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, and this information, together with gas exchange measurements, was used to model and compare their respective operational characteristics. Based on evidence from SEM 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 "sea-sawing" of osmotic and turgor pressure between guard and subsidiary cells during stomatal opening or closure. Such properties might underlie the success of grasses.


INTRODUCTION
Although the morphological diversity of stomata is widely documented (Haberlandt, 1884;Meidner and Mansfield, 1968;Allaway and Milthorpe, 1976;Ziegler, 1987;Willmer and Fricker, 1996), little is known of how this translates into functional diversity, and what the environmental context of this might be. Throughout the 400 Ma history of vascular plants on land, long-term decline in atmospheric CO 2 concentration and shifts in prevailing moisture patterns have placed selective pressures on stomata to increase epidermal conductance to CO 2 diffusion and also to increase transpiration efficiency (CO 2 fixed per unit water transpired). This posed two separate problems, upon which the combination of mutation and time might have worked to give rise to the current diversity of stomatal form and function. The first centred on the simple geometric practicalities of fitting enough functional stomatal units per unit leaf surface area to meet the desired CO 2 flux as atmospheric CO 2 concentration changed, or to service an increase in photosynthetic capacity. The second centred on the performance characteristics of any new stomatal structure or configuration, in relation to transpiration efficiency. Here, by examining the mechanical and performance characteristics of stomata in four different species, we explore the nature of these two problems and how they might have been resolved.
The mechanical characteristics of stomata are central to their performance in gas exchange regulation, but relatively little is known about these properties, particularly how they vary across different stomatal forms. The simple quantitative relationship between guard cell turgor (P g ), epidermal (or subsidiary) cell turgor (P e ) and stomatal aperture (a), which defines the operational potential of all stomata, is known for only a few species, and most of these have structurally similar stomata (Meidner and Bannister, 1979;Franks et al., 1998;Franks et al., 2001). No such data are available for the distinctive "dumbbell" shaped stomata of grasses, for example, or for the more mechanically isolated stomata that are common in many pteridophytes. Without this information on the mechanical diversity of stomata, the power to predict the behaviour of stomata in diverse types of vegetation, or to understand key stages in the evolution of plant gas exchange characteristics, remains limited. Our first objective was to address this shortfall by measuring and analysing the P g -P e -a relationship in four species with distinctively different stomatal morphologies: (i) the lycopod Huperzia prolifera; (ii) the fern Nephrolepis exaltata; (iii) the herbaceous angiosperm Tradescantia virginiana; (iv) the grass Triticum aestivum.
Stomata of the four species chosen for the study cover a broad morphological and evolutionary spectrum (Figure 1). H. prolifera is a living representative of one of the most ancient vascular plant taxa (Lycopodiaceae), with fossilised remains of its close relatives (having the same stomatal morphology) dating back to the lower Devonian (Stubblefield and Banks, 1978;Sun et al., 2005). Its stomata are anomocytic (lacking subsidiary cells), with large and comparatively fat guard cells, which undergo minimal swelling or lateral movement during stomatal opening. Based on these characteristics, it is regarded as archetypal (Ziegler, 1987), perhaps closely resembling the first stomata.
N. exaltata, like H. prolifera, is anomocytic, but fern stomata are structurally and functionally more advanced than those of Lycopods. Although the pattern of guard cell deformation during stomatal opening is similar to that of Lycopods, fern stomata of comparable guard cell dimensions achieve wider apertures, which assists with higher rates of gas exchange (N. exaltata exhibits photosynthetic rates more than three times that of H. prolifera under similar conditions; Franks, 2006). T. virginiana and T. aestivum are distinctive in that they both have a subsidiary cell running parallel to each guard cell.
Their guard cells exhibit substantial lateral movement and physical interaction with the subsidiary cells during stomatal opening, resulting in wide stomatal pores that facilitate high rates of photosynthetic gas exchange. While stomata of the other species are variants on the common "kidney" form, those of T. aestivum exhibit the characteristic dumb-bell shaped guard cells of grasses (Graminae). The functional significance of this uniquely different guard cell form remains unknown, although the capacity for rapid stomatal opening and closure in grasses is thought to be somehow linked to their unusual guard cell geometry (Johnsson et al., 1976;Hetherington and Woodward, 2003). It has further been proposed that superior dynamic performance of grass stomata could have facilitated the relatively recent spread and diversification of grasses during a period of global aridification 35-40 Ma ago (Hetherington and Woodward, 2003).
The second objective of the study was to investigate the role of guard cell morphology and mechanics in stomatal function, particularly in relation to its potential influence on the speed of stomatal opening and closure. Stomatal response time is important because it determines the extent to which leaf gas exchange can be optimised under fluctuating environmental conditions. Fast and appropriately damped response to changes in the environmental drivers of photosynthesis or transpiration rate can lead to greater transpiration efficiency. Grasses have long been known for their capacity for rapid stomatal response (Raschke and Fellows, 1971;Brogardh and Johnsson, 1975;Johnsson et al., 1976;Karlsson and Assmann, 1990;Grantz and Assmann, 1991;Assmann et al., 1992) but the underlying mechanism for this has remained a mystery, due partly to the absence of data on the mechanical interactions between guard and subsidiary cells in grasses. Our approach to unravelling this centrally important aspect of stomatal function was to revisit the findings of several classical studies on guard cell solute transport and, with new information on guard cell mechanical and geometric properties, formulate an osmo-mechanical model of stomatal movement that could explain the superior performance of grass stomata under dynamic environmental conditions. To illustrate these characteristics, the stomatal properties of the grass T. aestivum were compared against those of the three non-grass species.

RESULTS
The mechanical diversity of the four stomatal types is illustrated dramatically in the scanning electron micrographs of cryo-sectioned leaf material in Figures 2-5. Here the signature guard cell swelling and displacement characteristics of the different stomatal types are evident. In particular, H. prolifera and N. exaltata show little mechanical interaction between guard cells and epidermal cells as the guard cells swell to create the stomatal pore. H. prolifera displays the "Psilotum type" guard cell deformation (Ziegler, 1987), whereby the guard cell lower (leaf inner) wall expands into the sub-stomatal cavity during stomatal opening. N. exaltata shows the archetypal "Adiantum-type" guard cell deformation, whereby the guard cell upper and lower (leaf inner and outer) walls buckle outwards as the guard cells swell into a more rounded cross-section to create the stomatal pore. By contrast, both T. virginiana and T. aestivum guard cells undergo substantial lateral displacement into their adjacent subsidiary cells during stomatal opening, to the extent that the subsidiary cells are almost squashed in order to accommodate the open stoma. Of great significance is the fact that, since these leaves were sampled at very high humidity, we know that rates of transpirational water loss were minimal, and therefore the water potential of all cells in the image was close to zero (the plants being also well-watered). This means that turgor in all cells was maximal for the prevailing osmotic conditions. It is shown below that for the stomata in T.
virginiana and T. aestivum to have reached the apertures indicated, turgor in the subsidiary cells had to be significantly reduced, as full or even partial subsidiary cell turgor simply would not have allowed such wide apertures. Later, in the Discussion, we propose how this might be achieved.
The relationship between guard cell pressure (P g ) and stomatal aperture (as pore width, a; µm) at maximum and zero epidermal turgor is summarised for each species in Figure 6. A strong linear relationship was found between stomatal pore width and stomatal pore area in each species (data not shown), as was reported for T. virginiana by Franks and Farquhar (2001). Consistent with the evidence from the cryo-sections of open stomata (Figs 2-5), the aperture corresponding to any given P g was virtually unaffected by epidermal turgor (P e ) in H. prolifera and N. exaltata, but substantially influenced by P e in T. virginiana and T. aestivum. The small offset observed in H. prolifera ( Fig 6A) could be due to a small, generalised expansion of the epidermal cells at high turgor. At full epidermal turgor, T. virginiana stomata could not attain an aperture above about 7 µm, compared to its maximum of about 20 µm when P e was zero. Similarly, T. aestivum stomatal apertures were on average not greater than 2.5 µm at full epidermal turgor, compared to about 8 µm at zero epidermal turgor. This massive mechanical counteraction of stomatal opening by epidermal turgor in T. virginiana and T. aestivum is a negative side effect arising from the need for greater lateral displacement of guard cells to create a larger stomatal pore. Known technically as the "mechanical advantage" of epidermal cells over guard cells (DeMichelle and Sharpe, 1973;Cooke, 1976;Wu et al., 1985;Franks et al., 1998), this epidermal impediment to stomatal opening would potentially eliminate much of the gain from a more mobile guard cell pair. As indicated in Figure 6, the maximum apertures obtained by T. virginiana and T. aestivum, as verified in Figures 2-5, cannot be reached under conditions of high epidermal turgor (as was the case for the leaves in Figures 2-5) simply by maximising P g . Below we propose a mechanism for overcoming the mechanical advantage, and discuss some of the implications of such a mechanism in stomatal control.

How to meet the need for higher stomatal conductance.
There are likely to have been two main selective pressures for increasing maximum operating leaf diffusive conductance (g s ) in vascular plants. The first being the maintenance of a given rate of photosynthetic productivity as atmospheric CO 2 concentrations declined over much of the Paleozoic era (Crowley and Berner, 2001), and the second being competition for higher rates of photosynthetic gas exchange at a given atmospheric CO 2 concentration, which is facilitated by higher leaf diffusive conductance.
There are several strategies through which leaf diffusive conductance can be increased, all aimed ultimately at increasing the sum of stomatal pore area/depth per unit leaf area (diffusive conductance of a given stomatal pore being roughly proportional to the ratio of pore area/depth; Brown and Escombe, 1900). The simplest and possibly the most accessible option is to increase the number of stomata per unit leaf area, i.e. stomatal density (SD). Within limitations this seems to be a widely utilised strategy. There are numerous examples of plasticity in SD within species, with changes readily induced through exposure of developing leaves to changed atmospheric CO 2 concentrations (Woodward et al., 2002;Hetherington andWoodward, 2003), or drought (Cutter et al., 1977;Quarrie and Jones, 1977), or the drought stress hormone ABA (Bradford et al., 1983;Franks and Farquhar, 2001). However, in the case of increasing SD to obtain higher operating g s , there are practical limitations relating to space (maximum number of stomata of a given dimension per unit leaf area) and guard cell biochemistry (if the entire epidermis is guard cells, where will the guard cells import potassium from?). The spatial limitations on g s inherent to the four species in this study can be inferred from the illustrations in Figure 7, which show the relationship between projected maximum pore area (a max ) and area of the whole stomatal complex (pore plus guard cells; a sc ) for each species, at maximum stomatal aperture. Clearly, on this basis, T. aestivum has the greater potential leaf diffusive conductance, being able to pack in greater pore area per unit leaf area. This ratio of a max /a sc is quantified in Figure 8B, again showing the superiority of the T. aestivum guard cell design, with the difference in a max /a sc being more than 20-fold between H. prolifera and T. aestivum. The values of a max /a sc for T.
virginiana and T. aestivum would decrease slightly if subsidiary cells were included as essential components of the stomatal complex, but the trend in Figure 8B would remain the same.
Another potential strategy for increasing g s is, rather than only multiplying the number of stomata, to multiply number of stomata and reduce stomatal size. While the genetically-determined restrictions on this strategy might be greater than on only multiplying number of stomata per unit leaf area, the benefits are also greater. With a reduction in overall stomatal size comes a reduction in pore depth due to the smaller cross-sectional area of the guard cells, so with smaller stomata it is possible to achieve a greater leaf diffusive conductance per unit area occupied by stomata. Further analysis of this strategy is outside the scope of this paper, but many high-g s species do exhibit high densities of very small stomata (Willmer and Fricker, 1996).
The problem with the mechanical advantage. absence of an active compensating mechanism in the stomatal control system, the mechanical advantage dictates that stomatal aperture will open wider as evaporation potential increases, due to the increase in transpiration rate lowering epidermal turgor and facilitating the passive widening of the stomatal pores. Using the hydromechanical stomatal model described in Franks (2004), this effect is simulated for a stomatal opening sequence in Figure 9A, for a plant with stomatal characteristics similar to T. virginiana, and assuming no active compensation to counteract the increase in g s with increasing evaporative demand. Such a mode of operation would be highly destructive if it were to actually occur. However, it is almost universally observed that plants operate with lower (not higher) g s under higher evaporative demand (Lange et al., 1971;Schulze et al., 1972;Hall et al., 1976;Grantz, 1990;Franks and Farquhar, 1999). This is illustrated in Figure   9B and 9C for measured opening sequences on leaves of T. virginiana and T. aestivum, respectively, under two different values of leaf-to-air vapour pressure difference (D). In both cases the final steady state conductance to water vapour (g sw ) was substantially lower at higher D. Note also that there appears to be little enhancement of the initial rate of increase in g sw at higher D, compared to low D, suggesting a highly active compensating mechanism.

Overcoming the mechanical advantage
Based on the pressure probe results in Figure 6, it seems virtually impossible for T.
virginiana and T. aestivum stomata to reach the apertures observed in Figures 4 and 5 under humid conditions, yet clearly they did. The simplest explanation, suggested by the degree of deformation of T. aestivum subsidiary cells ( Figure 5) is that subsidiary cell turgor is much lower during maximum stomatal aperture, such as occurs under high humidity. The only way that this can be achieved at high cellular water potentials is if the osmotic pressure of subsidiary cells declines substantially, thus reducing the effect of the mechanical advantage, and allowing maximum lateral displacement of guard cells and maximum stomatal apertures. This effect is simulated in Figure 10, using the same hydromechanical feedback model as for the simulations in Figure 9A, but allowing Π e (effectively the osmotic pressure of subsidiary cells) to decline in association with the increase in guard cell osmotic pressure (Π g ; see Methods). This sea-sawing of relative osmotic and turgor pressures between subsidiary cells and guard cells, illustrated schematically in Figure 11, overcomes the problem of the mechanical advantage, and would allow T. aestivum to attain full apertures under high humidity, where it otherwise could not. Transfer of solutes (namely K + ) to guard cells via subsidiary and epidermal cells has long been recognised (Fujino, 1967;Fischer, 1968;Humble and Hsiao, 1969;Sawhney and Zelitch, 1969;Humble and Raschke, 1971;Pallaghy, 1971;Penny and Bowling, 1974;Dayanandan and Kaufman, 1975;Macrobbie and Lettau, 1980;Outlaw, 1983) but here we make the case for mandatory and opposite changes in osmotic and turgor pressure of guard and subsidiary cells where epidermal or subsidiary cells have a large mechanical advantage over guard cells. This requirement would diminish in species with diminished mechanical advantage (e.g. H. prolifera and N. exaltata in this study). A desirable side effect arising from this mechanism is that the rate of stomatal opening is increased (compare Figure 10A solid line with dashed line), as is the rate of closure in a reversal of the same process. Thus, the mechanical advantage, which arose as an unavoidable consequence of increased guard cell lateral movement to create wider stomatal pores, may have been harnessed in the manner described above to ultimately facilitate, rather than impede the operation of stomata. This facilitation enabled higher steady-state stomatal conductances to be achieved, and increased the rate at which stomatal aperture can change, thereby supporting increased rates of photosynthetic gas exchange and increased transpiration efficiency. Of course we cannot be sure which of increased lateral movement and shuttling of osmotica came first, and evolution may well have occurred in parallel.
Potassium shuttling between guard and subsidiary cells in relation to rapid stomatal opening was first discussed by Raschke and Fellows (1971)

in their study on
Zea mays, and later by Brogardh and Johnsson (1975). However, these authors considered only the speed of solute transfer and the potentially rapid rate of change of guard cell osmotic pressure due to the large reservoir of potassium in subsidiary cells immediately adjacent to guard cells of grasses. The requirement for, and advantages of, a substantial reduction in both the osmotic and turgor pressure of subsidiary cells during opening of graminoid stomata was not considered in detail at that time. Later work, which focussed on rapid responses in grass stomata exposed to a blue light stimulus ( Johnsson et al., 1976;Karlsson and Assmann, 1990;Grantz and Assmann, 1991;Assmann et al., 1992) also did not consider, from a quantitative perspective, the role of the mechanical advantage of subsidiary cells. Our measurements of the P g -P e -a relationship in the graminoid stomatal complex of T. aestivum and the integration of this information into a mechanistic model of stomatal movement has revealed how the combination of osmotic shuttling, high epidermal mechanical advantage and unique guard cell geometry in graminoid stomata allows them to open or close at a substantially faster rate than perhaps any other stomatal type.

Conclusions and further work
The results demonstrate that the morphological diversity of stomata translates into considerable mechanical and, ultimately, functional diversity. This study examined only the stomata of four species and, although it spanned a considerably broad morphological and evolutionary spectrum, there are many more stomatal forms yet to be examined in this way, and the picture is far from complete. By the same measure, we do not wish to generalise too extensively about the function of grass somata from our examination of just one species, but the results do provide a compelling case for the role of stomatal mechanics in the distinctive capabilities of this special group of plants. The findings highlight the importance of integrating mechanical and quantitative physical information about guard and adjacent cells in models of stomatal function in order to better describe and predict gas exchange regulation in diverse vegetation types.
structural modifications made here were 1) for the simulation in Figure 9A, Πg was held constant to demonstrate the effect of the mechanical advantage in the absence of osmotic compensation, 2) for the simulation in Figure 11, Π e was either fixed or made a function of Π g , such that Π e = a(b-Π g )/b, i.e. as Π g approaches b, Π e approaches zero, and 3) to generate time series for stomatal opening, the model was solved in discrete time steps for Π g increasing from zero according to ( ) where Π g0 is guard cell osmotic pressure at zero aperture (here 1.4 MPa), Π g(var) is the difference between Π g0 and Π g(max) (here 3.0 MPa), t is time from zero, and T is the time constant (here 600 s).      the massive impediment to stomatal opening (mechanical advantage) by epidermal turgor in T. virginiana and T. aestivum, compared to little or no effect in H. prolifera and N.
exaltata.   Note also that not only does the mechanism allow g ws to reach its full potential, but the rate of opening is also greatly increased. Figure 11. Schematic of the proposed "osmotic sea-saw" (combined opposite changes in both osmotic and turgor pressure between guard and subsidiary cells) in T. aestivum and other grass-type stomata. The mechanism reduces the large mechanical advantage that would otherwise prevent stomatal opening under high humidity, even if maximum turgor were generated in guard cells. A corollary is that the mechanism also greatly accelerates the rate of stomatal opening, helping to explain why T. aestivum has rates of stomatal opening more than an order of magnitude faster than any of the other species ( Figure 12).