Ultradian Oscillation of Growth Reveals Regulatory Mechanism in the Straightening Movement of Wheat Coleoptile

Plants regulate their shape and movements in accordance with their surrounding environment. This regulation occurs by a curving movement driven by differential growth. Recent studies has unraveled part of the mechanisms leading to differential growth though lateral polar auxin transport. However the real interplay between elongation, curvature variation, and accordingly the regulation process of growth distribution has not been really investigated so far. This issue is addressed in this study through gravitropic experiments on wheat coleoptiles, using a recently published kinematic approach, KimoRod. Here we show that median elongation is not affected by gravitropic perturbation. However kinematics studies reveal temporal oscillation of the median elongation rate. These oscillations propagate from the apex to the base during the movement with a characteristic velocity that is similar to auxin propagation in coleoptiles. The curvature variation exhibits a similar spatiotemporal pattern to the median elongation which reveals a nontrivial link between this two parameters and potential effect on perception and biomechanics of the tissue.

In a fluctuating environment organisms must constantly regulate their posture [1]. 2 Plants being usually clamped to the soil through their root system, their postural 3 control is directly related to the movement they display during development. The local 4 curvature of the plant organs is modified according to external and internal stimuli in 5 order to change the spatial organization of the plant. These movements are driven by 6 variation in growth between opposite side of the organ [2]. This asymmetry is currently regulation of the posture is critical to reach specific spatial orientation. Here, both the 22 perception and the active tropic curving is possible all along the elongation zone [6,10]. 23 Experiments have focused on the first instants of the gravitropic reaction [11][12][13], 24 neglecting the rest of the gravitropic movement. Others experiments have focused on 25 the apical orientation [12][13][14], neglecting the influence of the basal curvature on the 26 apical orientation [2,15]. This long-range effect of the basal curvature on the apical 27 orientation prevents to relate directly observations of the apical orientation with the 28 underlying dynamics of the plant organ. 29 Recently, we proposed to couple theoretical considerations with experimental 30 kinematics [3,15]. A general behavior of the gravitropic movement has been observed 31 among different species and organs and its control has been formalized in a unifying 32 model called the AC model. Gravitropism was shown to be only driven by a unique 33 number, B, "balance number", which expresses the ratio between two different 34 perceptions: perception of gravity and proprioception. Proprioception is described as 35 the ability of the plants to sense its own shape and responds accordingly, i.e. the organ 36 can perceive its own curvature and modify its differential growth in order to remain 37 straight [16]. If the number B is small, then proprioception tends to dominate the

43
This unifying model of gravitropism only accounts for a first order of the movement; 44 If the previously described general pattern is observed in every plants and species 45 studied in [3,15], experimental variations are often observed. In particular, plants tend 46 to present a stronger regulation of the movement than predicted by the AC model.

47
Many plants and organs does not overshoot the vertical in contradiction with prediction 48 from morphometric measurement. The existence of a stronger and finer regulation is 49 then expected. A joint regulation of longitudinal (median) elongation as well as of 50 differential growth may be implied. As the movement is related to the available 51 elongation, this regulation could not be understood properly without a clear and 52 complete kinematics of the movement. Here we propose to study the kinematics of an 53 organ in movements in order to identify new regulations that are linked to the postural 54 control.

55
Experiments on wheat coleoptiles were conducted (Fig. 1). This choice have been 56 influenced by the following factors : i. The organ never overshoot the vertical even for 57 large B [3]. ii. Coleoptiles are mostly cylindrical organs without leaves or cotyledons. It 58 is then easier to process image analysis than on an inflorescence, a hypocotyle or a stem 59 where lateral organs could hide some part of the studied organ. iii. The organ is a 60 germinative organ. It can be grown in the dark. Experiments can be conducted in the 61 absence of light without modifying the normal physiological behavior of the organ.

62
Thereby, phototropic effect can be avoided. 63 We recently developed a new tool to get the whole kinematics of an organ in 64 movement, KimoRod [17]. This tool is based on the edge detection of the organ through 65 a precise subpixellar algorithm. The median line is obtained with a very precise  The use of an accurate and precise tool to measure organ growth and curvature 71 opens the way to observe more details about the growth process. For instance, auxin is 72 known to propagate from the apex to the base, at least during the first instants of the 73 gravitropic response [4]. It has also been postulated that ultradian growth oscillation 74 might be observed in relation to the dynamics of the growth process itself [18,19]. The 75 spatial and and temporal resolution of KimoRod should be sufficient to observe those 76 mechanisms.  Time-lapse photography was taken every 15 minutes during 24 hours with the flash 88 light of the camera filtered by a "safe" green light filter (Lee 139 Primary Green). 89 Preliminary experiments showed that the intermittent green flashlight did not induce a 90 phototropic movement (the coleoptile is not directed towards the flash) neither any 91 greening. The markers did not alter elongation or bending of the organ. Geometric description of organ shape. The median line of an organ of total length L is in a plane defined by coordinates (x, y). The arc length s is defined along the median line, 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). A(s, t) is the local orientation of the organ with respect to the vertical and C(s, t) the local curvature. The two curves shown have the same apical angle A(0, t) = 0 but different shapes, so to specify the shape we need the form of A(s, t) or C(s, t) along the entire median line. Due to the symmetry of the system around the vertical axis, the angle A(s, t) is a zenith angle, zero when the organ is vertical and upright. For simplicity, clockwise angles are considered as positive.

106
The kinematics of the movement is obtained with the use of the KimoRod software [17] 107 (see Fig.3 for the geometry of the system). This software gives the median line of the Length of the growth zone, length of the curved zone and 117 balance number B

118
As proposed in [15], the balance number B can be measured as the ratio between the 119 length of the growth zone L gz and the length of the curved zone length of the curved of 120 the zone at steady state (when the organ reach an equlibrium shape), L c On each experiment the relative elongation growth rate of the median line (REGR) as a 122 function of the distance from the apex (s),Ė(s, t) is averaged over time An exponential function, A(s , t) = exp −s /Lc , is then fitted, and gives the characteristic 130 length of the curved zone. B can then be obtained directly from eq. 3. oscillations. Each clouds of points is then fitted with a line, so that the position of the 140 pulse along the median line, P(t), can be described by where v p is the velocity of propagation of the pulse from the apex to the base and t p is 142 the time of the pulse start.

166
This oscillatory behavior reveals a propagative mechanism of the elongation from the 167 apex to the base. The apex starts to elongate before the more basal part. The velocity 168 of propagation of the maximal elongation was comparable in all the experiments 169 v p = 12.6 ± 4.4mm.h −1 for the elongation ( Figure 6).  Temporal oscillations are also observed between curving phase in one direction (e.g.

178
DC/Dt > 0) and in the other direction (DC/Dt < 0) (Fig. 5.B and D). This pattern is 179 really similar to the pattern observed for the elongation (Fig. 5.A and C). Small all the experiments (Fig. 6). For tilted coleoptiles, the correlation of the median 196 elongation rate pattern with the material curvature variation pattern is also mostly 197 negative (Fig. 8.D). This negative correlation implies that the coleoptile tends to 198 straighten when the elongation rate is maximal whereas the coleoptile curves when the 199 elongation rate is small ( Fig. 5 and 8). In the case of untilted coleotpiles, the low values 200 of the curvature variation prevents to see this correlation ( Fig. 8.C), but this correlation 201 remains visible on the correlation of the oscillatory periods (Fig. 8.A).  This study reveals an oscillatory behavior of the relative elongation growth rate on 214 the median elongation (REGR) of the wheat coleoptile,Ė(s, t). Tobias Baskin [19] has 215 discussed the existence of ultradian oscillatory mechanism of growth but, these 216 oscillatory mechanisms have only been rarely reported, e.g. during the nutation of 217 sunflower hypocotyls [20]. However, this measurements are not realized on the median 218 line but on opposite sides of the organ. Oscillation of differential growth are expected to 219 account for the observed oscillatory movement [21]. The variation of the relative have also been measured on pollen tube due to pH variation [22] or calcium activity [23]. 222 But the pollen tube is a unique cell displaying tip growth and the characteristic scale of 223 the oscillations, less than a minute on 10um, are really different from the oscillations 224 observed on the wheat coleoptile, about two hours on 2cm.

225
By tracking the maxima of the elongation, propagation from the apex to the base is 226 revealed. This could be related to the propagation of auxin as the average velocity of 227 propagation of Auxin in coleoptile (12mm.h −1 according to [24][25][26]) is compatible with 228 our own observations (v p = 12.6 ± 4.4mm.h −1 ). Auxin is also known to play a major 229 role as a growth factor so it is a reasonable candidate to explain the propagation from 230 the apex to the base of the elongation.

231
However this remain insufficient to explain the oscillatory behavior of the elongation 232 and the associated characteristic time, 2.2h between 2 pulses. Oscillatory pulses of 233 auxin in a coleoptile have been measured [25,27,28], but the characteristic time between 234 2 pulses is around 25-30 minutes, 4 times faster than our observation. The dynamics of 235 auxin is then insufficient to account for the oscillations described in this study.

236
Similar oscillations of the curvature variation have also been revealed. this could be 237 related to experiment that tracked the apical part of coleoptile. An oscillatory 238 movement was revealed during gravitropic movement [13]. No conclusive mechanism were found as the kinematics only focused on the movement of the apical part of the 240 coleoptile. Our current observation provides a simple basis to this behavior. Global 241 measurements, such as the apical orientation, must be taken carefully as they can hide 242 more general local mechanisms such as oscillatory behavior and non-trivial relation 243 between curvature variation and elongation (see [17] for a discussion on the limits of 244 tracking the apical part of the organ only).

245
The characteristics of the oscillations of the curvature variation are similar to those 246 of the relative elongation growth rate on the median line. This relation is not trivial 247 indeed. The curvature variation can be expressed as a function of the elongation rate [3] 248 where ∆(s, t) accounts for the distribution of the differential growth on each side of the 249 coleoptile. While ∆(s, t) can be measured as the ratio between the variation of 250 curvature and the elongation rate curved can not be changed. As the curvature variation goes in different way depending 258 on the elongation oscillation, the differential growth term ∆(s, t) must be correlated to 259 the variation ofĖ(s, t).

260
To understand this non trivial correlation, different hypotheses can be postulated.

261
For instance, the general model of gravitropism has been described to be dependent on 262 two different parameters acting in an opposite way so that a dynamical equilibrium can 263 be reached [15]. Graviception tends to curve the coleoptile in order the stem to be 264 vertical whereas proprioception tends to straighten the stem. Depending on the value of 265 the elongation rate, one perception process could dominate the others.

266
Recent studies on the acto-myosin complex can provide a molecular and mechanistic 267 point of view on this question. It is now well known that the graviception is directly 268 related to the actin cytoskeleton [5,29,30]. The disruption of the actin cytoskeleton by 269 the use of drugs could enhance the response to the gravity, which would have then a 270 direct effect on the value of the graviceptive term β. A similar and opposite effect have 271 recently been revealed on the straightening of Arabidopsis inflorescence [31,32]. A 272 straightening deficiency is observed when the myosin complex is disrupted. The 273 influence of the proprioceptive term, γ, is then expected to be reduced. Finally the 274 configuration of the actin cytoskeleton is directly linked to the available auxin [28,33]. 275 This is amplified by an active feedback where the transport of the auxin is enhanced by 276 the actin cytoskeleton. This would provide a simple explanation of the observed relation 277 between curvature variation and elongation rate, where graviception and proprioception 278 can dominate different part of the dynamics due to the opposite effects of the 279 actin-myosin complex and its relation with auxin.