Modeling of the jasmonate signaling pathway in Arabidopsis thaliana with respect to pathophysiology of Alternaria blight in Brassica

The productivity of Oilseed Brassica, one of the economically important crops of India, is seriously affected by the disease, Alternaria blight. The disease is mainly caused by two major necrotrophic fungi, Alternaria brassicae and Alternaria brassicicola which are responsible for significant yield losses. Till date, no resistant source is available against Alternaria blight, hence plant breeding methods can not be used to develop disease resistant varieties. Jasmonate mediated signalling pathway, which is known to play crucial role during defense response against necrotrophs, could be strengthened in Brassica plants to combat the disease. Since scanty information is available in Brassica-Alternaria pathosystems at molecular level therefore, in the present study efforts have been made to model jasmonic acid pathway in Arabidopsis thaliana to simulate the dynamic behaviour of molecular species in the model. Besides, the developed model was also analyzed topologically for investigation of the hubs node. COI1 is identified as one of the promising candidate genes in response to Alternaria and other linked components of plant defense mechanisms against the pathogens. The findings from present study are therefore informative for understanding the molecular basis of pathophysiology and rational management of Alternaria blight for securing food and nutritional security.


Results
Description of constructed model. To date, a JA signaling model using Systems Biology Graphical Notation (SBGN) has not been constructed 49 . The goal of this study is to decipher the complexity of Arabidopsis-Alternaria pathosystem for understanding the pathophysiology of Alternaria blight in Brassica through quantitative and qualitative analysis of jasmonate biosynthesis pathway in terms of upstream signal and downstream response produced during pathogenesis process. These molecular mechanisms were modelled based on system biology approach to determine the duration of JA responses as well as try to identify key components involved in regulation of pathway during pathogenesis for achieving resistance against the disease. SBGN was utilized to assemble the relationship among different molecular species in the model based upon previous studies mined from scientific literatures and databases (Fig. 1). The model consists of 4 compartments, 44 species, 28 proteins, 14 simple molecules, 1 phenotype, and 37 reactions (Fig. 2).
Dynamic behaviour prediction of constructed model through simulation analysis. Present study explains the outcome of integrated systems based approach that explored the intricate nature of jasmonate signalling pathway during pathogenesis at molecular level. The rate laws produced by SBMLsqueezer were utilized to predict the dynamic behavior of the pathway ( Table 1). This could be useful for understanding the pathophysiology of Alternaria blight in Brassica for developing an efficient disease management strategy. The simulation jobs were run on hardware configuration comprises of intel corei3 processor of 2.40 GHz and 4GB RAM on 64 bit windows operating system laptop.
The real values for each molecular species in the model have not been used due to un-availability of experimental data for an individual cell. Simulation can decipher the behaviour of key molecular species in the presence and absence of pathogen elicitor for a particular disease. Defense responses through jasmonate signalling were predicted during pathogenesis of Alternaria blight in Arabidopsis thaliana.
In the absence of quantitative molecular data of an individual cell, it is difficult to estimate the relationship between species. Therefore, quantity is occupied in terms of amount to confirm their existence 40 . The values for each molecular species in the model ranged from 0.25 to 2.5. The value of pathogen is set at 0.25; receptor is set to equal of 0.5 due to its basal amount. The amounts of species are set at 0.5, 1 and 2, according to their activation and inactivation states, for example non-phosphorylated MAPKs are set at 0.5 and phosphorylated are set at 1; all the metabolites are set at 0.5 and all the enzymes involved in biosynthetic pathway are set at 1. The value of JA, MeJA and JA-IIe are considered as variable species and its values range from 0.5 to 1 to observe the dynamic behaviour of system. The value of COI1 is set in the range from 0.0 to 2 and that of SCF-COI1 complex is equal to 1.5; the amount of transcription factors is set to 1 and proteins is set to 2 as well as the amount of phenotypic response is set equal to 2.5.
Previous studies clearly demonstrated that when the intensity of abiotic and biotic stresses increases, the defense responses decrease rapidly in time dependent manner 15 . Here, the dynamic behaviour of the different species in the model was visualized during simulation with course of time. The variation in defense response with respect to COI1 is revealed in Fig. 3. When the COI1 interacts with jasmonate signal, it controls the modulation behaviour of various gene(s) involved in defense responses. It was predicted that when the expression level of COI1 increases the defense responses also increases, besides, when the expression of COI1 is slowed down the regulation of defense responses is down regulated in time dependent manner during plant-pathogen interaction (Fig. 3). The dynamic behaviour of plant system with respect to pathogenesis of Alternaria species and its effect on expression level of COI1 was shown in Fig. 3a,b, and c. PDF1.2 is one of plant defense gene playing essential role in disease resistance, during simulation analysis, it was predicted that its activity is also controlled by the activation of COI1. It was also predicted that when the expression of COI1 increases, the PDF1.2 is up-regulated. The fluctuations in the dynamic behaviour of PDF1.2 with respect to COI1 were also observed in different time scale ( Fig. 4a and b). The model has also perturbed with the variable quantity of COI1 to confirm its role in the regulation of defense responses quantitatively. It was found that the higher expression of COI1 modulates the cellular expression of defense related genes and provides protection to the crop plant systems (Fig. 4). It is well characterized that the COI1 is jasmonate receptor and responsible for triggering jasmonic acid mediated immunity in Arabidopsis thaliana through interaction with jasmonate signal and its expression in balanced way is essential to crop plants for defending pest and pathogen attack 6 . Present study decoded the fluctuation of COI1 at different amount with respect to time that can useful to maintaining its expression level in the balanced way during pathogenesis in future. Jasmonic acid and its structural analogs are known natural substrates that initiates the activity of COI1; Me-JA is one of the functional analogs of jasmonic acid which is known to promote COI1 interaction with JAZ1, which is responsible for defense responses, thus, we perturbed the model with different amount of Me-JA to predict the dynamic behaviour of COI1 (Fig. 5a). It was found that the dynamic activity of COI1 is controlled by the production of jasmonic acid and activity of its functional analogs (Fig. 5b,c and d).
Topological analysis of JA signalling network. The molecular interaction network of jasmonic acid has 81 nodes and 84 edges and all of the data were taken as scale free properties as anticipated from biological network 50,51 (Fig. 6). The average path length was used to measure the JA signalling network as directed and un-directed graph. The in-and out degree distributions for modelled network have power low exponent with approximate value a = 54.000, b = −1.848 and a = 74.000, b = −3.888 (R-squared value 1.000 and correlation 1.0) respectively. R-squared was computed on logarithmized value. Out and in degree power low distribution of JA network was analyzed, which explains the number of contacts per node, in order to determined hubs and verify the scale-free property 52,53 .
Network analysis revealed that the JA network has 81 node, 84 edges, 1 connected component node, 0 isolated node, 2.074 average number of neighbours, 6480 shortest path, 17.822 characteristics path length and 52 network diameter ( Table 2). The visualize parameter of NetworkAnalyzer was used to map the hub node in the network using the visual style to map node size "Degree" and node color "BetweenessCentrality" to determined the hub nodes. The BetweennessCentrality of each node is defined as a number between 0 and 1. It reveals the amount of control that this node exerts over the interactions of other nodes in the network 54 . The node JAZ1, JAZ3 and MYC2 was found as a hub node, which might play, a key regulatory role in Jasmonic acid mediated immunity (Fig. 7). Modeling and analysis of these networks would decode the complexity of agricultural trait and help us to bring out the hidden properties of the crop plant systems. A resolution image of whole network in modular view along with predicted hub nodes is shown in Fig. 7.

Discussion
Alternaria blight is one of the major threats to attain productivity of crucifers crops mainly Oilseed Brassica species such as Indian mustard, cabbage, broccoli, and oilseed rape. The yield losses from this disease could reach up to 80% 55 . Till date disease management through fungicide chemicals was the only option but these are practically insufficient in addition to being environmentally hazardous. In many European countries, organic agriculture has been transformed quickly through agricultural policy, which reports indicate opportunity of biological management of the disease 9 . Certain wild type plants in Brassica and Arabidopsis are known to show resistance or incompatible reactions to Alternaria. But their transferability to the agronomically important crops has been a limiting factor through breeding strategies due to several reasons including, genetic drag and self incompatibility, arising a major problem all over the world with no proven source of transferable resistance in any of the hosts 56,57 .
It is being felt that Alternaria brasscicola -Arabidopsis could be used as one of the excellent model system to understand phathophysiology of Alternaria blight in Brassica. Alternaria brassicae, being a hemibiotroph fungus displays necrotrophy at some stages of pathogenesis. It has been reported that Jasmonic acid plays important role in mounting the defense response towards necrotrophic fungal pathogens 17 . Deep insight in to the JA mediated signal transduction pathway involved during defense response will help in devising strategies for development of

SN Reactions
Kinetics equations 1 Necrotrophic fungal pathogen → PRRs Vre1 = vmax_re1 × Necrotrophic fungal pathogen/(kmc_re1_ Necrotrophic fungal pathogen + Necrotrophic fungal pathogen) Linolenic acid → HPOT catalyzed by Lipoxygenase   58 . Recent advances in integrated sciences have huge potential to handle such recalcitrant problem; therefore, the important components triggered during disease were investigated in the present study via modeling and simulation as well as network analysis of jasmonate signaling pathway in Arabidopsis thaliana. Jasmonate signaling pathway is well characterized pathway in plant systems for defense responses particularly in case of necrotrophic pathogens but the knowledge about the key element of pathway during pathogenesis in term of quantity remain unclear 5 . The developed model clearly demonstrated the fluctuations of key component involved in diseases resistance during simulation besides network analysis were also conducted to determine the value of topological  parameter of the JA network for mapping of hubs based on out degree visualization 59 . Degree is defined as a number of edges linked to a node, if it is a self loop; it shall be counted as two edges of a single node. In directed node, the degree distribution is of two types, in and out degree distribution. The number of coming edges to a node is called in-degree distribution and number of out-going edges is called out degree distribution of a node 60 . In case of biological network, the node and edge is defined in different ways; in metabolic network, the node is considered as metabolites and reactions are considered as edges; in protein-protein interaction network, protein is considered as node and edges are considered as bonding between one protein with other protein. Whereas, in case of gene regulatory network, the nodes are considered as gene and edges are known for its regulatory effect 52 .
The aim of modeling and simulation is to describe and understand the pathophysiology at molecular level where key regulatory element and its complex mechanisms that happen at several time scales were predicted. During simulation analysis at variable amount of jasmonic acid and its functional analogs, Me-JA; COI1 is predicted as one of the potential molecular target because it controls the expression of various defense related genes during pathogenesis. It was also predicted that the up and down regulation of COI1 during plant-pathogen interaction is totally linked to amount of jasmonic acid and its functional analogs. Besides, we have manually increased and decreased the amount of COI1 to determine the behaviour of system during pathogenesis 61 . Recent cloning and expression study conducted on COI1 gene of Aquilaria sinensis demonstrated that the Methyl jasmonate (MeJA), mechanical wounding and heat stress could significantly induce its expression level 62 . Network analysis has been publicized to be one of the powerful tools for decoding the key regulatory elements (hubs), which is   responsible for controlling the complex biological machinery during diseases 63 . Hub is a concept originated from the field of network science that refers to a node having number of links. Identification of hub nodes in complex networks has attracted a growing attention over the last decade 64,65 . In biology, a hub is metabolite, gene, or protein which is highly connected to the other nodes (is metabolite, gene, or protein) in a network and that is known to regulates several other pathways associated with the main pathway. Recent advances in plant disease resistance research have provided exciting novel insights into decoding of defense signaling network. Diverse number of components plays essential roles in the regulation of whole network through cross-communication in antagonistic or synergistic manners. Biological properties of hubs in JA signalling pathway are very significant as these are closely related to the well characterized components linked to the defense responses. Our finding demonstrated the highly connected nodes (hubs) such as JAZ1, JAZ3 and MYC2 but it was predicted that the expression of these hubs is managed by COI1. These hub nodes are involved in the regulation of defense machinery through interaction of COI1 with jasmonate signal. For that reason, COI1 is considered as one of the key components of JA pathway. Previous study suggested that COI1 has the structural traits for binding to jasmonyl-isoleucine (JA-IIe/Coronatine) 66 and determined as an intracellular signal with a hormone binding site 67 . Therefore, it may serve as a potential molecular target for triggering de novo resistance in crop plant systems during plant-pathogen interaction via engineering of jasmonic acid pathway for sustainable production of jasmonic acid and its functional analogs during pathogenesis or providing exogenous compounds as defense induces that can mimick the expression of COI1. It is evident that small molecule targeting COI1 leads to the production of appropriate defense whereas engineering of jasmonic acid pathway for proper production of jasmonic acid during diseases has a very complex and time taking process, therefore, we have concluded that there is a need of novel defense inducer molecule more efficient and stable as compared to jasmonic acid and its structural analogs to tackle today's problem of pathogen resistance by developing de novo resistance in crop plants for robust agricultural productivity and sustainability 5,6 . Biologically active small molecules have been verified previously for crop plant protection by producing de novo resistance 68,69 . In our knowledge, we have modeled JA signalling pathway first time to analyze the whole systems during plant-pathogen interaction. This integrated approach shows that computational demonstration can construct and explain precisely the complete observable fact of JA signalling during pathogenesis at molecular level. The constructed technical model describes the biochemical relationship of different molecular species and effect of pathogen in different unit time. These types of In silico finding provides a valuable hypothesis and mimics by the simulation analysis as in vitro test. The study exhibits that cellular reaction depends on the effective quantity of jasmonic acid and its functional analogs inside the cell 70 . As a result, the understanding of the integrated behaviour of model can be valuable to develop novel plant health and disease management strategies to fulfilling the demand of Brassica oilseed for rapidly growing world population.
COI1 was found as the most important molecular target. It can be utilizing to mimick jasmonic acid mediated immunity through engineering of the plant system or designing of the cost effective molecule, more efficient than naturally produced jasmonic acid for triggering de novo resistance during pathogenesis. During analysis, COI1 was found to control the expression of many defense related component in the model. Besides, other identified hubs node may also utilized for further investigation with respect to plant-pathogen interaction. A number of undiscovered effects of JA with their perturbed amount to its respective target can be predicted. This finding can be useful for experimental design and interpretation by using diseased and healthy plants. Nevertheless, it seems to be essential to examine more conditions that imitate realistic stress situation in an attempt to find out which methods need to be developed to cope with their usual environment. In term of agricultural significance, it is assumed that the availability of a constructed model further speed up the research for crop protection. Such type of models can be utilize in identification of molecular target and its dynamics at cellular and system level for management of Alternaria blight: a recalcitrant disease of Brassica through designing of defense inducer molecules that can able to trigger defense related pathway or application of genetic engineering approaches for sustainable agriculture.

Methods
Model construction. A comprehensive literatures survey was done to determine the relationship between different molecular components involved in Jasmonic acid biosynthesis pathway that triggers defense responses during plant-pathogen interaction in Arabidospis thaliana. A Systems Biology Graphical Notation (SBGN) for building of biological networks to express adequate information in a clearly visible and precise way was used 49 (Fig. 1). The Metabolic map of Jasmonic acid signalling pathway was constructed by CellDesigner4.4 and stored in Systems Biology Markup Language (SBML), a machine-readable format for representation of the biological network [71][72][73][74][75] . CellDesigner is a process diagram editor tool for representation of biological pathways using inbuilt symbols of systems biology graphical notation (Fig. 1). It is a graphical user interface that facilitates systems biologist to utilize available symbols of DNA, RNA, Protein, Simple molecule, Catalysis, Stimulation, Inhibition, Phosphorylation, activation, degradation etc for construction of pathway. The control panel menu in CellDesigner provides us simulation facilities by using SBML ODE Solver and Copasi, It facilitates to specify the particulars of constraints, varying quantity and leading parameter search as well as shared simulation with instinctive way 40 . Assignment of kinetic rate equations. SBMLsqueezer_v2.1 was applied to generate kinetic rate equations for each reaction of the constructed model through CellDesigner. This approach assists the modeling steps via programmed generation of equation and takes over the highly error-prone and complicate process of manually assigning kinetic equations 76 . It is a CellDesigner plugin that uses information from the system biology graphical notation (SBGN) representation of all components of network. SBMLsqueezer judges the Systems Biology Ontology (SBO) annotations to pull out this information 40,77 . The rate laws that can be produced by SBMLsqueezer consist of numerous types of generalized mass action, and comprehensive as well as generalized enzyme kinetics ( Table 1). Kinetic rate equations for metabolic reactions include uni-uni Michaelis-Menten kinetics, generalized hill equation for uni-uni reactions, Irreversible non-modulated non-interacting reactant enzymes, bi-uni enzyme reactions, bi-bi enzyme reactions, thermodynamics and convenience kinetics modular rate laws for enzymatic reactions 76,78 . Model simulation. To simulate the dynamic behavior of constructed model, SBML ODE Solver Library (SOSlib) was used through CellDesigner 71,79 , which enables us to run ordinary differential equations (ODE) based simulations. This is a frequently used method for quantitative analysis of biological systems in term of computational efficiency. SOSlib is a programming library for symbolic and numerical analysis of biochemical reaction network models encoded in the SBML 79 . CellDesigner is an integrated modeling and simulation platform that provides several third-party tools for interactive model simulation that is SOSlib 79 , COPASI 80 and Simulation Core Library 81 . We have employed deterministic algorithm for our constructed model. In studying model of biological systems, we need solution for a given set of parameter values with their assessment for dependency of other species in the model. The simulation engine itself was executed by the native library, and the results of simulation analysis were shown in a Graphical User Interface (GUI) window written in JAVA programming language 75,82 . Network analysis. Jasmonate signaling model generated in CellDesigner was exported in SBML format, which was imported in the Cytoscape 2.8.3 using Biological Network Manager (BiNoM) 83 . BiNoM is a Cytoscape plug in 84 to support the operation on biological networks represented in standard systems biology formats (SBML, SBGN, BioPAX) and to carry out studies on the complex network Structure 85 . Cytoscape is an open source software platform for integration, analysis and visualization of biological network 86 . Different types of plugins are available for various kinds of analysis, which facilitate us for decoding the complexity of biological networks. NetworkAnalyzer plugin 87 was applied for investigating and visualizing the important components of JA signaling pathway triggered during plant-pathogen interaction for devising the strategies to develop effective management system against Alternaria blight of Brassica 88 .