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

PLoS One. 2014 Nov 26;9(11):e113083. doi: 10.1371/journal.pone.0113083. eCollection 2014.


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Biomechanical Phenomena
  • Cattle
  • Cell Shape / physiology
  • Flagella / physiology*
  • Flagella / ultrastructure
  • Male
  • Mathematical Computing
  • Models, Statistical*
  • Motion
  • Movement / physiology*
  • Periodicity
  • Platyhelminths / anatomy & histology
  • Platyhelminths / physiology*
  • Principal Component Analysis
  • Spermatozoa / cytology
  • Spermatozoa / physiology

Grant support

SW and BMF received funding from the BMBF grant 031 A 099 ( The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.