A new discrete dynamic model of ABA-induced stomatal closure predicts key feedback loops

Abstract

Stomata, microscopic pores in leaf surfaces through which water loss and carbon dioxide uptake occur, are closed in response to drought by the phytohormone abscisic acid (ABA). This process is vital for drought tolerance and has been the topic of extensive experimental investigation in the last decades. Although a core signaling chain has been elucidated consisting of ABA binding to receptors, which alleviates negative regulation by protein phosphatases 2C (PP2Cs) of the protein kinase OPEN STOMATA 1 (OST1) and ultimately results in activation of anion channels, osmotic water loss, and stomatal closure, over 70 additional components have been identified, yet their relationships with each other and the core components are poorly elucidated. We integrated and processed hundreds of disparate observations regarding ABA signal transduction responses underlying stomatal closure into a network of 84 nodes and 156 edges and, as a result, established those relationships, including identification of a 36-node, strongly connected (feedback-rich) component as well as its in- and out-components. The network's domination by a feedback-rich component may reflect a general feature of rapid signaling events. We developed a discrete dynamic model of this network and elucidated the effects of ABA plus knockout or constitutive activity of 79 nodes on both the outcome of the system (closure) and the status of all internal nodes. The model, with more than 1024 system states, is far from fully determined by the available data, yet model results agree with existing experiments in 82 cases and disagree in only 17 cases, a validation rate of 75%. Our results reveal nodes that could be engineered to impact stomatal closure in a controlled fashion and also provide over 140 novel predictions for which experimental data are currently lacking. Noting the paucity of wet-bench data regarding combinatorial effects of ABA and internal node activation, we experimentally confirmed several predictions of the model with regard to reactive oxygen species, cytosolic Ca2+ (Ca2+c), and heterotrimeric G-protein signaling. We analyzed dynamics-determining positive and negative feedback loops, thereby elucidating the attractor (dynamic behavior) repertoire of the system and the groups of nodes that determine each attractor. Based on this analysis, we predict the likely presence of a previously unrecognized feedback mechanism dependent on Ca2+c. This mechanism would provide model agreement with 10 additional experimental observations, for a validation rate of 85%. Our research underscores the importance of feedback regulation in generating robust and adaptable biological responses. The high validation rate of our model illustrates the advantages of discrete dynamic modeling for complex, nonlinear systems common in biology.

Fig 1. The network of abscisic acid (ABA)-induced stomatal closure.

Edges that end in an arrowhead indicate positive interactions or regulatory relationships. Edges that end in a filled circle indicate negative interactions or regulatory relationships. Source nodes (nodes with no incoming edges) are represented by octagons; the rest are rectangles. Edges that represent direct interactions or regulatory relationships are indicated with black, and green edges represent indirect or inferred relationships. The color of the nodes represents their function, as follows: enzymes (red), signaling proteins (green), membrane-transport related nodes (blue), and secondary messengers and small molecules (orange). The full names of network components corresponding to each node label are indicated in S3 Table, and biological justification for the edges is provided in S1 Table, S2 Table, and S1 Text.

Fig 2. Feedbacks play a key role in the structural and dynamic properties of the abscisic acid (ABA)-induced stomatal closure network.

A. The network’s strongly connected component (SCC) comprises almost half of the nodes and more than two-thirds of the edges; it contains both positive and negative feedback loops. Nodes with a light green background are affected by nodes in the in-component, nodes with a blue background regulate nodes of the out-component, and nodes with a pink background interact with both the in-component and the out-component. The dashed edges indicate edges inferred during our network construction process. Even if all dashed edges were removed, 26 nodes would remain in the SCC. The dotted edge indicates a positive self-regulation inferred during the construction of the dynamic model. The nodes that make up the in-component, the SCC, and the out-component are listed in S4 Table. B-D. Stable motifs determine the final outcome (attractor) of the network. The node background indicates the stabilized state of the node; white represents 1 (ON) and black represents 0 (OFF). All stable motifs that are not self-loops are subsets of the SCC. B. Stable motifs associated with closure in response to sustained ABA. C and E. Stable motifs associated with lack of closure in the absence of ABA. The stable motif in E has 3 variants that share all the nodes and all the solid edges. Each variant also includes 2 to 6 additional nodes and 4 to 8 additional edges, which form additional feedback(s) and can be summarized as the indirect relationships shown as dashed edges. D. Stable motif associated with closure in the absence of ABA. Stabilization of this motif requires that Vacuolar Acidification first stabilizes in the ON state; this does not happen in any of the trajectories that start from our assumed initial condition representative of open stomata.

Fig 3. Node knockout (sustained OFF state) or constitutive activity (sustained ON state) can lead to a variety of divergences from the wild-type system’s response to abscisic acid (ABA), in agreement with experiments.

The percentage of closed stomata in the wild-type system reaches 100% in the presence of ABA (filled circles) and stays at 0% in the absence of ABA (open circles). A. Simulated knockouts that lead to ABA insensitivity (ost1) or reduced sensitivity to ABA (rboh, cytosolic pH [pH_c] clamp, phosphatidylcholine [PC] depletion). B. Examples of node knockouts that lead to ABA hyposensitivity (pldα, gapc1/2) or ABA hypersensitivity (abi1, abh1, Ca²⁺ ATPase knockout). C. Examples of constitutive node activation that lead to insensitivity to ABA (abi1 dominant mutant, constitutively active Ca²⁺_c ATPase), reduced ABA sensitivity (constitutive activity of ABA-insensitive 2 [ABI2] or protein phosphatase 2CA [PP2CA]), or ABA hyposensitivity (ROP11 constitutive activity). D. Examples of constitutive node activity that lead to ABA hypersensitivity: supply of phosphatidic acid (PA) and supply of reactive oxygen species (ROS), which we experimentally assess and confirm. Fewer than 30 time steps are illustrated in all panels simply to better display the differences among curves. The numerical data can be found in S1 Data.

Fig 4. Experimental validation of model predictions.

A,B. Wild-type ABA response of Ca²⁺_c oscillation in gpa1 null mutants. A. Representative ABA-induced oscillations in Ca²⁺_c using Y3.6 fluorescent reporter. The fluorescence emission ratio of yellow fluorescent protein (YFP) to cyan fluorescent protein (CFP) (YFP/CFP) was calculated from YFP and CFP emission intensities. Pseudo-colored scale bar refers to both wild-type Columbia accession (Col) and gpa1 data. B. The numbers of guard cells exhibiting different types of ABA-induced Ca²⁺_c oscillation in Col (n = 20), gpa1-3 (n = 18), and gpa1-4 (n = 19). C,D. ABA hypersensitivity in Arabidopsis thaliana stomatal closure upon external supply of Ca²⁺ or H₂O₂. Ca²⁺ or H₂O₂ alone does not induce closure at the low concentrations used here. C. CaCl₂ (50 μM) accelerates ABA (2 μM)-induced stomatal closure in epidermal peels at 1 h. D. H₂O₂ (0.1 μM) accelerates ABA (2 μM)-induced stomatal closure in epidermal peels at 1 h. The asterisk above the sample indicates statistical significance (Student t test p < 0.05) between this sample and the same sample within the ethanol (EtOH) (solvent control) group; the dagger symbol indicates statistical significance (Student t test p < 0.05) between the 2 samples within the ABA treatment group. Data are mean ± SE of 3 independent replicates with 64 stomata per replicate. The numerical data (for B, C, and D) can be found in S1 Data.

Fig 5. The system’s response to simulated constitutive activity or external supply of nodes in the absence of abscisic acid (ABA) depends on the initial activity of the protein phosphatases 2C (PP2Cs).

A. The PP2Cs are assumed to be ON in the initial state. The wild-type system in the absence of ABA (open circles) shows lack of closure in all simulations. Constitutively high concentration of cytosolic Ca²⁺ (Ca²⁺_c) or constitutive activity (CA) of Ca²⁺ ATPase similarly leads to lack of closure, but supply of reactive oxygen species (ROS) leads to a response similar to the response to ABA (Fig 3, closed circles). B. The PP2Cs are assumed to be OFF in the initial state. Now there is a nonzero probability of closure in the absence of ABA. Supply of ROS or sustained high Ca²⁺_c leads to a response similar to the response to ABA (Fig 3, closed circles), consistent with experimental observations. CA of the Ca²⁺ ATPase leads to the absence of closure in all simulations. The numerical data can be found in S1 Data.

Fig 6. The subnetwork from abscisic acid (ABA) to the anion channels includes the core ABA signaling chain as well as the entire strongly connected component (SCC).

As in Fig 1 and Fig 2, edges that end in an arrowhead signify activation and edges that end in a filled circle mean inhibition. For simplicity, certain linear chains, e.g., the Ca²⁺-dependent kinase (CPK)-mediated effect of Ca²⁺ on SLAC1 and SLAH3, have been compressed into single edges (shown with dashes). The 4 protein phosphatases 2C are merged into a single node (PP2Cs). ABA and RCARs are in the in-component, and SLAC1, QUAC1, and SLAH3 are in the out-component; the rest of the nodes are in the SCC. Nodes whose manipulation (knockout or, in the case of PP2Cs, constitutive activity) has been experimentally shown to cause decreased ABA sensitivity are marked with colored background (see Table 3). The colors indicate the response category for the simulated node manipulation: red means ABA insensitivity, orange marks reduced ABA sensitivity, and yellow means ABA hyposensitivity. The blue dash-dotted edge indicates our prediction that cytosolic Ca²⁺ inhibits the PP2Cs.