Nutations in plant shoots: endogenous and exogenous factors in the presence of mechanical deformations

Abstract

<jats:title>A<jats:sc>bstract</jats:sc></jats:title><jats:p>We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots, as driven by differential growth at the tip. We discuss the evolution laws for endogenous oscillators, straightening mechanisms and reorientations to directional cues, such as phototropic responses to a far light source and gravitropic reactions governed by the statoliths avalanche dynamics. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of a Hopf bifurcation reminiscent of flutter instabilities exhibited by structural systems under nonconservative loads. When also oscillations due to endogenous cues are present, their weight relative to those associated with the Hopf instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the flutter induced oscillations becomes dominant. Our findings suggest that the relative importance of the two mechanisms is an emergent property of the system that is affected by the amplitude of elastic deformations, and highlight the crucial role of elasticity in the analysis of circumnutations.</jats:p>

Nutations in Plant Shoots: Endogenous and Exogenous Factors in the Presence of Mechanical Deformations

“…This manuscript has been released as a pre-print at: www.biorxiv. org/content/10.1101/2020.07.06.188987v1 (Agostinelli et al, 2020a), and it includes content that appeared in DA's Ph.D. thesis (Agostinelli, 2020).…”

“…The authors would like to thank Alessandro Lucantonio for fruitful discussions and valuable suggestions. This manuscript has been released as a pre-print at: www.biorxiv.org/content/10.1101/2020.07.06.188987v1 (Agostinelli et al, 2020a ), and it includes content that appeared in DA's Ph.D. thesis (Agostinelli, 2020 ).…”

Multiscale integration of environmental stimuli in plant tropism produces complex behaviors

“…Circumnutation. Experiments suggest that, depending on the plant, circumnutation is driven by an internal oscillator, a time-delay response to gravity, or a combination of the two (87,88). Here, following the hypothesis of an internal oscillator, we show that the basic nutating motion emerges naturally from an internal oscillator at a single point combined with axial auxin transport (89).…”

Nutations in growing plant shoots as a morphoelastic flutter instability

“…Let double-struckE3 be the Euclidean space and choose a right-handed orthonormal basis falsefalse{bolde1,bolde2,bolde3falsefalse} such that the gravity vector is g := − e 2 . We follow Agostinelli et al [28] and model a growing slender organ as an unshearable and (elastically) inextensible rod of circular cross section. The current configuration of the rod has axis p ( s, t ) and orthonormal directors d j ( s, t ) for j = 1,2,3, where s ∈ [0, ℓ( t )] is the arc length coordinate.…”

“…In fact, nutations in growing plant shoots may be described as spontaneous oscillations caused by a flutter-like instability (a Hopf-type bifurcation) in a growing elastic system subject to gravity loading while sensing and actively responding to external stimuli. We have discussed the merits of this hypothesis in previous studies [28,29] and, in this paper, we study in detail the impact of different growth models on the qualitative and quantitative features of these spontaneous oscillations. To this aim, we model the system using the theory of morphoelastic growing rods discussed in [30].…”