Coupled ultradian growth and curvature oscillations during gravitropic movement in disturbed wheat coleoptiles

Abstract

To grow straight and upright, plants need to regulate actively their posture. Gravitropic movement, which occurs when plants modify their growth and curvature to orient their aerial organ against the force of gravity, is a major feature of this postural control. A recent model has shown that graviception and proprioception are sufficient to account for the gravitropic movement and subsequent organ posture demonstrated by a range of species. However, some plants, including wheat coleoptiles, exhibit a stronger regulation of posture than predicted by the model. Here, we performed an extensive kinematics study on wheat coleoptiles during a gravitropic perturbation (tilting) experiment in order to better understand this unexpectedly strong regulation. Close temporal observations of the data revealed that both perturbed and unperturbed coleoptiles showed oscillatory pulses of elongation and curvature variation that propagated from the apex to the base of their aerial organs. In perturbed coleoptiles, we discovered a non-trivial coupling between the oscillatory dynamics of curvature and elongation. The relationship between those oscillations and the postural control of the organ remains unclear, but indicates the presence of a mechanism that is capable of affecting the relationship between elongation rate, differential growth, and curvature.

Fig 1. Straightening movement of a wheat coleoptile, in the standard reading direction.

The white line is a 10 mm reference. The time between each frame is 150 minutes. The orange points on the coleoptile are the fluorescent markers used for the measurement of growth. Movies of all plants are available online [8, 9].

Fig 2. Picture of a coleoptile obtained from experiments.

The white line represents 10mm. Pictures are taken with a camera using a green flash bulb. A. RGB image taken directly from the camera. Although the coleoptile is a white organ, it appears green under flash lighting. B. Coleoptile image showing only the green color channel. Note that filtering out the orange markers does not modify the apparent shape of the coleoptile. C. Coleoptile image showing only the red color channel, leaving only the orange fluorescent markers visible for tracing.

Fig 3. Geometric description of the organ.

We define a set of coordinates (x, y) in the plane that intersects with the organ. The vertical direction y is aligned with the gravity field. The median line of an organ of total length L is defined by its curvilinear abscissa s, with s = 0 referring to the apex and s = L(t) referring to the base. In an elongating organ, only the part inside the growth zone, of length L_gz from the apex, is able to curve (with L_gz = L at early stages and L_gz < L later on [5]). The local orientation of the organ A(s, t) is defined at each point along the median with respect to the vertical. The angle is computed in radians so that a vertical upwards orientation is given by A(s, t) = 0 and an horizontal orientation by A(s, t) = π/2. Two curves are represented here with the same apical angle A(0, t) = 0 but different shapes. The measurement of A(s, t) along the entire median line is necessary to specify the full shape. The angle A(s, t) is a zenith angle, zero when the organ is locally vertical and upright. Clockwise angles are considered positive.

Fig 4. An idealized propagating wave, f(s,t)=sin(sTpvp+tTp).

The values of the function f(s, t) with respect to time t and curvilinear abscissa s.

Fig 5. Kinematics of gravitropic movement of two wheat coleoptiles (A-B from Fig 1).

Shown as color maps (kymograph) A-C. the orientation A(s, t) and B-D. the curvature with respect to time t and curvilinear abscissa s. As the coleoptile is elongating, the area covered is increasing with the time. As before, the angle is measured from the vertical in radians. The curvature is measured in mm⁻¹.

Fig 6. The maximal orientation of the tip, A_max(s = 0), as a function of the associated morphometric metric balance number B extracted from experiments.

The vertical line (B = 2.8) shows the transition between the plants that are predicted to not overshoot the vertical (on the left, in blue) and the plants that are predicted to overshoot the vertical (on the right, in green). The dashed shows the transition with the plants that have been observed to overshoot the vertical (on top, in red).

Fig 7. Relative elongation growth rate averaged on the whole experiment for each individual coleotpile.

A. non tilted coleoptiles and B. tilted coleoptiles Each position along the x-axes represents the data for an individual coleoptile. C. Relative Elongation Growth Rate averaged for all individuals. Red lines represent coleoptiles from the straight group, while blue lines represent data from tilted coleoptiles.

Fig 8. Relative elongation growth rate E˙(s,t) and curvature variation DC(s, t)/Dt of two indivduals coleoptiles.

A-B. untilted coleoptile, D-E coleoptile been tilted at 90° from the vertical. Color maps plotting $\dot{E}(s,t)$ in s⁻¹ (A and D) and the curvature variation DC(s, t)/Dt in mm⁻¹s⁻¹ (B and C) with respect to time t and curvilinear abscissa s (the arc length along the median measured from the apex s = 0 to the base of the organ s = L). Distribution of correlation between $\dot{E}(s,t)$ and DC(s, t)/Dt for all experiments (C. untilted and F. tilted).

Fig 9. Curvature variation for each individual coleotpile.

A. Averaged over the first 12 hours post-perturbation, and B. greater than 12h after perturbation (up to the end of the experiment). Red lines represent coleoptiles from the straight group, while blue lines represent data from tilted coleoptiles.