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

Abstract

Oscillations in cytosolic-free Ca(2+) concentration ([Ca(2+)]i) have been proposed to encode information that controls stomatal closure. [Ca(2+)]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 [Ca(2+)]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 [Ca(2+)]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.

Figure 1.

Macroscopic outputs of the OnGuard Arabidopsis model. Outputs resolved over a standard diurnal cycle (12 h light:12 h dark; dark period indicated by bar above) with 10 mm KCl, 1 mm CaCl₂, and pH 6.5 outside. The full set of model parameters and initializing variables will be found in Wang et al. (2012) and may be downloaded with the OnGuard software at www.psrg.org.uk. A to C, Outputs for the diurnal period 8.8 to 12.5 h from the start of the diurnal cycle (dark period indicated by bar above) for plasma membrane and tonoplast voltage (A), [Ca²⁺]_i (B), and stomatal aperture and the rate of opening/closing in stomatal aperture (C; =ΔAperture/Δt). Positive rates here indicate opening, and negative rates indicate closing. D, Expanded view of the rapid cycles in voltage, [Ca²⁺]_i, aperture, and the rates of opening/closing corresponding to the period (9.2–9.3 h) highlighted by the gray bars in A to C cross-referenced by numbers. Note the periodic, step-like decrease in aperture and its association with the periods of membrane depolarization and elevated [Ca²⁺]_i. Trials with diurnal fluence rates weighted to peak at 2, 6, or 10 h yielded a comparable series of oscillations, indicating that the kinetics of decay in primary ATP-dependent transport have no substantive influence on this behavior. E, Fourier spectral analysis of oscillation frequencies in voltage and [Ca²⁺]_i for the data in A to C. The plots show the relative amplitude of the component frequencies. Frequencies within the gray bars correspond to periodicities of approximately 6 to 26 min and show a prominent amplitude at 8.9 min (=1.9 mHz).

Figure 2.

Aperture closing rate as a function of the oscillation cycle period. Data from Figure 1 for each of the long oscillatory cycles and from a selection of the early, rapid cycles are plotted together with H⁺-ATPase current dynamics. H⁺-ATPase current determined as the difference in current at 0 mV between the hyperpolarized and depolarized phases of each oscillation cycle. Closing rates shown are corrected proportionally for the decay in K⁺ and anion electrochemical driving force during closure, which elevated the closing rates by approximately 20% to 25% for cycle periods of 10 min and longer. Inset, Closing rate as a function of the relative time fraction spent in the depolarized phase of the oscillation cycle. Note the slight hysteresis loop near the maximum rates of closure.

Figure 3.

Oscillation cycle period is a well-defined function of H⁺-ATPase activity but is largely independent of the Ca²⁺-ATPase and the major channel currents at the plasma membrane. Data are from each of the longer oscillations in Figure 1 and from a selection of the short oscillations. A, H⁺-ATPase current at 0 mV and the maximum hyperpolarization in the cycle. Note the discontinuity in cycle period around 0.7 pA. B, Ca²⁺-ATPase current at 0 mV and minimum hyperpolarization in the cycle. C and D, Ca²⁺ I_Ca and I_K,in currents at −200 mV and maximum hyperpolarization in the cycle. E, I_Cl current at −60 mV and minimum hyperpolarization in the cycle. Data for Mal²⁻ flux were equivalent to that for I_Cl, and for the outward-rectifying K⁺ channels were complementary to those for I_K,in and have been omitted from display.

Figure 4.

Outputs of the OnGuard Arabidopsis model with different extracellular Ca²⁺ concentrations. Outputs resolved as in Figure 1 but with 0.3 and 3 mm Ca²⁺ outside. A to C. Macroscopic outputs with 0.3 mm Ca²⁺ outside during the period from 8.8 to 17.2 h following the start of the diurnal cycle with plasma membrane and tonoplast voltage (A), [Ca²⁺]_i (B), and stomatal aperture and the rate of opening/closing in stomatal aperture (C; =ΔAperture/Δt). Positive rates here indicate opening, and negative rates indicate closing. Note the irregular oscillations in voltage and [Ca²⁺]_i and reduced rates of stomatal closure that extend into the dark period. Results with 3 mm Ca²⁺ are visually almost identical to those in Figure 1. D, Fourier analysis of oscillations in membrane [Ca²⁺]_i for the data in A to C and in with 3 mm Ca²⁺ outside. Data from Figure 1 are replotted in gray for reference. Note the loss in 0.3 mm Ca²⁺ of the prominent frequency near 1.9 mHz and the resolution of frequencies between approximately 0.5 and 1.8 mHz in 3 mm Ca²⁺. Higher order resonance frequencies are also well-resolved near 3 and 5 mHz when Ca²⁺ is elevated outside.

Figure 5.

Outputs of the OnGuard Arabidopsis model with the [Ca²⁺]_i sensitivity of the SLAC1 Cl⁻ channel increased by reducing its K_Ca from 600 nm to 400 nm. Compare outputs with those resolved in Figure 1. A to C, Macroscopic outputs for the period from 8.7 to 12.4 h following the start of the diurnal cycle with plasma membrane and tonoplast voltage (A), [Ca²⁺]_i (B), and stomatal aperture and the rate of opening/closing in stomatal aperture (C; =ΔAperture/Δt). Positive rates here indicate opening, and negative rates indicate closing. Note the elongation in voltage and [Ca²⁺]_i oscillations and their reduction in number. D, Fourier analysis of oscillations in [Ca²⁺]_i for the data in A to C. Data from Figure 1 are replotted in gray for reference. Note the shift in prominent frequency to 1.6 mHz (=12.4 min). Higher order frequencies are also well-resolved and displaced to lower values.