A model of stomatal closure driven by nonlinearities in soil-plant hydraulics

Predicting plant responses to drought is a long-standing research goal. Since stomata regulate gas-exchange between plants and the atmosphere, understanding their response to drought is fundamental. Current predictions of stomatal behavior during drought mainly rely on empirical models. These models may suit well to a specific set of plant traits and environmental growth conditions, but their predictive value is doubtful when atmospheric and soil conditions change. Stomatal optimization offers an alternative framework to predict stomatal regulation in response to drought for varying environmental conditions and plant traits. Models which apply this optimization principle posit that stomata maximize the carbon gain in relation to a penalty caused by water loss, such as xylem cavitation. Optimization models have the advantage of requiring a limited number of parameters and have been successfully used to predict stomatal response to drought for varying environmental conditions and species. However, a mechanism that enables stomata to optimally close in response to water limitations, and more precisely to a drop in the ability of the soil-plant continuum to sustain the transpiration demand, is not known. Here, we propose a model of stomatal regulation that is linked to abscisic acid (ABA) dynamics (production, degradation and transport) and that allows plants to avoid excessive drops in leaf water potential during soil drying and increasing vapor pressure deficit (VPD). The model assumes that: 1) stomatal conductance (g_s) decreases when ABA concentration close to the guard cells (C_ABA) increases; 2) C_ABA increases with decreasing leaf water potential (due to higher production); and 3) C_ABA decreases with increasing photosynthesis (e.g. due to faster degradation or transport to the phloem). Our model includes simulations of leaf water potential based on transpiration rate, soil water potential and variable hydraulic conductances of key elements (rhizosphere, root and xylem), and a function linking stomatal conductance to assimilation. It was tested for different soil properties and VPD. The model predicts that stomata close when the relation between assimilation and leaf water potential becomes nonlinear. In wet soil conditions and low VPD, when there is no water limitation, this nonlinearity is controlled by the relation between stomatal conductance and assimilation. In dry soil conditions, when the soil hydraulic conductivity limits the water supply, nonlinearity is controlled by the excessive drop of leaf water potential for increasing transpiration rates. The model predicts different relations between stomatal conductance and leaf water potential for varying soil properties and VPD. For instance, the closure of stomata is more abrupt in sandy soil, reflecting the steep decrease in hydraulic conductivity of sandy soils. In summary, our model results in an optimal behavior, in which stomatal closure avoids excessive (nonlinear) decrease in leaf water potential, similar to other stomatal optimization models. As based on ABA concentration which increases with decreasing leaf water potential but declines with assimilation, this model is a preliminary attempt to link optimization models to a physiological mechanism.