Phototropism pp 223-234 | Cite as

Quantitative Measurements of Curvature Along the Growth Axis in Tropic Responses Using Free Software Environments

  • Kotaro T. YamamotoEmail author
  • Ken Haga
Part of the Methods in Molecular Biology book series (MIMB, volume 1924)


Tropic responses in plants have usually been studied by measuring changes in the deflection angle of the organ tip. However, the measurement of other geometric parameters, such as curvature along the entire length, may give us better understanding of tropic responses, particularly in shoots. Here, we describe methods for obtaining quantitative measurements of local curvature and other parameters based on digital images of bending Arabidopsis hypocotyls using the free software packages, ImageJ and R.

Key words

Curvature Curve fit Hypocotyl bending ImageJ Partial derivative of curvature 



This work was funded in part by Grants-in-Aid from Ministry of Education, Culture, Sports, Science, and Technology, Japan, to K. T. Y. (19060008).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Biological Sciences, Faculty of ScienceHokkaido UniversitySapporoJapan
  2. 2.Department of Applied Chemistry, Faculty of Fundamental EngineeringNippon Institute of TechnologyMiyashiroJapan

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