Integrated Analysis of Cell Shape and Movement in Moving Frame

The cell movement and morphological change are two interrelated cellular processes. The integrated analysis is needed to explore the relationship between them. However, it has been challenging to investigate them as a whole. The cell trajectory can be described by its speed, curvature, and torsion. On the other hand, the 3-Dimensional (3D) cell shape can be studied by using a shape descriptor such as Spherical harmonic (SH) descriptor which is an extension of Fourier transform in 3D space. To integrate these shape-movement data, we propose a method to use a parallel-transport (PT) moving frame as the 3D-shape coordinate system. This moving frame is purely determined by the velocity vector. On this moving frame, the movement change will influence the coordinate system for shape analysis. By analyzing the change of the SH coefficients over time in the moving frame, we can observe the relationship between shape and movement. We illustrate the application of our approach using simulational and real datasets in this paper.