# The role of curvature and (de)curving in plant acclimation and tropisms

Félix Hartmann, Mélanie Decourteix, Bruno Moulia

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Félix Hartmann, Mélanie Decourteix, Bruno Moulia. The role of curvature and (de)curving in plant acclimation and tropisms. CurvoBio 2024, EuroCurvoBioNet (COST action CA22153), Aug 2024, Warsaw, Poland. **hal-04782429**

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Submitted on 14 Nov 2024

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Distributed under a Creative Commons Attribution 4.0 International License
The role of curvature and (de)curving
in plant acclimation and tropisms

Félix Hartmann, Mélanie Decourteix, Bruno Moulia

PIAF, INRAE / Université Clermont Auvergne, Clermont-Ferrand, France

28<sup>th</sup> August 2024

CurvoBio2024, Warsaw

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initially straight horizontal stem

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slight sagging under self weight

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curving upward

uniformly curved zone

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overshooting the vertical

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decurving

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steady-state shape

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s: spatial coordinate along the stem

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Curving and decurving
occur only in the growth
zone of the stem.

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Curvature changes when one side grows faster than the opposite one:

$$\dot{\epsilon}_2 > \dot{\epsilon}_1$$

$$\frac{dC(s, t)}{dt} = \frac{\dot{\epsilon}_2 - \dot{\epsilon}_1}{2R}$$
What is driving differential growth and, ultimately, curving?

Curving enables tropic movements in response to environmental stimuli.

Plant tropisms include

* gravitropism (positive in roots and negative in shoots);

* phototropism;

* hydrotropism (in roots);

* chemotropism (in roots);

* thigmotropism (response to touch);

* ... from Gilroy (2008) *Curr Biol*

<figure><img src="image_17.png" /></figure>

Current Biology

Stimuli are sensed and integrated into a unified tropic response:

$$ \frac{dC(s, t)}{dt} = f(\text{gravity}, \text{light}, \text{water gradient}, \text{chemical gradients}, \dots) $$
# Sensing the orientation with respect to gravity

## Statocytes and amyloplasts

*Statocytes* are cells in the endodermis which contain starch-filled plastids called *amyloplasts*.

Amyloplasts tend to avalanche to the bottom of statocytes.

<figure><img src="image_18.png" /></figure>

from Morita (2010) *Ann Rev Plant Biol*
Amyloplasts direct the flux of the growth hormone auxin

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The amyloplasts relocalize auxin transporters, which redirect the flux of auxin.
Amyloplasts direct the flux of the growth hormone auxin

When the stem is tilted, the amyloplasts flow to one side of the cell and
induce a net lateral flux of auxin.

<figure><img src="image_20.png" /></figure>

$$
J_{\text{lat}} \propto \sin A
$$

The lateral auxin gradient causes differential growth.
Simple model of gravitropic response

The auxin gradient across the stem is assumed proportional to the sine of the inclination angle. This is matched by the curving rate:

$$ \frac{dC(s, t)}{dt} = -\beta \sin A(s, t) $$

* β: gravitropic sensitivity (in m⁻¹ s⁻¹)

* A(s, t) inclination angle at position s and time t

<figure><img src="image_21.png" /></figure>

s: position along the stem
Simulation of the simple gravitropic model

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# Simulation of the simple gravitropic model

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The simulated stem oscillates indefinitely, never reaching a steady-state shape.

⇒ A **stabilizing feedback** is needed to converge toward a steady-state shape.
The plant proprioception hypothesis

Plants are endowed with the ability to sense their own local curvature, and to respond to it.

Gravi-proprioceptive model:

$$ \frac{dC(s, t)}{dt} = -\underbrace{\beta \sin A(s, t)}_{\text{gravitropic drive}} - \underbrace{\gamma C(s, t)}_{\text{proprioceptive drive}} $$

$\gamma$: proprioceptive sensitivity (in s⁻¹)
Simulation of the gravi-proprioceptive model

<figure><img src="image_24.png" /></figure>
# How can we demonstrate proprioception experimentally?

## Clinostat

A clinostat is a device used to rotate a plant around an horizontal axis and suppress gravity sensing.

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The rotation keeps the amyloplasts in suspension.

artificial system mimicking the motion of amyloplasts in a clinostat →

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A clinostat in action

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A typical proprioception experiment

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TILT bending up
under gravitropic drive

decurving / straightening
under pure proprioceptive drive
<figure><img src="image_29.png" /></figure>
Estimating $\gamma$ during the decurving/straightening phase

$$ \frac{dC(s, t)}{dt} = -\gamma C(s, t) \quad \implies \quad A_{\text{tip}}(t) - A_{\text{base}} = A_0 e^{-\gamma t} $$

Exponential fit on $A_{\text{tip}}$ - $A_{\text{base}}$:

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Semi-automatic estimation with the Interekt software (Hartmann et al., 2022).
Plant posture control as a curvature-based feedback loop

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from Hartmann, Decourteix and Moulia (2024) *Current Biology*
Transient curvature changes caused by external actions

<figure><img src="image_32.png" /><figcaption>*Reed culms bending under the wind.*</figcaption></figure>

* Transient bending stimuli are filtered out from proprioception.

* They do not lead to tropic responses in terms of $\frac{dc}{dt}$.

* But they do elicit growth responses.
Controlled bending stimuli on plant stems

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* A bending stimulus with a given curvature can by automatically applied during a few seconds.

* Stem growth is continuously measured.
Effect of bending treatment on stem elongation

Stem bending transiently inhibits elongation in tomato.

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# Effect of bending treatment on stem diameter growth

Stem bending transiently promotes diameter growth in young poplars.

<figure><img src="image_36.png" /></figure>
## Definition

*Thigmomorphogenesis* refers to all the growth responses of a plant which has sensed transient mechanical stimuli (wind, weight of the snow, animals, ...).

<figure><img src="image_37.png" /></figure>

As a result of thigmomorphogenesis, plants get acclimated to their mechanical environment, *i.e.* are more resistant to uprooting and stem breakage.
# Stem bending and strains (mechanical deformations)

Bending a stem induces mechanical deformations (strains) in the tissues.
Some cells are stretched, others are compressed.

initial
configuration

deformed
configuration

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strains
at the cellular level

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stretching

$$\epsilon = \frac{\delta L}{L_0} = \delta C \cdot R$$

<figure><img src="image_42.png" /></figure>

no straining

$$\epsilon = \frac{\delta L}{L_0} = 0$$

<figure><img src="image_43.png" /></figure>

compression

$$\epsilon = \frac{\delta L}{L_0} = -\delta C \cdot R$$
Linear relationship between strain and gene expression

The expression level of the transcription factor *Zinc Finger Protein 2* (ZFP2) is proportional to the magnitude of tissue strains.

<figure><img src="image_44.png" /></figure>

from Coutand et al. (2009) *Plant Physiology*

More than 2,000 genes are regulated in poplar after a bending stimulus (Pomiès et al., 2017, *BMC Genomics*).
# Thigmomorphogenesis as a developmental feedback loop

<figure><img src="image_45.png" /></figure>

from Hartmann, Decourteix and Moulia (2024) *Current Biology*
## Two extras

Interekt, a user-friendly software for tracking plant motions and measuring plant curvatures:

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An educational Youtube video on plant curvatures and tropisms:

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https://forgemia.inra.fr/felix.hartmann/interekt

https://youtu.be/kIBaJqnDovE
Collaborators from the PIAF Lab:

* Nathalie Leblanc-Fournier

* Nicole Brunel-Michac

* Valérie Legué

* Éric Badel

* Jérôme Franchel

* Kinza Khan (PhD student)

* Hugo Chauvet (former member)

And don't miss our easy-to-read
Primer on *Curvatures in plants*:
https://doi.org/10.1016/j.cub.2024.07.006

External collaborators:

* Yasmine Meroz (Tel Aviv U.)

* Julia Davies (Cambridge U.)

* Gary Stacey (Missouri U.)

* Jana Dlouhà and Thiéry
Constant (INRAE, Nancy)

* Olivier Pouliquen, Yoël Forterre
and Christophe Eloy
(Aix-Marseille U.)

<figure><img src="image_50.png" /></figure>
Bastien, R., Bohr, T., Moulia, B., and Douady, S. (2013). Unifying model of shoot gravitropism reveals proprioception as a central feature of posture control in plants. *Proceedings of the National academy of Sciences of the United States of America*, 110(2):755–760.

Coutand, C., Julien, J., Moulia, B., Maugen, J., and Guitard, D. (2000). Biomechanical study of the effect of a controlled bending on tomato stem elongation: global mechanical analysis. *Journal of Experimental Botany*, 51(352):1813–1824.

Coutand, C., Martin, L., Leblanc-Fournier, N., Decourteix, M., Julien, J.-L., and Moulia, B. (2009). Strain mechanosensing quantitatively controls diameter growth and ptazfp2 gene expression in poplar. *Plant Physiology*, 151(1):223–232.

Gilroy, S. (2008). Plant tropisms. *Current Biology*, 18(7):R275–R277.

Hartmann, F. P., Chauvet-Thiry, H., Franchel, J., Ploquin, S., Moulia, B., Leblanc-Fournier, N., and Decourteix, M. (2022). Methods for a quantitative comparison of gravitropism and posture control over a wide range of herbaceous and woody species. In Blancaflor, E. B., editor, *Plant Gravitropism*, Methods in Molecular Biology, pages 117–131. Humana, New York, NY, 2 edition.

Hartmann, F. P., Decourteix, M., and Moulia, B. (2024). Curvature in plants. *Current Biology*, 34(20):R991–R996.

Martin, L., Leblanc-Fournier, N., Julien, J.-L., Moulia, B., and Coutand, C. (2010). Acclimation kinetics of physiological and molecular responses of plants to multiple mechanical loadings. *Journal of Experimental Botany*, 61(9):2403–2412.

Morita, M. T. (2010). Directional gravity sensing in gravitropism. *Annual Review of Plant Biology*, 61(1):705–720. PMID: 19152486.

Moulia, B., Badel, E., Bastien, R., Duchemin, L., and Eloy, C. (2022). The shaping of plant axes and crowns through tropisms and elasticity: an example of morphogenetic plasticity beyond the shoot apical meristem. *New Phytologist*, 233(6):2354–2379.

Moulia, B., Douady, S., and Hamant, O. (2021). Fluctuations shape plants through proprioception. *Science*, 372(6540).

Pomiès, L., Decourteix, M., Franchel, J., Moulia, B., and Leblanc-Fournier, N. (2017). Poplar stem transcriptome is massively remodelled in response to single or repeated mechanical stimuli. *BMC Genomics*, 18(1):300.

Pouliquen, O., Forterre, Y., Bérut, A., Chauvet, H., Bizet, F., Legué, V., and Moulia, B. (2017). A new scenario for gravity detection in plants: the position sensor hypothesis. *Physical Biology*, 14:035005.