Abstract
ABSTRACTThe cell's movement and morphological change are two interrelated cellular processes. An integrated analysis is needed to explore the relationship between them. However, it has been challenging to investigate them as a whole. The cell's trajectory can be described by its speed, curvature, and torsion. On the other hand, the three-dimensional (3D) cell shape can be studied by using a shape descriptor such as spherical harmonic (SH) descriptor, which is an extension of a Fourier transform in 3D space. We propose a novel method using parallel-transport (PT) to integrate these shape-movement data by using moving frames 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 simulated and real datasets in this paper.
Highlights
IntroductionThe cell’s movement and morphological change are highly integrated
The cell’s movement and morphological change are highly integrated.They share many biological mechanisms controlled by the cytoskeleton, cell membrane, membrane proteins, and extracellular matrix (Friedl and Wolf, 2009; Ridley, 2003)
We propose a more natural way to align the rotation of a moving object such as a motile cell
Summary
The cell’s movement and morphological change are highly integrated. They share many biological mechanisms controlled by the cytoskeleton, cell membrane, membrane proteins, and extracellular matrix (Friedl and Wolf, 2009; Ridley, 2003). Almost all forms of the cell’s active movement need forces that are generated from dynamic shape change (Lämmermann and Sixt, 2009). It significantly facilitated researchers to study the dynamic interplay between shape and movement of the cell. We need the ability to objectively quantify the cell’s shape and movement.
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