Mechanics and hydraulics of pollen tube growth.

All kingdoms of life have evolved tip-growing cells able to mine their environment or deliver cargo to remote targets. The basic cellular processes supporting these functions are understood in increasing detail, but the multiple interactions between them lead to complex responses that require quantitative models to be disentangled. Here, I review the equations that capture the fundamental interactions between wall mechanics and cell hydraulics starting with a detailed presentation of James Lockhart's seminal model. The homeostatic feedbacks needed to maintain a steady tip velocity are then shown to offer a credible explanation for the pulsatile growth observed in some tip-growing cells. Turgor pressure emerges as a central variable whose role in the morphogenetic process has been a source of controversy for more than 50 yr. I argue that recasting Lockhart's work as a process of chemical stress relaxation can clarify how cells control tip growth and help us internalise the important but passive role played by turgor pressure in the morphogenetic process.

Design of a unidirectional water valve in Tillandsia.

The bromeliad Tillandsia landbeckii thrives in the Atacama desert of Chile using the fog captured by specialized leaf trichomes to satisfy its water needs. However, it is still unclear how the trichome of T. landbeckii and other Tillandsia species is able to absorb fine water droplets during intermittent fog events while also preventing evaporation when the plant is exposed to the desert's hyperarid conditions. Here, we explain how a 5800-fold asymmetry in water conductance arises from a clever juxtaposition of a thick hygroscopic wall and a semipermeable membrane. While absorption is achieved by osmosis of liquid water, evaporation under dry external conditions shifts the liquid-gas interface forcing water to diffuse through the thick trichome wall in the vapor phase. We confirm this mechanism by fabricating artificial composite membranes mimicking the trichome structure. The reliance on intrinsic material properties instead of moving parts makes the trichome a promising basis for the development of microfluidics valves.

A multi-scale model for fluid transport through a bio-inspired passive valve.

Tillandsia landbeckii is a rootless plant thriving in the hyper-arid Atacama Desert of Chile. These plants use unique cellulose-based microscopic structures called trichomes to collect fresh water from coastal fog. The trichomes rely on a passive mechanism to maintain an asymmetrical transport of water: they allow for the fast absorption of liquid water deposited by sporadic fog events while preventing evaporation during extended drought periods. Inspired by the trichome's design, we study fluid transport through a micrometric valve. Combining Grand Canonical Monte Carlo with Non-Equilibrium Molecular Dynamics simulations, we first analyze the adsorption and transport of a fluid through a single nanopore at different chemical potentials. We then scale up the atomic results using a lattice approach, and simulate the transport at the micrometric scale. Results obtained for a model Lennard-Jones fluid and TIP4P/2005 water were compared, allowing us to identify the key physical parameters for achieving a passive hydraulic valve. Our results show that the difference in transport properties of water vapor and liquid water within the cellulose layer is the basis for the ability of the Tillandsia trichome to function as a water valve. Finally, we predict a critical pore dimension above which the cellulose layer can form an efficient valve.

Optimal Design of Multilayer Fog Collectors.

The growing concerns over desertification have spurred research into technologies aimed at acquiring water from nontraditional sources such as dew, fog, and water vapor. Some of the most promising developments have focused on improving designs to collect water from fog. However, the absence of a shared framework to predict, measure, and compare the water collection efficiencies of new prototypes is becoming a major obstacle to progress in the field. We address this problem by providing a general theory to design efficient fog collectors as well as a concrete experimental protocol to furnish our theory with all the necessary parameters to quantify the effective water collection efficiency. We show in particular that multilayer collectors are required for high fog collection efficiency and that all efficient designs are found within a narrow range of mesh porosity. We support our conclusions with measurements on simple multilayer harp collectors.

Predicting Accumulation of Intermediate Compounds in Nitrification and Autotrophic Denitrification Processes: A Chemical Approach.

Nitrification and sulfur-based autotrophic denitrification processes can be used to remove ammonia from wastewater in an economical way. However, under certain operational conditions, these processes accumulate intermediate compounds, such as elemental sulphur, nitrite, and nitrous oxide, that are noxious for the environment. In order to predict the generation of these compounds, an analysis based on the Gibbs free energy of the possible reactions and on the oxidative capacity of the bulk liquid was done on case study systems. Results indicate that the Gibbs free energy is not a useful parameter to predict the generation of intermediate products in nitrification and autotrophic denitrification processes. Nevertheless, we show that the specific productions of nitrous oxide during nitrification, and of elemental sulphur and nitrite during autotrophic denitrification, are well related to the oxidative capacity of the bulk liquid.

Are microtubules tension sensors?

Mechanical signals play many roles in cell and developmental biology. Several mechanotransduction pathways have been uncovered, but the mechanisms identified so far only address the perception of stress intensity. Mechanical stresses are tensorial in nature, and thus provide dual mechanical information: stress magnitude and direction. Here we propose a parsimonious mechanism for the perception of the principal stress direction. In vitro experiments show that microtubules are stabilized under tension. Based on these results, we explore the possibility that such microtubule stabilization operates in vivo, most notably in plant cells where turgor-driven tensile stresses exceed greatly those observed in animal cells.

Lily Pollen Tubes Pulse According to a Simple Spatial Oscillator.

Polar growth is a fundamental mode of cell morphogenesis observed in nearly all major groups of organisms. Among polarly growing cells, the angiosperm pollen tubes have emerged as powerful experimental systems in large part because of their oscillatory growth, which provides a window into the network of interactions regulating morphogenesis. Empirical studies of oscillatory pollen tubes have sought to uncover the temporal sequence of cellular and molecular events that constitutes an oscillatory cycle. Here we show that in lily pollen tubes the distance or wavelength (λ = 6.3 ± 1.7 µm) over which an oscillatory cycle unfolds is more robust than the period of oscillation (τ = 39.1 ± 17.6 s) (n = 159 cells). Moreover, the oscillatory cycle is divided into slow and fast phases, with each phase unfolding over precisely one half of the wavelength. Using these observations, we show that a simple spatial bi-oscillator predicts the most common modes of oscillation observed in pollen tubes. These results call into question the traditional view of pollen tube morphogenesis as a temporal succession of cellular events. Space, not time, may be the most natural metric to inteprete the morphogenetic dynamics of these cells.

Wall mechanics and exocytosis define the shape of growth domains in fission yeast.

The amazing structural variety of cells is matched only by their functional diversity, and reflects the complex interplay between biochemical and mechanical regulation. How both regulatory layers generate specifically shaped cellular domains is not fully understood. Here, we report how cell growth domains are shaped in fission yeast. Based on quantitative analysis of cell wall expansion and elasticity, we develop a model for how mechanics and cell wall assembly interact and use it to look for factors underpinning growth domain morphogenesis. Surprisingly, we find that neither the global cell shape regulators Cdc42-Scd1-Scd2 nor the major cell wall synthesis regulators Bgs1-Bgs4-Rgf1 are reliable predictors of growth domain geometry. Instead, their geometry can be defined by cell wall mechanics and the cortical localization pattern of the exocytic factors Sec6-Syb1-Exo70. Forceful re-directioning of exocytic vesicle fusion to broader cortical areas induces proportional shape changes to growth domains, demonstrating that both features are causally linked.

Modes of deformation of walled cells.

The bewildering morphological diversity found in cells is one of the starkest illustrations of life's ability to self-organize. Yet the morphogenetic mechanisms that produce the multifarious shapes of cells are still poorly understood. The shared similarities between the walled cells of prokaryotes, many protists, fungi, and plants make these groups particularly appealing to begin investigating how morphological diversity is generated at the cell level. In this review, I attempt a first classification of the different modes of surface deformation used by walled cells. Five modes of deformation were identified: inextensional bending, equi-area shear, elastic stretching, processive intussusception, and chemorheological growth. The two most restrictive modes-inextensional and equi-area deformations-are embodied in the exine of pollen grains and the wall-like pellicle of euglenoids, respectively. For these modes, it is possible to express the deformed geometry of the cell explicitly in terms of the undeformed geometry and other easily observable geometrical parameters. The greatest morphogenetic power is reached with the processive intussusception and chemorheological growth mechanisms that underlie the expansive growth of walled cells. A comparison of these two growth mechanisms suggests a possible way to tackle the complexity behind wall growth.

Strategies for cell shape control in tip-growing cells.

PREMISE OF THE STUDY: Despite the large diversity in biological cell morphology, the processes that specify and control cell shape are not yet fully understood. Here we study the shape of tip-growing, walled cells, which have evolved a polar mode of cell morphogenesis leading to characteristic filamentous cell morphologies that extend only apically. METHODS: We identified the relevant parameters for the control of cell shape and derived scaling laws based on mass conservation and force balance that connect these parameters to the resulting geometrical phenotypes. These laws provide quantitative testable relations linking morphological phenotypes to the biophysical processes involved in establishing and modulating cell shape in tip-growing, walled cells. KEY RESULTS AND CONCLUSIONS: By comparing our theoretical results to the observed morphological variation within and across species, we found that tip-growing cells from plant and fungal species share a common strategy to shape the cell, whereas oomycete species have evolved a different mechanism.

Chemically mediated mechanical expansion of the pollen tube cell wall.

Morphogenesis of plant cells is tantamount to the shaping of the stiff cell wall that surrounds them. To this end, these cells integrate two concomitant processes: 1), deposition of new material into the existing wall, and 2), mechanical deformation of this material by the turgor pressure. However, due to uncertainty regarding the mechanisms that coordinate these processes, existing models typically adopt a limiting case in which either one or the other dictates morphogenesis. In this report, we formulate a simple mechanism in pollen tubes by which deposition causes turnover of cell wall cross-links, thereby facilitating mechanical deformation. Accordingly, deposition and mechanics are coupled and are both integral aspects of the morphogenetic process. Among the key experimental qualifications of this model are: its ability to precisely reproduce the morphologies of pollen tubes; its prediction of the growth oscillations exhibited by rapidly growing pollen tubes; and its prediction of the observed phase relationships between variables such as wall thickness, cell morphology, and growth rate within oscillatory cells. In short, the model captures the rich phenomenology of pollen tube morphogenesis and has implications for other plant cell types.

Universal rule for the symmetric division of plant cells.

The division of eukaryotic cells involves the assembly of complex cytoskeletal structures to exert the forces required for chromosome segregation and cytokinesis. In plants, empirical evidence suggests that tensional forces within the cytoskeleton cause cells to divide along the plane that minimizes the surface area of the cell plate (Errera's rule) while creating daughter cells of equal size. However, exceptions to Errera's rule cast doubt on whether a broadly applicable rule can be formulated for plant cell division. Here, we show that the selection of the plane of division involves a competition between alternative configurations whose geometries represent local area minima. We find that the probability of observing a particular division configuration increases inversely with its relative area according to an exponential probability distribution known as the Gibbs measure. Moreover, a comparison across land plants and their most recent algal ancestors confirms that the probability distribution is widely conserved and independent of cell shape and size. Using a maximum entropy formulation, we show that this empirical division rule is predicted by the dynamics of the tense cytoskeletal elements that lead to the positioning of the preprophase band. Based on the fact that the division plane is selected from the sole interaction of the cytoskeleton with cell shape, we posit that the new rule represents the default mechanism for plant cell division when internal or external cues are absent.

The mechanics of explosive dispersal and self-burial in the seeds of the filaree, Erodium cicutarium (Geraniaceae).

The filaree (Erodium cicutarium), a small, flowering plant related to geraniums, possesses a unique seed dispersal mechanism: the plant can fling its seeds up to half a meter away; and the seeds can bury themselves by drilling into the ground, twisting and untwisting in response to changes in humidity. These feats are accomplished using awns, helical bristles of dead but hygroscopically active tissue attached to the seeds. Here, we describe the kinematics of explosive dispersal and self-burial based on detailed high-speed and time-lapse videos. We use these observations to develop a simple mechanical model that accounts for the coiling behavior of the awn and allows comparison of the strain energy stored in the awn with the kinetic energy at launch. The model is used to examine tradeoffs between dispersal distance and reliability of the dispersal mechanism. The mechanical model may help in understanding the invasive potential of this species and provides a framework for examining other evolutionary tradeoffs in seed dispersal mechanisms among the Geraniaceae.

Foldable structures and the natural design of pollen grains.

Upon release from the anther, pollen grains of angiosperm flowers are exposed to a dry environment and dehydrate. To survive this process, pollen grains possess a variety of physiological and structural adaptations. Perhaps the most striking of these adaptations is the ability of the pollen wall to fold onto itself to prevent further desiccation. Roger P. Wodehouse coined the term harmomegathy for this folding process in recognition of the critical role it plays in the survival of the pollen grain. There is still, however, no quantitative theory that explains how the structure of the pollen wall contributes to harmomegathy. Here we demonstrate that simple geometrical and mechanical principles explain how wall structure guides pollen grains toward distinct folding pathways. We found that the presence of axially elongated apertures of high compliance is critical for achieving a predictable and reversible folding pattern. Moreover, the intricate sculpturing of the wall assists pollen closure by preventing mirror buckling of the surface. These results constitute quantitative structure-function relationships for pollen harmomegathy and provide a framework to elucidate the functional significance of the very diverse pollen morphologies observed in angiosperms.

Mechanics without muscle: biomechanical inspiration from the plant world.

Plant and animal biomechanists have much in common. Although their frame of reference differs, they think about the natural world in similar ways. While researchers studying animals might explore airflow around flapping wings, the actuation of muscles in arms and legs, or the material properties of spider silk, researchers studying plants might explore the flow of water around fluttering seaweeds, the grasping ability of climbing vines, or the material properties of wood. Here we summarize recent studies of plant biomechanics highlighting several current research themes in the field: expulsion of high-speed reproductive projectiles, generation of slow movements by shrinking and swelling cell walls, effects of ontogenetic shifts in mechanical properties of stems, flexible reconfiguration and material properties of seaweeds under crashing waves, and the development of botanically-inspired commercial products. Our hope is that this synopsis will resonate with both plant and animal biologists, encourage cross-pollination across disciplines, and promote fruitful interdisciplinary collaborations in the future.