You are here

Nutations in growing plant shoots: The role of elastic deformations due to gravity loading

Daniele Agostinelli
Friday, December 13, 2019 - 14:00

Nutations and circumnutations, namely, periodic movements in rapidly elongating plant organs such as roots, hypocotyls, shoots, branches, and flower stalks have fascinated scientists for over a century. A large body of literature has followed the seminal work by Darwin (1880).

Gradmann (1926) introduced the idea that circumnutations could be the result of delayed gravitropic responses: the deviation from the vertical line triggers a correcting movement that, due to a reaction time between perception and actuation, makes the plant overshoot giving rise to self-sustained oscillations.

Building on Gradmann's idea, we study the effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is numerically analyzed.

We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e. , spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose. 



  1. Darwin, C. , 1880. The Power of Movement in Plants. John Murray, London.
  2. Gradmann, H. , 1926. Die bewegungen der ranken und die überkrümmungstheorie. Jahrbücher für wissenschaftliche Botanik 65, 224–278 .
  3. D. Agostinelli, A. Lucantonio and G. Noselli and A. DeSimone., Nutations in growing plant shoots: The role of elastic deformations due to gravity loading, Journal of the Mechanics and Physics of Solids,

Sign in