The Developmental Basis of Stomatal Density and Flux

Equations for stomatal density and maximum theoretical stomatal conductance as functions of stomatal initiation rate, epidermal cell size, and stomatal size enable scaling from development to flux.Since the first published measurements of stomatal density by Johann Hedwig (1793) and Alexander von Humboldt (1798), the counting and measuring of stomata has been one of the most typical botanical activities, with an important role across fields of plant biology (Willmer and Fricker, 1996). Stomatal density (d) and size (s) are indicators of acclimation and adaptation to contrasting environments, and permit estimation of the theoretical anatomical maximum stomatal conductance (g_max; units: mol m⁻² s⁻¹; Brown and Escombe, 1900; Lawson et al., 1998; Franks and Beerling, 2009; Franks et al., 2009), which represents a first quantitative estimate of the anatomical constraint on maximum stomatal gas exchange. While decades of theory have focused on d and g_max, their basis in traits with a transparent relationship to epidermal development has not been expressed. We derived exact mathematical equations for d and g_max as functions of stomatal differentiation rate, also known as stomatal index (i, no. of stomata per no. of epidermal cells plus stomata), s, and epidermal cell size (e). These equations unify the quantitative understanding of epidermal development and maximum flux, revealing the developmental bases for d and g_max across genotypes or species, and enabling targeting of specific epidermal development traits in plant breeding for productivity.The genetic and developmental basis for high stomatal density and stomatal conductance is a research priority in plant physiology, agriculture, and paleobiology (Asl et al., 2011; Doheny-Adams et al., 2012; Dow et al., 2014; Franks et al., 2015; Roche, 2015; Wang et al., 2015b). Indeed, a higher g_max should benefit species under low CO₂, higher irradiance or nutrient supply, or under selection for high productivity or competition (Franks and Beerling, 2009; Taylor et al., 2012; Jones, 2014). Under the opposite conditions, a lower g_max would provide the potential benefits of reduced water loss and/or increased CO₂ gain relative to water loss (Franks and Beerling, 2009; Taylor et al., 2012; Jones, 2014; Franks et al., 2015). Decades of theory have focused on the basis of g_max in stomatal anatomy (Fig. 1, A–C). According to a classic formulation of g_max (Brown and Escombe, 1900) in a recently updated form,(1)where D (m² s⁻¹) represents the diffusivity in air of water or CO₂ (which differ by a factor of 1.6); ν the molar volume of air (m³ mol⁻¹); and d, a_max, and l, respectively, the stomatal density (pores m⁻²), the mean maximum area of a single stomatal pore (m²), and stomatal pore depth (m; Franks and Beerling, 2009; Franks et al., 2009). The most recent extensions of this equation incorporated basic assumptions about allometries among guard cell dimensions, which have become standard in the stomatal literature (e.g. Franks and Beerling, 2009; Franks et al., 2009; Taylor et al., 2012; Dow et al., 2014; McElwain et al., 2016) and enable the estimation of g_max as a function of d and s. In its simplest form:(2)where and such that b is a biophysical constant and m a morphological constant based on scaling factors representing the proportionality of stomatal length (L) and width (W), and pore length (p) and depth (l), with c = p/L, j = W/L, and h = l/W all treated as constant for the estimation of g_max (c, h, and j = 0.5 for nongrasses with kidney bean-shaped guard cells, or c = 0.5, h = 0.5, and j = 0.125 for grasses with their dumbbell-shaped guard cells; Franks and Beerling, 2009; McElwain et al., 2016), though these ratios can be allowed to vary for individual species or genotypes when more detailed information is available on stomatal dimensions (Franks and Farquhar, 2007; Franks et al., 2014).Open in a separate windowFigure 1.Anatomical variables determining maximum stomatal conductance (g_max). A to C, Stomatal dimensions (guard cell length, L; stomatal pore length, p; guard cell width, W; stomatal area, s; stomatal maximum pore area, a_max; stomatal depth, l) and epidermal development traits (epidermal cell area, e; stomatal index, i). D to F, The influence on stomatal density (d) and g_max of e and i: increasing i as from D to E would lead to higher d and g_max; reducing e as from E to F would lead to higher d and g_max. Larger s would also lead to lower d and g_max, though with a much smaller effect. Stomatal images after Beaulieu et al. (2008).The g_max estimated this way strongly predicted the operating stomatal conductance measured with leaf gas exchange systems (g_op) across Arabidopsis (Arabidopsis thaliana) genotypes under low CO₂, high humidity, and high red and blue light (Dow et al., 2014). However, across diverse species, the g_max values estimated by Equation 2 tend to be much higher than g_op (Feild et al., 2011; McElwain et al., 2016) for several reasons. First, for typical leaves transpiring even under the best conditions, the effective area of the stomatal pore (a’) is smaller than the anatomical maximum a_max, by an amount that varies across species, particularly as the actual pore geometry usually deviates from simplified cylindrical geometry (Franks and Farquhar, 2007). Second, as guard cells close under adverse conditions, a’ declines (Fanourakis et al., 2015). Third, there may be a substantial contribution of diffusion resistances in the intercellular airspaces, especially in the case of a partly cutinized substomatal chamber (Roth-Nebelsick, 2007; Feild et al., 2011). Fourth, leaf surface features such as hairs or papillae surrounding the stomata, or encryption of stomata, may affect the diffusion through stomata, and especially will influence the boundary layer, which in addition to stomatal conductance determines overall diffusional conductance and therefore gas exchange (Kenzo et al., 2008; Hassiotou et al., 2009; Maricle et al., 2009). Clearly, much more research is needed to establish models that include all the factors that determine the anatomical influence of stomata on gas exchange rates and to validate these against a wide diversity of plants, yet the anatomical maximum defined as in Equations 1 and 2 is a strong constraint: g_max correlates across diverse species with g_op and light-saturated photosynthetic rate (McElwain et al., 2016), and scales up, in combination with leaf area allocation, to the determination of ecosystem net primary productivity (Wang et al., 2015a). The anatomical g_max is therefore a theoretical value estimating the maximum stomatal diffusion capacity, and like other theoretical physiological variables, such as photosynthetic parameters including the maximum carboxylation rate (V_cmax), it cannot be reached in practice, but is useful for generating hypotheses regarding the capacity for stomatal diffusion in various domains, such as comparisons of genotypes or species, functional types, or trends in evolutionary time (Franks and Beerling, 2009; Doheny-Adams et al., 2012; Taylor et al., 2012; McElwain et al., 2016; de Boer et al., 2016).Despite the well-recognized importance of both d and g_max, there has been limited understanding of their genetic and developmental basis and their relationships to other epidermal traits. Ever since the seminal work of E.J. Salisbury early last century, d has been known to be positively associated with stomatal initiation rate, also known as stomatal index (i = no. of stomata per no. of epidermal cells plus stomata; Salisbury, 1927; Wengier and Bergmann, 2012), and negatively with mean epidermal cell area (e), as increases in e would space stomata apart (Fig. 1, D–F). Studies of plants of different species (Beaulieu et al., 2008; Brodribb et al., 2013) or of given species grown in different irradiance and vapor pressure deficit treatments (Carins Murphy et al., 2012, 2014) found that d related negatively to e. Further, a negative relationship of d with s within plant canopies or across species has been found numerous times and sometimes attributed to a “general association” or “trade-off” (e.g. Weiss, 1865; Grubb et al., 1975; Tichá, 1982; Hetherington and Woodward, 2003; Sack et al., 2003; Franks and Beerling, 2009; Brodribb et al., 2013; Wang et al., 2015a; de Boer et al., 2016). Yet, while numerous correlational studies within and across species have confirmed these relationships, their formal mathematical basis has remained unclear.To directly link g_max, and thus stomatal flux, to underlying epidermal development traits, we derived new equations for d and g_max as functions of e, i, and s, where e and s are projected cell areas (units: m²).As defined by Salisbury (1927), i is the number of stomata (n_s) divided by the sum of n_s and the number of epidermal cells (n_e):(3)Stomatal density (d) is related to n_s, n_e, s, and e as:(4)where area is that of the whole leaf (units: m²). Equation 4 can be rearranged as(4a)The ratio n_e/n_s can be expressed in terms of i by rearranging Equation 3:(5)Applying Equation 5 to Equation 4a gives(6)This equation gives d as a function of e, i, and s—traits with a transparent relationship to development, all being related to epidermal cell differentiation and expansion. Equation 6 can be applied to Equation 2 to give g_max as a function of e, i, and s:(7)These expressions rely on mean values for e, s, and i, so their accuracy may be affected by variation of these variables within leaves, or by variation in sampling methods as there exists no standard measurement protocol (see “Materials and Methods”). We tested the correctness of the derivation of Equation 6 and its applicability to real measurements of d, e, i, and s for abaxial leaf surfaces compiled from the published literature for 141 values from 81 species from 28 angiosperm families (“Supplemental Data”). We further checked for quantitative consistency between g_max as estimated from e, s, and i (Eq. 7) and the literature standard estimate of g_max from d and s (Eq. 2) using the same dataset. In both cases we found extremely tight correspondence (Fig. 2). Considering relationships within individual plant families for which ≥ 6 points were available showed similarly tight correspondence (R² = 0.96–1.0, P < 0.001, n = 6–30 for Betulaceae, Ericaceae, Fabaceae, Fagaceae, Orchidaceae, Rosaceae, and Sapindaceae; slopes and intercepts did not differ at P < 0.05 among families or from 1.0 and 0, respectively).Open in a separate windowFigure 2.Developmental basis for maximum stomatal flux variables: the estimation of abaxial leaf stomatal density (d; A) and theoretical maximum stomatal conductance (g_max; B) as functions of epidermal cell area (e), stomatal index (i), and stomatal area (s). A, Values estimated using Equation 6 plotted against reported values of d; B, values estimated using Equation 7 plotted against values estimated using Equation 2 with inputs of s and d as standard in the current literature. Data were compiled from single or mean values for leaves from published papers for seedlings (circles) and adults (squares) of 54 European woody species; four species of annual herbs of genus Gomphrena (Amaranthaceae; triangles); 22 species of genus Stanhopea, Orchidaceae (diamonds); and one grass species (Paspalum dilatatum, Poaceae; hexagon). The lines are ordinary least squares regressions fitted to the data with fixed zero intercept. The high R² values indicate the correctness of the derivation, its applicability to real measurements, and the quality of the measurements.These equations clarify precise geometric linkages among stomatal flux, anatomy, and development. We propose five examples of potentially powerful applications of these relationships to inform fundamental research across plant development, physiology, paleobiology, and crop science.

• (1) An expansion of available data on stomatal differentiation. Measurements of i can be technically challenging given the need to resolve all epidermal pavement cells in an image, but Equation 6 can be rearranged to allow estimation of i from measurements of d, e, and s, greatly expanding the data availability for this important developmental trait:(8)
• (2) Analysis of the developmental and genetic drivers of d and g_max across genotypes of a given species or across phylogenetically diverse species; i.e. quantifying how much of the variation in d and g_max arises due to differences in i, e, or s. Thus, the developmental basis for observed shifts in g_max in response to climate, CO₂, and lifeform evolution can be inferred using Equations 6 and 7.
• (3) Clarifying the quantitative role of shifts in genome and cell sizes (i.e. e and s) on g_max. The question of the role and impact of cell size is especially important given the strong developmental plasticity and evolutionary lability of cell size, and its relationship to other traits. For example, within some lineages, epidermal cell size correlates positively with genome size and leaf size and/or negatively with venation density (Beaulieu et al., 2008; Brodribb et al., 2013).
• (4) Resolving the coordinated shifts of stomatal traits in fossils and experimental plants, thereby improving inferences concerning shifts in response to global temperature and atmospheric CO₂. Previous studies of adaptation and acclimation in response to CO₂ have tended to quantify d and/or i (e.g. Beerling et al., 1998; Royer, 2001) and/or more rarely s and e (e.g. Ogaya et al., 2011; Haworth et al., 2014), and assumed that a shift in any one of these traits was an important marker of adaptation. Equations 6 and 7 allow estimation of the quantitative dependency of shifts in d and g_max on other variables.
• (5) Prediction of how each trait should be adjusted, through breeding or genetic manipulation, to optimize productivity through changes in g_max. Equations 6 and 7 clarify the separate roles of e, i, and s in determining higher g_max. Given the increasing resolution of the genetic basis for these traits in model species (e.g. Ferris et al., 2002; Delgado et al., 2011), these traits can be made specific targets for breeding for higher g_max and thereby for productivity. Other traits would also need to be targeted (e.g. hydraulic and photosynthetic traits) to enable higher productivity above and beyond the potential cost of constructing, maintaining, and operating additional stomatal apparatus (Assmann and Zeiger, 1987).

By linking leaf epidermal anatomy and development with physiological flux, these equations allow scaling from the differentiation and expansion of epidermal cells and stomata to plant productivity. Given ongoing improvement of models for the influence of the anatomy and dynamic behavior of stomata and of internal and external leaf tissues on gas exchange, consideration of these important traits in terms of their development will have potential applications across the widest range of fields in plant biology and earth system science.     

Regulation of autophagy and mitophagy by nutrient availability and acetylation

Normal cellular function is dependent on a number of highly regulated homeostatic mechanisms, which act in concert to maintain conditions suitable for life. During periods of nutritional deficit, cells initiate a number of recycling programs which break down complex intracellular structures, thus allowing them to utilize the energy stored within. These recycling systems, broadly named “autophagy”, enable the cell to maintain the flow of nutritional substrates until they can be replenished from external sources. Recent research has shown that a number of regulatory components of the autophagy program are controlled by lysine acetylation. Lysine acetylation is a reversible post-translational modification that can alter the activity of enzymes in a number of cellular compartments. Strikingly, the main substrate for this modification is a product of cellular energy metabolism: acetyl-CoA. This suggests a direct and intricate link between fuel metabolites and the systems which regulate nutritional homeostasis. In this review, we examine how acetylation regulates the systems that control cellular autophagy, and how global protein acetylation status may act as a trigger for recycling of cellular components in a nutrient-dependent fashion. In particular, we focus on how acetylation may control the degradation and turnover of mitochondria, the major source of fuel-derived acetyl-CoA.     

Effects of (22S,23S)-Homobrassinolide and Related Compounds on Membrane Potential and Transport of Egeria Leaf Cells

(22S,23S)-Homobrassinolide was tested for its effect on the electric cell potential, proton extrusion, ferricyanide reduction, and amino acid and sucrose uptake of leaves of Egeria densa Planchon. In the light, (22S,23S)-homobrassinolide and its derivative, 2α-3α-dihydroxy-5α-stigmast-22-en-6-one, were similar to each other and similar to fusicoccin in causing hyperpolarization and proton extrusion, whereas stigmasterol was less effective. In darkness, the three sterols showed comparable effects. (22S,23S)-Homobrassinolide slightly stimulated ferricyanide reduction and promoted uptake of sucrose and α-aminoisobutyric acid. The results are compatible with a stimulation of an electrogenic proton pump mechanism at the plasmalemma by (22S,23S)-homobrassinolide.     

Detection of Vibrio cholerae O1 in the aquatic environment by fluorescent-monoclonal antibody and culture methods

Vibrio cholerae O1 in plankton samples collected from ponds and rivers between February 1987 and January 1990 in Matlab, Bangladesh, was detected by the fluorescent-monoclonal antibody (FA) technique. Samples were collected at sites which were monitored fortnightly (fixed sites) as well as at sites that were part of a case-control study. FA results were compared with those obtained by conventional culture methods (CM). A total of 876 samples were collected; V. cholerae O1 was detected in 563 samples (64.27%) by the FA method and in 3 samples (0.34%) by CM. Of the fixed-site plankton samples, 439 (63.62%) were positive by FA and none were positive by CM. Of the 93 case sites sampled on the day after the occurrence of a case of cholera, 73 (78.49%) were positive for V. cholerae O1 by FA and 3 (3.2%) were positive by CM. In comparison, of the 93 first-day sample collections at control sites at the time a case of cholera occurred, only 51 (54.83%) were positive by FA and none were positive by CM. From the data, it is concluded that V. cholerae O1 is present throughout the year in the ponds and rivers of Bangladesh that were examined in this study and that V. cholerae can be detected by FA but not always by CM. The FA procedure was found to be very useful in detecting V. cholerae in plankton, with which it was associated and often occurred in large numbers in the nonculturable stage. Thus, studies investigating the significance of the role of environmental factors in the epidemiology of cholera can be performed effectively by using FA. Such studies are in progress.     

Optimal growth temperature for the isolation of Plesiomonas shigelloides, using various selective and differential agars.

The growth characteristics of known strains of Plesiomonas shigelloides were compared with those of Aeromonas species (the major competing species in environmental waters) on plesiomonas differential agar, inositol brilliant green bile salt, and modified salmonella-shigella agar at incubation temperatures of 37, 42, and 44 degrees C. Using local isolates from clinical and environmental sources, optimal growth conditions, as determined by colony counts and the colony characteristics, plesiomonas differential agar proved to be ideal when incubated at 44 degrees C. Contrary to earlier recommendations for 48 h incubation, the colonies could be recognized readily after an incubation of 24 h.     

Endothelial cells on an aged subendothelial matrix display heterogeneous strain profiles in silico

Within the artery intima, endothelial cells respond to mechanical cues and changes in subendothelial matrix stiffness. Recently, we found that the aging subendothelial matrix stiffens heterogeneously and that stiffness heterogeneities are present on the scale of one cell length. However, the impacts of these complex mechanical micro-heterogeneities on endothelial cells have not been fully understood. Here, we simulate the effects of matrices that mimic young and aged vessels on single- and multi-cell endothelial cell models and examine the resulting cell basal strain profiles. Although there are limitations to the model which prohibit the prediction of intracellular strain distributions in alive cells, this model does introduce mechanical complexities to the subendothelial matrix material. More heterogeneous basal strain distributions are present in the single- and multi-cell models on the matrix mimicking an aged artery over those exhibited on the young artery. Overall, our data indicate that increased heterogeneous strain profiles in endothelial cells are displayed in silico when there is an increased presence of microscale arterial mechanical heterogeneities in the matrix.     

Novel metabolites in phenanthrene and pyrene transformation by Aspergillus niger.

Aspergillus niger, isolated from hydrocarbon-contaminated soil, was examined for its potential to degrade phenanthrene and pyrene. Two novel metabolites, 1-methoxyphenanthrene and 1-methoxypyrene, were identified by conventional chemical techniques. Minor metabolites identified were 1- and 2-phenanthrol and 1-pyrenol. No 14CO2 evolution was observed in either [14C]phenanthrene or [14C]pyrene cultures.     

21-Hydroxylase deficiency: screening and incidence in Israel

BACKGROUND: Neonatal screening for congenital adrenal hyperplasia was introduced in 1977. However, even today only a few national screening programs exist and their cost effectiveness is still debatable. This study was conducted in order to evaluate the advisability of a national or regional screening program in Israel. METHODS: From June 1987 until December 1992 we screened a countrywide random sample of 113,846 newborns for 21-hydroxylase (21-OH) deficiency measuring 17alpha-OH progesterone (17-OHP) from blood spotted on filter paper. Between January 1993 and August 1995 we continued the screening program concentrating on the population of northern Israel. A total of 56,958 newborns were screened. We compared these findings with the incidence of 21-OH deficiency in the total population born in Israel during the years 1986-1991. RESULTS: In the countrywide screening program, 4 newborns (2 Arabs and 2 Jews) were found to have levels of 17-OHP between 409 and 2,049 nmol/l (2 males and 2 females). This constitutes a low incidence of 1 in 28,462 live births. In the north-Israel screening program 4 newborns (all Arabs) were detected (2 males and 2 females) constituting a much higher incidence of 1 in 14,240 live births. The data obtained from the archives revealed that the incidence of 21-OH deficiency nationwide during the years 1986-1991 was 1:19,000 live births, 1:30,000 for Jews and 1:8,000 for Arabs. The incidence of 21-OH deficiency among Arab newborns in the northern part of the country was as high as 1:5,000 (14:71,130). The female to male (F:M) ratio was 2.6:1 and the ratio of the salt-losing to the simple virilizing variant was 5:1. Two male patients were diagnosed prenatally, 21 patients (17 F and 4 M) during the first month after birth and 6 others subsequently. CONCLUSIONS: The high F:M ratio of 21-OH deficiency in the total population compared to a 1:1 ratio in our random screening programs suggests that 21-OH-deficient male patients in the general population might have been missed or died early due to a salt-losing crisis. The high incidence of this disease in the northern part of the country and especially among the Arabs, suggests that screening in this part of the country, especially among the Arab population, is warranted and might save the lives of some male patients.     

Plant hydraulics as a central hub integrating plant and ecosystem function: meeting report for ‘Emerging Frontiers in Plant Hydraulics’ (Washington,DC, May 2015)

Water plays a central role in plant biology and the efficiency of water transport throughout the plant affects both photosynthetic rate and growth, an influence that scales up deterministically to the productivity of terrestrial ecosystems. Moreover, hydraulic traits mediate the ways in which plants interact with their abiotic and biotic environment. At landscape to global scale, plant hydraulic traits are important in describing the function of ecological communities and ecosystems. Plant hydraulics is increasingly recognized as a central hub within a network by which plant biology is connected to palaeobiology, agronomy, climatology, forestry, community and ecosystem ecology and earth‐system science. Such grand challenges as anticipating and mitigating the impacts of climate change, and improving the security and sustainability of our food supply rely on our fundamental knowledge of how water behaves in the cells, tissues, organs, bodies and diverse communities of plants. A workshop, ‘Emerging Frontiers in Plant Hydraulics’ supported by the National Science Foundation, was held in Washington DC, 2015 to promote open discussion of new ideas, controversies regarding measurements and analyses, and especially, the potential for expansion of up‐scaled and down‐scaled inter‐disciplinary research, and the strengthening of connections between plant hydraulic research, allied fields and global modelling efforts.