Model for calcium dependent oscillatory growth in pollen tubes

The plant cell wall-dynamic, strong, and adaptable-is a natural shapeshifter

Mythology is replete with good and evil shapeshifters, who, by definition, display great adaptability and assume many different forms-with several even turning themselves into trees. Cell walls certainly fit this definition as they can undergo subtle or dramatic changes in structure, assume many shapes, and perform many functions. In this review, we cover the evolution of knowledge of the structures, biosynthesis, and functions of the 5 major cell wall polymer types that range from deceptively simple to fiendishly complex. Along the way, we recognize some of the colorful historical figures who shaped cell wall research over the past 100 years. The shapeshifter analogy emerges more clearly as we examine the evolving proposals for how cell walls are constructed to allow growth while remaining strong, the complex signaling involved in maintaining cell wall integrity and defense against disease, and the ways cell walls adapt as they progress from birth, through growth to maturation, and in the end, often function long after cell death. We predict the next century of progress will include deciphering cell type-specific wall polymers; regulation at all levels of polymer production, crosslinks, and architecture; and how walls respond to developmental and environmental signals to drive plant success in diverse environments.

AtFH5-labeled secretory vesicles-dependent calcium oscillation drives exocytosis and stepwise bulge during pollen germination

Pollen germination is an essential step for delivering sperm cells to the embryo sac for double fertilization in flowering plants. The cytosolic Ca2+ concentration ([Ca2+]cyt) and vesicle dynamics are critical for pollen germination, but their potential correlation in pollen grains is not fully understood. Here, we report that [Ca2+]cyt oscillates periodically at the prospective germination sites during pollen germination. The [Ca2+]cyt is mainly from extracellular Ca2+ ([Ca2+]ext) influx, which implicates the Ca2+-permeable ion channel cyclic nucleotide-gated channel 18 (CNGC18). The [Ca2+]cyt oscillations spatiotemporally correlate with the accumulation of secretory vesicles labeled by a formin protein AtFH5, and disruption of vesicle accumulation inhibits the [Ca2+]cyt oscillations. In turn, the [Ca2+]cyt oscillations promote exocytosis, which leads to stepwise cell extension during pollen germination. Together, these data provide a timeline of vesicle dynamics, calcium oscillation, and exocytosis during pollen germination and highlight the importance of the correlation of these events for pollen germination.

Mechanobiology of the cell wall – insights from tip-growing plant and fungal cells

The cell wall (CW) is a thin and rigid layer encasing the membrane of all plant and fungal cells. It ensures mechanical integrity by bearing mechanical stresses derived from large cytoplasmic turgor pressure, contacts with growing neighbors or growth within restricted spaces. The CW is made of polysaccharides and proteins, but is dynamic in nature, changing composition and geometry during growth, reproduction or infection. Such continuous and often rapid remodeling entails risks of enhanced stress and consequent damages or fractures, raising the question of how the CW detects and measures surface mechanical stress and how it strengthens to ensure surface integrity? Although early studies in model fungal and plant cells have identified homeostatic pathways required for CW integrity, recent methodologies are now allowing the measurement of pressure and local mechanical properties of CWs in live cells, as well as addressing how forces and stresses can be detected at the CW surface, fostering the emergence of the field of CW mechanobiology. Here, using tip-growing cells of plants and fungi as case study models, we review recent progress on CW mechanosensation and mechanical regulation, and their implications for the control of cell growth, morphogenesis and survival.

The legacy of kinesins in the pollen tube thirty years later

The pollen tube is fundamental in the reproduction of seed plants. Particularly in angiosperms, we now have much information about how it grows, how it senses extracellular signals, and how it converts them into a directional growth mechanism. The expansion of the pollen tube is also related to dynamic cytoplasmic processes based on the cytoskeleton (such as polymerization/depolymerization of microtubules and actin filaments) or motor activity along with the two cytoskeletal systems and is dependent on motor proteins. While a considerable amount of information is available for the actomyosin system in the pollen tube, the role of microtubules in the transport of organelles or macromolecular structures is still quite uncertain despite that 30 years ago the first work on the presence of kinesins in the pollen tube was published. Since then, progress has been made in elucidating the role of kinesins in plant cells. However, their role within the pollen tube is still enigmatic. In this review, I will postulate some roles of kinesins in the pollen tube 30 years after their initial discovery based on information obtained in other plant cells in the meantime. The most concrete hypotheses predict that kinesins in the pollen tube enable the short movement of specific organelles or contribute to generative cell or sperm cell transport, as well as mediate specific steps in the process of endocytosis.

Constrained Nonlinear and Mixed Effects Integral Differential Equation Models for Dynamic Cell Polarity Signaling

Polar cell growth is a process that couples the establishment of cell polarity with growth and is extremely important in the growth, development, and reproduction of eukaryotic organisms, such as pollen tube growth during plant fertilization and neuronal axon growth in animals. Pollen tube growth requires dynamic but polarized distribution and activation of a signaling protein named ROP1 to the plasma membrane via three processes: positive feedback and negative feedback regulation of ROP1 activation and its lateral diffusion along the plasma membrane. In this paper, we introduce a mechanistic integro-differential equation (IDE) along with constrained semiparametric regression to quantitatively describe the interplay among these three processes that lead to the polar distribution of active ROP1 at a steady state. Moreover, we introduce a population variability by a constrained nonlinear mixed model. Our analysis of ROP1 activity distributions from multiple pollen tubes revealed that the equilibrium between the positive and negative feedbacks for pollen tubes with similar shapes are remarkably stable, permitting us to infer an inherent quantitative relationship between the positive and negative feedback loops that defines the tip growth of pollen tubes and the polarity of tip growth.

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.

Insights into the Mechanisms of Heat Priming and Thermotolerance in Tobacco Pollen

Global warming leads to a progressive rise in environmental temperature. Plants, as sessile organisms, are threatened by these changes; the male gametophyte is extremely sensitive to high temperature and its ability to preserve its physiological status under heat stress is known as acquired thermotolerance. This latter can be achieved by exposing plant to a sub-lethal temperature (priming) or to a progressive increase in temperature. The present research aims to investigate the effects of heat priming on the functioning of tobacco pollen grains. In addition to evaluating basic physiological parameters (e.g., pollen viability, germination and pollen tube length), several aspects related to a correct pollen functioning were considered. Calcium (Ca2+) level, reactive oxygen species (ROS) and related antioxidant systems were investigated, also to the organization of actin filaments and cytoskeletal protein such as tubulin (including tyrosinated and acetylated isoforms) and actin. We also focused on sucrose synthase (Sus), a key metabolic enzyme and on the content of main soluble sugars, including UDP-glucose. Results here obtained showed that a pre-exposure to sub-lethal temperatures can positively enhance pollen performance by altering its metabolism. This can have a considerable impact, especially from the point of view of breeding strategies aimed at improving crop species.

PbrPOE21 inhibits pear pollen tube growth in vitro by altering apical reactive oxygen species content

Genome-wide identification, tissue-specific expression analysis and functional characterization of selected genes containing the pear Pollen Olea europaea I domain reveal their roles in pollen tube growth. Genes containing the Pollen Olea europaea I (POE) domain play crucial roles in diverse growth and developmental processes. Nevertheless, the specific functions of POE family members in progression of pollen tube growth (PTG) remain uncharacterized. We identified 45 PbrPOE genes in the pear (Pyrus bretschneideri) genome, clustered into seven subclasses. PbrPOE genes contained 1 to 11 exons and 0 to 10 introns, with exon/intron structure mostly conserved within each subclass. Whole-genome duplication has mainly contributed to the duplication pattern of PbrPOE genes in pear. Expression profiles of 45 PbrPOE genes in 12 different pear tissues revealed that six PbrPOE genes (PbrPOE6, 12, 21, 29, 35 and 41) of subclass B were highly expressed during the growth of the pear pollen tube in vitro. PbrPOE21 was selected for further functional analysis on the basis of its high and differential expression pattern in pollen. Antisense oligodeoxynucleotide assays demonstrated that PTG was augmented in vitro when PbrPOE21 expression was significantly inhibited. Moreover, pollen tube length in vitro was reduced when PbrPOE21 was transitorily over-expressed using particle bombardment technology. Exogenous PbrPOE21 recombinant protein inhibited PTG in vitro at an optimum concentration of 1.8 µM. PbrPOE21 also affected reactive oxygen species content in the pear pollen tube apex. We suggest that PbrPOE21 inhibits PTG in vitro by altering apical reactive oxygen species content.

Silver nanoparticles (AgNPs) induced impairment of in vitro pollen performance of Peltophorum pterocarpum (DC.) K. Heyne

Increasing use of silver nanoparticles (AgNPs) in myriad applications including electronics, medicines and agriculture has led to serious concerns regarding its release to plant ecosystems. Over the years, numerous studies have demonstrated the toxic impact of AgNPs in a variety of cell and tissue systems involved in vegetative growth across a wide range of plant species. However, assessing their impact on haploid phase of plant life cycle was restricted only to a study with Kiwifruit. In this study, in vitro pollen performance of Peltophorum pterocarpum at two endpoints i.e., germination and tube growth was assessed to evaluate the impact of nanoparticulate or ionic form of silver. Increasing concentrations of AgNO₃/AgNPs significantly reduced the pollen germination and retarded the tube growth. The EC 50 values indicated a more potent toxic effect of AgNPs than AgNO₃ on pollen germination as well as tube growth. Impairment of pollen performance was more pronounced at the stage of emergence of pollen tube. Extensive alterations in the muri and lumen of exine as revealed through SEM analysis and subsequent blockage of germpore might disrupt the emergence of pollen tube. The dynamics of pollen tube growth was analyzed with polynomial models of different degrees. A high degree of polynomial, the quintic model was able to approximate the real data points with highest coefficient of determination and smallest RMSE, compared to other models. An oscillating pattern of tube growth was portrayed with the passage of time in all the treatments that fits well with the established mechanistic oscillatory model of tube growth. It appears that exposure to AgNO₃/AgNPs inhibited pollen germination and retarded tube growth without affecting the oscillatory behavior of tip-growth.

Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis

Plant growth research produces a catalogue of complex open questions. We argue that plant growth is a highly mechanical process, and that mathematics gives an underlying framework with which to probe its fundamental unrevealed mechanisms. This review serves to illustrate the biological insights afforded by mathematical modelling and demonstrate the breadth of mathematically rich problems available within plant sciences, thereby promoting a mutual appreciation across the disciplines. On the one hand, we explain the general mathematical principles behind mechanical growth models; on the other, we describe how modelling addresses specific problems in microscale cell wall mechanics, tip growth, morphogenesis, and stress feedback. We conclude by identifying possible future directions for both biologists and mathematicians, including as yet unanswered questions within various topics, stressing that interdisciplinary collaboration is vital for tackling the challenge of understanding plant growth mechanics.

Cold stress affects cell wall deposition and growth pattern in tobacco pollen tubes

Cold is an abiotic stress seriously threatening crop productivity by decreasing biomass production. The pollen tube is a target of cold stress, but also a useful model to address questions on cell wall biosynthesis. We here provide (immuno)cytological data relative to the impact of cold on the pollen tube cell wall. We clearly show that the growth pattern is severely affected by the stress, since the typical pulsed-growth mechanism accompanied by the periodic deposition of pectin rings is absent/severely reduced. Additionally, pectins and cellulose accumulate in bulges provoked by the stress, while callose, which colocalizes with pectins in the periodic rings formed during pulsed growth, accumulates randomly in the stressed samples. The altered distribution of the cell wall components is accompanied by differences in the localization of glucan synthases: cellulose synthase shows a more diffuse localization, while callose synthase shows a more frequent cytoplasmic accumulation, thereby denoting a failure in plasma membrane insertion. The cell wall observations are complemented by the analysis of intracellular Ca2+, pH and reactive oxygen species (ROS): while in the case of pH no major differences are observed, a less focused Ca2+ and ROS gradients are present in the stressed samples. The standard oscillatory growth of pollen tubes is recovered by transient changes of turgor pressure induced by hypoosmotic media. Overall our data contribute to the understanding of the impact that cold stress has on the normal development of the pollen tube and unveil the cell wall-related aberrant features accompanying the observed alterations.

Elongation and shape changes in organisms with cell walls: A dialogue between experiments and models

The generation of anisotropic shapes occurs during morphogenesis of almost all organisms. With the recent renewal of the interest in mechanical aspects of morphogenesis, it has become clear that mechanics contributes to anisotropic forms in a subtle interaction with various molecular actors. Here, we consider plants, fungi, oomycetes, and bacteria, and we review the mechanisms by which elongated shapes are generated and maintained. We focus on theoretical models of the interplay between growth and mechanics, in relation with experimental data, and discuss how models may help us improve our understanding of the underlying biological mechanisms.

Cell mechanics of pollen tube growth

The pollen tube features particular traits that can only be understood when integrating cell biological with cell mechanical concepts. Firstly, regular temporal variations in the growth rate are governed by a feedback mechanism thought to involve mechanosensitive ion channels. Secondly, the tube uses invasive growth to penetrate the flower tissues with the aim to transport the male sperm cells to their target. Thirdly, the pollen tube is able to reorient its growth direction upon exposure to a guidance cue; the steering mechanism involves the sophisticated choreography of intracellular transport processes. Sophisticated imaging and micromanipulation techniques have been instrumental for the advancement in characterizing the biomechanical features of this crucial cell in the plant reproductive cycle.

Pollen tube growth and guidance: Occam's razor sharpened on a molecular arabinogalactan glycoprotein Rosetta Stone

Occam's Razor suggests a new model of pollen tube tip growth based on a novel Hechtian oscillator that integrates a periplasmic arabinogalactan glycoprotein-calcium (AGP-Ca²⁺ ) capacitor with tip-localized AGPs as the source of tip-focussed cytosolic Ca²⁺ oscillations: Hechtian adhesion between the plasma membrane and the cell wall of the growing tip acts as a piconewton force transducer that couples the internal stress of a rapidly growing wall to the plasma membrane. Such Hechtian transduction opens stretch-activated Ca²⁺ channels and activates H⁺ -ATPase proton pump efflux that dissociates periplasmic AGP-Ca²⁺ resulting in a Ca²⁺ influx that activates exocytosis of wall precursors. Thus, a highly simplified pectic primary cell wall regulates its own synthesis by a Hechtian growth oscillator that regulates overall tip growth. By analogy with the three cryptic inscriptions of the classical Rosetta Stone, the Hechtian Hypothesis translates classical AGP function as a Ca²⁺ capacitor, pollen tube guide and wall plasticizer into a simple but widely applicable model of tip growth. Even wider ramifications of the Hechtian oscillator may implicate AGPs in osmosensing or gravisensing and other tropisms, leading us yet further towards the Holy Grail of plant growth.

Oscillatory fungal cell growth

Cells are dynamic systems, the state of which undergoes constant alteration that results in morphological changes and movement. Many dynamic cellular processes that appear continuous are driven by underlying mechanisms that oscillate with distinct periods. For example eukaryotic cells do not grow continuously, but rather by pulsed extension of the periphery. Stepwise cell extension at the hyphal tips of several filamentous fungi was discovered 20 years ago, but only a few molecular details of the mechanism have been clarified since then. A recent study has provided evidence for correlations among intracellular Ca²⁺ levels, actin assembly, exocytosis and cell extension in growing hyphal tips. This suggests that pulsed Ca²⁺ influxes coordinate the temporal control of actin assembly and exocytosis, which results in stepwise cell extension. The coordinated oscillation of these machineries are likely to be ubiquitous among all eukaryotes. Indeed, intracellular Ca²⁺ levels and/or actin polymerization oscillate in mammalian and plant cells. This review summarizes the mechanisms of oscillation in several systems.

Frequency-associated transition from single-cell asynchronous motion to monotonic growth

This paper presents a Fourier analysis of the Ortega equation that examines the growth dynamics of plants, specifically the pollen tubes or non-meristematic zones of elongating coleoptiles. A frequency-induced transition from highly nonlinear (periodical) growth-like the one observed in pollen tubes-to monotonically ascending and asymptotically saturated (sigmoid-like) growth, which is anticipated within the framework of a 'two-fluid model', is shown. A dynamic phase diagram is calculated and presented in the form of a live video clip.

Exocytosis-coordinated mechanisms for tip growth underlie pollen tube growth guidance

Many tip-growing cells are capable of responding to guidance cues, during which cells precisely steer their growth toward the source of guidance signals. Though several players in signal perception have been identified, little is known about the downstream signaling that controls growth direction during guidance. Here, using combined modeling and experimental studies, we demonstrate that the growth guidance of Arabidopsis pollen tubes is regulated by the signaling network that controls tip growth. Tip-localized exocytosis plays a key role in this network by integrating guidance signals with the ROP1 Rho GTPase signaling and coordinating intracellular signaling with cell wall mechanics. This model reproduces the high robustness and responsiveness of pollen tube guidance and explains the connection between guidance efficiency and the parameters of the tip growth system. Hence, our findings establish an exocytosis-coordinated mechanism underlying the cellular pathfinding guided by signal gradients and the mechanistic linkage between tip growth and guidance.

Probing the effect of tip pressure on fungal growth: Application to Aspergillus nidulans

The study of fungal cells is of great interest due to their importance as pathogens and as fermenting fungi and for their appropriateness as model organisms. The differential pressure between the hyphal cytoplasm and the bordering medium is essential for the growth process, because the pressure is correlated with the growth rate. Notably, during the invasion of tissues, the external pressure at the tip of the hypha may be different from the pressure in the surrounding medium. We report the use of a method, based on the micropipette-aspiration technique, to study the influence of this external pressure at the hyphal tip. Moreover, this technique makes it possible to study hyphal growth mechanics in the case of very thin hyphae, not accessible to turgor pressure probes. We found a correlation between the local pressure at the tip and the growth rate for the species Arpergillus nidulans. Importantly, the proposed method allows one to measure the pressure at the tip required to arrest the hyphal growth. Determining that pressure could be useful to develop new medical treatments for fungal infections. Finally, we provide a mechanical model for these experiments, taking into account the cytoplasm flow and the wall deformation.

Segmentation of Pollen Tube Growth Videos Using Dynamic Bi-Modal Fusion and Seam Carving

The growth of pollen tubes is of significant interest in plant cell biology, as it provides an understanding of internal cell dynamics that affect observable structural characteristics such as cell diameter, length, and growth rate. However, these parameters can only be measured in experimental videos if the complete shape of the cell is known. The challenge is to accurately obtain the cell boundary in noisy video images. Usually, these measurements are performed by a scientist who manually draws regions-of-interest on the images displayed on a computer screen. In this paper, a new automated technique is presented for boundary detection by fusing fluorescence and brightfield images, and a new efficient method of obtaining the final cell boundary through the process of Seam Carving is proposed. This approach takes advantage of the nature of the fusion process and also the shape of the pollen tube to efficiently search for the optimal cell boundary. In video segmentation, the first two frames are used to initialize the segmentation process by creating a search space based on a parametric model of the cell shape. Updates to the search space are performed based on the location of past segmentations and a prediction of the next segmentation.Experimental results show comparable accuracy to a previous method, but significant decrease in processing time. This has the potential for real time applications in pollen tube microscopy.

Rapid and Inexpensive Method of Loading Fluorescent Dye into Pollen Tubes and Root Hairs

The most direct technique for studying calcium, which is an essential element for pollen tube growth, is Ca²⁺ imaging. Because membranes are relatively impermeable, the loading of fluorescent Ca²⁺ probes into plant cells is a challenging task. Thus, we have developed a new method of loading fluo-4 acetoxymethyl ester into cells that uses a cell lysis solution to improve the introduction of this fluorescent dye into pollen tubes. Using this method, the loading times were reduced to 15 min. Furthermore, loading did not have to be performed at low (4°C) temperatures and was successful at room temperature, and pluronic F-127 was not required, which would theoretically allow for the loading of an unlimited number of cells. Moreover, the method can also be used to fluorescently stain root hairs.

Gelsolin-Like Domain 3 Plays Vital Roles in Regulating the Activities of the Lily Villin/Gelsolin/Fragmin Superfamily

The villin/gelsolin/fragmin superfamily is a major group of Ca2+-dependent actin-binding proteins (ABPs) involved in various cellular processes. Members of this superfamily typically possess three or six tandem gelsolin-like (G) domains, and each domain plays a distinct role in actin filament dynamics. Although the activities of most G domains have been characterized, the biochemical function of the G3 domain remains poorly understood. In this study, we carefully compared the detailed biochemical activities of ABP29 (a new member of this family that contains the G1-G2 domains of lily ABP135) and ABP135G1-G3 (which contains the G1-G3 domains of lily ABP135). In the presence of high Ca2+ levels in vitro (200 and 10 μM), ABP135G1-G3 exhibited greater actin severing and/or depolymerization and nucleating activities than ABP29, and these proteins had similar actin capping activities. However, in the presence of low levels of Ca2+ (41 nM), ABP135G1-G3 had a weaker capping activity than ABP29. In addition, ABP29 inhibited F-actin depolymerization, as shown by dilution-mediated depolymerization assay, differing from the typical superfamily proteins. In contrast, ABP135G1-G3 accelerated F-actin depolymerization. All of these results demonstrate that the G3 domain plays specific roles in regulating the activities of the lily villin/gelsolin/fragmin superfamily proteins.

Arabidopsis RIC1 Severs Actin Filaments at the Apex to Regulate Pollen Tube Growth

Pollen tubes deliver sperms to the ovule for fertilization via tip growth. The rapid turnover of F-actin in pollen tube tips plays an important role in this process. In this study, we demonstrate that Arabidopsis thaliana RIC1, a member of the ROP-interactive CRIB motif-containing protein family, regulates pollen tube growth via its F-actin severing activity. Knockout of RIC1 enhanced pollen tube elongation, while overexpression of RIC1 dramatically reduced tube growth. Pharmacological analysis indicated that RIC1 affected F-actin dynamics in pollen tubes. In vitro biochemical assays revealed that RIC1 directly bound and severed F-actin in the presence of Ca(2+) in addition to interfering with F-actin turnover by capping F-actin at the barbed ends. In vivo, RIC1 localized primarily to the apical plasma membrane (PM) of pollen tubes. The level of RIC1 at the apical PM oscillated during pollen tube growth. The frequency of F-actin severing at the apex was notably decreased in ric1-1 pollen tubes but was increased in pollen tubes overexpressing RIC1. We propose that RIC1 regulates F-actin dynamics at the apical PM as well as the cytosol by severing F-actin and capping the barbed ends in the cytoplasm, establishing a novel mechanism that underlies the regulation of pollen tube growth.

Optimization of flow assisted entrapment of pollen grains in a microfluidic platform for tip growth analysis

A biocompatible polydimethylsiloxane (PDMS) biomicrofluidic platform is designed, fabricated and tested to study protuberance growth of single plant cells in a micro-vitro environment. The design consists of an inlet to introduce the cell suspension into the chip, three outlets to conduct the medium or cells out of the chip, a main distribution chamber and eight microchannels connected to the main chamber to guide the growth of tip growing plant cells. The test cells used here were pollen grains which produce cylindrical protrusions called pollen tubes. The goal was to adjust the design of the microfluidic network with the aim to enhance the uniformly distributed positioning of pollen grains at the entrances of the microchannels and to provide identical fluid flow conditions for growing pollen tubes along each microchannel. Computational fluid analysis and experimental testing were carried out to estimate the trapping efficiencies of the different designs.

Dissecting the regulation of pollen tube growth by modeling the interplay of hydrodynamics, cell wall and ion dynamics

Hydrodynamics, cell wall and ion dynamics are all important properties that regulate pollen tube growth. Currently, the two main pollen tube growth models, the cell wall model and the hydrodynamic model do not appear to be reconcilable. Here we develop an integrative model for pollen tube growth and show that our model reproduces key experimental observations: (1) that the hypertonic condition leads to a much longer oscillatory period and that the hypotonic condition halves the oscillatory period; (2) that oscillations in turgor are experimentally undetectable; (3) that increasing the extracellular calcium concentration or decreasing the pH decreases the growth oscillatory amplitude; (4) that knockout of Raba4d, a member of the Rab family of small GTPase proteins, decreases pollen tube length after germination for 24 h. Using the model generated here, we reveal that (1) when cell wall extensibility is large, pollen tube may sustain growth at different volume changes and maintain relatively stable turgor; (2) turgor increases if cell wall extensibility decreases; (3) increasing turgor due to decrease in osmolarity in the media, although very small, increases volume change. However, increasing turgor due to decrease in cell wall extensibility decreases volume change. In this way regulation of pollen tube growth by turgor is context dependent. By changing the osmolarity in the media, the main regulatory points are extracellular osmolarity for water flow and turgor for the volume encompassed by the cell wall. However, if the viscosity of cell wall changes, the main regulatory points are turgor for water flow and wall extensibility for the volume encompassed by the cell wall. The novel methodology developed here reveals the underlying context-dependent regulatory principle of pollen tube growth.

Annexin5 plays a vital role in Arabidopsis pollen development via Ca2+-dependent membrane trafficking

The regulation of pollen development and pollen tube growth is a complicated biological process that is crucial for sexual reproduction in flowering plants. Annexins are widely distributed from protists to higher eukaryotes and play multiple roles in numerous cellular events by acting as a putative "linker" between Ca2+ signaling, the actin cytoskeleton and the membrane, which are required for pollen development and pollen tube growth. Our recent report suggested that downregulation of the function of Arabidopsis annexin 5 (Ann5) in transgenic Ann5-RNAi lines caused severely sterile pollen grains. However, little is known about the underlying mechanisms of the function of Ann5 in pollen. This study demonstrated that Ann5 associates with phospholipid membrane and this association is stimulated by Ca2+ in vitro. Brefeldin A (BFA) interferes with endomembrane trafficking and inhibits pollen germination and pollen tube growth. Both pollen germination and pollen tube growth of Ann5-overexpressing plants showed increased resistance to BFA treatment, and this effect was regulated by calcium. Overexpression of Ann5 promoted Ca2+-dependent cytoplasmic streaming in pollen tubes in vivo in response to BFA. Lactrunculin (LatB) significantly prohibited pollen germination and tube growth by binding with high affinity to monomeric actin and preferentially targeting dynamic actin filament arrays and preventing actin polymerization. Overexpression of Ann5 did not affect pollen germination or pollen tube growth in response to LatB compared with wild-type, although Ann5 interacts with actin filaments in a manner similar to some animal annexins. In addition, the sterile pollen phenotype could be only partially rescued by Ann5 mutants at Ca2+-binding sites when compared to the complete recovery by wild-type Ann5. These data demonstrated that Ann5 is involved in pollen development, germination and pollen tube growth through the promotion of endomembrane trafficking modulated by calcium. Our results provide reliable molecular mechanisms that underlie the function of Ann5 in pollen.

No stress! Relax! Mechanisms governing growth and shape in plant cells

The mechanisms through which plant cells control growth and shape are the result of the coordinated action of many events, notably cell wall stress relaxation and turgor-driven expansion. The scalar nature of turgor pressure would drive plant cells to assume spherical shapes; however, this is not the case, as plant cells show an amazing variety of morphologies. Plant cell walls are dynamic structures that can display alterations in matrix polysaccharide composition and concentration, which ultimately affect the wall deformation rate. The wide varieties of plant cell shapes, spanning from elongated cylinders (as pollen tubes) and jigsaw puzzle-like epidermal cells, to very long fibres and branched stellate leaf trichomes, can be understood if the underlying mechanisms regulating wall biosynthesis and cytoskeletal dynamics are addressed. This review aims at gathering the available knowledge on the fundamental mechanisms regulating expansion, growth and shape in plant cells by putting a special emphasis on the cell wall-cytoskeleton system continuum. In particular, we discuss from a molecular point of view the growth mechanisms characterizing cell types with strikingly different geometries and describe their relationship with primary walls. The purpose, here, is to provide the reader with a comprehensive overview of the multitude of events through which plant cells manage to expand and control their final shapes.

Pressure-induced cell wall instability and growth oscillations in pollen tubes

In the seed plants, the pollen tube is a cellular extension that serves as a conduit through which male gametes are transported to complete fertilization of the egg cell. It consists of a single elongated cell which exhibits characteristic oscillations in growth rate until it finally bursts, completing its function. The mechanism behind the periodic character of the growth has not been fully understood. In this paper we show that the mechanism of pressure--induced symmetry frustration occurring in the wall at the transition-perimeter between the cylindrical and approximately hemispherical parts of the growing pollen tube, together with the addition of cell wall material, is sufficient to release and sustain mechanical self-oscillations and cell extension. At the transition zone, where symmetry frustration occurs and one cannot distinguish either of the involved symmetries, a kind of 'superposition state' appears where either single or both symmetry(ies) can be realized by the system. We anticipate that testifiable predictions made by the model (f is proportional to √P) may deliver, after calibration, a new tool to estimate turgor pressure P from oscillation frequency f of the periodically growing cell. Since the mechanical principles apply to all turgor regulated walled cells including those of plant, fungal and bacterial origin, the relevance of this work is not limited to the case of the pollen tube.

Mercury-sensitive water channels as possible sensors of water potentials in pollen

The growing pollen tube is central to plant reproduction and is a long-standing model for cellular tip growth in biology. Rapid osmotically driven growth is maintained under variable conditions, which requires osmosensing and regulation. This study explores the mechanism of water entry and the potential role of osmosensory regulation in maintaining pollen growth. The osmotic permeability of the plasmalemma of Lilium pollen tubes was measured from plasmolysis rates to be 1.32±0.31×10(-3) cm s(-1). Mercuric ions reduce this permeability by 65%. Simulations using an osmotic model of pollen tube growth predict that an osmosensor at the cell membrane controls pectin deposition at the cell tip; inhibiting the sensor is predicted to cause tip bursting due to cell wall thinning. It was found that adding mercury to growing pollen tubes caused such a bursting of the tips. The model indicates that lowering the osmotic permeability per se does not lead to bursting but rather to thickening of the tip. The time course of induced bursting showed no time lag and was independent of mercury concentration, compatible with a surface site of action. The submaximal bursting response to intermediate mercuric ion concentration was independent of the concentration of calcium ions, showing that bursting is not due to a competitive inhibition of calcium binding or entry. Bursting with the same time course was also shown by cells growing on potassium-free media, indicating that potassium channels (implicated in mechanosensing) are not involved in the bursting response. The possible involvement of mercury-sensitive water channels as osmosensors and current knowledge of these in pollen cells are discussed.

The cellular mechanics of an invasive lifestyle

Invasive behaviour is the hallmark of a variety of cell types of animal, plant, and fungal origin. Here we review the purpose and mechanism of invasive growth and migration. The focus is on the physical principles governing the process, the source of invasive force, and the cellular mechanism by which the cell penetrates the substrate. The current experimental methods for measuring invasive force and the modelling approaches for studying invasive behaviour are explained, and future experimental strategies are proposed.

Towards the Physics of Calcium Signalling in Plants

Calcium is an abundant element with a wide variety of important roles within cells. Calcium ions are inter- and intra-cellular messengers that are involved in numerous signalling pathways. Fluctuating compartment-specific calcium ion concentrations can lead to localised and even plant-wide oscillations that can regulate downstream events. Understanding the mechanisms that give rise to these complex patterns that vary both in space and time can be challenging, even in cases for which individual components have been identified. Taking a systems biology approach, mathematical and computational techniques can be employed to produce models that recapitulate experimental observations and capture our current understanding of the system. Useful models make novel predictions that can be investigated and falsified experimentally. This review brings together recent work on the modelling of calcium signalling in plants, from the scale of ion channels through to plant-wide responses to external stimuli. Some in silico results that have informed later experiments are highlighted.

Control of cell wall extensibility during pollen tube growth

In this review, we address the question of how the tip-growing pollen tube achieves its rapid rate of elongation while maintaining an intact cell wall. Although turgor is essential for growth to occur, the local expansion rate is controlled by local changes in the viscosity of the apical wall. We focus on several different structures and underlying processes that are thought to be major participants including exocytosis, the organization and activity of the actin cytoskeleton, calcium and proton physiology, and cellular energetics. We think that the actin cytoskeleton, in particular the apical cortical actin fringe, directs the flow of vesicles to the apical domain, where they fuse with the plasma membrane and contribute their contents to the expanding cell wall. While pH gradients, as generated by a proton-ATPase located on the plasma membrane along the side of the clear zone, may regulate rapid actin turnover and new polymerization in the fringe, the tip-focused calcium gradient biases secretion towards the polar axis. The recent data showing that exocytosis of new wall material precedes and predicts the process of cell elongation provide support for the idea that the intussusception of newly secreted pectin contributes to decreases in apical wall viscosity and to cell expansion. Other prime factors will be the localization and activity of the enzyme pectin methyl-esterase, and the chelation of calcium by pectic acids. Finally, we acknowledge a role for reactive oxygen species in the control of wall viscosity.

Transport logistics in pollen tubes

Cellular organelles move within the cellular volume and the effect of the resulting drag forces on the liquid causes bulk movement in the cytosol. The movement of both organelles and cytosol leads to an overall motion pattern called cytoplasmic streaming or cyclosis. This streaming enables the active and passive transport of molecules and organelles between cellular compartments. Furthermore, the fusion and budding of vesicles with and from the plasma membrane (exo/endocytosis) allow for transport of material between the inside and the outside of the cell. In the pollen tube, cytoplasmic streaming and exo/endocytosis are very active and fulfill several different functions. In this review, we focus on the logistics of intracellular motion and transport processes as well as their biophysical underpinnings. We discuss various modeling attempts that have been performed to understand both long-distance shuttling and short-distance targeting of organelles. We show how the combination of mechanical and mathematical modeling with cell biological approaches has contributed to our understanding of intracellular transport logistics.

The pollen tube paradigm revisited

The polar growth process characterizing pollen tube elongation has attracted numerous modeling attempts over the past years. While initial models focused on recreating the correct cellular geometry, recent models are increasingly based on experimentally assessed cellular parameters such as the dynamics of signaling processes and the mechanical properties of the cell wall. Recent modeling attempts have therefore substantially gained in biological relevance and predictive power. Different modeling methods are explained and the power and limitations of individual models are compared. Focus is on several recent models that use closed feedback loops in order to generate limit cycles representing the oscillatory behavior observed in growing tubes.

Persistent symmetry frustration in pollen tubes

Pollen tubes are extremely rapidly growing plant cells whose morphogenesis is determined by spatial gradients in the biochemical composition of the cell wall. We investigate the hypothesis (MP) that the distribution of the local mechanical properties of the wall, corresponding to the change of the radial symmetry along the axial direction, may lead to growth oscillations in pollen tubes. We claim that the experimentally observed oscillations originate from the symmetry change at the transition zone, where both intervening symmetries (cylindrical and spherical) meet. The characteristic oscillations between resonating symmetries at a given (constant) turgor pressure and a gradient of wall material constants may be identified with the observed growth-cycles in pollen tubes.

Calcium - a central regulator of pollen germination and tube growth

Pollen tubes grow rapidly by very fast rates and reach extended lengths to bring about fertilization during plant reproduction. The pollen tube grows exclusively at its tip. Fundamental for such local, tip-focused growth are the presence of internal gradients and transmembrane fluxes of ions. Consequently, vegetative pollen tube cells are an excellent single cell model system to investigate cell biological processes of vesicle transport, cytoskeleton reorganization and regulation of ion transport. The second messenger Ca(2+) has emerged as a central and crucial modulator that not only regulates but also integrates the coordination each of these processes. In this review we reflect on recent advances in our understanding of the mechanisms of Ca(2+) function in pollen tube growth, focusing on its role in basic cellular processes such as control of cell growth, vesicular transport and intracellular signaling by localized gradients of second messengers. In particular we discuss new insights into the identity and role of Ca(2+) conductive ion channels and present experimental addressable hypotheses about their regulation. This article is part of a Special Issue entitled:12th European Symposium on Calcium.

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.

The role of pectin in plant morphogenesis

The presence of a polysaccharidic cell wall distinguishes plant cells from animal cells and is responsible for fundamental mechanistic differences in organ development between the two kingdoms. Due to the presence of this wall, plant cells are unable to crawl and contract. On the other hand, plant cell size can increase by several orders of magnitude and cell shape can change from a simple polyhedron or cube to extremely intricate. This expansive cellular growth is regulated by the interaction between the cell wall and the intracellular turgor pressure. One of the principal cell wall components involved in temporal and spatial regulation of the growth process is pectin. Through biochemical changes to pectin composition and biochemical configuration, the properties of this material can be altered to trigger specific developmental processes. Here, the roles of pectin in three systems displaying rapid growth - the elongation zone of the root, the tip region of the pollen tube, and organ primordia formation at the shoot apical meristem - are reviewed.

An osmotic model of the growing pollen tube

Pollen tube growth is central to the sexual reproduction of plants and is a longstanding model for cellular tip growth. For rapid tip growth, cell wall deposition and hardening must balance the rate of osmotic water uptake, and this involves the control of turgor pressure. Pressure contributes directly to both the driving force for water entry and tip expansion causing thinning of wall material. Understanding tip growth requires an analysis of the coordination of these processes and their regulation. Here we develop a quantitative physiological model which includes water entry by osmosis, the incorporation of cell wall material and the spreading of that material as a film at the tip. Parameters of the model have been determined from the literature and from measurements, by light, confocal and electron microscopy, together with results from experiments made on dye entry and plasmolysis in Lilium longiflorum. The model yields values of variables such as osmotic and turgor pressure, growth rates and wall thickness. The model and its predictive capacity were tested by comparing programmed simulations with experimental observations following perturbations of the growth medium. The model explains the role of turgor pressure and its observed constancy during oscillations; the stability of wall thickness under different conditions, without which the cell would burst; and some surprising properties such as the need for restricting osmotic permeability to a constant area near the tip, which was experimentally confirmed. To achieve both constancy of pressure and wall thickness under the range of conditions observed in steady-state growth the model reveals the need for a sensor that detects the driving potential for water entry and controls the deposition rate of wall material at the tip.

Dynamic regulation of growing domains for elongating and branching morphogenesis in plants

With their continuous growth, understanding how plant shapes form is fundamentally linked to understanding how growth rates are controlled across different regions of the plant. Much of a plant's architecture is generated in shoots and roots, where fast growth in tips contrasts with slow growth in supporting stalks. Shapes can be determined by where the boundaries between fast- and slow-growing regions are positioned, determining whether tips elongate, branch, or cease to grow. Across plants, there is a diversity in the cell wall chemistry through which growth operates. However, prototypical morphologies, such as tip growth and branching, suggest there are common dynamic constraints in localizing chemical growth catalysts. We have used Turing-type reaction-diffusion mechanisms to model this spatial localization and the resulting growth trajectories, characterizing the chemistry-growth feedback necessary for maintaining tip growth and for inducing branching. The mechanism defining the boundaries between fast- and slow-growing regions not only affects tip shape, it must be able to form new boundaries when the pattern-forming dynamics break symmetry, for instance in the branching of a tip. In previous work, we used an arbitrary concentration threshold to switch between two dynamic regimes of the growth catalyst in order to define growth boundaries. Here, we present a chemical dynamic basis for this threshold, in which feedback between two pattern-forming mechanisms controls the extent of the regions in which fast growth occurs. This provides a general self-contained mechanism for growth control in plant morphogenesis (not relying on external cues) which can account for both simple tip extension and symmetry-breaking branching phenomena.

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.

Modeling pollen tube growth: feeling the pressure to deliver testifiable predictions

The frequency and amplitude of oscillatory pollen tube growth can be altered by changing the osmotic value of the surrounding medium. This has motivated the proposition that the periodic change in growth velocity is caused by changes in turgor pressure. Using mathematical modeling we recently demonstrated that the oscillatory pollen tube growth does not require turgor to change but that this behavior can be explained with a mechanism that relies on changes in the mechanical properties of the cell wall which in turn are caused by temporal variations in the secretion of cell wall precursors. The model also explains why turgor and growth rate are correlated for oscillatory growth with long growth cycles while they seem uncorrelated for oscillatory growth with short growth cycles. The predictions made by the model are testifiable by experimental data and therefore represent an important step towards understanding the dynamics of the growth behavior in walled cells.

A model of plasma membrane flow and cytosis regulation in growing pollen tubes

A model of cytosis regulation in growing pollen tubes is developed and simulations presented. The authors address the question on the minimal assumptions needed to describe the pattern of exocytosis and endocytosis reported recently by experimental biologists. Biological implications of the model are also treated. Concepts of flow and conservation of membrane material are used to pose an equation system, which describes the movement of plasma membrane in the tip of growing pollen tubes. After obtaining the central equations, relations describing the rates of endocytosis and exocytosis are proposed. Two cytosis receptors (for exocytosis and endocytosis), which have different recycling rates and activation times, suffice to describe a stable growing tube. Simulations show a very good spatial separation between endocytosis and exocytosis, in which separation is shown to depend strongly on exocytic vesicle delivery. In accordance to measurements, most vesicles in the clear zone are predicted to be endocytic. Membrane flow is essential to maintain cell polarity, and bi-directional flow seems to be a natural consequence of the proposed mechanism. For the first time, a model addressing plasma membrane flow and cytosis regulation were posed. Therefore, it represents a missing piece in an integrative model of pollen tube growth, in which cell wall mechanics, hydrodynamic fluxes and regulation mechanisms are combined.

Regulator or driving force? The role of turgor pressure in oscillatory plant cell growth

Turgor generates the stress that leads to the expansion of plant cell walls during cellular growth. This has been formalized by the Lockhart equation, which can be derived from the physical laws of the deformation of viscoelastic materials. However, the experimental evidence for such a direct correlation between growth rate and turgor is inconclusive. This has led to challenges of the Lockhart model. We model the oscillatory growth of pollen tubes to investigate this relationship. We couple the Lockhart equation to the dynamical equations for the change in material properties. We find that the correct implementation of the Lockhart equation within a feedback loop leading to low amplitude oscillatory growth predicts that in this system changes in the global turgor do not influence the average growth rate in a linear manner, consistent with experimental observations. An analytic analysis of our model demonstrates in which regime the average growth rate becomes uncorrelated from the turgor pressure.

Towards the creation of a systems tip growth model for a pollen tube

Essential features of pollen tube growth are polarization of extracellular ion fluxes, intracellular ion gradients, and oscillating dynamics. These features in pollen tube growth are regulated by a wide range of spatiotemporally organized functions such as exocytosis and endocytosis, actin cytoskeleton reorganization, cell wall deposition and assembly, intracellular signalling, fertilization, and self-incompatibility. Recently, by developing a compartmental model, we have demonstrated that the tip and shank in a pollen tube combine in an integrative and self-regulatory system of ion and growth dynamics. Recent developments in modelling and the wealth of experimental data can be used to develop a systems model that provides an integrative view of the the interactions between the different functions that affect pollen tube growth.

Modelling dynamic plant cells

A major challenge in plant biology is to understand how functions in plant cells emerge from interactions between molecular components. Computational and mathematical modelling can encapsulate the relationships between molecular components and reveal how biological functions emerge. We review recent progress in modelling in metabolism, growth, signalling and circadian rhythms in plant cells. We discuss challenges and opportunities for future directions.

A compartmental model analysis of integrative and self-regulatory ion dynamics in pollen tube growth

Sexual reproduction in higher plants relies upon the polarised growth of pollen tubes. The growth-site at the pollen tube tip responds to signalling processes to successfully steer the tube to an ovule. Essential features of pollen tube growth are polarisation of ion fluxes, intracellular ion gradients, and oscillating dynamics. However, little is known about how these features are generated and how they are causally related. We propose that ion dynamics in biological systems should be studied in an integrative and self-regulatory way. Here we have developed a two-compartment model by integrating major ion transporters at both the tip and shank of pollen tubes. We demonstrate that the physiological features of polarised growth in the pollen tube can be explained by the localised distribution of transporters at the tip and shank. Model analysis reveals that the tip and shank compartments integrate into a self-regulatory dynamic system, however the oscillatory dynamics at the tip do not play an important role in maintaining ion gradients. Furthermore, an electric current travelling along the pollen tube contributes to the regulation of ion dynamics. Two candidate mechanisms for growth-induced oscillations are proposed: the transition of tip membrane into shank membrane, and growth-induced changes in kinetic parameters of ion transporters. The methodology and principles developed here are applicable to the study of ion dynamics and their interactions with other functional modules in any plant cellular system.

Finite element model of polar growth in pollen tubes

Cellular protuberance formation in walled cells requires the local deformation of the wall and its polar expansion. In many cells, protuberance elongation proceeds by tip growth, a growth mechanism shared by pollen tubes, root hairs, and fungal hyphae. We established a biomechanical model of tip growth in walled cells using the finite element technique. We aimed to identify the requirements for spatial distribution of mechanical properties in the cell wall that would allow the generation of cellular shapes that agree with experimental observations. We based our structural model on the parameterized description of a tip-growing cell that allows the manipulation of cell size, shape, cell wall thickness, and local mechanical properties. The mechanical load was applied in the form of hydrostatic pressure. We used two validation methods to compare different simulations based on cellular shape and the displacement of surface markers. We compared the resulting optimal distribution of cell mechanical properties with the spatial distribution of biochemical cell wall components in pollen tubes and found remarkable agreement between the gradient in mechanical properties and the distribution of deesterified pectin. Use of the finite element method for the modeling of nonuniform growth events in walled cells opens future perspectives for its application to complex cellular morphogenesis in plants.