An Optimal Frequency in Ca2+ Oscillations for Stomatal Closure Is an Emergent Property of Ion Transport in Guard Cells

Oscillations in cytosolic-free Ca²⁺ concentration (Ca2+]_i) have been proposed to encode information that controls stomatal closure. Ca2+]_i oscillations with a period near 10 min were previously shown to be optimal for stomatal closure in Arabidopsis (Arabidopsis thaliana), but the studies offered no insight into their origins or mechanisms of encoding to validate a role in signaling. We have used a proven systems modeling platform to investigate these Ca2+]_i oscillations and analyze their origins in guard cell homeostasis and membrane transport. The model faithfully reproduced differences in stomatal closure as a function of oscillation frequency with an optimum period near 10 min under standard conditions. Analysis showed that this optimum was one of a range of frequencies that accelerated closure, each arising from a balance of transport and the prevailing ion gradients across the plasma membrane and tonoplast. These interactions emerge from the experimentally derived kinetics encoded in the model for each of the relevant transporters, without the need of any additional signaling component. The resulting frequencies are of sufficient duration to permit substantial changes in Ca2+]_i and, with the accompanying oscillations in voltage, drive the K⁺ and anion efflux for stomatal closure. Thus, the frequency optima arise from emergent interactions of transport across the membrane system of the guard cell. Rather than encoding information for ion flux, these oscillations are a by-product of the transport activities that determine stomatal aperture.Stomata in the leaf epidermis are the main pathway both for CO₂ entry for photosynthesis and for foliar water loss by transpiration. Guard cells surround the stomatal pore and regulate the aperture, balancing the often conflicting demands for CO₂ and water conservation. Guard cells open and close the pore by expanding and contracting through the uptake and loss, respectively, of osmotic solutes, notably of K⁺, Cl⁻, and malate²⁻ (Mal²⁻; Pandey et al., 2007; Kim et al., 2010; Roelfsema and Hedrich, 2010; Lawson and Blatt, 2014). These transport processes comprise the final effectors of a regulatory network that coordinates transport across the plasma membrane and tonoplast, and maintains the homeostasis of the guard cell. A number of well-defined signals—including light, CO₂, drought and the water stress hormone abscisic acid (ABA)—act on this network, altering transport, solute content, turgor and cell volume, and ultimately stomatal aperture.Much research has focused on stomatal closure, underscoring both Ca²⁺-independent and Ca²⁺-dependent signaling. Of the latter, elevated cytosolic-free Ca²⁺ concentration (Ca2+]_i) inactivates inward-rectifying K⁺ channels (I_K,in) to prevent K⁺ uptake and activates Cl⁻ (anion) channels (I_Cl) at the plasma membrane to depolarize the membrane and engage K⁺ efflux through outward-rectifying K⁺ channels (I_K,out; Keller et al., 1989; Blatt et al., 1990; Thiel et al., 1992; Lemtiri-Chlieh and MacRobbie, 1994). ABA, and most likely CO₂ (Kim et al., 2010), elevate Ca2+]_i by facilitating Ca²⁺ entry at the plasma membrane to trigger Ca²⁺ release from endomembrane stores, a process often described as Ca²⁺-induced Ca²⁺ release (Grabov and Blatt, 1998, 1999). The hormone promotes Ca²⁺ influx by activating Ca²⁺ channels (I_Ca) at the plasma membrane, even in isolated membrane patches (Hamilton et al., 2000, 2001), which is linked to reactive oxygen species (Kwak et al., 2003; Wang et al., 2013). In parallel, cADP-ribose and nitric oxide promote endomembrane Ca²⁺ release and Ca2+]_i elevation (Leckie et al., 1998; Neill et al., 2002; Garcia-Mata et al., 2003; Blatt et al., 2007). Best estimates indicate that endomembrane release accounts for more than 95% of the Ca²⁺ entering the cytosol to raise Ca2+]_i (Chen et al., 2012; Wang et al., 2012).One feature of stomatal response to ABA, and indeed to a range of stimuli both hormonal as well as external, is its capacity for oscillations both in membrane voltage and Ca2+]_i. Guard cell Ca2+]_i at rest is typically around 100 to 200 nm, as it is in virtually all living cells. In response to ABA, Ca2+]_i can rise above 1 μm—and locally, most likely above 10 μm—often in cyclic transients of tens of seconds to several minutes’ duration in association with oscillations in voltage and stomatal closure (Gradmann et al., 1993; McAinsh et al., 1995; Webb et al., 1996; Grabov and Blatt, 1998, 1999; Staxen et al., 1999; Allen et al., 2001). In principle, cycling in voltage and Ca2+]_i arises as closure is accelerated with a controlled release of K⁺, Cl⁻, and Mal²⁻ from the guard cell and is subject to extracellular ion concentrations (Gradmann et al., 1993; Chen et al., 2012). However, it has been proposed that these, and similar oscillations in a variety of plant cell models, serve as physiological signals in their own right (McAinsh et al., 1995; Ehrhardt et al., 1996; Taylor et al., 1996). In support of such a signaling role, experiments designed to impose Ca2+]_i (and voltage) oscillations in guard cells have yielded an optimal frequency for closure with a period near 10 min (Allen et al., 2001). Nonetheless, the studies offer no mechanistic explanation for this optimum that could validate a causal role in signaling, and none has been forthcoming since. Here we address questions of how such optimal frequencies in Ca2+]_i oscillation arise and their relevance for stomatal closure, using quantitative systems analysis of guard cell transport and homeostasis. Our findings indicate that oscillations in voltage and Ca2+]_i, and their optima associated with stomatal closure, are most simply explained as emerging from the interactions between ion transporters that drive stomatal closure. Thus, we conclude that these oscillations do not control, but are a by-product of the transport that determines stomatal aperture.