Systems dynamic modeling of the stomatal guard cell predicts emergent behaviors in transport, signaling, and volume control

The dynamics of stomatal movements and their consequences for photosynthesis and transpirational water loss have long been incorporated into mathematical models, but none have been developed from the bottom up that are widely applicable in predicting stomatal behavior at a cellular level. We previously established a systems dynamic model incorporating explicitly the wealth of biophysical and kinetic knowledge available for guard cell transport, signaling, and homeostasis. Here we describe the behavior of the model in response to experimentally documented changes in primary pump activities and malate (Mal) synthesis imposed over a diurnal cycle. We show that the model successfully recapitulates the cyclic variations in H⁺, K⁺, Cl⁻, and Mal concentrations in the cytosol and vacuole known for guard cells. It also yields a number of unexpected and counterintuitive outputs. Among these, we report a diurnal elevation in cytosolic-free Ca²⁺ concentration and an exchange of vacuolar Cl⁻ with Mal, both of which find substantiation in the literature but had previously been suggested to require additional and complex levels of regulation. These findings highlight the true predictive power of the OnGuard model in providing a framework for systems analysis of stomatal guard cells, and they demonstrate the utility of the OnGuard software and HoTSig library in exploring fundamental problems in cellular physiology and homeostasis.The guard cells, which surround stomatal pores in the epidermis of plant leaves, regulate the pore aperture to balance the often conflicting demands for CO₂ in photosynthesis with the need to conserve water by the plant. Stomatal transpiration accounts for much of the nearly 70% of global water usage associated with agriculture and has a profound impact on the water and carbon cycles of the world (Gedney et al., 2006; UNESCO, 2009). Recent studies have associated increases in continental water runoff with the rise in available CO₂ and decreases in stomatal transpiration (Gedney et al., 2006) and have suggested that stomatal behavior skews the impact of greenhouse gasses on fresh water resources (Betts et al., 2007). The past half century has generated a vast wealth of knowledge for guard cell transport, signaling, and homeostasis, resolving the properties of all of the major transporters and many of the signaling pathways that control them (Blatt, 2000a; Schroeder et al., 2001; Blatt et al., 2007; Wang and Song, 2008; McAinsh and Pittman, 2009). Even so, resolving many aspects of stomatal dynamics remains a challenge. These studies have yet to yield any detail about how the entire network of transporters works as a unit to modulate solute flux and regulate stomatal aperture. Quantitative systems analysis offers one approach to this problem that is now much needed. Efforts to model stomatal function to date generally have been driven by a top-down approach: The mechanics of stomatal movements are subsumed within a few empirical parameters of linear hydraulic pathways and conductances (Farquhar and Wong, 1984; Ball, 1987; Williams et al., 1996; Eamus and Shanahan, 2002; West et al., 2005). These models have proven useful at the plant and community levels; but they have not incorporated the essential detail to support an understanding of the molecular and cellular mechanics that drive stomatal movements.In the previous article (Hills et al., 2012) we introduced a computational approach to developing a dynamic model of the stomatal guard cell based on the HoTSig library and OnGuard software. We resolved an OnGuard model that takes account of all of the fundamental properties for transporters at the plasma membrane and tonoplast, the salient features of osmolite metabolism, and key homeostatic and dynamic signaling characteristics that have been described in the literature. The model successfully integrated a number of the steady-state characteristics of guard cells, recapitulating the patterns in guard cell response to the extracellular variables of KCl and CaCl₂ concentrations and to extracellular pH. Here we explore the capacity of the model to reproduce diurnal oscillations in guard cell membrane transport and malate (Mal) metabolism, and its consequences for the dynamics of guard cell volume, turgor pressure, and stomatal aperture. We demonstrate the true predictive power of the OnGuard model in generating a number of unexpected and counterintuitive outputs. Among these, the model yields counterintuitive changes in cytosolic-free Ca²⁺] (Ca2+]_i) and a daily exchange of Cl⁻ with Mal that are well documented in the literature, but have been suggested to require additional and complex levels of regulation. These behaviors are accounted for entirely by the known kinetic features of the transporters encoded in the model. Thus, the results demonstrate the predictive power of the OnGuard model as a framework from which to test the basic tenets of the stomatal behavior and to explore the interactions of transport and metabolism in the guard cell system.