COMMENTARY

Beyond the sine law of plant gravitropism

Jacques Dumais1 Faculdad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Viña del Mar 2562307, Chile

he great German plant physiolo- mechanistic justification in the sedimen- gist Wilhelm Pfeffer rightly tation pattern of statoliths. T claimed that “no plant is entirely The shortcomings of the sine law sur- without the power of movement” face when one attempts to build a regula- (1). If this fact remains underappreciated, tory model out of it. To develop such it is perhaps because plant movements a model, one must ask where gravity is typically unfold over minutes, hours, or sensed and how the sensing elements re- days, and thus exceed the attention span spond to a gravitropic stimulus. In the case of all but the most dedicated observer. of the root, gravity sensing is limited to the Among the large array of plant move- columella cells of the root cap (9, 10). The ments, the tropisms—that is, those move- signal is then transmitted to the elongation ments that are directed toward or away zone via a redistribution of auxin flow (11, from an external stimulus such as gravity 12). The stem, however, shows a notable or light—are the most fascinating because difference from the root. Experimental they highlight beautifully the sentient na- evidence indicates that the entire stem ture of plants and the goal-directedness of senses gravity and can responds to it lo- their growth habit. The pervasiveness of cally (13, 14) whereas the apex itself ap- plant tropisms is revealed when one stops pears to play no particular role, since to consider the unlikeliness that seeds decapitated plants respond normally to lodged haphazardly within the crevices of gravity (15). As Bastien et al. (3) clearly a rugged terrain should sprout stems that show, a stem whose distributed gravisens- reliably find their way up. Were it not for ing elements react to gravistimulation the ability of the young plants to sense according to the sine law would zigzag light and gravity, forests would be impen- about the vertical repeatedly without ever etrable tangles of stems and branches reaching a stable configuration. This growing in all directions. Their prevalence response arises because the basal Fig. 1. Shoot gravitropism beyond the sine law. elements of the stem keep responding to in the plant kingdom explains why trop- (A) Diagrams of a stem responding to gravity ac- isms have been an active area of research cording to the sine law. Sensing and curving are gravity and, therefore, keep curving up- since the beginning of the 19th century. By distributed over the entire length of the stem. ward long after the apical region of the end of the 19th century, the field had The orange arrows indicate the component of the stem has reached the vertical. As a re- reached such a level of development and the gravity vector (g)thatservesastheeffective sult of the sustained curving of the basal popularity that eminent biologists, in- bending stimulus (s). The stem repeatedly over- elements, the stem apex overshoots its cluding Charles Darwin and Pfeffer, could shoots the vertical because the basal part of target repeatedly (Fig. 1A). Moreover, the devote entire books to the topic (1, 2). the stem is still receiving a strong stimulus and is apical straightening that is an integral part therefore actively curving even as the apical part Given this long and illustrious tradition of the gravitropic response of stems is ’ approaches the vertical. (B) The gravitropic re- never fully achieved in a model based on of research, one might expect today s bi- sponse of Impatiens glandulifera sketched from ologists to have extracted all useful in- Pfeffer’s original photographs. This plant is a prime the sine law. It thus appears that a crucial formation from standard observational example of a gravitropic response with a large element is missing from the standard research of plant tropisms. A paper pub- bending number (B ∼ 9). It overshoots the vertical model of gravitropism. lished in PNAS should convince the twice, thus forming first a “C” andthena“S” The solution put forward by Bastien readers that much can still be learned from shape, but ultimately converges on a stable con- et al. (3) implicates a form of plant pro- fi careful, quantitative observation of bi- guration whereby a large section of the stem is prioception called autotropism. Auto- straight. The first two time points of the response tropism is the Newton’s first law of plant ological processes. In a systematic study of highlight the development of curvature over the shoot gravitropism in 11 taxa, Bastien tropisms; that is, in the absence of external extensive growth zone (Lgz), whereas the last time et al. (3) at once establish the universal point shows the curvature converging ultimately stimuli, plant organs maintain straight growth. Thus, elongating stem segments response to gravity as a process of initial to a much shorter length scale (Lc). The rapid stem curving followed by apical straight- convergence to an erect configuration is indicative that are not receiving a gravitropic stimu- ening and debunk the idea that current of the stabilizing effect of autotropic straighten- lus telling them to bend would naturally models of gravitropism offer a plausible ing in gravitropic responses. straighten under their internal autotropic explanation for the process. response. Autotropism was already known to Pfeffer and his contemporaries (1), and The standard model of gravitropism can approaches the vertical. Since its formu- be traced back to Julius Sachs, who stated ’ the counteracting role it plays with gravi- lation, Sachs sine law has been validated tropic curving has also been included in that the component of gravity acting at repeatedly, sometimes with minor mod- right angle to a plant axis (a stem or root) models (16, 17). Despite these precursors, ifications (5, 6). It was also noted that determines the strength of the stimulus the model put forward by Bastien et al. (3) (4). Accordingly, the gravitropic response the sedimentation of statoliths within should be proportional to the sine of the gravisensing cells would lead to some form angle between the organ axis and the of sinusoidal dependence on angle (7, 8). Author contributions: J.D. wrote the paper. vertical; thus, a stem placed horizontally Thus, the sine law, despite its simplicity, The author declares no conflict of interest. would show the strongest response, which offered a good fit of overall plant response See companion article on page 755. would then gradually decline as the stem to gravity and even enjoyed some level of 1E-mail: [email protected].

www.pnas.org/cgi/doi/10.1073/pnas.1219974110 PNAS | January 8, 2013 | vol. 110 | no. 2 | 391–392 Downloaded by guest on September 27, 2021 distinguishes itself by its simplicity and of a plant. The authors define a non- the gravitropic response has been com- — elegance it is, in fact, the minimal model dimensional bending number B as Lgz/Lc. pleted. Therefore, the stem approaches compatible with the two opposing “forces” This ratio captures explicitly the spatial the vertical smoothly without over- of gravitropic bending and autotropic aspect of the gravitropic response (i.e., it is shooting. For large B values, the length of straightening. the ratio of two important lengths in the the growth zone greatly exceeds the region ’ Unlike models based solely on Sachs system), but it also, implicitly, captures of final curvature. As a result, curvature sine law, the gravitropic/autotropic model a temporal feature of the gravitropic re- will initially develop over a large region put forward by the authors explains why sponse because the length of the growth of the stem before converging to a smaller the universal gravitropic response in plant zone (Lgz) is the initial distance over which stems proceeds from an initial overall region. In the convergence process, the the curvature is observed, and Lc is the stem will zigzag around the vertical, bending of the stem followed by basipetal final distance over which the stem will be forming first a “C” shape and possibly straightening (3, 18). As shown in their curved when the gravitropic response has a “S” shape. The largest B value recorded paper (3), a stem placed horizontally will been completed (Fig. 1B). It is the implicit rapidly converge to a steady-state solution so far, approximately 9, is for the Impa- where the stem angle (A) decreases expo- tiens plant studied by Pfeffer himself (Fig. nentially over the length (Lgz) of the Future research will have 1B). An infinite B is obtained if the grav- growth zone: to include autotropic itropic curving overpowers the autotropic π straightening. In this case, we recover AðsÞ¼ expðs=LcÞ for 0 ≤ s ≤ Lgz the sine law model and the plant never 2 straightening as an really settles into a steady-state ver- In this equation, Lc is the length scale integral part of shoot tical position. over which the stem angle changes when The beauty of the bending number the plant has completed its response to gravitropism. resides in the fact that it can be measured gravity. Lc is set by the relative strength of directly from images taken early and late temporal component of the bending the gravitropic (bending) and the auto- in the response of gravitropically stimu- number that makes it a useful metric of tropic (straightening) responses. If the lated plants (Fig. 1B). Simple length gravitropic responses in plants. For a plant gravitropic response dominates, Lc is to show an effective rectifying response to measurements performed on these two small, indicating that the stem angle endpoints can tell us everything that has changes over a short distance, thus im- gravity, it will need a zone of curvature occurred in the intervening time. Overall, posing a high local curvature. In contrast, production (i.e., growth zone) at least as the study of Bastien et al. (3) offers an a large Lc indicates a dominant autotropic long as the intrinsic length scale (Lc) set by reaction, which prevents the development the internal balance of gravitropic and exquisite example of the power of quanti- of strong curvature at any point along autotropic reactions. In other words, tative observations even in the context of the stem. bending numbers are typically greater than a century-old problem such as gravitrop- The major breakthrough of this work is 1. For B values close to 1, the length of the ism. Future research will have to include the conclusion that the two lengths Lgz and growth zone is comparable to the length autotropic straightening as an integral part Lc govern the entire gravitropic response over which curvature will be present when of shoot gravitropism.

1. Pfeffer W (1906) The Physiology of Plants (Clarendon 8. Larsen P (1969) The optimum angle of geotropic stim- 13. Fukaki H, Fujisawa H, Tasaka M (1996) Gravitropic re- Press, Oxford), Vol 3. ulation and its relation to the starch statolith hypoth- sponse of inflorescence stems in Arabidopsis thaliana. 2. Darwin C, Darwin F (1880) The Power of Movement in esis. Physiol Plant 22:469–488. Plant Physiol 110(3):933–943. Plants (John Murray, London). 9. Swarup R, et al. (2005) Root gravitropism requires lat- 14. Fukaki H, et al. (1998) Genetic evidence that the endo- 3. Bastien R, Bohr T, Moulia B, Douady S (2013) Unifying eral root cap and epidermal cells for transport and re- dermis is essential for shoot gravitropism in Arabidop- – model of shoot gravitropism reveals proprioception as sponse to a mobile auxin signal. Nat Cell Biol 7(11): sis thaliana. Plant J 14(4):425 430. a central feature of posture control in plants. Proc Natl 15. Firn RD, Digby J, Hall A (1981) The role of the shoot 1057–1065. Acad Sci USA 110:755–760. apex in geotropism. Plant Cell Environ 4:125–129. 10. Blancaflor EB, Fasano JM, Gilroy S (1998) Mapping the 4. Sachs J (1882) Über orthotrope und plagiotrope pflan- 16. Firn RD, Digby J (1979) A study of the autotropic functional roles of cap cells in the response of Arabi- zenteile. Arb Bot Inst Würzburg 2:226–284. straightening reaction of a shoot previously curved dopsis primary roots to gravity. Plant Physiol 116(1): 5. Iino M, Tarui Y, Uematsu C (1996) Gravitropism of during geotropism. Plant Cell Environ 2:149–154. 213–222. maize and rice coleoptiles: Dependence on the stimu- 17. Meskauskas A, Novak Frazer L, Moore D (1999) Math- 11. Friml J, Wisniewska J, Benková E, Mendgen K, Palme K lation angle. Plant Cell Environ 19(10):1160–1168. ematical modelling of morphogenesis in fungi: A key fl 6. Galland P (2002) Tropisms of Avena coleoptiles: Sine (2002) Lateral relocation of auxin ef ux regulator PIN3 role for curvature compensation (‘autotropism’)inthe law for gravitropism, exponential law for photogravi- mediates tropism in Arabidopsis. Nature 415(6873): local curvature distribution model. New Phytol 143(2): tropic equilibrium. Planta 215(5):779–784. 806–809. 387–399. 7. Audus LJ (1964) Geotropism and the modified sine 12. Ottenschläger I, et al. (2003) Gravity-regulated differ- 18. Moulia B, Fournier M (2009) The power and control of rule: An interpretation based on the amyloplast stato- ential auxin transport from columella to lateral root gravitropic movements in plants: A biomechanical and lith theory. Physiol Plant 17:737–745. cap cells. Proc Natl Acad Sci USA 100(5):2987–2991. systems biology view. J Exp Bot 60(2):461–486.

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