The highly ordered spatial organization of microtubule bundles in the mitotic spindle is crucial for its proper functioning. The recent discovery of twisted shapes of microtubule bundles and spindle chirality suggests that the bundles extend along curved paths in three dimensions, rather than being confined to a plane. This, in turn, implies that rotational forces, i.e., torques, exist in the spindle in addition to the widely studied linear forces. However, studies of spindle architecture and forces are impeded by a lack of a robust method for the geometric quantification of microtubule bundles in the spindle. In this work, we describe a simple method for measuring and evaluating the shapes of microtubule bundles by characterizing them in terms of their curvature and twist. By using confocal microscopy, we obtain three-dimensional images of spindles, which allows us to trace the entire microtubule bundle. For each traced bundle, we first fit a plane and then fit a circle lying in that plane. With this robust method, we extract the curvature and twist, which represent the geometric information characteristic for each bundle. As the bundle shapes reflect the forces within them, this method is valuable for the understanding of forces that act on chromosomes during mitosis.

有丝分裂纺锤体中微管束的高度有序的空间组织对其正常功能至关重要。最近对微管束扭曲形状和纺锤体手性的发现表明，微管束沿着三个维度的弯曲路径延伸，而不是局限于一个平面。这反过来意味着除了广泛研究的线性力之外，主轴中还存在旋转力，即扭矩。然而，由于缺乏对纺锤体中微管束的几何量化的稳健方法，对纺锤体结构和力的研究受到阻碍。在这项工作中，我们描述了一种通过表征微管束的曲率和扭曲来测量和评估微管束形状的简单方法。通过使用共焦显微镜，我们获得了纺锤体的三维图像，这使我们能够追踪整个微管束。对于每个追踪的束，我们首先拟合一个平面，然后拟合位于该平面上的一个圆。通过这种稳健的方法，我们提取了代表每个束的几何信息特征的曲率和扭曲。由于束的形状反映了它们内部的力，因此这种方法对于理解有丝分裂过程中作用于染色体的力很有价值。