Stochastic processes in gravitropism

Engineering Transport via Collisional Noise: A Toolbox for Biology Systems

The study of noise assisted-transport in quantum systems is essential in a wide range of applications, from near-term NISQ devices to models for quantum biology. Here, we study a generalized XXZ model in the presence of stochastic collision noise, which allows describing environments beyond the standard Markovian formulation. Our analysis through the study of the local magnetization, the inverse participation ratio (IPR) or its generalization, and the inverse ergodicity ratio (IER) showed clear regimes, where the transport rate and coherence time could be controlled by the dissipation in a consistent manner. In addition, when considering various excitations, we characterized the interplay between collisions and system interactions, identifying regimes in which transport was counterintuitively enhanced when increasing the collision rate, even in the case of initially separated excitations. These results constitute an example of an essential building block for the understanding of quantum transport in structured noisy and warm-disordered environments.

Role of the Earth's Motions in Plant Orientation - Planetary Mechanism

According to the proposed theory, the starch-rich particles (statoliths) help the plant to convert the signals from Earth's motions into the signals necessary for the plant to perceive its orientation relative to the gravity vector while moving freely because of inertia in the sensory cells (statocytes) of roots and stems. Motions of the Earth are never constant, which, in particular, refers to the so-called polar motions and oscillations of the planet's rotation axis. Statoliths at any given moment move in the cytoplasmic liquid of statocytes due to inertial motion initiated by the action of the Earth's movements, maintaining the trajectory set by the previous movement of the oscillating planet. Unlike statoliths, the walls of a statocyte move in space along with the entire plant and with the Earth, in strict accordance with the current direction of motion of the planet's axis. This leads to the inevitable collision of statoliths with the statocytic wall/membrane. Cytoplasmic liquid, as a substance that is not able to maintain its shape, does not interfere with the inertial motions of the statoliths and collision with the wall of the statocyte. By striking the membrane, statoliths cause the release of ions and other factors at the impact site, which further participate in the gravitropic process. Pressure of the sediment of statoliths at the bottom of the statocyte, as well as position of this sediment, are not the defining factors of gravitropism.

Fluctuations shape plants through proprioception

Plants constantly experience fluctuating internal and external mechanical cues, ranging from nanoscale deformation of wall components, cell growth variability, nutating stems, and fluttering leaves to stem flexion under tree weight and wind drag. Developing plants use such fluctuations to monitor and channel their own shape and growth through a form of proprioception. Fluctuations in mechanical cues may also be actively enhanced, producing oscillating behaviors in tissues. For example, proprioception through leaf nastic movements may promote organ flattening. We propose that fluctuation-enhanced proprioception allows plant organs to sense their own shapes and behave like active materials with adaptable outputs to face variable environments, whether internal or external. Because certain shapes are more amenable to fluctuations, proprioception may also help plant shapes to reach self-organized criticality to support such adaptability.

Modelling the spatial crosstalk between two biochemical signals explains wood formation dynamics and tree-ring structure

In conifers, xylogenesis during a growing season produces a very characteristic tree-ring structure: large, thin-walled earlywood cells followed by narrow, thick-walled latewood cells. Although many factors influence the dynamics of differentiation and the final dimensions of xylem cells, the associated patterns of variation remain very stable from one year to the next. While radial growth is characterized by an S-shaped curve, the widths of xylem differentiation zones exhibit characteristic skewed bell-shaped curves. These elements suggest a strong internal control of xylogenesis. It has long been hypothesized that much of this regulation relies on a morphogenetic gradient of auxin. However, recent modelling studies have shown that while this hypothesis could account for the dynamics of stem radial growth and the zonation of the developing xylem, it failed to reproduce the characteristic tree-ring structure. Here, we investigated the hypothesis of regulation by a crosstalk between auxin and a second biochemical signal, by using computational morphodynamics. We found that, in conifers, such a crosstalk is sufficient to simulate the characteristic features of wood formation dynamics, as well as the resulting tree-ring structure. In this model, auxin controls cell enlargement rates while another signal (e.g. cytokinin, tracheary element differentiation inhibitory factor) drives cell division and auxin polar transport.

What is quantitative plant biology?

Quantitative plant biology is an interdisciplinary field that builds on a long history of biomathematics and biophysics. Today, thanks to high spatiotemporal resolution tools and computational modelling, it sets a new standard in plant science. Acquired data, whether molecular, geometric or mechanical, are quantified, statistically assessed and integrated at multiple scales and across fields. They feed testable predictions that, in turn, guide further experimental tests. Quantitative features such as variability, noise, robustness, delays or feedback loops are included to account for the inner dynamics of plants and their interactions with the environment. Here, we present the main features of this ongoing revolution, through new questions around signalling networks, tissue topology, shape plasticity, biomechanics, bioenergetics, ecology and engineering. In the end, quantitative plant biology allows us to question and better understand our interactions with plants. In turn, this field opens the door to transdisciplinary projects with the society, notably through citizen science.

Development of gravitropic response: unusual behavior of flax phloem G-fibers

The major mechanism of gravitropism that is discussed for herbal plants is based on the nonuniform elongation of cells located on the opposite stem sides, occurring in the growing zone of an organ. However, gravitropic response of flax (Linum usitatissimum L.) is well-pronounced in the lower half of developing stem, which has ceased elongation long in advance of plant inclination. We have analyzed the stem curvature region by various approaches of microscopy and found the undescribed earlier significant modifications in primary phloem fibers that have constitutively developed G-layer. In fibers on the pulling stem side, cell portions were widened with formation of "bottlenecks" between them, leading to the "sausage-like" shape of a cell. Lumen diameter in fiber widening increased, while cell wall thickness decreased. Callose was deposited in proximity to bottlenecks and sometimes totally occluded their lumen. Structure of fiber cell wall changed considerably, with formation of breaks between G- and S-layers. Thick fibrillar structures that were revealed in fiber cell wall by light microscopy got oblique orientation instead of parallel to the fiber axis one in control plants. The described changes occurred at various combinations of gravitational and mechanical stimuli. Thus, phloem fibers with constitutively formed gelatinous cell wall, located in nonelongating parts of herbal plant, are involved in gravitropism and may become an important element in general understanding of the gravity effects on plants. We suggest flax phloem fibers as the model system to study the mechanism of plant position correction, including signal perception and transduction.

Thermodynamical journey in plant biology

Nonequilibrium irreversible thermodynamics constitute a meaningful point of view suitable to explore life with a rich paradigm. This analytical framework can be used to span the gap from molecular processes to plant function and shows great promise to create a holistic description of life. Since living organisms dissipate energy, exchange entropy and matter with their environment, they can be assimilated to dissipative structures. This concept inherited from nonequilibrium thermodynamics has four properties which defines a scale independent framework suitable to provide a simpler and more comprehensive view of the highly complex plant biology. According to this approach, a biological function is modeled as a cascade of dissipative structures. Each dissipative structure, corresponds to a biological process, which is initiated by the amplification of a fluctuation. Evolution of the process leads to the breakage of the system symmetry and to the export of entropy. Exporting entropy to the surrounding environment corresponds to collecting information about it. Biological actors which break the symmetry of the system and which store information are by consequence, key actors on which experiments and data analysis focus most. This paper aims at illustrating properties of dissipative structure through familiar examples and thus initiating the dialogue between nonequilibrium thermodynamics and plant biology.