Supplementary Material for: On the variability in cell and nucleus shape

Cell morphology is an important regulator of cell function. Many abnormalities in cellular behavior can be discerned from changes in the shape of the cell and its organelles, typically the nucleus. Two major challenges for developing such phenotypic assays are reconstructing 3D surfaces of individual cells and nuclei from confocal images and developing characterizations of these surfaces for comparisons. We demonstrate two algorithms - 3D Active Contours and 3D Condensed-Attention UNet to segment cells and nuclei from confocal images. The cell and nuclear surfaces are then converted into vectors using a reversible, spherical transform - i.e. shapes can be recovered from the vectors. Typical methods for characterizing shapes using size, shape, and image parameters such as area, volume, shape factor, solidity, and pixel intensities are not amenable to such reverse transformation. Our vector representation's Principal Component Analysis (PCA) shows that the significant modes of variability among cell and nucleus shapes are scaling and flattening. We benchmark these modes using a known mechanical model for nucleus morphology. Subsequent modes alter the eccentricity of the nucleus and translate and rotate it with respect to the cell. Our vector-space representation of cell and nucleus shape helps physically interpret the variability sources. It may further help to guide mechanical models and identify molecular mechanisms driving cell and nuclear shape changes. The source code and the data used in this article are available at: https://github.com/iitgoa-ml/3d-cells-nuclei-segmentation

细胞形态是调控细胞功能的重要因素。诸多细胞行为异常均可通过细胞及其细胞器（通常为细胞核）的形态变化得以识别。开发此类表型分析实验所面临的两大核心挑战，在于从共聚焦图像中重建单个细胞与细胞核的三维表面，以及构建这些表面的表征方法以实现对比分析。本研究提出两种算法——3D主动轮廓（3D Active Contours）与3D压缩注意力UNet（3D Condensed-Attention UNet），用于从共聚焦图像中分割细胞与细胞核。随后，我们利用可逆球面变换将细胞与细胞核表面转换为向量形式——即通过该向量可还原出原始形态。传统形状表征方法多基于尺寸、形态及图像参数（如面积、体积、形状因子、紧实度与像素强度），但这类方法无法支持此类逆向变换。针对我们的向量表征进行的主成分分析（Principal Component Analysis，PCA）结果显示，细胞与细胞核形态的主要变异模式为缩放与扁平化。我们利用已有的细胞核形态力学模型对这些变异模式进行了基准验证。后续变异模式则会改变细胞核的偏心率，并使其相对于细胞发生平移与旋转。我们提出的细胞与细胞核形态向量空间表征方法，有助于从物理层面解析形态变异的来源。该方法还可辅助指导力学模型的构建，并助力阐明驱动细胞与细胞核形态改变的分子机制。本文所用源代码与数据集已公开于：https://github.com/iitgoa-ml/3d-cells-nuclei-segmentation