The relation between stomatal aperture and gas exchange under consideration of pore geometry and diffusional resistance in the mesophyll

The quantitative relation between stomatal aperture and gas exchange through the stomatal pore can be described by physical models derived from Fick's first law of diffusion. Such models, usually based on a simplified pore geometry, are used to calculate leaf conductance from stomatal pore dimensions or vice versa. In this study a combination of gas-exchange measurements and simultaneous microscopical observations of stomatal apertures was used to empirically determine this relationship. The results show a substantial deviation between measured stomatal conductance and that calculated from the simplified models. The main difference is a much steeper increase of conductance with aperture at small apertures. When the calculation was based on a realistic pore geometry derived from confocal laser scanning microscopy, a good fit to the experimentally found relationship could be obtained if additionally a significant contribution of a mesophyll diffusional resistance was taken into account.     

Modelling of stomatal density response to atmospheric CO2

Stomatal density tends to vary inversely with changes in atmospheric CO(2) concentration (C(a)). This phenomenon is of significance due to: (i) the current anthropogenic rise in C(a) and its impact on vegetation, and (ii) the potential applicability for reconstructing palaeoatmospheric C(a) by using fossil plant remains. It is generally assumed that the inverse change of stomatal density with C(a) represents an adaptation of epidermal gas conductance to varying C(a). Reconstruction of fossil C(a) by using stomatal density is usually based on empirical curves which are obtained by greenhouse experiments or the study of herbarium material. In this contribution, a model describing the stomatal density response to changes in C(a) is introduced. It is based on the diffusion of water vapour and CO(2), photosynthesis and an optimisation principle concerning gas exchange and water availability. The model considers both aspects of stomatal conductance: degree of stomatal aperture and stomatal density. It is shown that stomatal aperture and stomatal density response can be separated with stomatal aperture representing a short-term response and stomatal density a long-term response. The model also demonstrates how the stomatal density response to C(a) is modulated by environmental factors. This in turn implies that reliable reconstructions of ancient C(a) require additional information concerning temperature and humidity of the considered sites. Finally, a sensitivity analysis was carried out for the relationship between stomatal density and C(a) in order to identify critical parameters (= small parameter changes lead to significant changes of the results). Stomatal pore geometry (pore size and depth) represents a critical parameter. In palaeoclimatic studies, pore geometry should therefore also be considered.     

Stomatal responses to humidity in isolated epidermes

The ability of guard cells to hydrate and dehydrate from the surrounding air was investigated using isolated epidermes of Tradescantia pallida and Vicia faba . Stomata were found to respond to the water vapour pressure on the outside and inside of the epidermis, but the response was more sensitive to the inside vapour pressure, and occurred in the presence or absence of living, turgid epidermal cells. Experiments using helium–oxygen air showed that guard cells hydrated and dehydrated entirely from water vapour, suggesting that there was no significant transfer of water from the epidermal tissue to the guard cells. The stomatal aperture achieved at any given vapour pressure was shown to be consistent with water potential equilibrium between the guard cells and the air near the bottom of the stomatal pore, and water vapour exchange through the external cuticle appeared to be unimportant for the responses. Although stomatal responses to humidity in isolated epidermes are the result of water potential equilibrium between the guard cells and the air near the bottom of the stomatal pore, stomatal responses to humidity in leaves are unlikely to be the result of a similar equilibrium.     

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.     

Computer-based studies of diffusion through stomata of different architecture

BACKGROUND AND AIMS: The influence of stomatal architecture on stomatal conductance and on the developing concentration gradient was explored quantitatively by comparing diffusion rates of water vapour and CO(2) occurring in a set of three-dimensional stoma models. The influence on diffusion of an internal cuticle, a sunken stoma, a partially closed stoma and of substomatal chambers of two different sizes was considered. METHODS: The study was performed by using a commercial computer program based on the Finite Element Method which allows for the simulation of diffusion in three dimensions. By using this method, diffusion was generated by prescribed gas concentrations at the boundaries of the substomatal chamber and outside of the leaf. The program calculates the distribution of gas concentrations over the entire model space. KEY RESULTS: Locating the stomatal pore at the bottom of a stomatal antechamber with a depth of 20 microm decreased the conductance significantly (at roughly about 30 %). The humidity directly above the stomatal pore is significantly higher with the stomatal antechamber present. Lining the walls of the substomatal chamber with an internal cuticle which suppresses evaporation had an even stronger effect by reducing the conductance to 60 % of the original value. The study corroborates therefore the results of former studies that water will evaporate preferentially at sites in the immediate vicinity to the stomatal pore if no internal cuticle is present. The conductance decrease affects only water vapour and not CO(2). Increasing the substomatal chamber increases CO(2) uptake, whereas transpiration increases if an internal cuticle is present. CONCLUSIONS: Variation of stomatal structure may, with unchanged pore size and depth, profoundly affect gas exchange and the pathways of liquid water inside the leaf. Equations for calculation of stomatal conductance which are solely based on stomatal density and pore depth and size can significantly overestimate stomatal conductance.     

A surrogate measure of stomatal aperture

It is proposed that a measurement of the peristomatal groove distance (PGD) of guard cells on surface impressions of leaf epidermis can act as a surrogate measure of stomatal aperture. To test this idea, investigations were carried out on two species, one in which it is possible to make direct measurements of pore width with relative ease (Commelina communis L.) and one whose stomata are so small that this is difficult (Phaseolus vulgaris L.). Leaf water vapour conductance measurements were first taken with a porometer, then, without delay, a silicone rubber impression of the leaf was made of the area directly under the porometer cup. From a positive replica of this impression, stomatal aperture, PGD and pore length were measured. The correlations between stomatal aperture and PGD and between PGD and stomatal conductance were positive and highly significant. Because a causal relationship between stomatal aperture and PGD is expected, linear regression was used to obtain equations for converting PGD measurements into estimates of stomatal aperture. These account for 91.7% of the variation of aperture in the case of C. communis and 70.7% in P. vulgaris, suggesting that PGD measurements have potential as an alternative measure of pore width in cases where direct measurements would be both difficult and subject to excessive measurement error or bias.     

The relative role of stomata in transpiration and assimilation

Summary The ways in which transpiration and assimilation depend on stomatal aperture are compared. It is shown that transpiration and assimilation are equally sensitive to change of stomatal aperture when the internal resistance to assimilation is equal to an effective resistance to evaporation which exists because of the coupling of heat and vapour exchanges between leaf and atmosphere. Generally the ratio of transpiration to assimilation changes with stomatal aperture in a manner which is determined by the relative magnitude of these resistances and on temperature. Some possible implications in relation to the optimal behaviour of stomata are discussed.Work done while J.H.T. held a New Zealand D.S.I.R. Fellowship.     

The citrus leaf cuticle in relation to measurement of leaf water potential using thermocouple psychrometers*

Abstract. Cuticular resistance to water vapour diffusion is an important aspect of thermocouple psychrometry and may introduce significant error in the measurement of leaf water potential (Ψ). The effect of the citrus (Citrus mitis Blanco) leaf cuticle on water vapour movement was studied using the times required for vapour pressure equilibration during thermocouple psychrometric measurement of Ψ. Cuticular abrasion with various carborundum powders was used to reduce the diffusive resistance of both the adaxial and abaxial leaf surfaces, and the extent of the disruption to the leaf was investigated with light and electron microscopy. Cuticular abrasion resulted in reduced equilibration times due to decreased cuticular resistance and greater water vapour movement between the leaf and the psychrometer chamber. Equilibration times were reduced from over 5 h in the unabraded control leaves to 1 h with cuticle abrasion. This was associated with the decrease in diffusive resistance with cuticular abrasion from over 55 s cm^?1 to less than 8 s cm^?1 for both the adaxial and abaxial leaf surfaces. Scanning electron micrographs of the abraded leaf tissue revealed considerable disruption of the stomatal ledge and of the guard cells, surface smoothing and displacement of waxes into the stomatal aperture, and damage to veins. Observations with the transmission electron microscope revealed frequent disruption of epidermal cell walls, and damage to both the cytoplasmic and vacuolar membranes.     

From reproduction to production,stomata are the master regulators

The best predictor of leaf level photosynthetic rate is the porosity of the leaf surface, as determined by the number and aperture of stomata on the leaf. This remarkable correlation between stomatal porosity (or diffusive conductance to water vapour g_s) and CO₂ assimilation rate (A) applies to all major lineages of vascular plants (Figure 1) and is sufficiently predictable that it provides the basis for the model most widely used to predict water and CO₂ fluxes from leaves and canopies. Yet the Ball–Berry formulation is only a phenomenological approximation that captures the emergent character of stomatal behaviour. Progressing to a more mechanistic prediction of plant gas exchange is challenging because of the diversity of biological components regulating stomatal action. These processes are the product of more than 400 million years of co‐evolution between stomatal, vascular and photosynthetic tissues. Both molecular and structural components link the abiotic world of the whole plant with the turgor pressure of the epidermis and guard cells, which ultimately determine stomatal pore size and porosity to water and CO₂ exchange (New Phytol., 168, 2005, 275). In this review we seek to simplify stomatal behaviour by using an evolutionary perspective to understand the principal selective pressures involved in stomatal evolution, thus identifying the primary regulators of stomatal aperture. We start by considering the adaptive process that has locked together the regulation of water and carbon fluxes in vascular plants, finally examining specific evidence for evolution in the proteins responsible for regulating guard cell turgor.     

The Effect of Epidermal Cell Water Potential on Stomatal Response to Illumination of Leaf Discs of Vicia faba

Illuminated leaf discs of Vicia faba were brought into equilibrium with a series of mannitol solutions. The width of stomatal aperture and the osmotic potential of guard cells and epidermal cells were determined. It was found that the maximal aperture was obtained when epidermal cells were at about incipient plasmolysis and that any increase in their turgor pressure brought about a decrease in stomatal aperture. These findings emphasize the importance of epidermal cells in determining the width of the stomatal pore.     

The kinetics of stomatal responses to VPD in Vicia faba: electrophysiological and water relations models

Abstract. An Ohm's law analogy is frequently employed to calculate parameters of leaf gas exchange. For example, resistance to water vapour loss is calculated as the quotient of vapour pressure difference (VPD) and vapour loss by transpiration. In the present research, this electrical analogy was extended. Steady-state transpiration as a function of VPD, assayed in leaflets of Vicia faba using gas exchange techniques, was compared with steady-state K⁺ current magnitude as a function of voltage in isolated guard cell protoplasts of Vicia faba, assayed using the patch clamping technique in the whole cell configuration. An electrophysiological model originally developed to explain the kinetics of current changes following step changes in voltage across a cell membrane was used to fit the kinetics of transpiration changes following step changes in VPD applied to leaflets of Vicia faba. Following step increases in VPD, transpiration exhibited an initial increase, reflecting the increased driving force for water loss and, for large step increases in VPD, a transient decrease in stomatal resistance. Transpiration subsequently declined, reflecting stomatal closure. By analogy to electrophysiological responses, it is hypothesized that the humidity parameter that is sensed by guard cells is VPD. Two models based on epidermal water relations were also applied to transpiration kinetics. In the first model, the transient increase in transpiration following a step increase in VPD was attributed partially to an increase in the Physical driving force (VPD) and partially to a transient decrease in stomatal resistance resulting from reduced epidermal backpressure. In the second model, the transient decrease in stomatal resistance was attributed to a direct response of the guard cells to VPD. Both models based on water relations gave good fits of the data, emphasizing the need for further study regarding the metabolic nature of the guard cell response to humidity.     

Short- and Long-term Stomatal Responses to Fluctuations in Environment in Southern European Greenhouses

Stomatal behaviour in cucumber (Cucumis sativus L.) was analysed and modelled as a function of different greenhouse environmental parameters, under variable summer conditions. Solar radiation was the main regulating factor. During the day, large atmospheric vapour pressure deficit increased transpiration which was followed by a reduction in stomatal aperture, suggesting the presence of a feedback response to water stress. However, stomatal behaviour was more sensitive to high atmospheric vapour pressure deficit when this was accompanied by a rapid decrease of solar radiation. The response to the difference between leaf and air temperature was also influenced by air vapour pressure deficit and duration of plant exposure to high evaporative demand. Calculation of the crop water stress index showed that the air vapour pressure deficit of 1 kPa used in the control treatment probably caused water stress and induced some hardening, a necessary condition for adaptation to summer climate in southern Europe. The importance of the interaction between climatic parameters and plant response in greenhouse environmental management is analysed. Classical models of stomatal resistance are also discussed.     

Testing a vapour‐phase model of stomatal responses to humidity

This study tests two predictions from a recently proposed model for stomatal responses to humidity and temperature. The model is based on water potential equilibrium between the guard cells and the air at the bottom of the stomatal pore and contains three independent variables: g_s⁰, Z and Θ. g_s⁰ is the value of stomatal conductance that would occur at saturating humidity and will vary among leaves and with CO₂ and light. The value of Z is determined primarily by the resistance to heat transfer from the epidermis to the evaporating site and the value of Θ is determined primarily by the resistance to water vapour diffusion from the evaporating site to the guard cells. This leads to the two predictions that were tested. Firstly, the values of Z and Θ should be constant for leaves of a given species grown under given conditions, although g_s⁰ should vary among leaves and with light and CO₂. And secondly, the ratio of Z to Θ should be higher in leaves having their stomata in crypts because the distance for heat transfer is greater than that for water vapour diffusion. Data from three species, Nerium oleander, Pastinaca sativum and Xanthium strumarium support these two predictions.     

Interpretation of an empirical model for stomatal conductance in terms of guard cell function

An empirical model for stomatal conductance (g), proposed by Leuning (1995, this issue) as a modification of Ball, Woodrow & Berry's (1987) model, is interpreted in terms of a simple, steady-state model of guard cell function. In this model, stomatal aperture is a function of the relative turgor between guard cells and epidermal cells. The correlation between g and leaf surface vapour pressure deficit in Leuning's model is interpreted in terms of stomatal sensing of the transpiration rate, via changes in the gradient of total water potential between guard cells and epidermal cells. The correlation between g, CO₂ assimilation rate and leaf surface CO₂ concentration in Leuning's model is interpreted as a relationship between the corresponding osmotic gradient, irradiance, temperature, intercellular CO₂ concentration and stomatal aperture itself. The explicit relationship between osmotic gradient and stomatal aperture (possibly describing the effect of changes in guard cell volume on the membrane permeability for ion transport) results in a decrease in the transpiration rate in sufficiently dry air. Possible extension of the guard cell model to include stomatal responses to soil water status is discussed.     

Guard cells elongate: relationship of volume and surface area during stomatal movement

Stomata in the epidermis of photosynthetically active plant organs are formed by pairs of guard cells, which create a pore, to facilitate CO2 and water exchange with the environment. To control this gas exchange, guard cells actively change their volume and, consequently, surface area to alter the aperture of the stomatal pore. Due to the limited elasticity of the plasma membrane, such changes in surface area require an exocytic addition or endocytic retrieval of membrane during stomatal movement. Using confocal microscopic data, we have reconstructed detailed three-dimensional models of open and closed stomata to precisely quantify the necessary area to be exo- and endocytosed by the guard cells. Images were obtained under a strong emphasis on a precise calibration of the method and by avoiding unphysiological osmotical imbalance, and hence osmocytosis. The data reveal that guard cells of Vicia faba L., whose aperture increases by 111.89+/-22.39%, increase in volume and surface area by 24.82+/-6.26% and 14.99+/-2.62%, respectively. In addition, the precise volume to surface area relationship allows quantitative modeling of the three-dimensional changes. While the major volume change is caused by a slight increase in the cross section of the cells, an elongation of the guard cells achieves the main aperture change.     

A new, vapour-phase mechanism for stomatal responses to humidity and temperature

A new mechanism for stomatal responses to humidity and temperature is proposed. Unlike previously-proposed mechanisms, which rely on liquid water transport to create water potential gradients within the leaf, the new mechanism assumes that water transport to the guard cells is primarily through the vapour phase. Under steady-state conditions, guard cells are assumed to be in near-equilibrium with the water vapour in the air near the bottom of the stomatal pore. As the water potential of this air varies with changing air humidity and leaf temperature, the resultant changes in guard cell water potential produce stomatal movements. A simple, closed-form, mathematical model based on this idea is derived. The new model is parameterized for a previously published set of data and is shown to fit the data as well as or better than existing models. The model contains mathematical elements that are consistent with previously-proposed mechanistic models based on liquid flow as well as empirical models based on relative humidity. As such, it provides a mechanistic explanation for the realm of validity for each of these approaches.     

Photosynthesis and Transpiration as a Function of Gaseous Diffusive Resistances in Orange Leaves

The CO₂ and H₂O vapour exchange of single attached orange, Citrus sinensis (L.), leaves was measured under laboratory conditions using infrared gas analysis. Gaseous diffusive resistances were derived from measurements at a saturating irradiance and at a leaf temperature optimum for photosynthesis. Variation in leaf resistance (within the range 1.6 to 60 s cm^-1) induced by moisture status, or by cyclic oscillations in stomatal aperture, was associated with changes in both photosynthesis and transpiration. At low leaf resistance (ri less than 10 s cm^-1) the ratio of transpiration to photosynthesis declined with reduced stomatal aperture, indicating a tighter stomatal control over H₂O vapour loss than over CO₂ assimilation. At higher leaf resistance (ri greater than 10 s cm^-1) changes in transpiration and photosynthesis were linearly related, but leaf resistance and mesophyll resistance were also positively correlated, so that strictly stomatal control of photosynthesis became more apparent than real. This evidence, combined with direct measurements of CO₂ diffusive resistances (in a -O₂ gas stream) emphasised the presence of a significant mesophyll resistance; i.e., an additional and rate limiting resistance to CO₂ assimilation over and above that encountered by H₂O vapour escaping from the leaf.     

Stomatal encryption by epicuticular waxes as a plastic trait modifying gas exchange in a Mediterranean evergreen species (Quercus coccifera L.)

The adaptive benefit of stomatal crypts remains a matter of controversy. This work studies the effect on gas exchange of cuticular rims that overarch the stomatal pore in the Mediterranean species Quercus coccifera L. growing under Mediterranean (lower relative humidities and high summer temperatures) or oceanic conditions (higher daily relative humidities and mild temperatures). After microscopic assessment of the leaf surfaces and stomatal architecture, the impact of the cuticular ‘cup’ on gas exchange was evaluated by employing three‐dimensional finite element models. Here, we provide evidence for a high plasticity of the Q. coccifera cuticular cup, with much larger vents under oceanic conditions compared to small vents under Mediterranean conditions. This structure adds a substantial fixed resistance thereby strongly decreasing gas exchange under Mediterranean conditions. The cuticular cup, which also increases leaf internal humidity, might buffer the rapid changes in vapour pressure deficit (VPD) often observed under Mediterranean conditions. Since water loss of guard and adjacent epidermal cells regulates stomatal aperture, we suggest that this structure allows an efficient regulation of stomatal conductance and optimum use of resources under high VPD. This study provides evidence that plasticity of stomatal architecture can be an important structural component of hydraulic adaptation to different climate conditions.     

Stomatal control of transpiration from a developing sugarcane canopy

Abstract. Stomatal conductance of single leaves and transpiration from an entire sugarcane (Saccharum spp. hybrid) canopy were measured simultaneously using independent techniques. Stomatal and environmental controls of transpiration were assessed at three stages of canopy development, corresponding to leaf area indices (L) of 2.2, 3.6 and 5.6. Leaf and canopy boundary layers impeded transport of transpired water vapour away from the canopy, causing humidity around the leaves to find its own value through local equilibration rather than a value determined by the humidity of the bulk air mass above the canopy. This tended to uncouple transpiration from direct stomatal control, so that transpiration predicted from measurement of stomatal conductance and leaf-to-air vapour pressure differences was increasingly overestimated as the reference point for ambient vapour pressure measurement was moved farther from the leaf and into the bulk air. The partitioning of control between net radiation and stomata was expressed as a dimensionless decoupling coefficent ranging from zero to 1.0. When the stomatal aperture was near its maximum this coefficient was approximately 0.9, indicating that small reductions in stomatal aperture would have had little effect on canopy transpiration. Maximum rates of transpiration were, however, limited by large adjustments in maximum stomatal conductance during canopy development. The product of maximum stomatal conductance and L. a potential total canopy conductance in the absence of boundary layer effects, remained constant as L increased. Similarly, maximum canopy conductance, derived from independent micrometeorological measurements, also remained constant over this period. Calculations indicated that combined leaf and canopy boundary layer conductance decreased with increasing L such that the ratio of boundary layer conductance to maximum stomatal conductance remained nearly constant at approximately 0.5. These observations indicated that stomata adjusted to maintain both transpiration and the degree of stomatal control of transpiration constant as canopy development proceeded.