|dc.description.abstract||The phytohormone abscisic acid (ABA) is an endogenous messenger in plant abiotic stress responses. Drought stress increases the level of ABA triggering the fastest adaptive physiological response of plants- closure of stomata, individual pores surrounded by two guard cells on the surface of leaves. Understanding gene/protein expression involved in stomatal closure has great importance to genetic modification of plants to survive under severe climatic conditions. However, systems level information that defines the communication pattern of the related network of cellular molecules is not yet properly understood. Stomatal closure, in broad terms, is a combined result of organic and inorganic ion regulation to release water from the guard cells through osmosis (reduction of turgor) and the rearrangement of the cell structure to facilitate stomatal movement.
This study integrated fragmentary information collected from the literature to define the dynamics of ABA signalling in the rapid closure of stomata through three computational approaches (synchronous Boolean, asynchronous Boolean and normalized HillCube models). Our network consists of 56 nodes and their interaction dynamics (127 interactions) defined in accordance with the past experimental results. In our network, the input node represents the ABA signal to the system. Intermediary nodes represent proteins, second messengers, small molecules, plant lipids and several cellular conditions. These intermediary nodes link the system signal to the global cellular response (stomatal closure) through a series of interconnected network edges (reactions), predominantly representing enzyme catalysis, various post-translational modification activities and ion transport. The first main task was to update and extend the existing ABA network, with the addition of 22 elements and 84 reactions. After completing the network topology with the available biological knowledge, we then studied the topological properties of the ABA signalling network and found that the network displays scale-free properties with RbOH, SLAC1, Ca²⁺, PP2C, PA, Depolarization and Actin as network hubs to define the functional modules of the system.
The first modelling attempt in this study was to check the system dynamics of the ABA signalling system with a synchronous Boolean model and compare the model results with the current mathematical model available in the literature. Our model resulted rapid stomatal closure with in several arbitrary time steps and then converged the system dynamics to eight limit cycle attractors. These eight attractors represented the synchronous steady state dynamics of the ABA signalling system and provided the evidence for experimentally observed Ca²⁺ oscillations in the guard cells. We found that the advancement of network topology improved the understanding of network functioning while preserving the core behaviour observed in the Li et al. (2006)ᵇ model. The study was mainly conducted to identify the essential components of ABA signalling as the most important regulators of the system were decided by the topology. The results revealed that destruction of the ABA receptor complex (PYR/PYL, PP2C and SnRK2 proteins) made the stomata insensitive to closure as the result of a disruption of signal transmission to downstream regulators. It was identified that the plasma membrane outward ion channels, GORK and SLAC1, are crucial for pumping out water to facilitate guard cell turgor reduction. Inhibition of MAPK kinases (an important regulator of SLAC1), cytosolic alkalization (pH) and membrane depolarization also had a drastic effect on stomatal closure. Loss of the function of actin rearrangement resulted in loss of stomatal closure as structural rearrangements of the guard cells are necessary to facilitate cell shrinkage. Disruption of reactive oxygen species or their regulators (RBOH, PA, PLD or RCN1), plant-specific actin binding protein SCAB1 and overexpression of AtRAC1 showed drastic effects on structural rearrangements. Perturbation analysis revealed that the number of elements crucial to stomatal closure comprised about 30% of the network and, thus, stomatal closure was robust against perturbation to the other 70% of network elements. These results were in agreement with experimental findings and indicated a potential redundancy and/or the secondary role of a large percentage of elements with respect to stomatal closure.
The second major modelling attempt was to incorporate time delays into the network updating method to study the steady state dynamics of the ABA signalling network through an asynchronous Boolean model. The study was mainly conducted to identify the biologically reliable dynamics of ABA signalling system as the synchronous Boolean model lacks the temporal order of state transitions in the system. Results of this study revealed that the model successfully captured the temporal hierarchy of ABA signalling events, as observed in the experimental literature. The system achieved the stomatal closure within five minutes at the earliest and reached limit cycle attractors during steady state dynamics. Biologicaly most reliable attractor identified by the model resembled experimentally-observed oscillatory behaviour of Ca²⁺ with the measured frequency and transient periods. The model explained that the attractor was a result of the regulatory activities of 14 non-stationary nodes (defined by Ca²⁺) and the frozen states of the remainder of the network nodes. Evaluation of the role of Ca²⁺ in the ABA signalling network found that redundancy of [Ca²⁺]cyt signalling within the ABA signalling system during stomatal closure played a large role in protecting the system against various disturbances and accelerating stomatal closure by the fast regulation of SLAC1 channel. Our model further predicted that if ABA enhance the sensitivity of the network regulatory proteins to [Ca²⁺]cyt, ABA can hand over the system regulation to [Ca²⁺]cyt under the condition that [Ca²⁺]cyt can independently regulate the enzyme, PLC. This finding corresponded with the biological hypothesis in the literature that ABA enhances the Ca²⁺sensitivity of some proteins.
The third modelling attempt of the research was to identify the minimal model to represent steady state dynamics of the system and model it with continuous dynamics using the normalized HillCube approach to better understand the properties of the system. The transformation of the Boolean dynamics of the core model (consisting of attractor nodes) into continuous dynamics successfully reproduced the limit cycle attractor of the ABA signalling system with defined parameters, such as 10 minute transient periods and the peak height of Ca²⁺ oscillations equals to 400-600 nM. The model found that the ABA system oscillations were sensitive to small changes in the regulation of Ca²⁺ efflux systems. It further revealed that the system attractor has the potential to decode the Ca²⁺ signature to achieve steady state regulation of downstream effectors through Ca²⁺ sensor proteins, which could be important and probably used for the maintenance of stomatal closure. The model was able to predict the kinetic parameters for downstream regulations of CDPK to achieve their steady state regulation for maintenance of stomatal closure.||en