Modeling Stomatal Conductance

Abstract

Robust models of stomatal conductance are greatly needed to predict plant-atmosphere interactions in a changing climate and to integrate new knowledge in physiology and ecological theory. Recent years have brought major advances in the experimental and theoretical understanding underpinning both process-based and optimality-based approaches to modeling stomatal function. I review these advances, highlight areas in need of more research, and argue that these modeling approaches are poised to supersede the long-dominant empirical approach. A reliable and general model for leaf stomatal conductance (g s) has long been one of the holy grails of plant physiology. By controlling the exchange of water and carbon dioxide between plants and the atmosphere, stomata play a central role in the regulation of leaf and plant water status and transport, photosynthesis, drought sensitivity and tolerance, competition for soil resources, and even landscape and global hydrology (Hetherington and Woodward, 2003). An integrative formal theory—a mathematical model—that links stomatal function to plant traits and environmental variables would thus have incalculable value, both for making forward predictions and for drawing inferences about the physiology and ecology of observed stomatal behavior. My aim in this article is to summarize recent progress toward such models of stomatal conductance. Stomatal conductance has historically been predicted almost exclusively using empirical or phenomenological models, such as the widely used Jarvis and Ball-Berry families of models (Jarvis, 1976; Ball et al., 1987). Such models are perfectly adequate for forward prediction in situations where their parameters can be estimated with confidence, and indeed, these models continue to inform gas exchange projections across the modeling community (e.g. Oleson et al., 2008). However, the phenomenology of stomatal behavior in seed plants is by now very well established, so little further progress is likely in the area of empirical modeling, nor is it likely worth pursuing given that empirical models cannot provide insight about the underlying controls on gas exchange, but can only summarize and project what we already know about stomata. (Some aspects of the phenomenology of stomatal behavior in nonseed plants remain unresolved, such as the responses to CO2 and abscisic acid [e.g. Brodribb and McAdam, 2011; Chater et al., 2011; Ruszala et al., 2011; Brodribb and McAdam, 2017]; empirical models have yet to be thoroughly validated for these taxa, so progress remains possible on that front.) This article will therefore focus on process-based (“mechanistic”) and goal-directed (“optimality”) approaches to predicting and interpreting stomatal function. In what follows, I will very briefly review the background to each of these approaches, describe important advances over the last decade or so, and then suggest directions for continuing work. I prefer to avoid reproducing equations and instead refer readers to articles cited herein for mathematical details. Most models of stomata based on physiological mechanisms simulate two key variables: guard cell volume, or turgor pressure, and guard cell osmotic content, or osmotic pressure. The rationale for this approach is that stomatal aperture increases when guard cells expand in volume (Franks et al., 1995, 1998, 2001) and that shifts in guard cell volume often result from osmotic water movements driven by active regulation of guard cell ion transport and carbon metabolism (note that guard cell water movements can also occur passively as a result of changes in local water potential). Guard cell volume, or turgor, is typically predicted from mass balance; that is, by assuming that water potential is dictated by a steady-state balance between water supply from elsewhere in the leaf or plant and evaporative water loss to the atmosphere. Water balance can also predict the effects of turgor in adjacent epidermal or subsidiary cells, whose “backpressure” opposes stomatal opening (Meidner and Edwards, 1975; Franks et al., 1995, 1998; Vialet-Chabrand et al., 2017). Several improvements have emerged in recent years in this basic conceptual framework for process-based modeling of g s. These advances primarily involve three areas: improved understanding of stomatal hydromechanical diversity and its role in responses to water stress; growing awareness of the multiplicity of mechanisms underlying stomatal responses to both light and CO2, including the role of mesophyll photosynthesis; and advances in kinetics-based modeling of guard cell osmotic pressure and volume. I discuss advances in these areas below. Some interesting features of stomatal behavior arise from the hydraulic and mechanical context in which guard cells function in the intact leaf. For example, in seed plants, the immediate passive effect of a decline in water potential in the vicinity of guard cells is to open stomatal pores (Darwin, 1898; Iwanoff, 1928; Powles et al., 2006; Buckley et al., 2011). This may seem counterintuitive, given that reduced water potential should cause guard cells to lose water and thus decrease in volume. However, the surrounding epidermal cells also lose water, which reduces their backpressure on the guard cells and produces a net opening movement known as the initial “wrong-way” response (WWR; Shackel and Brinckmann, 1985; Franks et al., 1998; Mott and Franks, 2001). This occurs whether leaf water status is perturbed by changing water supply (soil water potential, ψ soil, or plant hydraulic conductance, K plant) or evaporative demand (leaf to air water vapor mole fraction difference, Ɗw). However, the WWR is eventually followed by a “right-way” response (RWR) in which apertures decline below their initial values (Rufelt, 1963; Raschke, 1970; Comstock and Mencuccini, 1998; Buckley et al., 2011). The RWR is apparently caused by an actively mediated adjustment of guard cell osmotic pressure that is slower than, and subsequent to, the initial and more rapid change in epidermal and guard cell volumes (Darwin, 1898; Grantz and Zeiger, 1986; Grantz, 1990; Buckley, 2005). Several models capture these basic phenomena (e.g. Cowan, 1972; Delwiche and Cooke, 1977; Haefner et al., 1997; Buckley et al., 2003; Franks, 2004). In the last decade, several important refinements to this picture of stomatal hydromechanics have emerged—refinements that influence stomatal function and have implications for how to model stomata on a mechanistic basis. Painstaking work using cell pressure probes to construct pressure-aperture relationships for guard cells and subsidiary cells (Meidner and Edwards, 1975; Zimmermann and Steudle, 1975; Franks et al., 1995, 1998) has shown that angiosperm stomata often cannot achieve their maximum apertures unless the adjacent subsidiary cells experience a marked drop in turgor pressure at the same time that the guard cells increase their turgor pressures (Franks and Farquhar, 2007). This is because the effect of epidermal backpressure on stomatal aperture is unusually strong in angiosperms, and particularly in grasses. An important consequence is that stomatal aperture can change very quickly in grasses, which Franks and Farquhar (2007) noted may enable them to respond more quickly to environmental cues, thus possibly helping to explain the ecological success and rapid diversification of grasses. The mechanical diversity of stomata spans in both directions: whereas the epidermal effect is especially strong in grasses, Franks and Farquhar (2007) found it to be very weak or even negligible in ferns. This may have significance for understanding the evolution of stomatal responses to water status. Brodribb and McAdam (2011) found that stomata in ferns and other seedless vascular plants (SVPs) lack a WWR to humidity, which is consistent with a weak epidermal effect, but more importantly means that these species may not require an actively mediated response to overcome the epidermal effect and produce a RWR—the passive effect of water potential on guard cell turgor may be sufficient. The same authors also found that SVPs are largely insensitive to exogenous abscisic acid (ABA), giving rise to the hypothesis that seed plants evolved guard cell ABA sensitivity as a mechanism to drive the osmotic shifts needed to overcome the greater opposing force of their epidermal cells. However, other evidence shows that the genes required for ABA-mediated stomatal closure are present in all major lineages of extant land plants (Lind et al., 2015) and that some mosses (Chater et al., 2011) and lycophytes (Ruszala et al., 2011) do in fact respond to exogenous ABA. A possible resolution of these viewpoints is that it was not the existence but rather the magnitude and importance of active responses that increased over evolutionary time. A long-standing hypothesis for stomatal closure in drying soil is the notion that ABA is generated in droughted roots and transported through the transpiration stream to stomata, where it induces stomatal closure (Davies and Zhang, 1991; Tardieu and Simonneau, 1998). This hypothesis was challenged by data showing normal drought responses in wild-type shoots grafted onto ABA-deficient rootstock (Holbrook et al., 2002; Christmann et al., 2005). Although the debate over the root-ABA hypothesis is not resolved, recent years have brought some new insights. For example, Rodriguez-Dominguez et al. (2016) found that a stomatal response to water status originating entirely within the leaf, initiated by changes in leaf turgor, could explain most or all of the observed soil drought response in three woody species (Fig. 1C), with at most a minor role for leaf-exogenous signals. A great deal of evidence suggests that leaf-endogenous ABA production may help to explain stomatal responses to both atmospheric and soil drought (Wright and Hiron, 1969; Loveys and Kriedemann, 1973; Xie et al., 2006; Bauer et al., 2013). More McAdam et al. (2016) that stomatal closure in air in angiosperms, but not in is by a in ABA production within caused by increased of genes that key in the ABA (Fig. These active responses consistent with the typically observed to the RWR in recent evidence suggests leaf ABA may also leaf hydraulic conductance, which could changes in leaf turgor by stomata et al., 2013). Stomatal responses to leaf turgor integrate effects of several other stomatal responses arise from the effect of leaf water potential, which the of environmental and plant Recent work has the of modeling these responses on a mechanistic by showing that the effect of leaf water potential on stomatal conductance is mediated by of ABA in response to reduced leaf turgor McAdam et al., and stomatal responses to soil drought can be almost entirely by effects mediated by leaf turgor et al., These can be the hydromechanical framework For example, in the influence of epidermal turgor on stomatal aperture would in the epidermal mechanical in the model of Buckley et al. which is a model with a pressure-aperture or more in pressure-aperture in the model given by Franks which in the of an actively mediated response of guard cell osmotic pressure to leaf water status would in models as in the magnitude of the sensitivity of g to leaf turgor the or evaporative demand the Franks Tardieu et al. have shown how the of leaf ABA from production in roots and in a water transport can be and this approach could be to for leaf-endogenous ABA and with approaches that for stomatal More data are needed about the of the leaf-endogenous ABA response a general model can be have been to predict stomatal responses to light and CO2 on a mechanistic in intact because the mechanisms remain Farquhar and that the effects of and CO2 on stomatal conductance very to their effects on mesophyll cell predicted by a model et al., and this model as an empirical of g s. a as a more mechanistic that the light and CO2 responses are actively mediated may on the of and from the of to CO2 as a of this for modeling Buckley et al. used Farquhar and model to predict guard cell osmotic in their model of stomatal conductance. The predictions from these models are consistent with experimental evidence that mesophyll is in in the stomatal responses to light and For example, both responses are or by and Zeiger, and et al., 2002; et al., More recent work has shown that these responses are weak or in epidermal but are when are on actively mesophyll et al., McAdam and and that the may be mediated by a vapor ion that the of the guard cell et al., that the these responses is to the of of the transport which would these with other data showing that the responses are of the or CO2 or transport 1998; et al., et al., 2008). The of mesophyll is for normal stomatal responses to light and CO2 in and the from the mesophyll may be a A to of stomatal aperture to changes in and CO2 observed in intact epidermal and epidermal onto mesophyll of stomatal aperture in epidermal to of a in an the with and a between the and epidermal to transport of the from Mott et al. and Mott et al. evidence shows that stomata can also respond to light and CO2 of mesophyll example, CO2 responses in and et al., and the existence of a and response to light was years et al., 1986; et al., and 2017). et al. (2016) found that the light response is at driven by of that to stomatal This is consistent with work on guard cells and and epidermal and Zeiger, that ion cannot explain stomatal behavior and that metabolism is also and 2017). recent work suggests at one mechanism that could produce a response of g to leaf hydraulic conductance increases in response to (e.g. et al., 2002; et al., et al., et al., which may water to the vicinity of guard cells, stomatal The mechanism of this response is but it may involve of in or other leaf cells et al., the of vapor transport toward the from mesophyll by light et al., et al., and Mott (2011) further that the stomatal response to could also be by vapor transport to within the leaf, the is the of within the modeling suggests the is typically the of the leaf evaporative et al., et al., these the existence of mechanisms underlying the stomatal responses to light and models of g in intact have to capture these responses on a mechanistic basis. However, the framework (e.g. the and Franks can such mechanisms as to be example, responses mediated by guard cell ion transport or water transport conductance would be by the active regulation of guard cell osmotic pressure or plant hydraulic conductance, a result of the mechanistic of guard cell ion transport, models of stomatal conductance typically predict guard cell osmotic pressure from about mechanisms at a of as However, guard cell ion transport are now well to prediction of of osmotic pressure from of the of ion transport and and 2017). et al. a of guard cell water and driven by knowledge of the of and and other and et al. that this model observed of guard cell its recent this modeling framework has already generated new of guard cell For example, et al. used the model to explain how of the stomatal to of ion stomatal effects of on et al. (2016) that been to play a role in stomatal fact from the mechanisms that the an effect rather a cause of the underlying This modeling framework can also be used to predict how of the of transport and stomatal function et al., which is for both and progress toward a model of stomatal conductance advances in several including of the response of g to leaf turgor mediated by leaf-endogenous ABA including the of both ABA and on the mechanism and role of changes in leaf hydraulic conductance that influence g of the of the pressure within the leaf, which in which of hydraulic conductance should be used to predict the turgor example, the in the then the hydraulic conductance would be the in the because water potential greatly between these Buckley et al., the mechanistic by Mott et al. and the light and CO2 and about how vapor transport within effects of light and on and et al., with process-based models of stomatal conductance, water transport, and to the of guard cell transport in the of the intact leaf. models are often by the modeling community because parameters that can be very to even in a key is to process-based models with and estimated parameters and links to more have shown how this be in by the model for et al., et al., Rodriguez-Dominguez et al., An important is to continue these and other process-based models to new experimental knowledge and to and them more across species and An approach to modeling stomata is based on the hypothesis that evolution has likely for mechanisms of stomatal regulation that to the between carbon and water The in this area has been the work of Farquhar and and Farquhar that carbon is for a given of water loss over some time (e.g. one g so that the carbon of water where A and are net CO2 and transpiration remains over time and to an the of This most stomatal responses to environmental and at with work prediction of a of to CO2 et al., and the of empirical models for g based on that et al., the of this on understanding of the and physiology of gas exchange cannot be with process-based models, the has to for two it not explain how to or the in to environmental or and is required to predictions from the unless one negligible mesophyll and et al., to the is that it a response of stomata to increased atmospheric CO2 when is by the of or which most data (e.g. 1998). The decade has a of and progress in to this of it at the CO2 response and the to variables or it entirely by the in a In this I will summarize recent and work in this and suggest for continuing when atmospheric CO2 increases The this response CO2 or but the an opening response light and This has been by two recent of et al. noted that is in plants in a and that an of the the CO2 response one a that in to a the However, Buckley and and Buckley et al. (2016) that the shifts in CO2 from of the plant at time which would also cause shifts in other parameters that are as at the time such as maximum hydraulic conductance and et al. (2011) a resolution to the CO2 response noted that the Ball-Berry of empirical models et al., for most stomatal but a response to then that a of is to the Ball-Berry model and that the between g and A in Ball-Berry is thus to the The stomatal model is a of when is by and shifts to an but has not been that the of to predict the a response in light is important for modeling in a is likely to shifts only in very where can atmospheric CO2 to the air the are more likely to be at the of such so the of a and light may only be for in The a supply of water for transpiration over some time and the of that water with other the of the However, water supply as soil between and as plant so the of A would so that soil water each this would the of carbon to water but is given the of how should increase g should a drought to carbon in soil and also from using water, and et al. that should decline over time plants are evolutionary of the Recent work has these in new new the and ecological of the which may the toward more of for predicting stomatal behavior. For example, et al. (2016) how should and predicted a decline in over time drought and a between stomatal conductance and soil with closure at soil water et al. (2016) a approach that time and the that plants carbon CO2 the carbon caused by leaf water to stomatal in other et al. (2016) not the in but would and of by water that A was an evolutionary competition for water, the soil water potential by an plant is insensitive to changes in that transpiration also a for g that was to an of by et al. both predict stomatal opening in response to increased et al. (2016) their model A with an A which as to the theory. However, the is to A with A in the which approach by a global with to g s. et al. a model very to that of et al. in which both the and and thus the was as the loss of hydraulic to and the function was the of A to its value, A at a CO2 to the stomatal conductance that would cause ψ leaf to the for This is to A A with to g is the fraction of the of K to so it that the carbon of with for example, when K has by of its the are of A However, may be as the hydraulic of potential rather a The by et al. (2016) and et al. has some For example, evidence suggests that the is often across of the of g in species not are to their turgor loss (e.g. et al., et al., and effects of water on at ψ leaf do occur and evidence for such effects is in the such effects are not In where both predict that stomata should open as as However, this with evidence that stomata often water loss even in the of (e.g. et al., 2002; et al., such a when competition is or soil is only to or rapid it is when at time because it to rapid of water that could be used more and therefore more and decrease with in of the important and that are only at time For example, from ψ example, the of of that water more and thus more as to and the of in the by carbon in hydraulic transport A more general for predicting in the for and thus g would a that all of these as well as their for photosynthesis, and of This the to all including water, and and all whether or and et al. to such a and more recent work by et al. et al. and and Buckley, Buckley et al., has A central result is that shifts in the carbon of water are to the carbon of that water, as well as parameters other in Buckley et al., which in suggests that the and of water loss by cannot predict shifts in (Fig. these to in the and would on and thus g even when the carbon of transpiration are that influence the of the carbon of increase in leaf carbon that would result from an increase in water in stomatal conductance and therefore water loss to immediate carbon and from reduced water which However, carbon between and the carbon of prediction of and stomatal conductance, should these as well as the immediate and of in stomatal conductance. is it was a decade that has great potential for predicting stomatal conductance in More work is needed to the from recent of et al. et al. (2016) and et al. (2016) that and whose parameters are The in to and environmental parameters a to of the and years between initial to on a and the more recent of in this et al., et al., Buckley et al., The carbon of water potential in the model is a of where work is and this more we need to and then means of them across the of have been estimated and shown to be consistent with in and have not been is that these are in the using loss to water but these capture only the balance between two of production and the is what the as with the function in these experimental and theoretical work is therefore needed to these and the the to stomatal function over time that major and the the stomatal responses to environmental parameters a predicted by from shifts in g that are driven by changes in plant and it be to predict shifts in the and result from change et al., Buckley et al., would be most and to the to predict the as but as with the this will require work to the underlying for links to now and models with a in physiology and whose parameters and that can be by of these models will not only the of forward but also the and of the mathematical that to relationships traits and environmental across would also provide a more between and and the knowledge at by and a for to inform and and to continuing of these is possible in a by empirical I Farquhar and three for This work was by the the and and the and

Abstract of "Modeling Stomatal Conductance" by Thomas N. Buckley, https://doi.org/10.1104/pp.16.01772, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.