Shape and dynamics of tip-growing cells

Study of impacts of two types of cellular aging on the yeast bud morphogenesis

Understanding the mechanisms of the cellular aging processes is crucial for attempting to extend organismal lifespan and for studying age-related degenerative diseases. Yeast cells divide through budding, providing a classical biological model for studying cellular aging. With their powerful genetics, relatively short cell cycle, and well-established signaling pathways also found in animals, yeast cells offer valuable insights into the aging process. Recent experiments suggested the existence of two aging modes in yeast characterized by nucleolar and mitochondrial declines, respectively. By analyzing experimental data, this study shows that cells evolving into those two aging modes behave differently when they are young. While buds grow linearly in both modes, cells that consistently generate spherical buds throughout their lifespan demonstrate greater efficacy in controlling bud size and growth rate at young ages. A three-dimensional multiscale chemical-mechanical model was developed and used to suggest and test hypothesized impacts of aging on bud morphogenesis. Experimentally calibrated model simulations showed that during the early stage of budding, tubular bud shape in one aging mode could be generated by locally inserting new materials at the bud tip, a process guided by the polarized Cdc42 signal. Furthermore, the aspect ratio of the tubular bud could be stabilized during the late stage as observed in experiments in this work. The model simulation results suggest that the localization of new cell surface material insertion, regulated by chemical signal polarization, could be weakened due to cellular aging in yeast and other cell types, leading to the change and stabilization of the bud aspect ratio.

Conserved physical mechanisms of cell and tissue elongation

Living organisms have the ability to self-shape into complex structures appropriate for their function. The genetic and molecular mechanisms that enable cells to do this have been extensively studied in several model and non-model organisms. In contrast, the physical mechanisms that shape cells and tissues have only recently started to emerge, in part thanks to new quantitative in vivo measurements of the physical quantities guiding morphogenesis. These data, combined with indirect inferences of physical characteristics, are starting to reveal similarities in the physical mechanisms underlying morphogenesis across different organisms. Here, we review how physics contributes to shape cells and tissues in a simple, yet ubiquitous, morphogenetic transformation: elongation. Drawing from observed similarities across species, we propose the existence of conserved physical mechanisms of morphogenesis.

A fitness landscape instability governs the morphological diversity of tip-growing cells

Cellular morphology affects many aspects of cellular and organismal physiology. This makes it challenging to dissect the evolutionary basis for specific morphologies since various cellular functions may exert competing selective pressures on this trait, and the influence of these pressures will depend on the specific mechanisms of morphogenesis. In this light, we combined experiment and theory to investigate the complex basis for morphological diversity among tip-growing cells from across the tree of life. We discovered that an instability in the widespread mechanism of "inflationary" tip growth leads directly to a bifurcation in the common fitness landscape of tip-growing cells, which imposes a strict global constraint on their morphologies. This result rationalizes the morphology of an enormous diversity of important fungal, plant, protistan, and bacterial systems. More broadly, our study elucidates the principle that strong evolutionary constraints on complex traits, like biological form, may emerge from emergent instabilities within developmental systems.

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.

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.

Myosin XI drives polarized growth by vesicle focusing and local enrichment of F-actin in Physcomitrium patens

In tip-growing plant cells, growth results from myosin XI and F-actin-mediated deposition of cell wall polysaccharides contained in secretory vesicles. Previous evidence showed that myosin XI anticipates F-actin accumulation at the cell's tip, suggesting a mechanism where vesicle clustering via myosin XI increases F-actin polymerization. To evaluate this model, we used a conditional loss-of-function strategy by generating moss (Physcomitrium patens) plants harboring a myosin XI temperature-sensitive allele. We found that loss of myosin XI function alters tip cell morphology, vacuolar homeostasis, and cell viability but not following F-actin depolymerization. Importantly, our conditional loss-of-function analysis shows that myosin XI focuses and directs vesicles at the tip of the cell, which induces formin-dependent F-actin polymerization, increasing F-actin's local concentration. Our findings support the role of myosin XI in vesicle focusing, possibly via clustering and F-actin organization, necessary for tip growth, and deepen our understanding of additional myosin XI functions.

Physics-informed deep learning characterizes morphodynamics of Asian soybean rust disease

Medicines and agricultural biocides are often discovered using large phenotypic screens across hundreds of compounds, where visible effects of whole organisms are compared to gauge efficacy and possible modes of action. However, such analysis is often limited to human-defined and static features. Here, we introduce a novel framework that can characterize shape changes (morphodynamics) for cell-drug interactions directly from images, and use it to interpret perturbed development of Phakopsora pachyrhizi, the Asian soybean rust crop pathogen. We describe population development over a 2D space of shapes (morphospace) using two models with condition-dependent parameters: a top-down Fokker-Planck model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. We discover a variety of landscapes, describing phenotype transitions during growth, and identify possible perturbations in the tip growth machinery that cause this variation. This demonstrates a widely-applicable integration of unsupervised learning and biophysical modeling.

Quantitative cell biology of tip growth in moss

KEY MESSAGE

Here we review, from a quantitative point of view, the cell biology of protonemal tip growth in the model moss Physcomitrium patens. We focus on the role of the cytoskeleton, vesicle trafficking, and cell wall mechanics, including reviewing some of the existing mathematical models of tip growth. We provide a primer for existing cell biological tools that can be applied to the future study of tip growth in moss. Polarized cell growth is a ubiquitous process throughout the plant kingdom in which the cell elongates in a self-similar manner. This process is important for nutrient uptake by root hairs, fertilization by pollen, and gametophyte development by the protonemata of bryophytes and ferns. In this review, we will focus on the tip growth of moss cells, emphasizing the role of cytoskeletal organization, cytoplasmic zonation, vesicle trafficking, cell wall composition, and dynamics. We compare some of the existing knowledge on tip growth in protonemata against what is known in pollen tubes and root hairs, which are better-studied tip growing cells. To fully understand how plant cells grow requires that we deepen our knowledge in a variety of forms of plant cell growth. We focus this review on the model plant Physcomitrium patens, which uses tip growth as the dominant form of growth at its protonemal stage. Because mosses and vascular plants shared a common ancestor more than 450 million years ago, we anticipate that both similarities and differences between tip growing plant cells will provide mechanistic information of tip growth as well as of plant cell growth in general. Towards this mechanistic understanding, we will also review some of the existing mathematical models of plant tip growth and their applicability to investigate protonemal morphogenesis. We attempt to integrate the conclusions and data across cell biology and physical modeling to our current state of knowledge of polarized cell growth in P. patens and highlight future directions in the field.

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.

Apical pollen tube wall curvature correlates with growth and indicates localized changes in the yielding of the cell wall

The shape of the apical region of lily pollen tube changes rhythmically as the growth rate of the tube oscillates becoming alternately more prolate then back to oblate. We quantified shape change by calculating the curvature of the cross-sectional edge of the pollen tube tip and cross-correlating curvature changes with growth rate. The apical region takes the form of a partial elliptical spheroid, with variation in the length and location of the minor axis. During oscillation curvature profiles show a sharp increase in curvature at the "shoulders" of the apex when oblate, 4-7 μm from the flatter central zone. As the tip becomes more prolate, the "shoulders" decrease rapidly in curvature and move towards the growth axis as curvature at the tip increases. We understand curvature changes to represent differential changes in local wall expansion rates, driven by uniform turgor pressure and mediated by changes in wall polysaccharides. To become more oblate, the tip region must become less extensible than the "shoulder" region. And, as the tip becomes more prolate, the increased curvature must be due to increased local expansion. We found that changes in the growth velocity of the "shoulders" of the cell measured as the progress of the cell edge along the growth axis are cyclically out of phase with growth velocity at the tip such that the shoulder regions lag for part of the oscillation cycle, then "catch up" as the growth rate at the tip reaches a maximum and begins to decline. In this way the cell becomes oblate. Cell shape and growth rate oscillate in concert and are functionally related. Spatial change in edge growth rate points to important cellular locations for further investigation of vesicle movement and exocytosis, calcium gradients, and actin dynamics in lily pollen tubes.

Type V myosin focuses the polarisome and shapes the tip of yeast cells

The polarisome is a cortical proteinaceous microcompartment that organizes the growth of actin filaments and the fusion of secretory vesicles in yeasts and filamentous fungi. Polarisomes are compact, spotlike structures at the growing tips of their respective cells. The molecular forces that control the form and size of this microcompartment are not known. Here we identify a complex between the polarisome subunit Pea2 and the type V Myosin Myo2 that anchors Myo2 at the cortex of yeast cells. We discovered a point mutation in the cargo-binding domain of Myo2 that impairs the interaction with Pea2 and consequently the formation and focused localization of the polarisome. Cells carrying this mutation grow round instead of elongated buds. Further experiments and biophysical modeling suggest that the interactions between polarisome-bound Myo2 motors and dynamic actin filaments spatially focus the polarisome and sustain its compact shape.

Coordinating cell polarization and morphogenesis through mechanical feedback

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis.

Role of combined cell membrane and wall mechanical properties regulated by polarity signals in cell budding

Budding yeast, Saccharomyces cerevisiae, serves as a prime biological model to study mechanisms underlying asymmetric growth. Previous studies have shown that prior to bud emergence, polarization of a conserved small GTPase Cdc42 must be established on the cell membrane of a budding yeast. Additionally, such polarization contributes to the delivery of cell wall remodeling enzymes and hydrolase from cytosol through the membrane, to change the mechanical properties of the cell wall. This leads to the hypothesis that Cdc42 and its associated proteins at least indirectly regulate cell surface mechanical properties. However, how the surface mechanical properties in the emerging bud are changed and whether such change is important are not well understood. To test several hypothesised mechanisms, a novel three-dimensional coarse-grained particle-based model has been developed which describes inhomogeneous mechanical properties of the cell surface. Model simulations predict alternation of the levels of stretching and bending stiffness of the cell surface in the bud region by the polarized Cdc42 signals is essential for initiating bud formation. Model simulations also suggest that bud shape depends strongly on the distribution of the polarized signaling molecules while the neck width of the emerging bud is strongly impacted by the mechanical properties of the chitin and septin rings. Moreover, the temporal change of the bud mechanical properties is shown to affect the symmetry of the bud shape. The 3D model of asymmetric cell growth can also be used for studying viral budding and other vegetative reproduction processes performed via budding, as well as detailed studies of cell growth.

Mechanical force-induced morphology changes in a human fungal pathogen

Background

The initial step of a number of human or plant fungal infections requires active penetration of host tissue. For example, active penetration of intestinal epithelia by Candida albicans is critical for dissemination from the gut into the bloodstream. However, little is known about how this fungal pathogen copes with resistive forces upon host cell invasion.

Results

In the present study, we have used PDMS micro-fabrication to probe the ability of filamentous C. albicans cells to penetrate and grow invasively in substrates of different stiffness. We show that there is a threshold for penetration that corresponds to a stiffness of ~ 200 kPa and that invasive growth within a stiff substrate is characterized by dramatic filament buckling, along with a stiffness-dependent decrease in extension rate. We observed a striking alteration in cell morphology, i.e., reduced cell compartment length and increased diameter during invasive growth, that is not due to depolarization of active Cdc42, but rather occurs at a substantial distance from the site of growth as a result of mechanical compression.

Conclusions

Our data reveal that in response to this compression, active Cdc42 levels are increased at the apex, whereas active Rho1 becomes depolarized, similar to that observed in membrane protrusions. Our results show that cell growth and morphology are altered during invasive growth, suggesting stiffness dictates the host cells that C. albicans can penetrate.

Modelling fungal hypha tip growth via viscous sheet approximation

In this paper we present a new model for single-celled, non-branching hypha tip growth. The growth mechanism of hypha cells consists of transport of cell wall building material to the cell wall and subsequent incorporation of this material in the wall as it arrives. To model the transport of cell wall building material to the cell wall we follow Bartnicki-Garcia and Gierz in assuming that the cell wall building material is transported in straight lines by an isotropic point source. To model the dynamics of the cell wall, including its growth by new material, we use the approach of Campàs and Mahadevan, which assumes that the cell wall is a thin viscous sheet sustained by a pressure difference. Furthermore, we include a novel equation which models the hardening of the cell wall as it ages. We validate the new model by comparing it to experimental data.

Role of mechanical cues and hypoxia on the growth of tumor cells in strong and weak confinement: A dual in vitro-in silico approach

Characterization of tumor growth dynamics is of major importance for cancer understanding. By contrast with phenomenological approaches, mechanistic modeling can facilitate disclosing underlying tumor mechanisms and lead to identification of physical factors affecting proliferation and invasive behavior. Current mathematical models are often formulated at the tissue or organ scale with the scope of a direct clinical usefulness. Consequently, these approaches remain empirical and do not allow gaining insight into the tumor properties at the scale of small cell aggregates. Here, experimental and numerical studies of the dynamics of tumor aggregates are performed to propose a physics-based mathematical model as a general framework to investigate tumor microenvironment. The quantitative data extracted from the cellular capsule technology microfluidic experiments allow a thorough quantitative comparison with in silico experiments. This dual approach demonstrates the relative impact of oxygen and external mechanical forces during the time course of tumor model progression.

In vivo interactions between myosin XI, vesicles and filamentous actin are fast and transient in Physcomitrella patens

The actin cytoskeleton and active membrane trafficking machinery are essential for polarized cell growth. To understand the interactions between myosin XI, vesicles and actin filaments in vivo, we performed fluorescence recovery after photobleaching and showed that the dynamics of myosin XIa at the tip of the spreading earthmoss Physcomitrella patens caulonemal cells are actin-dependent and that 50% of myosin XI is bound to vesicles. To obtain single-particle information, we used variable-angle epifluorescence microscopy in protoplasts to demonstrate that protein myosin XIa and VAMP72-labeled vesicles localize in time and space over periods lasting only a few seconds. By tracking data with Hidden Markov modeling, we showed that myosin XIa and VAMP72-labeled vesicles exhibit short runs of actin-dependent directed transport. We also found that the interaction of myosin XI with vesicles is short-lived. Together, this vesicle-bound fraction, fast off-rate and short average distance traveled seem be crucial for the dynamic oscillations observed at the tip, and might be vital for regulation and recycling of the exocytosis machinery, while simultaneously promoting vesicle focusing and vesicle secretion at the tip, necessary for cell wall expansion.

Formal description of plant morphogenesis

Plant morphogenesis may be characterized by complex feedback mechanisms between signals specifying growth and by the growth of the plant body itself. Comprehension of such feedback mechanisms is an ongoing research task and can be aided with formal descriptions of morphogenesis. In this review, we present a number of established mathematical paradigms that are useful to the formal representation of plant shape, and of biomechanical and biochemical signaling. Specifically, we discuss work from a range of research areas including plant biology, material sciences, fluid dynamics, and computer graphics. Treating plants as organized systems of information processing allows us to compare these different mathematical methods in terms of their expressive power of biological hypotheses. This is an attempt to bring together a large number of computational modeling concepts and make them accessible to the analytical as well as empirical student of plant morphogenesis.

Systematic mapping of cell wall mechanics in the regulation of cell morphogenesis

Walled cells of plants, fungi, and bacteria come with a large range of shapes and sizes, which are ultimately dictated by the mechanics of their cell wall. This stiff and thin polymeric layer encases the plasma membrane and protects the cells mechanically by opposing large turgor pressure derived mechanical stresses. To date, however, we still lack a quantitative understanding for how local and/or global mechanical properties of the wall support cell morphogenesis. Here, we combine subresolution imaging and laser-mediated wall relaxation to quantitate subcellular values of wall thickness (h) and bulk elastic moduli (Y) in large populations of live mutant cells and in conditions affecting cell diameter in the rod-shaped model fission yeast. We find that lateral wall stiffness, defined by the surface modulus, σ = hY, robustly scales with cell diameter. This scaling is valid across tens of mutants spanning various functions-within the population of individual isogenic strains, along single misshaped cells, and even across the fission yeasts clade. Dynamic modulations of cell diameter by chemical and/or mechanical means suggest that the cell wall can rapidly adapt its surface mechanics, rendering stretched wall portions stiffer than unstretched ones. Size-dependent wall stiffening constrains diameter definition and limits size variations; it may also provide an efficient means to keep elastic strains in the wall below failure strains, potentially promoting cell survival. This quantitative set of data impacts our current understanding of the mechanics of cell walls and its contribution to morphogenesis.

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.

Mechanical feedback coordinates cell wall expansion and assembly in yeast mating morphogenesis

The shaping of individual cells requires a tight coordination of cell mechanics and growth. However, it is unclear how information about the mechanical state of the wall is relayed to the molecular processes building it, thereby enabling the coordination of cell wall expansion and assembly during morphogenesis. Combining theoretical and experimental approaches, we show that a mechanical feedback coordinating cell wall assembly and expansion is essential to sustain mating projection growth in budding yeast (Saccharomyces cerevisiae). Our theoretical results indicate that the mechanical feedback provided by the Cell Wall Integrity pathway, with cell wall stress sensors Wsc1 and Mid2 increasingly activating membrane-localized cell wall synthases Fks1/2 upon faster cell wall expansion, stabilizes mating projection growth without affecting cell shape. Experimental perturbation of the osmotic pressure and cell wall mechanics, as well as compromising the mechanical feedback through genetic deletion of the stress sensors, leads to cellular phenotypes that support the theoretical predictions. Our results indicate that while the existence of mechanical feedback is essential to stabilize mating projection growth, the shape and size of the cell are insensitive to the feedback.

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.

Forces that shape fission yeast cells

One of the major challenges of modern cell biology is to understand how cells are assembled from nanoscale components into micrometer-scale entities with a specific size and shape. Here I describe how our quest to understand the morphogenesis of the fission yeast Schizosaccharomyces pombe drove us to investigate cellular mechanics. These studies build on the view that cell shape arises from the physical properties of an elastic cell wall inflated by internal turgor pressure. Consideration of cellular mechanics provides new insights into not only mechanisms responsible for cell-shape determination and growth, but also cellular processes such as cytokinesis and endocytosis. Studies in yeast can help to illuminate approaches and mechanisms to study the mechanobiology of the cell surface in other cell types, including animal cells.

Non-equilibrium Membrane Homeostasis in Expanding Cellular Domains

Many cell behaviors involve cell-shape transformations that impose considerable changes in the cell's surface area, requiring a constant adaptation of the cell's plasma membrane area to prevent cell lysis. Here, we theoretically describe the interplay between the plasma membrane dynamics and a physically connected cell cortex or wall, accounting for spatial variations in membrane recycling and tension. In-plane membrane net flows result naturally from these dynamics and, in the presence of an expanding cell cortex or wall, regions of converging or diverging flow patterns emerge. These flow patterns can potentially explain the spatial localization/segregation of membrane proteins in processes such as cell polarization. We also identify the relevant parameters that control membrane homeostasis and derive the range of parameters for which homeostatic states exist.

Combined elevated temperature and soil waterlogging stresses inhibit cell elongation by altering osmolyte composition of the developing cotton (Gossypium hirsutum L.) fiber

Soil waterlogging events and high temperature conditions occur frequently in the Yangtze River Valley, yet the effects of these co-occurring stresses on fiber elongation have received little attention. In the current study, the combined effect of elevated temperature (ET) and soil waterlogging (SW) more negatively affected final fiber length (reduced by 5.4%-11.3%) than either stress alone by altering the composition of osmotically active solutes (sucrose, malate, and K⁺), where SW had the most pronounced effect. High temperature accelerated early fiber development, but limited the duration of elongation, thereby limiting final fiber length. Treatment of ET alone altered fiber sucrose content mainly through decreased source strength and the expression of the sucrose transporter gene GhSUT-1, making sucrose availability the primary determinant of final fiber length under ET. Waterlogging stress alone decreased source strength, down-regulated GhSUT-1 expression and enhanced SuSy catalytic activity for sucrose reduction. Waterlogging treatment alone also limited fiber malate production by down-regulating GhPEPC-1 & -2. However, combined elevated temperature and waterlogging limited primary cell wall synthesis by affecting GhCESAs genes and showed a negative impact on all three major osmotic solutes through the regulation of GhSUT-1, GhPEPC-1 & -2 and GhKT-1 expression and altered SuSy activity, which functioned together to produce a shorter fiber length.

Widening perspectives on regenerative processes through growth

Defining the basic mechanisms behind regeneration requires comparison to both development and homeostasis. How is organ size achieved in animals during normal development, and how is it reconstituted in animals capable of regenerating organs and body parts lost to injury? Are the mechanisms regulating size and allometry evolutionarily conserved? In recent years, discoveries in the fields of signalling, physiology, developmental biology and regeneration using a growing and diverse collection of model organisms have begun to shed mechanistic insight into these problems. Growth, central to embryonic development, tissue homeostasis and regeneration, was the unifying concept at the recent Molecular and Cellular Basis for Growth and Regeneration Keystone meeting.

Dynamics of cell wall elasticity pattern shapes the cell during yeast mating morphogenesis

The cell wall defines cell shape and maintains integrity of fungi and plants. When exposed to mating pheromone, Saccharomyces cerevisiae grows a mating projection and alters in morphology from spherical to shmoo form. Although structural and compositional alterations of the cell wall accompany shape transitions, their impact on cell wall elasticity is unknown. In a combined theoretical and experimental approach using finite-element modelling and atomic force microscopy (AFM), we investigated the influence of spatially and temporally varying material properties on mating morphogenesis. Time-resolved elasticity maps of shmooing yeast acquired with AFM in vivo revealed distinct patterns, with soft material at the emerging mating projection and stiff material at the tip. The observed cell wall softening in the protrusion region is necessary for the formation of the characteristic shmoo shape, and results in wider and longer mating projections. The approach is generally applicable to tip-growing fungi and plants cells.

NADPH oxidases as electrochemical generators to produce ion fluxes and turgor in fungi, plants and humans

The NOXs are a family of flavocytochromes whose basic structure has been largely conserved from algae to man. This is a very simple system. NADPH is generally available, in plants it is a direct product of photosynthesis, and oxygen is a largely ubiquitous electron acceptor, and the electron-transporting core of an FAD and two haems is the minimal required to pass electrons across the plasma membrane. These NOXs have been shown to be essential for diverse functions throughout the biological world and, lacking a clear mechanism of action, their effects have generally been attributed to free radical reactions. Investigation into the function of neutrophil leucocytes has demonstrated that electron transport through the prototype NOX2 is accompanied by the generation of a charge across the membrane that provides the driving force propelling protons and other ions across the plasma membrane. The contention is that the primary function of the NOXs is to supply the driving force to transport ions, the nature of which will depend upon the composition and characteristics of the local ion channels, to undertake a host of diverse functions. These include the generation of turgor in fungi and plants for the growth of filaments and invasion by appressoria in the former, and extension of pollen tubes and root hairs, and stomatal closure, in the latter. In neutrophils, they elevate the pH in the phagocytic vacuole coupled to other ion fluxes. In endothelial cells of blood vessels, they could alter luminal volume to regulate blood pressure and tissue perfusion.

Fruiting Branch K(+) Level Affects Cotton Fiber Elongation Through Osmoregulation

Potassium (K) deficiency in cotton plants results in reduced fiber length. As one of the primary osmotica, K(+) contributes to an increase in cell turgor pressure during fiber elongation. Therefore, it is hypothesized that fiber length is affected by K deficiency through an osmotic pathway, so in 2012 and 2013, an experiment was conducted to test this hypothesis by imposing three potassium supply regimes (0, 125, 250 kg K ha(-1)) on a low-K-sensitive cultivar, Siza 3, and a low-K-tolerant cultivar, Simian 3. We found that fibers were longer in the later season bolls than in the earlier ones in cotton plants grown under normal growth conditions, but later season bolls showed a greater sensitivity to low-K stress, especially the low-K sensitive genotype. We also found that the maximum velocity of fibre elongation (V max) is the parameter that best reflects the change in fiber elongation under K deficiency. This parameter mostly depends on cell turgor, so the content of the osmotically active solutes was analyzed accordingly. Statistical analysis showed that K(+) was the major osmotic factor affecting fiber length, and malate was likely facilitating K(+) accumulation into fibers, which enabled the low-K-tolerant genotype to cope with low-K stress. Moreover, the low-K-tolerant genotype tended to have greater K(+) absorptive capacities in the upper fruiting branches. Based on our findings, we suggest a fertilization scheme for Gossypium hirsutum that adds extra potash fertilizer or distributes it during the development of late season bolls to mitigate K deficiency in the second half of the growth season and to enhance fiber length in late season bolls.

Mechanics and morphogenesis of fission yeast cells

The integration of biochemical and biomechanical elements is at the heart of morphogenesis. While animal cells are relatively soft objects which shape and mechanics is mostly regulated by cytoskeletal networks, walled cells including those of plants, fungi and bacteria are encased in a rigid cell wall which resist high internal turgor pressure. How these particular mechanical properties may influence basic cellular processes, such as growth, shape and division remains poorly understood. Recent work using the model fungal cell fission yeast, Schizosaccharomyces pombe, highlights important contribution of cell mechanics to various morphogenesis processes. We envision this genetically tractable system to serve as a novel standard for the mechanobiology of walled cell.

Phosphorylation-dependent inhibition of Cdc42 GEF Gef1 by 14-3-3 protein Rad24 spatially regulates Cdc42 GTPase activity and oscillatory dynamics during cell morphogenesis

The 14-3-3 protein Rad24 modulates the availability of Cdc42 GEF Gef1, spatially regulating Cdc42 activity during cell morphogenesis. Gef1 is sequestered in the cytoplasm upon 14-3-3 interaction, mediated by Orb6 kinase. The resulting competition for Gef1 promotes anticorrelated Cdc42 oscillations at cell tips.

Active Cdc42 GTPase, a key regulator of cell polarity, displays oscillatory dynamics that are anticorrelated at the two cell tips in fission yeast. Anticorrelation suggests competition for active Cdc42 or for its effectors. Here we show how 14-3-3 protein Rad24 associates with Cdc42 guanine exchange factor (GEF) Gef1, limiting Gef1 availability to promote Cdc42 activation. Phosphorylation of Gef1 by conserved NDR kinase Orb6 promotes Gef1 binding to Rad24. Loss of Rad24–Gef1 interaction increases Gef1 protein localization and Cdc42 activation at the cell tips and reduces the anticorrelation of active Cdc42 oscillations. Increased Cdc42 activation promotes precocious bipolar growth activation, bypassing the normal requirement for an intact microtubule cytoskeleton and for microtubule-dependent polarity landmark Tea4-PP1. Further, increased Cdc42 activation by Gef1 widens cell diameter and alters tip curvature, countering the effects of Cdc42 GTPase-activating protein Rga4. The respective levels of Gef1 and Rga4 proteins at the membrane define dynamically the growing area at each cell tip. Our findings show how the 14-3-3 protein Rad24 modulates the availability of Cdc42 GEF Gef1, a homologue of mammalian Cdc42 GEF DNMBP/TUBA, to spatially control Cdc42 GTPase activity and promote cell polarization and cell shape emergence.

Morphogenesis of the Fission Yeast Cell through Cell Wall Expansion

The shape of walled cells such as fungi, bacteria, and plants are determined by the cell wall. Models for cell morphogenesis postulate that the effects of turgor pressure and mechanical properties of the cell wall can explain the shapes of these diverse cell types. However, in general, these models await validation through quantitative experiments. Fission yeast Schizosaccharomyces pombe are rod-shaped cells that grow by tip extension and then divide medially through formation of a cell wall septum. Upon cell separation after cytokinesis, the new cell ends adopt a rounded morphology. Here, we show that this shape is generated by a very simple mechanical-based mechanism in which turgor pressure inflates the elastic cell wall in the absence of cell growth. This process is independent of actin and new cell wall synthesis. To model this morphological change, we first estimate the mechanical properties of the cell wall using several approaches. The lateral cell wall behaves as an isotropic elastic material with a Young's modulus of 50 ± 10 MPa inflated by a turgor pressure estimated to be 1.5 ± 0.2 MPa. Based upon these parameters, we develop a quantitative mechanical-based model for new end formation that reveals that the cell wall at the new end expands into its characteristic rounded shape in part because it is softer than the mature lateral wall. These studies provide a simple example of how turgor pressure expands the elastic cell wall to generate a particular cell shape.

SNARE VTI13 plays a unique role in endosomal trafficking pathways associated with the vacuole and is essential for cell wall organization and root hair growth in arabidopsis

BACKGROUND AND AIMS

Root hairs are responsible for water and nutrient uptake from the soil and their growth is responsive to biotic and abiotic changes in their environment. Root hair expansion is a polarized process requiring secretory and endosomal pathways that deliver and recycle plasma membrane and cell wall material to the growing root hair tip. In this paper, the role of VTI13 (AT3G29100), a member of the VTI vesicular soluble NSF attachment receptor (SNARE) gene family in Arabidopsis thaliana, in root hair growth is described.

METHODS

Genetic analysis and complementation of the vti13 root hair phenotypes of Arabidopsis thaliana were first used to assess the role of VTI13 in root hair growth. Transgenic lines expressing a green fluorescent protein (GFP)-VTI13 construct were used to characterize the intracellular localization of VTI13 in root hairs using confocal microscopy and immunotransmission electron microscopy.

KEY RESULTS

VTI13 was characterized and genetic analysis used to show that its function is required for root hair growth. Expression of a GFP-VTI13 fusion in the vti13 mutant background was shown to complement the vti13 root hair phenotype. GFP-VTI13 localized to both the vacuole membrane and a mobile endosomal compartment. The function of VTI13 was also required for the localization of SYP41 to the trans-Golgi network. Immunohistochemical analysis indicated that cell wall organization is altered in vti13 root hairs and root epidermal cells.

CONCLUSIONS

These results show that VTI13 plays a unique role in endosomal trafficking pathways associated with the vacuole within root hairs and is essential for the maintenance of cell wall organization and root hair growth in arabidopsis.

How and why cells grow as rods

The rod is a ubiquitous shape adopted by walled cells from diverse organisms ranging from bacteria to fungi to plants. Although rod-like shapes are found in cells of vastly different sizes and are constructed by diverse mechanisms, the geometric similarities among these shapes across kingdoms suggest that there are common evolutionary advantages, which may result from simple physical principles in combination with chemical and physiological constraints. Here, we review mechanisms of constructing rod-shaped cells and the bases of different biophysical models of morphogenesis, comparing and contrasting model organisms in different kingdoms. We then speculate on possible advantages of the rod shape, and suggest strategies for elucidating the relative importance of each of these advantages.

Symmetry breaking in spore germination relies on an interplay between polar cap stability and spore wall mechanics

The morphogenesis of single cells depends on their ability to coordinate surface mechanics and polarity. During germination, spores of many species develop a polar tube that hatches out of a rigid outer spore wall (OSW) in a process termed outgrowth. However, how these awakening cells reorganize to stabilize this first growth axis remains unknown. Here, using quantitative experiments and modeling, we reveal the mechanisms underlying outgrowth in fission yeast. We find that, following an isotropic growth phase during which a single polarity cap wanders around the surface, outgrowth occurs when spores have doubled their volume, concomitantly with the stabilization of the cap and a singular rupture in the OSW. This rupture happens when OSW mechanical stress exceeds a threshold, releases the constraints of the OSW on growth, and stabilizes polarity. Thus, outgrowth exemplifies a self-organizing morphogenetic process in which reinforcements between growth and polarity coordinate mechanics and internal organization.

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.

Model of fission yeast cell shape driven by membrane-bound growth factors and the cytoskeleton

Fission yeast serves as a model for how cellular polarization machinery consisting of signaling molecules and the actin and microtubule cytoskeleton regulates cell shape. In this work, we develop mathematical models to investigate how these cells maintain a tubular shape of approximately constant diameter. Many studies identify active Cdc42, found in a cap at the inner membrane of growing cell tips, as an important regulator of local cell wall remodeling, likely through control of exocyst tethering and the targeting of other polarity-enhancing structures. First, we show that a computational model with Cdc42-dependent local cell wall remodeling under turgor pressure predicts a relationship between spatial extent of growth signal and cell diameter that is in agreement with prior experiments. Second, we model the consequences of feedback between cell shape and distribution of Cdc42 growth signal at cell tips. We show that stability of cell diameter over successive cell divisions places restrictions on their mutual dependence. We argue that simple models where the spatial extent of the tip growth signal relies solely on geometrical alignment of confined microtubules might lead to unstable width regulation. Third, we study a computational model that combines a growth signal distributed over a characteristic length scale (as, for example, by a reaction-diffusion mechanism) with an axis-sensing microtubules system that places landmarks at positions where microtubule tips touch the cortex. A two-dimensional implementation of this model leads to stable cell diameter for a wide range of parameters. Changes to the parameters of this model reproduce straight, bent, and bulged cell shapes, and we discuss how this model is consistent with other observed cell shapes in mutants. Our work provides an initial quantitative framework for understanding the regulation of cell shape in fission yeast, and a scaffold for understanding this process on a more molecular level in the future.

Fission yeast is a rod-shaped organism that is studied, in part, as a model for how cells develop and regulate their shape. Despite extensive work identifying effects of genetic mutations and pharmacological treatments on the shape of these cells, there is a lack of mathematical and computational models examining how internal cell signals and the cytoskeleton organize to remodel the cell wall, direct growth at cell tips, and maintain tubular shape. In this work we describe how the spatial distribution of regulatory protein signal at growing cell tips relates to cell diameter. Further, we describe the consequences of this signal depending on the shape of the cell, namely its length and diameter. Finally, we propose a computational model for understanding growth and shape that includes an axis-sensing microtubule system, landmarks delivered to cell tips along those microtubules, and a growth zone signal that moves around but is attracted to the landmarks. This picture explains a large number of reported abnormal shapes in terms of only a few modular components.

Dynamic microtubules and endomembrane cycling contribute to polarity establishment and early development of Ectocarpus mitospores

Many zygotes and spores of brown algae are photosensitive and establish a developmental axis in accordance with directional light cues. Ectocarpus siliculosus is being advanced as a genetic and genomic model organism for investigating brown alga development, and this report investigates photopolarization of the growth axis of mitospores. When exposed to unidirectional light, mitospores photopolarized and established a growth axis such that germination was preferentially localized to the shaded hemisphere of the spore body. The roles of the microtubule cytoskeleton and endomembrane cycling in the photopolarization process were investigated using pharmacological agents. Disruption of microtubule dynamics progressively reduced the percentage of mitospores that photopolarized, while inhibition of vesicle secretion blocked photopolarization nearly completely. Chronic treatment with these pharmacological agents severely affected algal morphogenesis. Microtubules in mitospores and algal filaments were imaged by confocal microscopy. Mitospores contained a radial microtubule array, emanating from a centrosome associated with the nuclear envelope. At germination, the radial array gradually transitioned into a longitudinal array with microtubules extending into the emerging apex. At mitosis, spindles were aligned with the growth axis of cylindrical cells in the filament, and the division plane bisected the spindle axis. These studies demonstrate that dynamic membrane cycling and microtubule assembly play fundamental roles in photopolarization and provide a foundation for future genetic and genomic investigations of this important developmental process.

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 spatial distribution of the exocyst and actin cortical patches is sufficient to organize hyphal tip growth

In the hyphal tip of Candida albicans we have made detailed quantitative measurements of (i) exocyst components, (ii) Rho1, the regulatory subunit of (1,3)-β-glucan synthase, (iii) Rom2, the specialized guanine-nucleotide exchange factor (GEF) of Rho1, and (iv) actin cortical patches, the sites of endocytosis. We use the resulting data to construct and test a quantitative 3-dimensional model of fungal hyphal growth based on the proposition that vesicles fuse with the hyphal tip at a rate determined by the local density of exocyst components. Enzymes such as (1,3)-β-glucan synthase thus embedded in the plasma membrane continue to synthesize the cell wall until they are removed by endocytosis. The model successfully predicts the shape and dimensions of the hyphae, provided that endocytosis acts to remove cell wall-synthesizing enzymes at the subapical bands of actin patches. Moreover, a key prediction of the model is that the distribution of the synthase is substantially broader than the area occupied by the exocyst. This prediction is borne out by our quantitative measurements. Thus, although the model highlights detailed issues that require further investigation, in general terms the pattern of tip growth of fungal hyphae can be satisfactorily explained by a simple but quantitative model rooted within the known molecular processes of polarized growth. Moreover, the methodology can be readily adapted to model other forms of polarized growth, such as that which occurs in plant pollen tubes.

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.

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.

Dislocation-mediated growth of bacterial cell walls

Recent experiments have illuminated a remarkable growth mechanism of rod-shaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference [Garner EC, et al., (2011) Science 333:222-225], [Domínguez-Escobar J, et al. (2011) Science 333:225-228], [van Teeffelen S, et al. (2011) PNAS 108:15822-15827]. We view these as dislocations in the partially ordered peptidoglycan structure, activated by glycan strand extension machinery, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Generation and motion of these interacting defects lead to surprising effects arising from the cylindrical geometry, with important implications for growth. We also discuss how long range elastic interactions and turgor pressure affect the dynamics of the fraction of actively moving dislocations in the bacterial cell wall.

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.