Setup of a Comprehensive ABA Signalling Network

Scale-free networks are well recognized in modelling complex natural systems as they are quite common in various types of biological systems. Scale-free networks are networks whose

degree distribution follows a power law (P(k) ~ k-γ_{) (Aldridge, 2005) and consist of a few highly}

connected nodes (hubs) and a large number of sparsely connected nodes. “The degree of a node in a network is the number of connections the node has to other nodes. If a network is directed then the nodes have two different degrees, the in-degree, which is the number of incoming edges, and the out-degree, which is the number of outgoing edges” (Wikipedia, 2014).

In 2003, Hetherington and Woodward proposed the guard cell signalling network as a scale-free network displaying robustness on node removal, instability on hub removal and system acclimation under a variety of environmental conditions with a rhythmic behaviour (Hetherington & Woodward, 2003). However, the scale-free properties of ABA signalling are neither fully understood nor tested with rigorous mathematical analysis, as Hetherington and Woodward assumed that the guard cell network observed at that time was too small to study scale-free properties with mathematical approaches (Hetherington & Woodward, 2003).

The existing ABA signalling network used to study the system properties is a protein-

protein signalling network simulated by Li et al. (2006)b_{. The authors gathered all the}

information available on protein interactions in guard cell ABA signalling and synthesized them with a synchronous Boolean approach (as discussed in Chapter 2). Their objectives were to study the topology of the network paths that connected ABA to the ultimate response (stomatal closure) and to identify essential elements which upset the global behaviour of the

network through simulating node perturbations. However, Li et al. (2006)b _{stressed that their}

results may be altered as a result of network topology changes with novel biological findings, as well as with the availability of kinetic data, which can alter the order of network updates according to the relative reaction speeds. They further declared that their network was not large enough to prove that ABA signalling had the properties of a scale-free network.

Our network is drawn as a sign directed graph amending the information available in the

biological literature. Taking the 43 node network identified by Li et al. (2006)b _{as the base}

network, we expanded it by adding newly discovered proteins and interactions and removing, wherever possible, existing nodes/links that were redundant or irrelevant with no harm to the network, using a reverse engineering approach.

3.1.2 Sign Directed Graph

In graph theory, a sign directed graph is a set of nodes/vertices (reactive molecules in a biological system) connected by a set of directed edges/arcs. Each edge is an arrow representing an interaction between two nodes, which can be any type of regulatory reaction identified in

biology. All edges are directed from the head node, the source/regulator of the tail node, to the node which is being regulated (target or tail). The representation of a sign directed graph (SG) can be in a formal form as in Eq. 3.1.

SG={V, E} (3.1)

where, set V and set E, respectively, represent the vertices and edges.

Figure 3.1 displays the sign directed graph for our ABA signalling network, which

comprises 56 nodes and 127 interactionsbased on fragmentary biological information sourced

from an extensive and comprehensive survey of the literature, as explained in Chapter 2.Here,

the direction of the edges reflects the propagation of the signal flow between signalling molecules, such as proteins, small molecules and ion channels (represented as nodes). All interactions involved in this network are summarized in Table 3.1 (this table is at the end of the chapter for reference).

In the preliminary assessment, we probed the network from its functional perspective. The goal of ABA signalling is to close stomata to prevent water loss under drought conditions. Upon the drought induced ABA signal entering the guard cell, signalling must accomplish the tasks required for stomatal closure. This primarily involves removing water from the cell and facilitating the safe movement of the cell membrane to shrink the cell volume subsequent to removal of water from the guard cells. Guard cells are in equilibrium with the surrounding environment and water moves in and out according to the osmotic pressure differential. Key

to this regulation is osmolytes (positively and negatively charged ions such as K+_{, Cl}-_/NO

3 - _and

malate2-_{). The more ions inside the cell, the more water enters it and the fewer ions inside the}

cell, the more water leaves it. Therefore, releasing water requires the removal of ions from guard cells that sets up an outward osmotic potential gradient. However, opening of the ion channels in the cell membrane required for releasing water happens only under depolarized (enhanced positive charge) conditions in the membrane. This requires that negative ions be released from the cell so the internal environment of the cell is more positively charged. Therefore, depolarization of the cell membrane is one of the main tasks of ABA signalling. The node ‘polarization’ in Figure 3.1 represents this phenomenon along with the molecules that

support it. Once the membrane is depolarized, K+ _{out channels open to release K}+ _{along with}

water. The K+ _{out channel concerned is GORK, shown at the bottom right corner of the box,}

which contains teal coloured nodes in the bottom left side of Figure 3.1 (next to closure, which indicates the final state of the stomata, whether open or closed).

When water is released, the cell shrinks. However, unless the skeleton of the cell supports it, the cell can undergo collapse. Therefore, parallel to the release of water, cytoskeleton rearrangements, such as filament relaxation, must take place. This activity is shown in the upper right corner of Figure 3.1 (yellow nodes). The release of water and filaments rearrangement are directly initiated by ABA. Another important aspect of ABA is maintenance of stomatal

closure. The role of Ca2+ _{in supporting the closure and its maintenance has been reported in the}

literature. Ca2+ _{is shown in the middle of Figure 3.1 (pink nodes) and the sheer number of}

connections involved with this node indicates that Ca2+ _{is an important element in the system.}

There are also other highly connected nodes, including ABA (top-most node in Figure 3.1), SnRK2 (first protein released by ABA – shown in the bottom left corner area of Figure 3.1 in yellow), RbOH (top left region in Figure 3.1 (purple nodes)) and closure, etc. These and other nodes are analyzed for scale-free properties of the network in this chapter. More details and their interactions will be revealed as the discussion progresses, in this chapter and the subsequent results chapters.

Figure 3.1: Sign directed graph of the ABA signalling network (regular arrows (black) represent positive interactions, diamond-head arrows (red) represent inhibitory

interactions and dashed line arrows represent putative relationships)