# A Dual Inhibition-Stimulation Mechanism at the Basis of Phyllotaxis?

Landry Duguet, Etienne Farcot, Guillaume Cerutti, Carlos Galvan-Ampudia, Teva Vernoux, Christophe Godin

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Landry Duguet, Etienne Farcot, Guillaume Cerutti, Carlos Galvan-Ampudia, Teva Vernoux, et al. A Dual Inhibition-Stimulation Mechanism at the Basis of Phyllotaxis?. Shaping Life 3, Jun 2025, Cassis, France. 2025. [hal-05286619](https://hal.science/hal-05286619v1)

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Submitted on 27 Sep 2025

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# A Dual Inhibition-Stimulation Mechanism at the Basis of Phyllotaxis?

Landry Duguet¹, Etienne Farcot², Guillaume Cerutti¹,
Carlos Galvan-Ampudia¹, Teva Vernoux¹, Christophe Godin¹

¹Laboratoire Reproduction et Développement des Plantes, ENS de Lyon, CNRS, INRAE, Inria, France
²Department of Mathematics, University of Nottingham

## Abstract

Phyllotaxis, the arrangement of plant leaves around stems, demonstrates strikingly **regular patterns**. For the last decades, researchers have sought to uncover the **molecular actors** regulating the **positioning of organs**, called primordia, at the tip of the stem in the shoot apical meristem (SAM). The local **accumulation** of the phytohormone **auxin** initiates primordia. A main regulator of auxin distribution is the **PIN** proteins, which are **polar auxin exporters**. Numerical **simulations** modeling auxin transport by PIN polarities were able to produce **phyllotactic patterns** due to a lateral **inhibition mechanism**, in which emergent **convergences** of PIN polarities were thought to **drain auxin** from primordia surroundings, making it **impossible** for new **organs** to **initiate** nearby. However, recent **3D live quantifications** of auxin and PIN polarities **challenge** the **realism** of these models. In particular, **no convergent sites of PIN polarities** are observed. We **analyze** the quantified **PIN distributions** and show that the **changes of intensity of PIN polarities**, which were overlooked so far, constitute the **main component** of the **convergence** of PIN polarities. Together with the directions of PIN polarities, they create an **evolving pattern** which **depletes auxin** nearby the primordia, but also **promotes its accumulation** further away. This **dual inhibition-stimulation mechanism** promotes a **new interpretation** for phyllotaxis.

<figure><img src="image_1.png" /><figcaption>Fig. 1: The shoot apical meristem of Arabidopsis thaliana (left) The plant model Arabidopsis thaliana. (up) inflorescence stage. (down) Confocal image of its shoot apical meristem. (right) The SAM and its developing primordia. Red arrows indicate tissue growth.</figcaption></figure>

## The classical view

Lateral inhibition of organogenesis by growing primordia can produce the majority of **phyllotactic patterns** [1].

* The SAM is crowded with organs,

* outward tissue growth creates space for the **initiation** of new primordia (Fig. 1).

This **inhibition** mechanism is at the **foundation** of the **auxin transport models** used to simulate phyllotaxis (Fig. 2). **Cells** are assumed to **allocate PIN** proteins **toward** their **neighbors** with **higher auxin** concentrations [2,3]. This results in the **emergence** of **auxin accumulations** at the center of **convergent PIN polarities**.

<figure><img src="image_2.png" /><figcaption>Fig. 2: The classical view is based on inhibition
Primordia (P) develop convergent PIN polarities. It drains
auxin from the surrounding, inhibiting the formation of new
organs nearby. A new auxin accumulation forms at the
farthest place from the primordia. From this process results
the formation of phyllotactic patterns.</figcaption></figure>

## New microscopic observations

* **PIN polarities** are quantified in 3D and through time in four SAMs [4] (Fig. 3).

* a novel **high spatio-temporal resolution** ratiometric **sensor** of auxin degradation [5] has been used for 21 SAMs [4].

* **global polarisation** of PIN toward the center of the SAM, without local convergence sites.

* **presence of high auxin concentrations in the center** of the SAM (Fig. 3).

These unprecedented observations **question** the **realism** of the classical view.

<figure><img src="image_3.png" /><figcaption>Fig. 3: Unprecedented quantifications reveal PIN polarities and the auxin distribution</figcaption></figure>

(left) PIN quantification is based on two signals, one for PIN proteins and one for the cell wall.

(center) An automatic 3D algorithm quantifies the PIN polarities for each cell wall section.

(right) PIN polarities globally converging to the center +Auxin accumulation in the center.

<figure><img src="image_4.png" /><figcaption>Fig. 4: Defining PIN net polarity vectors</figcaption></figure>

The net polarity vector (red) sums the vectors (black) of the differences of PIN concentration between the two sides of each wall section surrounding a cell.

## PIN net polarity analysis - Directions

* **Deviations** compared to radial direction quantified by orthoradial projections (Fig. 5).

* Converging and diverging deflections of PIN net polarities aligned with organ positioning.

<figure><img src="image_5.png" /><figcaption>Fig. 5: PIN polarities form deflections correlated with the phyllotactic pattern</figcaption></figure>

(left) Orthoradial projections (red/blue) of the net polarity vectors. (right) Quantification of the changes of orthoradial direction of PIN net polarities.

* Early primordia (-1, 0, 1) = convergent deflection pattern,

* Later stages (3, 4, 5) = diverging deflection pattern.

## The divergence(s) of PIN net vectors

* The divergence operator quantifies the **ability** of a PIN pattern to **concentrate** or **scatter auxin fluxes**.

Let the vector field: **v** = *i* **d**, with *i* the intensity, **d** the direction (||**d**||=1).

$$ \nabla \cdot \mathbf{v} = \nabla i \cdot \mathbf{d} + i \nabla \cdot \mathbf{d} \quad (1) $$

decomposes the divergence into an **intensity** and a **directional** contribution.

<figure><img src="image_6.png" /></figure>

## PIN net polarity analysis - Intensities

* **Observations of discrepancies** in PIN net vectors **intensities**.

* A frontier of intense polarities (nearby the organs) transports auxin out of the periphery, and makes it **accumulate** in the center.

<figure><img src="image_7.png" /><figcaption>Fig. 6: The intensities of PIN net polarities are tightly regulated through time</figcaption></figure>

Intensities of the net polarity vectors (green) at 0H (left) and 14H (right).

* Net polarities more intense in periphery than center,

* Decrease nearby P-1 and P0,

* Increase in the sectors of P1, P2, P3.

<caption>Fig. 7: Intensities of PIN net polarity vectors contribute to the divergence</caption>

Mean patterns of the divergence of the net polarity vectors (center) and its **intensity** (left) and **direction** (right) components.

* **Most converging zones** correspond to the high auxin concentrations of early primordia.

* The **intensity component** has the **strongest** contribution for each individual (data not shown)

* Rather than purely directionally convergent sites as in Fig. 2, PIN polarities create convergent points by changing their intensities.

## Conclusion

* **Intensities** of PIN polarities, overlooked so far, are **non-negligible regulators of the auxin distribution**. This has been confirmed via an **auxin transport model** (data not shown).

* **Analysis of PIN polarities** indicates a **dual** effect on the auxin distribution (Fig. 8).

<figure><img src="image_8.png" /><figcaption>Fig. 8: A dual inhibition-stimulation mechanism ?</figcaption></figure>

* **Spreading directions** and increasing intensities create local auxin depletions (yellow), inhibiting the development of new primordia.

* Further away from the primordia, the intensities decrease and the directions meet, contributing to the accumulation of auxin. This stimulates the formation of new primordia.

This **duality** corresponds to a recent **theoretical model** [6]. It renews our **interpretation** and **opens** new perspectives for **biological experiments**, such as finding **regulators** of PIN net **intensities**, or trying to **perturb** the **stimulation mechanism**.

## References

[1] Douady, S., & Couder, Y. (1996). Phyllotaxis as a dynamical self organizing process part I: the spiral modes resulting from time-periodic iterations. Journal of theoretical biology, 178(3), 255-273.

[2] Jönsson, H., Heisler, M. G., Shapiro, B. E., Meyerowitz, E. M., & Mjolsness, E. (2006). An auxin-driven polarized transport model for phyllotaxis. Proceedings of the national academy of sciences, 103(5), 1633-1638.

[3] Smith, R. S., Guyomarc'h, S., Mandel, T., Reinhardt, D., Kuhlemeier, C., & Prusinkiewicz, P. (2006). A plausible model of phyllotaxis. Proceedings of the National Academy of Sciences, 103(5), 1301-1306.

[4] Galvan-Ampudia, C. S., Cerutti, G., Legrand, J., Brunoud, G., Martin-Arevalillo, R., Azais, R., ... & Vernoux, T. (2020). Temporal integration of auxin information for the regulation of patterning. Elife, 9, e55832.

[5] Brunoud, G., Wells, D. M., Oliva, M., Larrieu, A., Mirabet, V., Burrow, A. H., ... & Vernoux, T. (2012). A novel sensor to map auxin response and distribution at high spatio-temporal resolution. Nature, 482(7383), 103-106.

[6] Yonekura, T., & Sugiyama, M. (2024). A new mathematical model of phyllotaxis to solve the genuine puzzle spiromonostichy. Journal of Plant Research, 137(1), 143-155.