An analysis of the mechanics of guard cell motion

This paper presents a mechanical analysis of the cellular deformations which occur during the opening and closing of stomata. The aperture of the stomatal pore is shown to be a result of opposing pressures of the guard and adjacent epidermal cells. The analysis indicates that the epidermal cells have a mechanical advantage over the guard cells. With no mechanical advantage, an equal reduction in the turgor pressure of both guard and epidermal cells would have a neglible effect upon stomatal aperture. However, due to the mechanical advantage of the surrounding cells, the stomatal aperture increases with equal reductions in turgor, until the adjacent epidermal cells become flaccid. The minimum diffusion resistance of the pore occurs at this point. Further reductions in guard cell turgor lead to closure of the pore. The analysis further demonstrates how the shape, size, wall thickness and material properties of the guard cell walls influence their behavior.     

PECTATE LYASE LIKE12 patterns the guard cell wall to coordinate turgor pressure and wall mechanics for proper stomatal function in Arabidopsis

Plant cell deformations are driven by cell pressurization and mechanical constraints imposed by the nanoscale architecture of the cell wall, but how these factors are controlled at the genetic and molecular levels to achieve different types of cell deformation is unclear. Here, we used stomatal guard cells to investigate the influences of wall mechanics and turgor pressure on cell deformation and demonstrate that the expression of the pectin-modifying gene PECTATE LYASE LIKE12 (PLL12) is required for normal stomatal dynamics in Arabidopsis thaliana. Using nanoindentation and finite element modeling to simultaneously measure wall modulus and turgor pressure, we found that both values undergo dynamic changes during induced stomatal opening and closure. PLL12 is required for guard cells to maintain normal wall modulus and turgor pressure during stomatal responses to light and to tune the levels of calcium crosslinked pectin in guard cell walls. Guard cell-specific knockdown of PLL12 caused defects in stomatal responses and reduced leaf growth, which were associated with lower cell proliferation but normal cell expansion. Together, these results force us to revise our view of how wall-modifying genes modulate wall mechanics and cell pressurization to accomplish the dynamic cellular deformations that underlie stomatal function and tissue growth in plants.     

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

Plant cell morphogenesis depends critically on two processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by the stresses resulting from the cell's turgor pressure. We developed a model of plant cell morphogenesis that is a first attempt at integrating these two processes. The model is based on the theories of thin shells and anisotropic viscoplasticity. It includes three sets of equations that give the connection between wall stresses, wall strains and cell geometry. We present an algorithm to solve these equations numerically. Application of this simulation approach to the morphogenesis of tip-growing cells illustrates how the viscoplastic properties of the cell wall affect the shape of the cell at steady state. The same simulation approach was also used to reproduce morphogenetic transients such as the initiation of tip growth and other non-steady changes in cell shape. Finally, we show that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells.     

Polar growth in pollen tubes is associated with spatially confined dynamic changes in cell mechanical properties

Cellular morphogenesis involves changes to cellular size and shape which in the case of walled cells implies the mechanical deformation of the extracellular matrix. So far, technical challenges have made quantitative mechanical measurements of this process at subcellular scale impossible. We used micro-indentation to investigate the dynamic changes in the cellular mechanical properties during the onset of spatially confined growth activities in plant cells. Pollen tubes are cellular protuberances that have a strictly unidirectional growth pattern. Micro-indentation of these cells revealed that the initial formation of a cylindrical protuberance is preceded by a local reduction in cellular stiffness. Similar cellular softening was observed before the onset of a rapid growth phase in cells with oscillating growth pattern. These findings provide the first quantitative cytomechanical data that confirm the important role of the mechanical properties of the cell wall for local cellular growth processes. They are consistent with a conceptual model that explains pollen tube oscillatory growth based on the relationship between turgor pressure and tensile resistance in the apical cell wall. To further confirm the significance of cell mechanics, we artificially manipulated the mechanical cell wall properties as well as the turgor pressure. We observed that these changes affected the oscillation profile and were able to induce oscillatory behavior in steadily growing tubes.     

Stomatal action directly feeds back on leaf turgor: new insights into the regulation of the plant water status from non‐invasive pressure probe measurements

Uptake of CO₂ by the leaf is associated with loss of water. Control of stomatal aperture by volume changes of guard cell pairs optimizes the efficiency of water use. Under water stress, the protein kinase OPEN STOMATA 1 (OST1) activates the guard‐cell anion release channel SLOW ANION CHANNEL‐ASSOCIATED 1 (SLAC1), and thereby triggers stomatal closure. Plants with mutated OST1 and SLAC1 are defective in guard‐cell turgor regulation. To study the effect of stomatal movement on leaf turgor using intact leaves of Arabidopsis, we used a new pressure probe to monitor transpiration and turgor pressure simultaneously and non‐invasively. This probe permits routine easy access to parameters related to water status and stomatal conductance under physiological conditions using the model plant Arabidopsis thaliana. Long‐term leaf turgor pressure recordings over several weeks showed a drop in turgor during the day and recovery at night. Thus pressure changes directly correlated with the degree of plant transpiration. Leaf turgor of wild‐type plants responded to CO₂, light, humidity, ozone and abscisic acid (ABA) in a guard cell‐specific manner. Pressure probe measurements of mutants lacking OST1 and SLAC1 function indicated impairment in stomatal responses to light and humidity. In contrast to wild‐type plants, leaves from well‐watered ost1 plants exposed to a dry atmosphere wilted after light‐induced stomatal opening. Experiments with open stomata mutants indicated that the hydraulic conductance of leaf stomata is higher than that of the root–shoot continuum. Thus leaf turgor appears to rely to a large extent on the anion channel activity of autonomously regulated stomatal guard cells.     

In vivo extraction of Arabidopsis cell turgor pressure using nanoindentation in conjunction with finite element modeling

Turgor pressure in plant cells is involved in many important processes. Stable and normal turgor pressure is required for healthy growth of a plant, and changes in turgor pressure are indicative of changes taking place within the plant tissue. The ability to quantify the turgor pressure of plant cells in vivo would provide opportunities to understand better the process of pressure regulation within plants, especially when plant stress is considered, and to understand the role of turgor pressure in cellular signaling. Current experimental methods do not separate the influence of the turgor pressure from the effects associated with deformation of the cell wall when estimates of turgor pressure are made. In this paper, nanoindentation measurements are combined with finite element simulations to determine the turgor pressure of cells in vivo while explicitly separating the cell‐wall properties from the turgor pressure effects. Quasi‐static cyclic tests with variable depth form the basis of the measurements, while relaxation tests at low depth are used to determine the viscoelastic material properties of the cell wall. Turgor pressure is quantified using measurements on Arabidopsis thaliana under three pressure states (control, turgid and plasmolyzed) and at various stages of plant development. These measurements are performed on cells in vivo without causing damage to the cells, such that pressure changes may be studied for a variety of conditions to provide new insights into the biological response to plant stress conditions.     

The mechanical diversity of stomata and its significance in gas-exchange control

Given that stomatal movement is ultimately a mechanical process and that stomata are morphologically and mechanically diverse, we explored the influence of stomatal mechanical diversity on leaf gas exchange and considered some of the constraints. Mechanical measurements were conducted on the guard cells of four different species exhibiting different stomatal morphologies, including three variants on the classical "kidney" form and one "dumb-bell" type; this information, together with gas-exchange measurements, was used to model and compare their respective operational characteristics. Based on evidence from scanning electron microscope images of cryo-sectioned leaves that were sampled under full sun and high humidity and from pressure probe measurements of the stomatal aperture versus guard cell turgor relationship at maximum and zero epidermal turgor, it was concluded that maximum stomatal apertures (and maximum leaf diffusive conductance) could not be obtained in at least one of the species (the grass Triticum aestivum) without a substantial reduction in subsidiary cell osmotic (and hence turgor) pressure during stomatal opening to overcome the large mechanical advantage of subsidiary cells. A mechanism for this is proposed, with a corollary being greatly accelerated stomatal opening and closure. Gas-exchange measurements on T. aestivum revealed the capability of very rapid stomatal movements, which may be explained by the unique morphology and mechanics of its dumb-bell-shaped stomata coupled with "see-sawing" of osmotic and turgor pressure between guard and subsidiary cells during stomatal opening or closure. Such properties might underlie the success of grasses.     

Loss of stability: a new look at the physics of cell wall behavior during plant cell growth

In this article we investigate aspects of turgor-driven plant cell growth within the framework of a model derived from the Eulerian concept of instability. In particular we explore the relationship between cell geometry and cell turgor pressure by extending loss of stability theory to encompass cylindrical cells. Beginning with an analysis of the three-dimensional stress and strain of a cylindrical pressure vessel, we demonstrate that loss of stability is the inevitable result of gradually increasing internal pressure in a cylindrical cell. The turgor pressure predictions based on this model differ from the more traditional viscoelastic or creep-based models in that they incorporate both cell geometry and wall mechanical properties in a single term. To confirm our predicted working turgor pressures, we obtained wall dimensions, elastic moduli, and turgor pressures of sequential internodal cells of intact Chara corallina plants by direct measurement. The results show that turgor pressure predictions based on loss of stability theory fall within the expected physiological range of turgor pressures for this plant. We also studied the effect of varying wall Poisson's ratio nu on extension growth in living cells, showing that while increasing elastic modulus has an understandably negative effect on wall expansion, increasing Poisson's ratio would be expected to accelerate wall expansion.     

Metabolomics of red‐light‐induced stomatal opening in Arabidopsis thaliana: Coupling with abscisic acid and jasmonic acid metabolism

Environmental stimuli‐triggered stomatal movement is a key physiological process that regulates CO₂ uptake and water loss in plants. Stomata are defined by pairs of guard cells that perceive and transduce external signals, leading to cellular volume changes and consequent stomatal aperture change. Within the visible light spectrum, red light induces stomatal opening in intact leaves. However, there has been debate regarding the extent to which red‐light‐induced stomatal opening arises from direct guard cell sensing of red light versus indirect responses as a result of red light influences on mesophyll photosynthesis. Here we identify conditions that result in red‐light‐stimulated stomatal opening in isolated epidermal peels and enlargement of protoplasts, firmly establishing a direct guard cell response to red light. We then employ metabolomics workflows utilizing gas chromatography mass spectrometry and liquid chromatography mass spectrometry for metabolite profiling and identification of Arabidopsis guard cell metabolic signatures in response to red light in the absence of the mesophyll. We quantified 223 metabolites in Arabidopsis guard cells, with 104 found to be red light responsive. These red‐light‐modulated metabolites participate in the tricarboxylic acid cycle, carbon balance, phytohormone biosynthesis and redox homeostasis. We next analyzed selected Arabidopsis mutants, and discovered that stomatal opening response to red light is correlated with a decrease in guard cell abscisic acid content and an increase in jasmonic acid content. The red‐light‐modulated guard cell metabolome reported here provides fundamental information concerning autonomous red light signaling pathways in guard cells.     

A conserved functional role of pectic polymers in stomatal guard cells from a range of plant species

Guard cell walls combine exceptional strength and flexibility in order to accommodate the turgor pressure-driven changes in size and shape that underlie the opening and closing of stomatal pores. To investigate the molecular basis of these exceptional qualities, we have used a combination of compositional and functional analyses in three different plant species. We show that comparisons of FTIR spectra from stomatal guard cells and those of other epidermal cells indicate a number of clear differences in cell-wall composition. The most obvious characteristics are that stomatal guard cells are enriched in phenolic esters of pectins. This enrichment is apparent in guard cells from Vicia faba (possessing a type I cell wall) and Commelina communis and Zea mays (having a type II wall). We further show that these common defining elements of guard cell walls have conserved functional roles. As previously reported in C. communis, we show that enzymatic modification of the pectin network in guard cell walls in both V. faba and Z. mays has profound effects on stomatal function. In all three species, incubation of epidermal strips with a combination of pectin methyl esterase and endopolygalacturonase (EPG) caused an increase in stomatal aperture on opening. This effect was not seen when strips were incubated with EPG alone indicating that the methyl-esterified fraction of homogalacturonan is key to this effect. In contrast, arabinanase treatment, and incubation with feruloyl esterase both impeded stomatal opening. It therefore appears that pectins and phenolic esters have a conserved functional role in guard cell walls even in grass species with type II walls, which characteristically are composed of low levels of pectins.     

Microtubule dynamics are involved in stomatal movement ofVicia faba L.

Summary To obtain a full picture of microtubule (MT) behavior during the opening and closure of guard cells we have microinjected living guard cells ofVicia faba with fluorescent tubulin, examined fine detail by freeze shattering fixed cells, and used drug treatments to confirm aspects of MT dynamics. Cortical MTs in fully opened guard cells are transversely oriented from the ventral wall to the dorsal wall. When the stomatal aperture was decreased by darkness, these MTs became twisted and patched and broken down into diffuse fragments when stomata were closed. When the closed stomata were opened in response to light, the MTs in guard cells changed from the diffused, transitional pattern back to one in which MTs are transversely oriented from stomatal pore to dorsal wall. This observation indicates a linkage between these MT changes and stomatal movement. To confirm this, we used the MT-stabilizing agent taxol and the MT-depolymerizing herbicide oryzalin and observed their effects on the stomatal aperture and MT dynamics. Both drugs suppressed light-induced stomatal opening and dark-induced closure. MTs are known to be necessary for maintaining the static kidney shape of guard cells; the present data now show that the dynamic properties of polymeric tubulin accompany changes in shape with stomatal movement and may be functionally involved in stomatal movement.     

A constraint–relaxation–recovery mechanism for stomatal dynamics

Models of guard cell dynamics, built on the OnGuard platform, have provided quantitative insights into stomatal function, demonstrating substantial predictive power. However, the kinetics of stomatal opening predicted by OnGuard models were threefold to fivefold slower than observed in vivo. No manipulations of parameters within physiological ranges yielded model kinetics substantially closer to these data, thus highlighting a missing component in model construction. One well‐documented process influencing stomata is the constraining effect of the surrounding epidermal cells on guard cell volume and stomatal aperture. Here, we introduce a mechanism to describe this effect in OnGuard2 constructed around solute release and a decline in turgor of the surrounding cells and its subsequent recovery during stomatal opening. The results show that this constraint–relaxation–recovery mechanism in OnGuard2 yields dynamics that are consistent with experimental observations in wild‐type Arabidopsis, and it predicts the altered opening kinetics of ost2 H⁺‐ATPase and slac1 Cl^? channel mutants. Thus, incorporating solute flux of the surrounding cells implicitly through their constraint on guard cell expansion provides a satisfactory representation of stomatal kinetics, and it predicts a substantial and dynamic role for solute flux across the apoplastic space between the guard cells and surrounding cells in accelerating stomatal kinetics.     

A Computational Framework for 3D Mechanical Modeling of Plant Morphogenesis with Cellular Resolution

The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.     

Guard cell photosynthesis is critical for stomatal turgor production,yet does not directly mediate CO2‐ and ABA‐induced stomatal closing

Stomata mediate gas exchange between the inter‐cellular spaces of leaves and the atmosphere. CO₂ levels in leaves (Ci) are determined by respiration, photosynthesis, stomatal conductance and atmospheric [CO₂]. [CO₂] in leaves mediates stomatal movements. The role of guard cell photosynthesis in stomatal conductance responses is a matter of debate, and genetic approaches are needed. We have generated transgenic Arabidopsis plants that are chlorophyll‐deficient in guard cells only, expressing a constitutively active chlorophyllase in a guard cell specific enhancer trap line. Our data show that more than 90% of guard cells were chlorophyll‐deficient. Interestingly, approximately 45% of stomata had an unusual, previously not‐described, morphology of thin‐shaped chlorophyll‐less stomata. Nevertheless, stomatal size, stomatal index, plant morphology, and whole‐leaf photosynthetic parameters (PSII, qP, qN, F_V′/F_M′) were comparable with wild‐type plants. Time‐resolved intact leaf gas‐exchange analyses showed a reduction in stomatal conductance and CO₂‐assimilation rates of the transgenic plants. Normalization of CO₂ responses showed that stomata of transgenic plants respond to [CO₂] shifts. Detailed stomatal aperture measurements of normal kidney‐shaped stomata, which lack chlorophyll, showed stomatal closing responses to [CO₂] elevation and abscisic acid (ABA), while thin‐shaped stomata were continuously closed. Our present findings show that stomatal movement responses to [CO₂] and ABA are functional in guard cells that lack chlorophyll. These data suggest that guard cell CO₂ and ABA signal transduction are not directly modulated by guard cell photosynthesis/electron transport. Moreover, the finding that chlorophyll‐less stomata cause a ‘deflated’ thin‐shaped phenotype, suggests that photosynthesis in guard cells is critical for energization and guard cell turgor production.     

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.     

The chemiosmotic model of stomatal opening revisited

Stomata are light‐activated biological valves in the otherwise gas‐impermeable epidermis of aerial organs of higher plants. Stomata often regulate rates of photosynthesis and transpiration in ways that optimize whole‐plant carbon gain against water loss. Each stoma is flanked by a pair of opposing guard cells. Stomatal opening occurs by light‐activated increases in the turgor pressure of guard cells, which causes them to change shape so that the stomatal pore between them widens. These increases in turgor pressure oppose increases in cellular osmotic pressure that result from uptake of K⁺. K⁺ uptake occurs by a chemiosmotic mechanism in response to light‐activated extrusion of H⁺ outward across the plasma membrane of the guard cell. The initial changes in cellular membrane potential lead to the opening of inward‐rectifying K⁺ channels, after which K⁺ is taken up along its electrochemical gradient. Changes in membrane potential resulting from K⁺ uptake may be balanced by accumulation of Cl^?ions by guard cells and/or by synthesis of malic acid within each cell. Malic acid also acts to buffer increases in cytosolic pH caused by H⁺ extrusion. This review describes how the application of patch‐clamp technology to guard cell protoplasts has enabled investigators to elucidate the mechanisms by which H⁺ is extruded from guard cells, the types of ion channels present in the guard cell plasma membrane, how those ion channels are regulated, and the signal transduction processes that trigger stomatal opening and closing.     

Origins of Escherichia coli Growth Rate and Cell Shape Changes at High External Osmolality

In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope, followed by an active recovery. After recovery, and if the external osmolality remains high, cells have been shown to grow more slowly, smaller, and at reduced turgor pressure. Despite the fact that the active recovery is a key stress response, the nature of these changes and how they relate to each other is not understood. Here, we use fluorescence imaging of single cells during hyperosmotic shocks, combined with custom made microfluidic devices, to show that cells fully recover their volume to the initial, preshock value and continue to grow at a slower rate immediately after the recovery. We show that the cell envelope material properties do not change after hyperosmotic shock, and that cell shape recovers along with cell volume. Taken together, these observations indicate that the turgor pressure recovers to its initial value so that reduced turgor is not responsible for the reduced growth rate observed immediately after recovery. To determine the point at which the reduction in cell size and turgor pressure occurs after shock, we measured the volume of E. coli cells at different stages of growth in bulk cultures. We show that cell volume reaches the same maximal level irrespective of the osmolality of the media. Based on these measurements, we propose that turgor pressure is used as a feedback variable for osmoregulatory pumps instead of being directly responsible for the reduction in growth rates. Reestablishment of turgor to its initial value might ensure correct attachment of the inner membrane and cell wall needed for cell wall biosynthesis.     

Origins of Escherichia coli Growth Rate and Cell Shape Changes at High External Osmolality

In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope, followed by an active recovery. After recovery, and if the external osmolality remains high, cells have been shown to grow more slowly, smaller, and at reduced turgor pressure. Despite the fact that the active recovery is a key stress response, the nature of these changes and how they relate to each other is not understood. Here, we use fluorescence imaging of single cells during hyperosmotic shocks, combined with custom made microfluidic devices, to show that cells fully recover their volume to the initial, preshock value and continue to grow at a slower rate immediately after the recovery. We show that the cell envelope material properties do not change after hyperosmotic shock, and that cell shape recovers along with cell volume. Taken together, these observations indicate that the turgor pressure recovers to its initial value so that reduced turgor is not responsible for the reduced growth rate observed immediately after recovery. To determine the point at which the reduction in cell size and turgor pressure occurs after shock, we measured the volume of E. coli cells at different stages of growth in bulk cultures. We show that cell volume reaches the same maximal level irrespective of the osmolality of the media. Based on these measurements, we propose that turgor pressure is used as a feedback variable for osmoregulatory pumps instead of being directly responsible for the reduction in growth rates. Reestablishment of turgor to its initial value might ensure correct attachment of the inner membrane and cell wall needed for cell wall biosynthesis.     

STOMATAL MECHANICS

A model of stomatal movement due to changes in turgor is presented which systematically illustrates the role of certain anatomical features. During the expansion of paired guard cells, there are two physical constraints that cause the guard cells to bend and thus open the stomatal pore. The radial orientation of the micellae is shown to be the crucial feature which directly transmits the movement of the dorsal wall of the polar and central section to the stomatal slit. Furthermore, it is necessary that either the overall length of the entire stomatal apparatus or length of the common wall between the polar segments of the guard cells be constrained during the expansion of the guard cells. The model also shows that asymmetrically thickened guard cell walls are not necessary to cause bending of the guard cell. The ideas set forth in our model are consistent with the opening movements of both elliptical and grass-type stomata.     

Distribution of mechanical stress in the Escherichia coli cell envelope

The cell envelope in Gram-negative bacteria comprises two distinct membranes with a cell wall between them. There has been a growing interest in understanding the mechanical adaptation of this cell envelope to the osmotic pressure (or turgor pressure), which is generated by the difference in the concentration of solutes between the cytoplasm and the external environment. However, it remains unexplored how the cell wall, the inner membrane (IM), and the outer membrane (OM) effectively protect the cell from this pressure by bearing the resulting surface tension, thus preventing the formation of inner membrane bulges, abnormal cell morphology, spheroplasts and cell lysis. In this study, we have used molecular dynamics (MD) simulations combined with experiments to resolve how and to what extent models of the IM, OM, and cell wall respond to changes in surface tension. We calculated the area compressibility modulus of all three components in simulations from tension-area isotherms. Experiments on monolayers mimicking individual leaflets of the IM and OM were also used to characterize their compressibility. While the membranes become softer as they expand, the cell wall exhibits significant strain stiffening at moderate to high tensions. We integrate these results into a model of the cell envelope in which the OM and cell wall share the tension at low turgor pressure (0.3 atm) but the tension in the cell wall dominates at high values (>1 atm).