Comparison of Current Model Results with the Li et al (2006) b Model

In this section, we discuss the major findings of both models comparing the corresponding results.

(A)

(B)

Figure 5.5: Comparison of the sign directed graphs of the two modelling studies. A) Sign

directed graph of the Li et al. (2006)b _{model; B) sign directed graph of our study (red}

nodes indicate the proteins, small molecules or cellular conditions common to both models)

Figure 5.5 depicts the sign directed graphs used in both studies. Figure 5.5 (B), the sign directed graph of the current research, shows the topological differences between the two models by indicating the common nodes in both models in red. According to Figure 5.5, we recognize that 34 nodes are common to both models. The first major topological difference we

observe between the two models is signal perception through the ABA receptor complex (compare two nodes, ABI1 and OST1 in Figure 5.5 (A) and the ABA receptor complex box in Figure 5.5 (B)), which is, currently, identified as a crucial functional module of ABA

signalling. In the Li et al. (2006)b _{model, they considered PP2C (ABI1 in their model) and}

SnRK2 (OST1 in their model) as two independent nodes but our model clearly defines their significance to the ABA signalling network. For example, SnRK2 is currently known as one of the major functioning proteins to initiate the ABA signalling process but such a role was not

defined in the Li et al. (2006)b _{model. Furthermore, PP2C is the regulator of SnRK2 in our}

model.

The lipid regulation pathway and ROS production in both models are comparable but the

Li et al. (2006)b _{model lacks the feedback regulatory loop between sphingolipid (S1P) and PA,}

which is an essential regulation discovered recently for the self-regulation of sphingolipid induced PA production (compare the top middle boxes in Figure 5.5(A) and the lipid signalling box in Figure 5.5(B)).

Guard cell osmoregulation is defined differently in the two models. The Li et al. (2006)b

model considered a common anion channel (node AnionEM in Figure 5.5(A)) for the

regulation of all anions (Cl-/NO3- and malate2-) and two K+ efflux channels (KAP and KOUT)

for the regulation of cations. The KAP channel in the Li et al. (2006)b _{model represents K}+

efflux through rapidly activating K+ _{channels in the plasma membrane. In our study we do not}

consider KAP because the recent literature revealed that GORK is the only available K+ _efflux

channel in the guard cell membrane. As a result, our model displays no functional redundancy

in the GORK channel, as it is solely responsible for the K+ _{efflux from plant guard cells.}

Further, the regulation of anions is expanded in our model with current knowledge about different ion channels (SLAC1, QUAC, and ATALMT6) (osmoregulation box in Figure 5.5(B)) so the significance of each channel to the global output of the system can be revealed. Due to the lack of knowledge about structural rearrangement at the time, actin regulation

is poorly defined in the Li et al. (2006)b _{model. Comparatively, our model captures more}

scientific knowledge on guard cell structural rearrangements and connect them with several other important functional sets in the system. However, current knowledge about this functional set still lacks a proper understanding of the connectivity between the actin regulatory proteins and their regulations.

Components of the Ca2+ _{regulatory pathway are nearly similar but the definition of the Ca}2+

signature is considerably contradictory between the two models. For example, Ca2+ _{release by}

the internal organelles is regulated by four independent regulators (InSP3, InSP6, cGMP and

cADPR) in the Li et al. (2006)b _{model (middle left region in Figure 5.5 (A)) but we assume}

that these four regulators are not independent (InSP6 is the phosphorylated product of InSP3 and cGMP enhances the production of cADPR); therefore, our model considers them as two regulatory paths (calcium signalling box in Figure 5.5(B)). Further, our model considers the

contribution of structural rearrangements to cytosolic Ca2+ _{increase through stretched activated}

Ca2+ _{channels in the plasma membrane, which is missing in the previous model. Moreover, the}

previous model considered the Ca2+ _{efflux system as a single node (Ca}2+_{ATPase node in Figure}

5.5(A)) regulated by Ca2+_{. We are certain that the Ca}2+ _{efflux system consists of two effluxes}

(Ca2+_{-ATPase and CAX) that are differently regulated by their corresponding regulators.}

Therefore, our model considers the individual regulations of Ca2+ _{effluxes (Calcium signalling}

box in Figure 5.5(B)) assuming that this expansion helps identify biologically evidenced attractors with our asynchronous Boolean model in the next chapter.

The discussion above emphasized the topological differences between the Li et al. (2006)b

model and our model. As shown in the discussion, it is clear that there has been a considerable amount of new knowledge (important regulators and regulatory links) incorporated into our model. The following section discusses how this new contribution advances the model results to generate new insights.

Both models approach the main goal, stomatal closure, in a similar way within several time steps in response to a constant ABA input. In both models, the majority of nodes approach their steady state values within a few time steps and their steady state values are independent of the initial conditions. These findings display a common ground for both models with regard to stomatal closure.

Initial theoretical analysis of the stable behavior of the system (attractors) from the two models reveals that the principal regulatory mechanisms are common in both cases but there are case specific characteristics. This is a good indication that the addition of new nodes or regulatory paths has not violated the fundamentals of system regulation such that the attractors

are a result of Ca2+ _{governed regulatory mechanisms in both models. The attractors of the Li}

et al. (2006)b _{model are simple limit cycles, consisting of a set of 12 dynamic nodes, including}

Ca2+_{, Ca}2+_{-ATPase, PLC, InSP3, NO, cGMP, cADPR, K}+ _{efflux from the vacuole to the}

cytosol, and K+_{efflux through rapidly activating K}+_{efflux channels at the plasma membrane}

(KAP), with the remainder of the network nodes in a frozen state (the original attractor was not published in their paper but we obtained a part of their attractor that had been published elsewhere (Saadatpour et al., 2010)). In comparison, our model results in simple limit cycle

attractors with 14 non-stationary nodes (PLC, InSP3, InSP6, NO, cADPR, cGMP, CDPK, Ca2+_,

CBL, Ca2+_{-ATPase, CaM, CAX, CIPK, and ATALMT6). Of these 14 nodes, there are 7 nodes}

common in both models; these are PLC, InSP3, NO, cADPR, cGMP, Ca2+ _{and Ca}2+_-ATPase.

Figure 5.6 compares the dynamic part of the major attractors found in the two models. The major difference between the two systems is the length of the attractors. The attractors from

the Li et al. (2006)b _{model are 4 states long (Figure 5.6(B)), whereas the lengths of the attractors}

found in our study is 7 states (Figure 5.6 (A)). The difference between the two attractors is due to different regulatory mechanisms considered in the two models. However, we believe that the state transition patterns in our attractors are more representative of the ABA system as our model traces novel and more realistic regulatory paths in the system.

Figure 5.6: Comparison of steady state behaviour of the ABA signalling network

(oscillatory nodes only) resulted from; A) our model; and B) the Li et al. (2006)b _model.

Red circles represent the inactive states of nodes and green represents the active nodes

Comparison of Figures 5.6 (A) and (B) confirms that the Li et al. (2006)b _{model produces}

more frequent system oscillations by repeatedly visiting shorter limit cycles. We cannot argue about the reliability of this feature as both models are synchronous; hence, they could not capture the temporal organization of system events. However, we notice that the Hamming

distance of the attractors are comparatively higher in the Li et al. (2006)b _{model (Hamming}

distance = 5.25 & 6). If shorter Hamming distances are favoured in evolutionary biology and are more robust against small system perturbations, we can argue that our system (Hamming distance = 3.85) is comparatively more robust.

The Li et al. (2006)b _{model suggests that the steady state system behaviour of the ABA}

signalling network is due to Ca2+ _{governed regulatory mechanisms but the models lacks}

knowledge of how Ca2+ _{proceeds with its signal transduction through various Ca}2+ _regulatory

proteins, which is important in order to know how and why the system makes use of the Ca2+

signature during steady state dynamics. Both models support the fact that Ca2+ _{elevation in the}

system accelerates stomatal closure prior to reaching the system attractors (Ca2+ _{oscillations)}

but that ABA-induced stomatal closure can happen independent of Ca2+ _{elevation. However,}

the Li et al. (2006)b _{model does not discuss how disruption of Ca}2+ _{signalling leads to slower}

stomatal response than in the WT system. Our system demonstrates the cause of Ca2+ _induced

rapidity in relation to regulation of the SLAC1 channel. In conclusion, both models highlight

the importance of Ca2+ _{for fast activation of stomatal closure as well as maintenance of stomatal}

closure but our model provides more clarity with proper reasoning.

Both models support the fact that disruption of sparsely connected nodes does not lead to negative qualitative effects on the stomatal response. Similarly, both models agree with the perturbation results obtained from disrupting the lipid signalling pathway, which makes stomata oscillate as a result. Moreover, both models discover that the loss of membrane

depolarization, disruption of anion efflux, and the loss of actin cytoskeleton reorganization

create stomatal insensitivity to ABA. Our model further suggests that elimination of the receptor complex (PYR, PP2C and SnRK2) completely blocks ABA induced stomatal closure

as a result of impaired SLAC1 activation, actin rearrangement, ROS production and Ca2+

signalling, but in the Li et al. (2006)b _{model SnRK2 mutants are still responsive to ABA.}

SnRK2 appears to be a potential hub in our model, but in the Li et al. (2006)b _{model it is yet}

another sparsely connected node. Similarly, ROS is a clear hub in our model, which communicates with all the functional nodes in the ABA signalling system. Disruption of ROS produces similar behaviour to SnRK2, making stomata insensitive to ABA, but the Li et al.

(2006)b _{model predicts ABA hyposensitivity when ROS is eliminated. This proves that some}

of the important elements or their roles are not well represented in the Li et al. (2006)b _model.

According to our model, Ca2+_{, PP2C, ROS, SLAC1, RbOH, depolarization, actin, PA, pH,}

SnRK2, GORK, malate, MAPK and a few other Ca2+ _{related nodes are identified as network}

hubs. The Li et al. (2006)b _{model concluded that Ca}2+_{, depolarization, pH, ROS, anion efflux,}

and K+_{efflux through outwardly rectifying K}+ _{channels are network hubs. The network hubs}

identified by the Li et al. (2006)b _{model (6 elements) appears to be a subset of network hubs}

identified by our model indicating that we have targeted more potential elements for genetic studies.

In summary, we believe that our model is rich with a number of advancements and new knowledge generated but fundamentally both models preserve the core characteristics of the ABA signalling network.