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.     

Evolutionary Connectionism: Algorithmic Principles Underlying the Evolution of Biological Organisation in Evo-Devo,Evo-Eco and Evolutionary Transitions

The mechanisms of variation, selection and inheritance, on which evolution by natural selection depends, are not fixed over evolutionary time. Current evolutionary biology is increasingly focussed on understanding how the evolution of developmental organisations modifies the distribution of phenotypic variation, the evolution of ecological relationships modifies the selective environment, and the evolution of reproductive relationships modifies the heritability of the evolutionary unit. The major transitions in evolution, in particular, involve radical changes in developmental, ecological and reproductive organisations that instantiate variation, selection and inheritance at a higher level of biological organisation. However, current evolutionary theory is poorly equipped to describe how these organisations change over evolutionary time and especially how that results in adaptive complexes at successive scales of organisation (the key problem is that evolution is self-referential, i.e. the products of evolution change the parameters of the evolutionary process). Here we first reinterpret the central open questions in these domains from a perspective that emphasises the common underlying themes. We then synthesise the findings from a developing body of work that is building a new theoretical approach to these questions by converting well-understood theory and results from models of cognitive learning. Specifically, connectionist models of memory and learning demonstrate how simple incremental mechanisms, adjusting the relationships between individually-simple components, can produce organisations that exhibit complex system-level behaviours and improve the adaptive capabilities of the system. We use the term “evolutionary connectionism” to recognise that, by functionally equivalent processes, natural selection acting on the relationships within and between evolutionary entities can result in organisations that produce complex system-level behaviours in evolutionary systems and modify the adaptive capabilities of natural selection over time. We review the evidence supporting the functional equivalences between the domains of learning and of evolution, and discuss the potential for this to resolve conceptual problems in our understanding of the evolution of developmental, ecological and reproductive organisations and, in particular, the major evolutionary transitions.     

Estimating abdominal adipose tissue with DXA and anthropometry

Objective: To identify an anatomically defined region of interest (ROI) from DXA assessment of body composition that when combined with anthropometry can be used to accurately predict intra‐abdominal adipose tissue (IAAT) in overweight/obese individuals. Research Methods and Procedures: Forty‐one postmenopausal women (age, 49 to 66 years; BMI, 26 to 37 kg/m²) underwent anthropometric and body composition assessments. ROI were defined as quadrilateral boxes extending 5 or 10 cm above the iliac crest and laterally to the edges of the abdominal soft tissue. A single‐slice computed tomography (CT) scan was measured at the L3 to L4 intervertebral space, and abdominal skinfolds were taken. Results: Forward step‐wise regression revealed the best predictor model of IAAT area measured by CT (r² = 0.68, standard error of estimate = 17%) to be: IAAT area (centimeters squared) = 51.844 + DXA 10‐cm ROI (grams) (0.031) + abdominal skinfold (millimeters) (1.342). Interobserver reliability for fat mass (r = 0.994; coefficient of variation, 2.60%) and lean mass (r = 0.986, coefficient of variation, 2.67%) in the DXA 10‐cm ROI was excellent. Discussion: This study has identified a DXA ROI that can be reliably measured using prominent anatomical landmarks, in this case, the iliac crest. Using this ROI, combined with an abdominal skinfold measurement, we have derived an equation to predict IAAT in overweight/obese postmenopausal women. This approach offers a simpler, safer, and more cost‐effective method than CT for assessing the efficacy of lifestyle interventions aimed at reducing IAAT. However, this warrants further investigation and validation with an independent cohort.     

The channel-forming protein proaerolysin remains a dimer at low concentrations in solution

Proaerolysin, the proform of the channel-forming protein aerolysin, is secreted as a dimer by Aeromonas sp. The protein also exists as a dimer in the crystal, as well as in solution, at least at concentrations in the region of 500 microg/ml. Recently it has been argued that proaerolysin becomes monomeric at concentrations below 100 microg/ml and that only the monomeric form of the protoxin can bind to cell surface receptors (Fivaz, M., Velluz, M.-C., and van der Goot, F. G. (1999) J. Biol. Chem. 274, 37705-37708). Here we show, using non-denaturing polyacrylamide electrophoresis, chemical cross-linking, and analytical ultracentrifugation, that proaerolysin remains dimeric at the lowest concentrations of the protein that we measured (less than 5 microg/ml) and that the dimeric protoxin is quite capable of receptor binding.     

VE-cadherin: adhesion at arm's length

VE-cadherin was first identified in the early 1990s and quickly emerged as an important endothelial cell adhesion molecule. The past decade of research has revealed key roles for VE-cadherin in vascular permeability and in the morphogenic events associated with vascular remodeling. The details of how VE-cadherin functions in adhesion became apparent with structure-function analysis of the cadherin extracellular domain and with the identification of the catenins, a series of cytoplasmic proteins that bind to the cadherin tail and mediate interactions between cadherins and the cytoskeleton. Whereas early work focused on the armadillo family proteins -catenin and plakoglobin, more recent investigations have identified p120-catenin (p120^ctn) and a related group of armadillo family members as key binding partners for the cadherin tail. Furthermore, a series of new studies indicate a key role for p120^ctn in regulating cadherin membrane trafficking in mammalian cells. These recent studies place p120^ctn at the hub of a cadherin-catenin regulatory mechanism that controls cadherin plasma membrane levels in cells of both epithelial and endothelial origin. endothelial cell; cytoskeleton; -catenin; p120^ctn; cell adhesion; vascular endothelial cadherin     

Isolation of a putative progenitor subpopulation of alveolar epithelial type 2 cells

Alveolar epithelial type 2 cells (AEC2) isolated from hyperoxia-treated animals exhibit increases in both proliferation and DNA damage in response to culture. AEC2 express the zonula adherens proteins E-cadherin, -, - and -catenin, desmoglein, and pp120, as demonstrated by Western blotting. Immunohistochemical analysis of cultured AEC2 showed expression of E-cadherin on cytoplasmic membranes varying from strongly to weakly staining. When cultured AEC2 placed in suspension were labeled with fluorescent-tagged antibodies to E-cadherin, cells could be sorted into at least two subpopulations, either dim or brightly staining for this marker. With the use of antibody to E-cadherin bound to magnetic beads, cells were physically separated into E-cadherin-positive and -negative subpopulations, which were then analyzed for differences in proliferation and DNA damage. The E-cadherin-positive subpopulation contained the majority of damaged cells, was quiescent, and expressed low levels of telomerase activity, whereas the E-cadherin-negative subpopulation was undamaged, proliferative, and expressed high levels of telomerase activity.     

Food hoarding is increased by food deprivation and decreased by leptin treatment in Syrian hamsters

Compensatory increases in food intake are commonly observed after a period of food deprivation in many species, including laboratory rats and mice. Thus it is interesting that Syrian hamsters fail to increase food intake after a period of food deprivation, despite a fall in plasma leptin concentrations similar to those seen in food-deprived rats and mice. In previous laboratory studies, food-deprived Syrian hamsters increased the amount of food hoarded. We hypothesized that leptin treatment during food deprivation would attenuate food-deprivation-induced increases in hoarding. Baseline levels of hoarding were bimodally distributed, with no hamsters showing intermediate levels of hoarding. Both high (HH) and low hoarding (LH) hamsters were included in each experimental group. Fifty-six male hamsters were either food deprived or given ad libitum access to food for 48 h. One-half of each group received intraperitoneal injections of leptin (4 mg/kg) or vehicle every 12 h during the food-deprivation period. Within the HH group, the hoarding score increased significantly in food-deprived but not fed hamsters (P < 0.05). Leptin treatment significantly decreased hoarding in the food-deprived HH hamsters (P < 0.05). The LH hamsters did not increase hoarding regardless of whether they were food deprived or had ad libitum access to food. These results are consistent with the idea that HH hamsters respond to energetic challenges at least in part by changing their hoarding behavior and that leptin might be one factor that mediates this response.