A System of Subsystems: Hierarchical Modularity of Guard Cell ABA Signalling Network defines its  Evolutionary Success

doi:10.21203/rs.3.rs-2214954/v1

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A System of Subsystems: Hierarchical Modularity of Guard Cell ABA Signalling Network defines its Evolutionary Success

https://doi.org/10.21203/rs.3.rs-2214954/v1

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Biological functions are accomplished by extensive molecular signalling networks that are too complex to comprehend their meaning. This study aims to exploit computational network analysis on a model system to unravel network complexity to gain insights into the principles of organization of molecular networks. Plants respond to drought stress by stomatal closure, the most rapid physiological response in plant leaves where aperture between two guard cells closes rapidly to prevent water loss. ABA (Abscisic acid) signalling network that accomplishes stomatal closure in guard cells is thought to be an evolutionarily well conserved system organized to control the stomatal aperture in response to drought stress. However, functional organization and evolutionary success of this system is yet to be explored for gaining deeper insights into the operation and success of this system. This study views this signaling system from a holistic perspective and hypothesizes that it is an interconnected system of subsystems evolved to facilitate the communication flow of the whole system to respond to the signals by means of a collection of feedback processes with shifting dominance in time and space. Further, it is known that topological properties of biological networks can reveal the influence of structural properties on the functional and dynamical properties of a system. Therefore, this study exploits topology analysis of an updated ABA signalling network using graph theoretic measures involving topological dissimilarity based node clustering to explore its modularity to characterize it as a system of subsystems. The paper explains the hierarchical modules identified by topological distance measures and hub elements identified by centrality measures. Network was decomposed into three subsystems comprising seven functional modules along with a number of hub elements that provided an easy to understand view of ABA signaling. This system of subsystems view enabled by modularity revealed a meaningful and coherent organization of the structure and function of the complex ABA network. Further, ABA signaling network was found to be a scale-free network that defines its evolutionary success.

Biological sciences/Systems biology/Complexity

Biological sciences/Plant sciences

ABA signalling

topological properties

hierarchical modules

systems

subsystems

structural and functional organization

scale-free network

All biological functions are accomplished by extensive and interconnected molecular signalling networks. The increasing amounts of data and information collected over the last decade have revealed the extent of complexity of these networks and challenge to understanding the principles of their organization and function. Computational network analysis can contribute to unravelling network complexity. This study aims to exploit network analysis methods to explore a well-studied model system in order to probe deep into its principles of structural and functional organisation. Guard cells are a well-developed model system for understanding how cell components interact within a signalling network of a single cell. This involves a large number of interconnected molecules that convey the drought signal sensed by plant hormone Abscisic acid (ABA) to prevent plant water loss by closing stomata. The ABA signalling network facilitates stomatal closure via safe movement of the cell membrane to shrink the guard cell volume by removing water from it through osmosis. This requires an outward osmotic potential gradient generated by the removal of charged osmolytes such as K⁺, Cl⁻/${\text{NO}}_{\text{3}}^{\text{-}}$ and malate²⁻ from guard cells. When water is released, the guard cell shrinks. However, unless the skeleton of the cell supports it, the cell can undergo collapse. Therefore, in parallel to the release of water, cytoskeleton rearrangements must take place. ABA signalling network coordinates both osmoregulation and structural rearrangements in parallel in a way that ultimately leads to safe stomatal closure and then evokes the regulatory mechanisms needed to keep stomata closed until the plant become stress free.

Biological signalling networks are designed in such a way that they can reveal important properties and principles about the functional organization of the network. We rewired and greatly expanded the existing ABA signalling system with 34 proteins and 43 interactions [20] to comprise 56 nodes and 127 interactions, by amending fragmentary biological information sourced from an extensive and comprehensive literature survey (Supplementary Fig. 1). It is not an easy task to consider each and every molecule’s task in a complex and large web of interacting elements; therefore, identification of subsystems and their relationships in spatial and temporal placement of the network will provide the context to highlight the biological importance and contribution of each event, task or molecule to the final output.

ABA signalling network is hypothesized to have scale-free topology as is the majority of other biological networks [2]. Scale-free networks are networks whose degree distribution (the number of connections per node) obeys a power low of the form h(k) ≈ k^− q (k is the degree and q is the exponent) indicating the presence of a small number of highly connected (high-degree) nodes (hubs) and a large number of parsley connected (low-degree) nodes [3]. As scale-free topology tends to display a highly clustered nature in real world networks, it can be assumed that the ABA signalling network can more likely be clustered into hierarchical modules. Hierarchical modularity is a novel concept in recent literature for identification of organizational principles of complex networks [4], [5]. The modularity concept assumes that the functionality of a networked system can be partitioned into a bundle of functional segments by decomposing the network based on various topological properties, such as betweenness centrality (a measure of the centrality of a node in a network), topological overlap (similarity of nodes in terms of the common nodes they are connected to) and global structure analysis. Centrality measures are useful to identify the most important players (hubs) in a system.

Topological overlap represents a measure of agreement between the neighbourhoods of a given pair of nodes, which gives an indication of the size of the set of common neighbours shared by each pair of nodes. It helps exclude spurious connections and identify similar nodes and define the neighbourhoods of nodes based on their similarities that could indicate a potential functional group. Global structure analysis studies the topological structure of a network to understand the organizational principles of the network. All these methods help decompose a network into a distinguishable set of functional subnetworks by measuring the similarity/dissimilarity between the network nodes. By doing this, we can gain a better understanding of the relationships between different parts of the network, which can help us gain deeper insights into the principles used by the network for functional coordination of a large number of elements to achieve the network goal. Further, it will help gain deeper insights into the biology by allowing scope for suggesting possible functions for members of a subgroup by comparing them to known functions of other subgroup members.

Therefore, this study aims to analyse the topological properties of the expanded ABA signalling network to understand the underlying organizational principles and functional properties of the network from a systems point of view that sees a system as an assembly of subsystems. This paper discusses some important clusters based on topological overlap properties and centrality measures of the ABA signalling network to reveal the hierarchical modularity of the network and shows how it enables a greatly meaningful interpretation of the functional organization of the system.

2.1. Scale Free Properties of the Network

A network with scale-free property is defined as a network whose degree (node connectivity) distribution follows a power law, at least asymptotically as $h\left(k\right)\tilde{k}^{-q}$, where h(k) is the fraction of vertices in a network that have degree k, and q is the power low exponent.

2.2. Hierarchical Modularity

Hierarchical modularity is a novel and popular concept in recent literature for identification of organization principles of complex networks. The modularity concept assumes that the functionality of a system can be partitioned into a bundle of functional segments, such that the functionality of each segment is independent and separable from each other but the boundaries between segments are not necessarily clear-cut. However, it cannot be ignored that there can be reactions that do not appear together in the wiring graph but still can be functionally correlated due to feedback loops. It cannot be expected to have perfect separation of functional subgroups using any of the existing topological approaches. In fact, such separations may not even be biologically plausible. Therefore, our aim is to reasonably decompose the ABA signalling network into meaningful subsets with the aid of the available decomposing methods discussed in section 2.3 below.

2.3. Decomposition of the ABA Signalling Network

The first step in clustering is to choose a proper distance measure to distinguish the dissimilarities between the nodes of the network. Of various decomposition methods available in the literature, ‘path lengths’ between nodes are identified as the best dissimilarity measure for clustering nodes [18]. This is because closely related functional reactions should, biologically, have short path lengths. Hierarchical classification based on the dissimilarity between nodes should, therefore, satisfy the requirement that each node within a subset should be more densely and strongly connected to other nodes in the subset, compared to the interactions with nodes from other subsets.

In this study, the shortest path concept involving topological overlap is used to obtain the best clustering criteria within the ABA signalling network, as described below.

Topological overlap represents a measure of agreement between the neighbourhoods of a given pair of nodes, which gives an indication of the size of the set of common neighbours shared by each pair of nodes. This can be used to define a dissimilarity measure which can then be used to identify functional modules using a clustering algorithm. The similarity matrix (Eq. 1) contains the shortest path distance based on the ‘geodesic distance’ from node i to node j (t_ij) for each pair of nodes in the network computed from Eq. 2. From this, a dissimilarity measure in introduced as in Eq. 3 and dissimilarity matrix defined as in Eq. 4. This concept is best executed in the GTOM (generalized topological overlap measure) algorithm in MATLAB and it is recommended to refer to [6] for the details of this methodology. The Eqs. 1–4 were also adapted from [6]. The Eqs. 1 and 2 show how GTOM values are calculated for a neighbourhood of size m.

$${T}^{\left[m\right]}=\left[{ t}_{ij}^{\left[m\right]} \right]$$

where,${T}^{\left[m\right]}$ is GTOM matrix of size N x N, m is neighbourhood size, and ${ t}_{ij}^{\left[m\right]}$ is the m^th order topological overlap measure between node i and j.

$${t}_{ij}^{\left[m\right]}=\left\{\begin{array}{c} \frac{\left|{N}_{m}\left(i\right) \bigcap {N}_{m}\left(j\right)\right| +{ a}_{ij}}{min\left\{\left|{N}_{m}\left(i\right)\right|,\left|{N}_{m}\left(j\right)\right|\right\} + 1-{a}_{ij}} if i\ne j\\ \\ 1 if i=j\end{array}\right.$$

where, ${N}_{m}\left(i\right)$ represents the neighbours of node i at m^th distance, ${N}_{m}\left(j\right)$ represents the neighbours of node j at m^th distance, ${N}_{m}\left(i\right) \bigcap {N}_{m}\left(j\right)$ represents the common neighbours of node i and j at m^th distance, |.| represents the cardinality of the inside argument, and${ a}_{ij}$ is the adjacency measure (adjacency measure is a simple representation of connectivity in a graph, which represents the connection pattern of the network nodes by means of a matrix of size N x N (N is the number of nodes in the network) whose (i,j) entry a_ij is 1 if nodes i and j are connected, and 0 otherwise. The adjacency matrix is symmetric around the diagonal for undirected graphs. Defined this way, the similarity measure can fluctuate between 0–1. Therefore, the index assumes 0 for its minimum value if there are no common neighbours and no direct link between the pair. The maximum value 1 is assigned to any pair of nodes if the two nodes are directly linked and the neighbours of one node are a subset of the other.

As ${T}^{\left[m\right]}$ represents the similarity between each pair of nodes, it is necessary to convert this into a dissimilarity measure ${(d}_{ij}^{T,\left[m\right]} )$ using Eq. 3 for individual pairs of nodes and Eq. 4 for the whole dissimilarity matrix. In the implementation of Eq. 3, m is increased within a range and the most suitable m that provides the greatest discrimination is selected.

$${d}_{ij}^{T,\left[m\right]}=1-{t}_{ij}^{\left[m\right]}$$

$${D}^{T,\left[m\right]}=\left[{d}_{ij}^{T,\left[m\right]} \right]$$

In this study GTOM based dissimilarity measures were calculated with the Matlab GTOM algorithm and the clustering was based on the Ward’s linkage method on Matlab.

The topological overlap dissimilarity matrix is symmetric around the diagonal because undirected adjacency matrix was used in this study to better represent the total connectivity of the network nodes. Therefore, different hierarchical modules are located on the diagonal and represented as a series of squares. In general, modules are clearer with increasing neighbourhood size such that the higher the size of the neighbourhood, considered up to a threshold value, the higher the sensitivity for the specificity of clusters.

2.4. Centrality Measures of the ABA Signalling Network

Centrality indicates the centrality of a node in a network and it helps identify influential nodes that exert a larger control on the system. Centrality analysis was performed with Cytoscape software (version 3.8.0) [19], using “cytoHubba” plug-in [10], in which a biological network is defined as G = (V, E), where V is the collection of nodes within the network and E is the edge set. Given a node v, N(v) denotes the collections of its neighbors. Node ranking methods adopted from cytoHubba [10] are as below.

Maximum Neighborhood Component (MNC(v)) = |E(MC(v))|, where MC(v) is the maximum connected component of the G[N(v)], G[N(v)] is the induced subgraph of G by N(v) and E(MC(v)) is the collection of edges in MC(v). So this defines the maximum number of edges.
Maximal Clique Centrality ($MCC\left(v\right))={\sum }_{c\in s\left(v\right)}\left(\left|c\right|-1\right)!$, where S(v) is the collection of maximal cliques which contain v, and (|C|-1)! is the product of all positive integers less than |C|.
Density of Maximum Neighborhood Component (DMNC(v)) = |E(MC(v))|/|V(MC(v))|^ε, where ε = 1.7, E(MC(v)) is the collection of edges in MC(v) and V(MC(v)) is the collection of nodes within MC(v). So this defines number of edges per node.
Degree method (deg(v)) =|N(v)|. This defines the number of connections for a node. This can be defined for incoming (in-degree), outgoing (out-degree) or total connections for a node.
Edge Percolated Component $\left(EPC\left(v\right)\right)= \frac{1}{\left|v\right|}\sum _{k=1}^{1000}\sum _{tϵv}{\delta }_{vt}^{k}$. If G_k is the reduced network randomly generated at the k^th time and if nodes u and v are connected in G_k, set ${\delta }_{vt}^{k}$ is 1; otherwise ${\delta }_{vt}^{k}$=0 (given a threshold (0 ≤ the threshold ≤ 1); cytoHubba creates 1000 reduced networks by assigning a random number between 0 and 1 to every edge and remove edges if their associated random numbers are less than the threshold. This explores persistent connections for a node.
Bottleneck $\left(BN\left(v\right)\right)=\sum _{s\in v}{p}_{s}\left(v\right),$ where ${p}_{s}\left(v\right)=1$if more than |V(T_s)|/4 paths from node s to other nodes in T_s meet at vertex v; otherwise ${p}_{s}\left(v\right)=0$. T_s is the shortest path tree rooted at node s and V(T_s) is the collection of nodes within T_s. This seeks nodes that are on the pathway between many nodes.
Betweenness (BC(v))=$\sum _{s\ne t\ne v\in C\left(v\right)}\frac{{\sigma }_{st}\left(v\right)}{{\sigma }_{st}}$, where ${\sigma }_{st}$ is the number of shortest paths from node s to t. BC(v) indicates the proportion of ${\sigma }_{st}$that goes through node v. This quantifies the proportion of shortest paths between from s to t that goes through node v.
Closeness (CL(v)) = $\sum _{w\in v}\frac{1}{dist (v,w)}$, where the length of a shortest path between nodes u and v is denoted as dist(u, v).

3.1 ABA network is scale-free pointing to its evolutionary success

Results confirmed that the ABA signalling system is a scale free system where the ‘in-degree’ distribution (the number of in-coming connections of a node) of the network can be represented by $\text{p}\left(\text{k}\right)\text{=0.43(}{\text{k}}^{\text{-1.15}}\text{)}$ and the ‘out-degree’ (number of out-going connections) by $\text{p}\left(\text{k}\right)\text{=0.52(}{\text{k}}^{\text{-1.5}}\text{)}$ with MSE (mean square error) <0.001. As stated before, scale-free topology coexists with a high clustering nature in real world networks; thus, it is possible that the ABA signalling network is more likely clustered into hierarchical modules. High clustering also indicates a small number of highly connected nodes (hubs) and a large number of sparsely connected nodes. This allows the network scope for diversity pointing to its evolutionary success.

3.2 ABA network displays modular functional hierarchy

Figure 1 shows how the topological overlap measure decomposes the ABA signalling network based on a neighbourhood size of 1 and 2. Figures 1A and 1B illustrate the dendrogram and the heat map clustering according to dissimilarity measures of neighbourhood size 1 and 2, respectively. According to the results, the network was meaningfully divided into a set of distinguishable clusters and these clusters represented a true biological functional hierarchy. Theoretically, topological overlap measure based clustering shows asymptotic behaviour resulting in larger and tighter modules along the heat map diagonal when the neighbourhood increases above a certain size because all pairs of nodes within a connected network component will be highly interconnected (meets the network diameter) [6]. However, as the size of the neighbourhood increases, the specificity of the interconnectedness decreases. Therefore, neighbourhood size 2 is proposed as the best for biological networks in the literature because higher neighborhood sizes tend to lump nodes together resulting in loss of resolution [7].

Clusters separated by the dendrogram and heat map in Fig. 1 were analogous to each other in that the size of the red boxes along the diagonal of heat map corresponds to the clustering organization in the corresponding dendrogram (see dashed lines connecting the dendrogram and heat map for greater visibility of the clusters). These clusters represent the functional units in the ABA signalling. As neighbourhood size 2 reveals clusters more clearly, three topologically distinct functional modules were identified (by pruning at Ward distance 1.4 in Fig. 1(B)) in the system;

and they represent: osmoregulation (ion channels and regulatory proteins), lipid signalling (inositol, sphingolipid and other lipids) and Ca²⁺ regulation (see clusters separated by dashed lines in Fig. 1(B)). Closer observation of each of these three modules on the dendrogram shows that there is potential for forming even more specific functional modules within each cluster as evidenced by the sub-clusters within the clusters that can be had at various levels of pruning (heights in the dendrogram in Fig. 1). However, more regulatory molecules need to be discovered to better explain these sub-clusters.

The most prominent cluster on the heat map (lower right red square in Fig. 1(B)) represents the lipid signalling pathways in the ABA system. This prominence may be due to functionally well-preserved regulatory mechanisms. In the dendrogram, sphingolipids and phospholipids (mainly PA) (red cluster on the dendrogram) were separated from other lipids at Ward distance of 1.0 because they form a feedback regulatory loop displaying a noticeable functional independence from other lipids by contributing to ROS producing pathway. It also contained nodes involved in phosphatidic acid (PA) production and RbOH activation (See Supplementary Figure S1 for detail interactions and the summary description presented later). The second lipid signalling functional set (pink sub-cluster on the dendrogram) mainly contained nodes involved in regulating the Ca²⁺ influx from the internal organelles via Ca²⁺ 1 PLC feedback regulation.

The second cluster representing osmotic regulation (green group on the dendrogram in Fig. 1B) further specifies the functionality within this main cluster, separating ion channels and their regulatory proteins (mainly PP2C regulation) into two modules.

The third cluster mostly represented Ca²⁺ regulation (dark blue grouping on the dendrogram) of the system but structural rearrangement (actin) is shown to be very closely associated with the Ca²⁺ regulatory part. Interestingly, actin rearrangement is currently thought to be an ‘independent’ functional module in the ABA signalling network but our results could not place it in an independent module. It indicates that these two functional sets are heavily dependent on each other making it difficult to further subdivide this cluster but many questions remain unanswered about the connections between the actin cytoskeleton and calcium. For example, calcium-stimulated protein kinases involved in phosphorylating ABPs (Acting Binding Proteins) and their phosphorylation substrates have yet to be identified [8]. Moreover, there are gaps in understanding of how the actin cytoskeleton regulates the activity of calcium-permeable channels. Further, actin regulatory proteins were scattered in other functional modules even though these proteins did not share a true functional similarity with rest of the members in the corresponding modules. This may indicate multiple roles of actin and/or structural rearrangement that are not yet known. Future studies should therefore focus on the signal transduction of calcium to change the actin cytoskeleton and the mechanism(s) through which calcium homeostasis is regulated by the actin cytoskeleton [8]. Additionally, this third Ca²⁺ dominant cluster reveals a close link to membrane depolarization (yellow group on the dendrogram). Membrane depolarization is due to the activity of various ion channels including Ca²⁺. This close relationship may indicate a predominant role of Ca²⁺ in membrane polarization.

The above three main functional clusters (subsystems) are highlighted on the ABA signalling digraph in Fig. 2 using the same colours as in the dendrogram under the same headings - lipid regulation, osmoregulation and Ca²⁺ and Actin regulation. Figure 2 highlights these three as seven functional modules as indicated on the dendrogram in different colours representing: immediate downstream effectors of ABA (light blue box), inositol pathway (pink box) and sphingolipid and phosphatidic acid pathway (red box); ion channels (teal box) and ion channel regulation (mainly via PP2C) (green box); depolarization (pale yellow box) and Ca²⁺ and actin regulatory pathways (dark blue box).

The light blue cluster, which was topologically closely associated with lipid signalling, did not represent any specific signalling pathway but, instead, the reception of the ABA signal by various lipids, proteins and enzymes on the plasma membrane. This may not currently have a true biological meaning beyond signal transfer, as the majority of the reactions in this subset are putative connections where elements of true regulations are yet to be discovered.

3.3 Hub nodes of the ABA network

The roles of different nodes within a network are often understood through centrality analysis to quantify the capacity of a node to influence, or be influenced by, other nodes [9] and to identify key players (hubs) in biological processes. Top ten nodes ranked by eight centrality measures, Maximum Neighborhood Component (MNC), Maximal Clique Centrality (MCC), Density of Maximum Neighborhood Component (DMNC), degree and four centralities based on shortest paths (Bottleneck (BN), Closeness, Betweenness and Edge Percolated Component (EPC)) using cytoHubba [10] are shown in Table 1. Overall, results of all the centrality measures were comparable and most produced the same results. Hub elements of the ABA signalling network identified by these global and local centrality measures were, primarily, SLAC1, RbOH, PP2C, ACTIN, DEPOLAR and Ca²⁺ (yellow nodes in Fig. 2) and, potentially, ROS, CDPK, MAPK and PA (red nodes in Fig. 2). They acted as central elements in each of the three main functional subsystems and in six of the seven modules indicating their importance for the functioning of the system. For example, SLAC1 (Slow activating anion channel) plays a crucial role in osmoregulation of the system via membrane depolarization and slac1

Table 1

Top ten elements in the network identified by different Local and Global centrality measures.
Local				Global
MNC	MCC	DMNC	Degree	EPC	BN	Closeness	Betweenness
PP2C	CA	CDPK	CA	CA	CA	CA	CA
CDPK	PP2C	SLAC1	PP2C	PP2C	ACTIN	PP2C	PP2C
SLAC1	SLAC1	MAPK	SLAC1	SLAC1	PA	ROS	ACTIN
MAPK	CDPK	ACTIN	ROS	Depolar	PP2C	RBOH	PA
Depolar	Depolar	pH	Depolar	ROS	RBOH	ACTIN	ROS
CA	MAPK	ABH1	RBOH	RBOH	Depolar	SLAC1	RBOH
PIP2	ACTIN	RBOH	ABA	CDPK	SLAC1	Depolar	SLAC1
SNRK2	ROS	CAM	PA	PH	PLD	CDPK	ABA
ACTIN	RBOH	ICA	ACTIN	MAPK	ROS	MAPK	PLD
pH	ABA	MALATE	MALATE	SNRK2	GPA1	PA	Depolar
MNC - Maximum Neighborhood Component, MCC - Maximal Clique Centrality, DMNC - Density of Maximum Neighborhood Component, EPC - Edge Percolated Component, and BN – Bottleneck

mutants are strongly ABA insensitive [11]. ROS are central to cation efflux, Ca²⁺ signalling, as well as actin rearrangement. Ca²⁺ signalling is believed to play a secondary role in stomatal closure and be primarily responsible for closure maintenance. PP2C, the principal negative regulator of the ABA signalling network, is tightly regulated with many connections as inhibition of PP2C is the most fundamental need of the system to sustain the proper functioning of the osmoregulation and structural rearrangements required for stomatal closure under stressed conditions. Actin, representing actin rearrangement, is essential for collapse-free cell shrinkage.

3.4 Functional Flow of the ABA signaling network

Considering the spatial arrangement (as discussed above) and temporal behaviour of these modules incorporating timing for their signalling events (temporal behaviour of this system based on timing of events from literature and from an asynchronous Boolean model discussed in [12, 13]), the functional flow of the ABA signalling network can be abstracted as depicted in Fig. 3. Specifically, after a comprehensive review of the biological literature on the relevant time durations (half activity) for each reaction corresponding to the network edges in the ABA network, an asynchronous updating scheme was introduced to the model and system dynamics were studied [12, 13]. Integration of asynchrony in a deterministic manner in the asynchronous Boolean model captured the order of the events happening inside the ABA system through precise information processing. It follows the order of events happening in the network from the reception of the signal to the generation of output - stomatal closure. Figure 3 shows the integration of signal transduction through various signalling components between ABA reception and stomatal closure. From a high-level perspective, the functional flow of this network starts at the plasma membrane of the guard cell followed by the cytoplasm and internal organelles. All these components are cross-linked and connected with a series of feedback loops towards accomplishing the goal of stomatal closure.

From a detailed functional perspective, at the plasma membrane, the first module to respond to the ABA signal is all the membrane proteins and lipids, which are directly regulated by ABA (Fig. 3, panel (A)). This includes the ABA receptor complex (activated in less than a minute) and several other enzymes (for clarity, individual elements are not shown in Fig. 3). Enzyme activation at the

plasma membrane leads to the activities of lipid signalling pathways (e.g., PI3KP, PI4KP, SpHK and PLD) that are activated within the first few minutes (phospholipid within a minute and sphingolipid in two to four minutes). This confirms that as the building blocks of the plasma membrane, lipids are the first to receive and quickly proceed with the signal transduction. Lipid signalling modules proceed with the signalling mainly by invoking Ca²⁺, actin and oxidative signalling pathways (ROS and NO). Some enzymes (e.g., primarily SnRK2, MAPK, and CDPK) act on regulating ion channel protein modifications and pH changes in the cytoplasm (panel(B) of Fig. 3 and Ion channel regulation functional module (green box) in Fig. 2). As can be seen, almost all elements are related to both Ca²⁺ and osmoregulation (panel (C) in Fig. 3)

By means of these processes, ABA boosts the activities of all the functional modules identified in the network. These modules cross link with each other to achieve specific tasks needed for stomatal closure (C-E panels in Fig. 3), while maintaining their activities by a number of feedback loops. Of them, the fastest visible cell behaviour is ion channel activities regulating osmosis of the guard cell which takes place within two minutes from receiving the ABA signal (note the green arrows in Fig. 3). Osmotic regulation is basically achieved through the regulation of ion channels, depending on the gating properties of the respective channels. These channels can either be regulated by post-translational modifications (mainly phosphorylation) of channel proteins and/or voltage sensing. It can be assumed that post-translational modification initiates anion efflux (Cl-/${\text{NO}}_{\text{3}}^{\text{-}}$ and malate2-). As a result, the electrical properties of the plasma membrane become more positive facilitating the voltage potentials required for opening of the voltage sensitive channels for K⁺ efflux. According to the time scales observed in the literature [12], it can be assumed that guard cell osmoregulation starts by pumping out both anions and cations (K⁺). Inhibition of influxes of K⁺ appears secondary as regulation of these events happen on a slower time scale. However, Ca2 + signalling proceeds with its activities before the inhibition of these influxes.

It is reported in the literature that structural rearrangements follow osmotic regulation. Topologically, actin reorganization and Ca²⁺ regulatory subsets are closely connected and are grouped in the same functional module (dendrogram in Fig. 1, dark blue box in Fig. 2 and purple arrows in Fig. 3). This clustering can be accepted because both oxidative pathways and lipid dependent pathways directly regulate actin and Ca2 + signalling pathways (refer to the orange coloured arrows from both to actin via actin regulatory processes and to purple arrows from both to Ca²⁺ in Fig. 3). Furthermore, Ca²⁺ and actin are linked by a positive feedback loop where Ca²⁺ activates actin and actin, in turn, through other regulators (from Ca²⁺ to actin via actin regulatory processes (orange coloured arrows) and from actin to Ca²⁺ via ion channels/pumps (purple coloured arrows) in Fig. 3), regulates Ca²⁺. Ca²⁺ signalling is initiated by ROS (via channel protein modifications) and inositol signalling and then by NO and actin. All of them make feedback regulatory loops with Ca²⁺, making Ca²⁺ the most connected element in the system (note the relative abundance of purple arrows in Fig. 3). These signal transduction mechanisms progressively reduce the cell turgor and affect structural rearrangements in a coordinated manner to support safe cell shrinkage without collapse (Panel (D) in Fig. 3) to achieve the output of the biological system, i.e. stomatal closure (Panel (E) in Fig. 3).

Guard cell signalling is a complex system that plants use to control the stomatal aperture. In this study, we assembled an updated ABA network and studied its topological properties using graph theoretic measures and related the topological properties to functional organisation of the network. Results showed that the network is scale free and coherently organized as a system of subsystems. Specifically, there are three main self-organized functional subsystems linked together to carry the ABA signal to close stomata. These subsystems are mainly: Lipid signalling, Osmoregulation and Ca²⁺ (and actin) signaling. These 3 main subsystems can be further decomposed into seven functional modules which include signal perception, sphingolipid signalling, inositol signalling, ion channels, ion channel regulatory proteins, Ca²⁺ and Actin signalling. These modules in turn comprises an interconnected set of proteins, lipids, small molecules and various other conditions (e.g. pH) of the guard cells. The interconnections among the modules facilitate the communication flow of the whole system to respond to the stress signals by means of a collection of feedback processes and their relative dominance in time and space.

In systems thinking, this tight binding by feedback loops, which function differently in time and space with a defined hierarchy, provides the ABA network with increased resilience to function in a variable environment with minimum time delay.

Osmoregulation (basically SLAC1 regulation) and Ca²⁺ signalling, being hubs in the system, are tightly connected with many of the other functional modules. Of these two, the largest number of positive and/or negative feedback loops connect Ca²⁺ signalling to the majority of modules, placing it as the core reinforcement in the system.

Decomposition of the ABA signalling network based on the topological differences shared by neighbourhood sizes 1 and 2 identified three main self-organized functional subsystems that are linked to carry the ABA signal to close the stomata. We identified that decomposition is relatively distinctive for neighbourhood size 2, which displays higher Ward distances (discrimination) between the functional subsystems. Both neighbourhood sizes 1 and 2 identify lipid signalling, Ca²⁺ signalling and guard cell osmoregulation (ion channels and regulatory enzymes) representing guard cell turgor reduction as the three functionally separable hierarchical subsystems in the system. Six of the seven modules, that these three subsystems decompose into, as highlighted in Fig. 2, are mostly centred around hub elements in the ABA signalling network identified by the centrality measures of the network, displaying the functional specificity of each module (Ca²⁺, Actin, RbOH, SLAC1, PP2C, depolarization and then to a lesser extent, PA, ROS, CDPK, MAPK and ABA).

In general, there is no clear functional boundaries between these modules to consider them as totally independent functional sets from the others according to the current knowledge. For example, structural rearrangement is thought to represent one clear functional module in the ABA signalling network but our results show that it overlaps with the functional module of Ca²⁺ signalling either due to their close interaction or due to a lack of proper knowledge about all the functional proteins and regulatory mechanisms of actin regulation in guard cells. Importantly, a close link between actin and Ca²⁺ signaling has been shown in volume regulation in mammalian cell cycle [14]–[17]; therefore, a similar close relationship may be possible in stomatal closure.

The main findings of our study can be summarised as follows:

The ABA signalling system is an evolutionarily successful system as it is a scale free system that hypothetically provides a larger space to reach the global output through diverse arrangements of signalling events.
There are 3 main subsystems representing lipid signalling, Ca²⁺ signalling and guard cell osmoregulation which can be further subdivided into seven functional modules of signal perception, sphingolipid signalling, inositol signalling, ion channels, PP2C regulation, Ca²⁺ signalling and depolarization.
Potential hubs of the network, mainly Ca²⁺, Actin, RbOH, SLAC1, PP2C, depolarization and then to a lesser extent, PA, ROS, CDPK, MAPK and ABA define the functional specificity of the network representing major events in the ABA system, such as signal perception, lipid signalling, osmoregulation, Ca²⁺ signalling and structural rearrangement.
Ca²⁺ signalling acts as the core reinforcement in the system.
The tight binding by feedback loops, which function differently in time and space with a defined hierarchy, provides the ABA network with increased resilience to function in a variable environment with minimum time delay.

We hypothesized the potential existence of subsystems in the ABA network and that identification of these subsystems and their relationships in the spatial and temporal placements of the network would allow to highlight the biological importance and contribution of each event, task or molecule, and show their coordination to the final output more realistically and meaningfully than considering every molecule’s task individually in a complex environment. Accordingly, this research for the first time studied the topological properties of the ABA signalling network and revealed the existence of three subsystems with seven interlinked functional modules that are hierarchically organized in time and space to robustly achieve stomatal closure. Results further revealed that some of the known functional modules of the network are masked by the size of the ABA signalling network as it is still too small to distinguish all hierarchical modules due to the limited understanding of the correct regulatory mechanisms. Therefore, these properties should be studied in future research using a more expanded network topology.

Supplementary Materials: The following are available online. Figure S1: Detailed view of the extended ABA signalling network as a sign directed graph

Author Contributions: P.W. and S.S. designed the research and wrote the manuscript, P.W. conducted the analyses and prepared the figures, S.S. supervised the research and provided critique and overview and edited the manuscript.

Acknowledgments: This work was supported by a Commonwealth Scholarship. A thesis has previously been published [12] that contains this work.

Conflicts of Interest: The authors declare no conflict of interest.

Y. Wu, X. Zhang, J. Yu, and Q. Ouyang, “Identification of a Topological Characteristic Responsible for the Biological Robustness of Regulatory Networks,” PLOS Comput. Biol., vol. 5, no. 7, p. e1000442, Jul. 2009.
A. M. Hetherington and F. I. Woodward, “The role of stomata in sensing and driving environmental change,” Nature, vol. 424, no. 6951, pp. 901–908, 2003.
T. G. Lewis, “Scale-Free Networks,” in Network science: Theory and applications, John Wiley & Sons, 2011, p. 177:215.
E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabási, “Hierarchical organization of modularity in metabolic networks,” Science (80-.)., vol. 297, no. 5586, pp. 1551–1555, 2002.
J. A. Papin, J. L. Reed, and B. O. Palsson, “Hierarchical thinking in network biology: the unbiased modularization of biochemical networks,” Trends Biochem. Sci., vol. 29, no. 12, pp. 641–647, 2004.
A. M. Yip and S. Horvath, “Gene network interconnectedness and the generalized topological overlap measure,” BMC Bioinformatics, vol. 8, no. 1, p. 22, 2007.
A. Li and S. Horvath, “Network neighborhood analysis with the multi-node topological overlap measure,” Bioinformatics, vol. 23, no. 2, pp. 222–231, Jan. 2007.
D. Qian and Y. Xiang, “Actin Cytoskeleton as Actor in Upstream and Downstream of Calcium Signaling in Plant Cells,” Int. J. Mol. Sci., vol. 20, no. 6, 2019.
S. Oldham, B. Fulcher, L. Parkes, A. Arnatkevic̆iūtė, C. Suo, and A. Fornito, “Consistency and differences between centrality measures across distinct classes of networks,” PLoS One, vol. 14, no. 7, p. e0220061, Jul. 2019.
C.-H. Chin, S.-H. Chen, H.-H. Wu, C.-W. Ho, M.-T. Ko, and C.-Y. Lin, “cytoHubba: identifying hub objects and sub-networks from complex interactome,” BMC Syst. Biol., vol. 8, no. S4, p. S11, 2014.
T. Vahisalu et al., “SLAC1 is required for plant guard cell S-type anion channel function in stomatal signalling,” Nature, vol. 452, no. 7186, p. 487, 2008.
K. P. Waidyarathne, “Modelling dynamics of Abscisic Acid (ABA) signalling network in plant guard cells to induce stomatal closure in response to drought stress,” Lincoln University, 2015. researcharchive.lincoln.ac.nz
P. Waidyarathne and S. Samarasinghe, “Boolean Calcium Signalling Model Predicts Calcium Role in Acceleration and Stability of Abscisic Acid-Mediated Stomatal Closure,” Sci. Rep., vol. 8, no. 1, 2018.
C. Rosenmund and G. L. Westbrook, “Calcium-induced actin depolymerization reduces NMDA channel activity,” Neuron, vol. 10, no. 5, pp. 805–814, 1993.
E. T. O’Brien, E. D. Salmon, and H. P. Erickson, “How calcium causes microtubule depolymerization,” Cell Motil. Cytoskeleton, vol. 36, no. 2, pp. 125–135, 1997.
Y. Wang, M. P. Mattson, and K. Furukawa, “Endoplasmic reticulum calcium release is modulated by actin polymerization,” J. Neurochem., vol. 82, no. 4, pp. 945–952, 2002.
D. Gremm and A. Wegner, “Gelsolin as a calcium-regulated actin filament‐capping protein,” Eur. J. Biochem., vol. 267, no. 14, pp. 4339–4345, 2000.
H.-W. Ma, X.-M. Zhao, Y.-J. Yuan, and A.-P. Zeng, “Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph,” Bioinformatics, vol. 20, no. 12, pp. 1870–1876, 2004.
P. Shannon et al., “Cytoscape: a software environment for integrated models of biomolecular interaction networks,” Genome Res., vol. 13, no. 11, pp. 2498–2504, 2003.
S. Li,, S.M. Assmann, and R. Albert. Predicting essential components of signal transduction networks: A dynamic model of guard cell abscisic acid signaling. PLoS Biol. 4, 1732–1748 (2006).

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A System of Subsystems: Hierarchical Modularity of Guard Cell ABA Signalling Network defines its Evolutionary Success

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Abstract

Figures

1. Introduction

2. Materials And Methods

2.1. Scale Free Properties of the Network

2.2. Hierarchical Modularity

2.3. Decomposition of the ABA Signalling Network

2.4. Centrality Measures of the ABA Signalling Network

3. Results

3.1 ABA network is scale-free pointing to its evolutionary success

3.2 ABA network displays modular functional hierarchy

3.3 Hub nodes of the ABA network

3.4 Functional Flow of the ABA signaling network

4. Discussion And Conclusions: A System Of Subsystems

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