Prospective guidance in a free-swimming cell

Jonathan T. Delafield-Butt*, Gert Jan Pepping, Colin D. McCaig, David N. Lee

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

11 Citations (Scopus)


Abstract A systems theory of movement control in animals is presented in this article and applied to explaining the controlled behaviour of the single-celledParamecium caudatum in an electric field. The theory-General Tau Theory-is founded on three basic principles: (i) all purposivemovement entails prospectively controlling the closure of action-gaps (e.g. a distance gap when reaching, or an angle gap when steering); (ii) the sole informational variable required for controlling gaps is the relative rate of change of the gap (the time derivative of the gap size divided by the size), which can be directly sensed; and (iii) a coordinated movement is achieved by keeping the relative rates of change of gaps in a constant ratio. The theory is supported by studies of controlled movement in mammals, birds and insects. We now show for the first time that it is also supported by single-celled paramecia steering to the cathode in a bi-polar electric field. General Tau Theory is deployed to explain this guided steering by the cell. This article presents the first computational model of prospective perceptual control in a non-neural, single-celled system.

Original languageEnglish
Pages (from-to)283-293
Number of pages11
JournalBiological Cybernetics
Issue number4-5
Early online date22 Jun 2012
Publication statusPublished - Jul 2012

Bibliographical note

This study has been funded by a seed-corn grant from the Carnegie Trust for the Universities of Scotland and the Moray Endowment Fund; analyses were made possible by the Edinburgh Fund, an E.U. Nest Adventure grant, TACT, a Leverhulme Trust Fellowship to DNL. The authors wish to express their thanks to Ariel Dynamics Inc. for their help in tracking algorithms and Eric Lucey for assistance with electrical operation.


  • Cellular guidance
  • Galvanotaxis
  • General Tau Theory
  • Paramecium
  • Tau-coupling


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