Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies

TL;DR

This paper demonstrates shape mode analysis as an effective method to describe and differentiate complex biological shapes and movements, such as flagella oscillations and flatworm postures, using principal component analysis.

Contribution

It introduces shape mode analysis as a concise, quantitative approach for characterizing biological shape dynamics and distinguishing species based on shape variability.

Findings

Flagellar oscillations reconstructed as a limit cycle.

Distinct flatworm body postures linked to locomotion modes.

Species discrimination achieved despite shape variability.

Abstract

We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of flagellar oscillations, paying particular attention to the periodicity of angular data. As a second example, we analyze non-convex boundary outlines of gliding flatworms, which allows us to expose stereotypic body postures that can be related to two different locomotion mechanisms. Further, shape mode analysis based on principal component analysis allows to discriminate different flatworm species, despite large motion-associated shape variability. Thus, complex shape dynamics is characterized by a small number of shape scores that change in time. We present this method using descriptive examples, explaining abstract mathematics in a graphic way.