Spatiotemporal Integration in Plant Tropisms

Abstract

Tropisms, growth-driven responses to environmental stimuli, cause plant organs to respond in space and time and reorient themselves. Classical experiments from nearly a century ago reveal that plant shoots respond to the integrated history of light and gravity stimuli rather than just responding instantaneously. We introduce a temporally non-local response function for the dynamics of shoot growth formulated as an integro-differential equation whose solution allows us to qualitatively reproduce experimental observations associated with intermittent and unsteady stimuli. Furthermore, an analytic solution for the case of a pulse light stimulus expresses the response function as function of experimentally tractable variables for the phototropic response of Arabidopsis hypocotyls. All together, our model enables us to predict tropic responses to time-varying stimuli, manifested in temporal integration phenomena, and sets the stage for the incorporation of additional effects such as multiple stimuli, gravitational sagging etc.Plant tropisms are the growth-driven responses of a plant organ which reorients itself in the direction of an environmental stimulus such as light, termed phototropism, or gravity, termed gravitropism. Tropisms driven by a directional stimulus lead to the asymmetric redistribution of a growth hormone such as auxin [1-5] which then directs growth. For example, in Fig. 1a we show snapshots of the negatively gravitropic response of a wheat seedling placed horizontally at time t = 0, where the seedling shoot detects the direction of gravity and grows to oppose it. This response is dynamical, and one might suspect that if the stimulus is changed intermittently, the spatiotemporal response itself will be complex. In the simple experiment described above, gravity acts continuously on the shoot with a constant magnitude. Thus it is not possible to distinguish between a response that integrates the stimulus over time and one that acts instantaneously. However experimental observations of gravitropism and phototropism dating back more than a century have shown that plants respond to time varying stimuli in a way that suggests that they do integrate the stimuli in time. For example, different combinations of stimuli that are intermittent in time [6][7][8][9][10] or which have reciprocal ratios of intensity and duration [11][12][13][14][15][16][17][18], so that the time-integrated stimulus is constant, lead to the same response, as shown in the insets in Figs. 2 and 3. Explanations of shoot phototropism assume that this follows from photobiology [19]. However, the fact that this phenomenon has also been observed in the context of gravitropism suggests that one must look for a common signal transduction pathway, naturally implicating the polar transport of the growth hormone auxin that is * Electronic address: jazz@tauex.tau.ac.il † Electronic address: lmahadev@g.harvard.edu critical in mediating tissue growth, which is indeed driven by either gravity or light. Furthermore, these observations of responses to ...

A Framework for Collective Behavior in Plant Inspired Growth-Driven Systems, Based on Kinematics of Allotropism

“…However this can be generalized to explicitly account for growth following previous work 2014. In addition, elasticity [58] and more complex integration of stimuli [51] can be integrated, as well as a generalization to 3D [50]. Moreover, this model assumes the signal is emitted from a point at the tip, however it is possible to consider the signals emitted from a more extended part of the organ, by assuming the signal is additive.…”

“…the model is general, making minimal assumptions about the building blocks of the system, it successfully accounts for the experimentally observed gravitropic kinematics of different organs from 11 angiosperms. The model also accounts for the kinematics of growing organs [49] in 3D [50], and has also been generalized to take into account time varying stimuli [51]. However, it is limited to the case of distant stimuli yielding a parallel vector field, such as gravity or sunlight, which approach any point along a plant from the same angle, and at the same intensity.…”

A perspective on plant robotics: from bioinspiration to hybrid systems

“…Later, further generalizations provided descriptions of goaldirected movements (tropisms) as well as search movements/actuation (the intrinsic periodic movements called circumnutations), in three-dimensions (see also figure 2(f)) [33,[46][47][48][49]. Another layer of complexity comes from the inclusion of memory, based on the observations that plants do not respond instantaneously, but rather to a history within tropic responses [50,51]. Memory provides the framework for basic behavioral processes, allowing to integrate stimuli, compare stimuli over time, and at the basis of decision-making-to name a few functions.…”