行Voronoï分析,结果发现:肌动蛋白、β-血影蛋白N端、原肌球蛋白、锚蛋白的xpeak分别为0.86、0.86、0.86、0.84,Cv分别为0.37、0.37、0.39、0.40(表1)。这些结果说明上述4种骨架膜蛋白与CD59相比呈较均匀的分布,但锚蛋白较其他骨架蛋白的分布更具随机性。

图 4. 不同红细胞膜骨架蛋白SMLM图像的Voronoï分析和最近距离分析。(a)红细胞肌动蛋白;(b)β-血影蛋白N端;(c)原肌球蛋白;(d)锚蛋白;(e)红细胞膜骨架超微结构模型示意图

Fig. 4. Voronoï analysis and nearest distance analysis for SMLM images of different membrane skeletal proteins in erythrocytes. (a) Erythrocyte actin; (b) N terminus of β-spectrin; (c) TMOD; (d) ankyrin; (e) schematic of ultrastructural model of erythrocyte membrane skeleton

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表 1. 红细胞中不同蛋白的分布参数

Table 1. Distribution parameters of different proteins in erythrocyte

Type of proteinsPeak value of γ distribution corresponds to the x-axis coordinate xpeakCoefficient of variation CvPeak of the nearest distance dmax /nm
CD590.780.4550
Actin0.860.3770
N terminus of β-spectrin0.860.3770
TMOD0.860.3980
Ankyrin0.840.4060

查看所有表

同时,笔者还分析了4种蛋白的最近距离分布,其中肌动蛋白、β-血影蛋白N端、原肌球蛋白的最近距离峰值分别为70、70、80 nm[如图4(a)~(c)所示],与先前的研究结果一致12,这表明红细胞三角晶格骨架长度约为80 nm。如图4(d)所示,锚蛋白最近距离峰值为60 nm,这提示锚蛋白可能与其他骨架蛋白存在分布差异。根据已有的红细胞膜骨架模型[如图4(e)所示],肌动蛋白、β-血影蛋白N端和原肌球蛋白均位于连接复合体上,即三角晶格网络的节点上,而锚蛋白定位于β-血影蛋白的第14~15片段处,即位于血影蛋白四聚体上约四分之三的位置处。41-42。因此,节点蛋白会比位于血影蛋白上的锚蛋白的分布更加均匀,而本文通过Voronoï和最近距离分析得到的结果很好地证明了两类骨架蛋白分布特性的细微差别。

3.4 缺失和扰动对均匀分布点集Voronoï图的影响

理论上,对于均匀分布的点集,其Voronoï图的xpeak数值应该为1。但SMLM成像过程中荧光标记不全导致的信息缺失和红细胞晶格骨架本身的扰动都会在很大程度上影响该数值,因此本文对三角晶格膜骨架节点蛋白SMLM图像进行Voronoï分析后实际得到的xpeak数值为0.86。首先探究仅存在点缺失情况下xpeak的变化趋势。创建间距为80 nm的三角晶格点阵,经计算点阵密度约为180 μm-2,如图5(a)所示。而SMLM成像的骨架蛋白密度约为70~100 μm-2,这说明SMLM成像的红细胞骨架蛋白信息存在缺失。因此,对点阵设置0.05~0.8(即5%~80%)的随机缺失并进行Voronoï分析,观察其损失函数和xpeak的变化。结果显示:随着缺失率增大,Voronoï图的伽马分布拟合损失函数以及xpeak均逐渐减小,但损失函数依旧保持在10-3量级,说明拟合效果较差,如图5(b)所示。当晶格密度缺失至与SMLM测得的肌动蛋白约80 μm-2的密度(缺失率约为0.55)相符时,虽然xpeak约为0.86,但伽马函数拟合效果在10-3量级,拟合效果较差,同时最近距离分布也与实验测得的分布不相符。这说明单纯的三角晶格缺失不足以描述红细胞骨架的分布模式。

图 5. 仅存在缺失对Voronoï分析结果的影响。(a)晶格模拟点集缺失后的Voronoï分割;(b)(c)缺失率对损失函数和xpeak的影响;(d)(e)模拟点集缺失率为0.55时,Voronoï图的伽马分布和最近距离分析

Fig. 5. Effects of deletion alone on Voronoï analysis results. (a) Voronoï tessellation of simulated points with lattice distribution after deletion; (b)(c) effect of deletion ratio on loss function and xpeak; (d)(e) γ distribution of Voronoï diagram and nearest distance analysis of simulated points with 0.55 deletion ratio

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进一步,以SMLM成像得到的红细胞肌动蛋白密度(约为80 μm-2)为基准,通过自编的MATLAB程序模拟了缺失和扰动同时存在对均匀分布蛋白xpeak数值的影响,模拟结果如图6所示。首先生成间隔为80 nm的周期性三角晶格分布点,然后将所有点的位置施加不同程度的随机扰动,并随机移除部分点,使点密度与SMLM成像测得的肌动蛋白点簇的密度相同,然后进行Voronoï分割,如图6(a)所示。探究了不同扰动率(0~0.5)下损失函数的变化趋势。扰动率指的是点相对于晶格间距(80 nm)发生的随机位置偏移率,可使用MATLAB中的randn函数实现扰动率与晶格间距乘积的标准随机正态分布位移。扰动率最小为0,即点自身没有位置偏移;扰动率最大为1,即每个点产生距自身位置至多80 nm的随机移动。扰动率为0时,伽马函数的拟合结果在10-3量级,这是因为无扰动的缺失晶格分布不满足泊松分布,因此伽马分布的拟合效果较差,如图6(b)所示。随着扰动率增大,损失函数逐渐减小并趋于平缓,表明伽马拟合效果越来越好。本文还分析了不同扰动率下xpeak的变化趋势,结果显示扰动率为0.15时xpeak为0.86[如图6(c)所示],同时该条件下最近距离分析显示得到的最大值对应的距离为70 nm[如图6(d)所示],与实验结果[如图5(a)所示]一致。这些结果说明人红细胞三角晶格骨架存在0.15左右的扰动。

图 6. 扰动和缺失对Voronoï分析结果的影响。(a)晶格模拟点集扰动和缺失后的Voronoï分割;(b)(c)扰动率对损失函数和xpeak的影响;(d)模拟点集在0.15扰动率下的最近距离分析

Fig. 6. Effects of disturbance and deletion on Voronoï analysis results. (a) Voronoï tessellation of simulated points with lattice distribution after disturbance and deletion; (b)(c) effect of disturbance ratio on loss function and xpeak; (d) nearest distance analysis of simulated points with 0.15 disturbance ratio

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4 结论

针对红细胞膜骨架SMLM超分辨图像的分析问题,提出了一种基于Voronoï图的解决方案。骨架蛋白的SMLM图像具有点簇特征,根据这一特征提取点簇质心并进行Voronoï多边形分割,同时引入Voronoï多边形面积伽马分布图峰值对应的x轴坐标xpeak和Voronoï多边形变异系数Cv等参量,并辅以最近距离峰值,对红细胞膜蛋白和骨架蛋白点簇的空间分布特性进行定量分析和表征。结果显示:在细胞膜上可自由移动的CD59膜蛋白为随机分布;肌动蛋白、β-血影蛋白N端和原肌球蛋白等三角晶格节点蛋白呈现相对均匀的分布,扰动率约为0.15,而位于血影蛋白骨架上的锚蛋白的分布均匀性稍差于晶格节点蛋白。这些结果证明了基于Voronoï的分析方法在评价红细胞膜骨架蛋白分布特性方面的有效性,该方法可推广至多样SMLM点簇图像的深层信息提取与分析。

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杨建宇, 胡芬, 侯梦迪, 董浩, 陈靖, 潘雷霆. 人红细胞膜骨架超分辨图像的Voronoï分析[J]. 中国激光, 2023, 50(15): 1507104. Jianyu Yang, Fen Hu, Mengdi Hou, Hao Dong, Jing Chen, Leiting Pan. Voronoï Analysis for Super‑Resolution Image of Human Erythrocyte Membrane Skeleton[J]. Chinese Journal of Lasers, 2023, 50(15): 1507104.

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