Abstract
Plant-insect interaction system has been a widely studied model of the ecosystem. Attempts have long been made to understand the numerical behaviour of this counter system and make improvements in it from initial simple analogy based approach with predator-prey model to the recently developed mathematical interpretation of plant-insect interaction including concept of plant immune interventions Caughley and Lawton (1981). In our current work, we propose an improvement in the model, based on molecular interactions behind plant defense mechanism and it’s effect on the plant growth and insect herbivory. Motivated from an interaction network of plant biomolecules given by Louis and Shah (2014) and extending the model of Chattopadhyay, et al (2001), we propose here a mathematical model to show how plant insect interaction system is governed by the molecular components inside. Insect infestation mediated induction of Botrytis Induced Kinase-1 (BIK-1) protein causes inhibition of Phyto Alexin Deficient-4 (PAD4) protein. Lowered PAD4, being responsible for initiating plant defense mechanism, results in degraded plant immune potential and thus causes loss of plant quality. We adapt these interactions in our model to show how they influence the plant insect interaction system and also to reveal how silencing BIK-1 may aid in enhanced production of plant biomass by increasing plant immunity mediated by increase in PAD4 and associated antixenotic effects. We hypothesize the significance of BIK-1 inhibition which could result in the improvement of the plant quality. We explain the interaction system in BIK-1 inhibition using mathematical model. Further, we adopted the plethora of computational modeling and simulations techniques to identify the mechanisms of molecular inhibition.
Introduction
Insects are amongst the major threat to several economic and staple crops. Aphids make a significant bunch of contribution to this class of organism and annual crop loss1. Where insects have natural tendency to feed on plants and pose threat to their growth rate; plants also respond these herbivore attacks by initiating their defense mechanisms2,3,4,5. Altogether, these two form an ecological model of predator-prey system 6. We implement here the top-down approach of systems biology to further explain this model in mathematical expressions as well as to explain how molecular components behind this interaction helps or can be used for regulating this ecological system7. Though, a plethora of research works published till date have put forth the mathematical model of plant-insect interaction but none of those have yet included the molecular control responsible for this phenomenon8,9,10,11,12,13. In this work, we present a two-step workflow; of which one is to design a mathematical model of plant-insect interaction network in effect of molecular components behind their response; while other relates to the search of possible inhibitor against one of the key component of this network. At last we will returnto our mathematical model with an added component and show how this inhibition may affectnetwork and contribute towards protection of plants by synergizing itsdefense mechanism.
Some key research focused on elucidating the signaling mechanisms of plant defense systems has revealed molecular interactions involved in plant defense response14,15,16,17,18,19, 20, 21. A small module of such signaling mechanism have been reviewed and reported by Louis and Shah, (2014) 22. Proposed model is an extension to Plant-Insect interaction model supposed to analyze the synchronization between molecular level as well as community level change of phase of system components and their dynamic behavior. Moreover, we expect to analyze the change in behavior of our network’s dynamicity in effect of any perturbation in system at molecular level.
Our motivation to this work lies in studying trends of plant response on insect infestation causing rapid induction in PAD4 concentration. This increase in PAD4 concentration helps transcribing several other genes including those responsible for deterring insects and protecting plants from their attack 21, 14, 23. This response is accompanied by rise in Botrytis induced kinase (BIK1) protein concentration 22. BIK1 is a key molecule in plant defense system, as it seems to confer defense resistance against some insect herbivores in several plants. Phosphorylation of FLS2 and BAK1 proteins as well as association with Flg22 initiates BIK1 mediated defense signaling in such plants. As a final outcome of this signaling response, plants act through JA and SA mediated defense mechanism 24, 25. While in case of green peach aphid attack, BIK1 is induced by insect infestation and is an experimentally validated inhibitor of PAD4 protein14.
Thus, in case of aphid attack sap feeding herbivores, insect infestation is not restricted because of PAD4 inhibition in effect of BIK1 expression. While, in BIK1 mutants, basal activity of PAD4 is up regulated and improves crop quality by hindering their infestation by insects21. This makes BIK1 to be an important target of for inhibitor design against insect infestation of plants. Since, it seems quite difficult for any small molecule to cross cell wall barrier for entering inside cell and making it feasible for our inhibitor to serve this purpose. But we assume that the cell wall barrier inplants to be accessible by projected molecule upon leaf puncture during aphid attack and deliver its purpose in the cytoplasmic environment of plant. This will make a small molecular inhibition process of BIK1 and may serve our purpose of improving plant growth rate through increased release of antixenotic phytochemicals, i.e. Ethylene 15, 16. Thus, in light of knowledge to this interaction and its anticipated effect on plant insect interaction system, Fig 1 shows a schematic diagram of the interaction network between Plants and Insects as well as their resultant influence on molecular components attached to it. We also try to demonstrate with the help of our mathematical model how inhibition of BIK1 can help restricting insect infestation and enhance plant biomass production.
Methods
Mathematical model
Efforts here in this work have been made to bring together Plant-Insect interaction model and its regulatory aspects in effect of molecular interactions involved. We restricted on basic behavioural interaction assuming sap feeding insects cause serious damage to plant stem and make it more difficult to recover as well as to simplify the computational complexity and focus on theme study of behavioral changes in effect of molecular interactions. This model consists of two parts, both of which showing dynamic progression of plant-insect interaction in effect of underlying BIK1-PAD4 interactions22; with an added inhibitor of BIK1 in the second step. Here, plants (x1) were considered as prey of growth rate k1 as well as an assumption of long recovery time. Thus plants were considered to be damaged in any condition at a rate of k2 in this predator-prey model. While, infestation of plants causeincrease in survival potency of insects (x2) and promotes reproduction with the factor of k3. While reproduction of plant specieswas independent of any interaction and grew with the rate of r times its own population, but was limited by the carrying capacity of environment K. Since, there was no predator for insects in our model; they were limited by their own death rate of k4. Further extension of this model was based on interaction of molecular components found during literature survey10, 12. Acording to which, we have introduced numerical dependencies of Plant-insect interaction system on underlying molecular interaction between PAD4 and BIK1.
Table 1 shows the list of components participating in this model. Rate constants of these interactions were decided to be arbitrary constants of such a range that does not makes any significant change to the model with or without these components. Parameters of added components in such range was seemed logical and justified because of our assumption that these molecular interactions already existed but not included while designing these plant-insect interaction models. Thus, literature based knowledge of antixenotic effects of PAD4 (x3) was translated in to this model with an effective rate of k5 depending on its availability to insects21, 23. Synthesis of PAD4 was predicted to be at the rate of k6 based on infestation caused by insects, while its natural degradation was supposed to be at the rate of k7 of its own concentration19, 20. Since BIK1 (x4) had been responsible for inhibiting the actions of PAD4, this BIK1 based PAD4 inhibition was considered to be at the rate of k814.As suggested by literature survey, BIK1 was considered to be produced upon interaction of plants and insectsat therate of k926, 27, 28. While, it’s natural degradation rate was predicted to be k10. List of all reaction channels and their rate of progression have been shown in Table 2.
With all the parameters and reaction channels in hand, mathematical model was translated into ODEs. System of equations 1, 2, 3 and 4a holds quality of an intact system.
We used Runge-Kutta’s fourth order differential equation solver and PERL programming for simulation of this model29. It was made sure through model simulation, that no significant difference is being observed in network progression while extending the network with added PAD4 and BIK1.
For, our purpose of studying effect of BIK1 inhibition on Plant insect interaction, we deliberately introduced a hypothetical inhibitor (InBIK1)in the model working at an effective rate of k11. This change in network has been incorporated in the form of equation 4a replaced by equation 4b in our earlier system of ODEs. Simulation of this model is supposed to show a prediction of effect exerted by plants on the insect herbivores through enhanced antixenotic properties or more appropriately, an enhanced release of Ethylene through the plants15, 16. While, we fixed the minimum value limit of BIK1 decline to zero concentration for avoiding any negative value if achieved.
BIK1 structure prediction and inhibition
As suggested by our mathematical model and experimental evidence the importance of BIK1 inhibition resulting in the higher PAD4 concentration in plant species thus inhibiting the aphid attack on plants. Based on the computational modeling and molecular dynamics simulation approaches we identify possible lead molecules, which can act as inhibitors to BIK1 in plants30, 31. Due to unavailable crystal structure, we decided to choose ab intio structure modeling through Phyre2 web server and minimized structural energy through FG-MD webserver. There onwards, we tested our protein structure for structural validation through Ramachandran plot analysis of Phi-Psi angle allowance as well as ProSA analysis for structural comparison with other PDB based structures. Emphasis structural validation was made to reach closest comparison of its crystal structure result.
Sequence information and structure modeling
We retrieved the intact BIK1 protein sequence of Arabidopsis thaliana (NP_181496.1, 395 residues) from NCBI-Protein databank resource (https://www.ncbi.nlm.nih.gov/protein/). Figure 2a shows the information of GOR4 detected secondary structures available in sequence as well as active site region of the protein sequence detected from PSI-BLAST are shown in Fig 2b. GOR4 analysis predicted that BIK1 protein sequence consist of 137 amino acids i.e. 34.68% protein in alpha helix form, 62 amino acids i.e. 15.70% protein in extended strand form and random coil of 196 i.e 49.62% amino acid residues 32.
PDB directed PSI-BLAST results were obtained to detect the feasibility of this protein’s homology modeling 34. Below 40% similarity index of BIK1 protein sequence with any crystal structure persuded us to build our protein’s structure through ab initio structure modeling techniques 35, 36, 37. Moreover, low similarity of this protein was confirmed from any of proteins in humans. This also strengthens our idea of using inhibitor of this protein during agricultural practices, without posing any threat to humans upon consumption in small amounts. We submitted our sequence to Phyre2 webserver for ab initio structure modeling at Intensive mode of setting. Shown below in Fig 3 is the structure obtained with 90% accuracy score and 80% query coverage 38.
At this stage, obtained PDB file was subjected to Fragment Guided Molecular Dynamic simulation server of I-TASSER for minimization of energy in PDB structure and get a structure with most stable conformation of predicted model 39. With this structure, we used RAMPAGE server Ramachandran analysis for structure validation confirming occurrence of 89.7% residues in favored region and 8.1% residues in allowed region (Fig 4a) 40. We also processed our protein through ProSA-web server to calculate the Z-score of this structure and Knowledge Based Energy diagram for the amino acid residues in this structure (Fig 4b & 4c) 41. Z-score for this protein structure was obtained -6.79 amongst all available structures in RCSB-PDB.
Thus, validating the all structural aspects of this model at in silico platform, we moved ahead in direction finding an inhibitor for this protein.
Active site prediction
This protein model was then analyzed through METAPOCKET server as well as DogSiteScorer web server for studying surface topology of BIK1 protein structure and finding probable active sites 42, 43, 44. Table 3 shown below is an extension of active site region analysis through CD-search database and confirms the active region of BIK1 protein through results obtained from Pfam, Conserved Domain search, TIGR, PLN, COG and SMART motif search results45. We have summarized the participating amino acid residues in the active region of this protein in accordance with results obtained from PSI-BLAST. We also correlated PSI-BLAST confirmed active site region of this protein with surface topology result of DogSiteScorer server and submitted our protein for METAPOCKET analysis43, 33, 46. Correlation of these two analysis confirmed P_2 from DogSiteScorer analysis as the active and binding region of this protein.
Our results from METAPOCKET detected same location with exactly same amino acids as Pocket 1 and strengthened our knowledge of the active site residues Table 4 shows a summary of DogSiteScorer detected pockets at the surface of BIK1 protein with details.
Comparing the results of DogSiteScorer, METAPOCKET and PSI-BLAST based study as well as manually detecting the location of participating amino acids, we concluded P_2 as the active site.
Figure 5 shown above is a structural representation of P_2 pocket of BIK1 structure specificying active site residues.
Protein preparation
The modelled structure of BIK-1 was subjected to Protein Preparation Wizard utility in Maestro (Schrödinger, Inc.). Hydrogen atoms were added to the resulting structure, which was minimised to overcome bad steric contacts. During receptor grid preparation wizard, OPLS/AA charges49 were automatically assigned by Glide version 7.1 (Schrödinger, Inc.).
Ligand preparation
Structure files of Maybridge screening collection were obtained from its website (http://www.maybridge.com). There are approximately 53,000 organic molecules available at this time for screening purpose. Considering the LigPrep program (Schrödinger, Inc.), possible tautomers were generated using ionization states at pH 7. OPLS ligand charges were also assigned by the program to these structures at default setting.
Docking studies
Docking calculations were completed in three stages. First stage included docking of all the possible tautomers of the available molecules of Maybridge library using High-Throughput Virtual Screening (HTVS) mode. The molecules which had Glide Score (GScore) below -6.0 were selected for next stage docking. In the second stage, Standard Precision (SP) mode was considered. Those molecules which had GScore below -8.0 were considered for final stage of docking. This stage included molecular docking using Extra-Precision (XP) mode of glide. The results were analysed and interpreted on the basis of visual inspection of molecular interactions with the protein using the Maestro (Schrödinger, Inc.).
Molecular Dynamics
Molecular Dynamics (MD) simulations were carried out to validate the docking results. For this simulation, we have considered the GROningenMAchine for Chemical Simulations50 (GROMACS) v5.0.7 package. Topology file for the protein was prepared considering ‘GROMOS96 43a1’ force field51 and ligand topology was prepared over PRODRG server52. The solvated system was found to have a net charge of -2.0. Therefore, two sodium ions were added to neutralize the system. In next stage, solvated, neutral system was minimized using the steepest descent method, followed by position restraint dynamics, also known as equilibration run inclusive of NVT (Number of particles, Volume and Temperature) and NPT (Number of particles, Pressure and Temperature). Soon after the system was equilibrated, a 20 nanoseconds (ns) long production simulation (MD run) was initiated. The output files of the MD run were processed for analysis of the simulation performed using GROMACS. To interpret the hydrogen bonds occupancy for specific residues of BIK-1, VMD53 was used.
Results and Discussion
Mathematical model
We simulated our model on numerical basis and demonstrated how molecular responses during insect infestation of plants can be utilized in favor of human benefits by increasing plant growth rate by cessation of insect infestation. Fig 6a shows a damping oscilation of plant growth in normal conditions of insect infestation. In this plot, plant biomass accumulation stabilizes at 2.2533 concentration scale of this system in comparison to 105 carrying capacity supported in this model, while insect population stabilizes to the value of 0.3256. Thus, this system at ecological level became stationary by the end of 2507th time scale at about two percent or less of the total carrying capacity of the ecosystem for plants. Meanwhile, molecular concentration of PAD4 and BIK1 also proceed through an oscilatory response as shown in Fig 6b. By the end of 2525th time scale, both of these molecular components became stable at 0.8811 for PAD4 and 7.3318 for BIK1. These two plots can be easily correlated for PAD4 dependent insect population as well as respective plant quality. Fig 6c shows how relative amount of plant biomass vary in response to insect population. As soon as insect population increases, plant biomass dives down its relative amount. While, molecular dependency of plant biomass and insect population can be correlated with BIK1 and PAD4 concentration inside cell as seen in Fig 6d. As soon as BIK1 concentration rises, it drops down the relative concentration of PAD4 protein inside cell; this in response helps insects through lowered PAD4 based antixenotic effect and negatively affects relative plant biomass in the system.
Fig 7 shown below summarizes the variation in system behaviour in response to introduction of BIK1-inhibitor at about 310th time scale till next 20 time steps at the rate of 0.1 concentration scale per time step. We observed in Fig 7b, that BIK1 inhibition significantly increased the PAD4 concentration in plants and helped them deteriorating the insects to cease on their feeding preference.
This inhibition resultantly helped keeping insects away from plants and increasing their biomass production as shown in Fig 7a. Thus, according to Fig 7d molecular control of BIK1 action directly influenced the action of PAD4 protein in the system, hence helped plant biomass growth rate to increase and get stable at about 5.7886 biomass scale by the end of 634th time scale in contrast to 2.2533 during regular infection scenario. Meanwhile, by the end of 656th time scale, BIK1 concentration reached zero level of concentration and stabilized PAD4 at 18.1944. Thus, according to numerical simulation and their result analysis, we concluded BIK1 inhibiton as the key mechanism to increase the plant growth. We, furthermore suggest that the numerical simulation may not have been able to completely mimic the real scenario and have only partly symbolized the effect of this inhibition. But, it might have a more influencial effect on the ecological system as some of the wet lab results showing effects of BIK1 silencing have indicated more promising plant growth.
Virtual Screening and Molecular Docking
Predicted binding site of BIK-1 was considered for glide grid preparation and has been targeted for docking of molecules. All the possible tautomers of ∼53, 000 molecules were docked using HTVS mode of Glide. Around 23, 000 molecules had glide score equal to or below -6.00. These molecules were considered for molecular docking via SP mode of glide. There were around 1300 molecules which had glide score -8.0 or less. These molecules were further docked using XP mode of glide. HTVS and SP mode of glide offers molecular docking at lower computational costs than XP mode of glide. XP mode of glide is an important method as it has the ability to weed out the false positives at the same time providing a better correlation between both the good poses as well as good scores. From the XP glide docking results, the top 86 molecules having glide score less than or equal to -10.0 were short-listed for detailed analysis. Visual inspection of the docked complex was carried out. Based on maximum number of interactions of ligand (hydrogen bond, hydrophobic interactions etc) with the amino acid residues constituting the binding site the list was ranked. The top two ligands (i.e. RF03436 and SPB07243) had maximum interactions with the binding site of the protein (Table 5). Ligand interaction diagram in maestro provides vital information about the type of interactions between the ligands in complex with proteins.
Molecular interactions
Ligand interaction diagram of RF03436 (Fig 8) reveals that the molecule interacts with the protein via hydrogen bonds with amino acid residues constituting the binding site of the protein (i.e. Gly74, Met153, Ser157, Asn160). Moreover, there is also a pi-cation interaction with Arg164, a binding site residue. Several residues of the protein were found to form hydrophobic contacts with the RF03436 (Fig 8).
Another view of the docked complex (Fig 9) reveals the position of the docked RF03436 within the binding site of BIK-1.
For SPB07243, the ligand interaction diagram (Fig 10) describes that the molecule is making hydrogen bonds with various binding site residues of the protein like Val72, Gly74 and Met153. In addition, the ligand is also making pi-pi interaction with Phe78 and pi-cation interaction with Lys83, which are also the binding site residue of the protein. Several hydrophobic interactions are also involved between SPB07243 and the target protein (Fig 10).
The position of the docked SPB07243 within the protein can be viewed in the structural representation (Fig 11). Thus, molecular docking studies suggest that the molecules will more likely interact with the binding site of the BIK-1 and acts as possible antagonist to undergo desired mechanism.
Molecular Dynamic simulation
To further investigate the stability of the docked complex, 20 ns long MD simulations were carried out for each complex. Each 20 ns long MD simulation run provided a vital confirmation to the docking studies. The energy graph (Fig 12), illustrates the association and dissociation of the ligand molecule with the receptor during the course of simulation. For RF03436 (black), the molecule was adjusting itself into the docked site throughout the simulation. It implies that the molecule, RF03436 was not able to adjust itself in the docked conformation and hence there were interaction energy variation throughout the simulation. However, for SPB07243 (red), the interaction energy was found rather stable (Fig 12). There was sudden drift in the interaction energy at two instances (i.e. at 4 ns and 16 ns), both the time, the -50 KJ/mol drift was noticed. It is estimate that the ligand found better position during the course of simulation. It was vital to identify the primary residues of the BIK-1, which primarily involved in the hydrogen bonding with ligands during the 20 ns long MD simulation. Higher number of hydrogen bonds corresponds to higher strength of the protein ligand complex and hence, its stability. Therefore, VMD analysis was carried out.
The analysis revealed that SPB07243 is better molecule for BIK-1 as compared to RF03436. For, RF03436, maximum contribution of hydrogen bonds were made by Tyr214 (23.88%) and Lys155 (11.34%), as evident from the Fig 13A. Among these two residues, only Lys155 is the constituent of the binding site of the protein. In contrast to this, SPB07243 makes hydrogen bonds primarily with Ser219 (48.25%) and Asn207 (12.49%), as evident from Fig 13B.
Both the residues are constituent of the binding site of BIK-1. RMSD of the ligand from its initial position was also evaluated. For both the ligands, the RMSD stabilizes at 8 ns, confirming that both the ligand has found better position in the binding site (Fig 14).
Comparatively, it was found that the RMSD was least for SPB07243. Thus, it can be concluded that SPB07243 could act as better antagonist for BIK-1. Hence, it may be used as bio pesticide against several hemipterans responsible for a huge amount of annual crop loss and significantly increase the rate of plant biomass production.
Conclusion
We studied through a proposed extension of plant-insect interaction network about how their molecular counterparts of plant immune system interact as well as significantly control the ecological response. We studied the behavior of insect infestation on plants and how these are regulated by PAD4 concentration. Our study based on mathematical model and simulation strongly supports the experimental evidences claiming BIK1 based plant quality control. Based on experimental claims, our model’s further extension also helped studying effect of BIK1 inhibition through InBIK1 in plants resulting as increased plant biomass production. We successfully showed how at the introduction of an inhibitor to BIK1 may help this system to bring down BIK1 activity and influence the PAD4 action. Due to physical limitations of real life scenario, we had to restrict the minimum BIK1 concentration to zero as it reached negative values for some instants and promoted PAD4 activity exponentially high. Results of this model simulation with inhibitor showed how we can enhance crop production by inhibitor based strategies of crop protection from insect infestation.
As an applied part of our proposed model, our work also included the Search for possible inhibitors against BIK1. Out of 53,000 molecules from Maybridge library, there are 88 molecules which can possibly participate in the inhibition mechanisms of BIK-1. However, RF03436 and SPB07243 from the list of 88 possible BIK-1 inhibitors are suggested to be most efficient on the basis of their molecular interactions with the protein. The molecular dynamics simulation studies carried out for the two molecules bound to the protein advocates the higher stability of the BIK-1 and SPB07243 complex. To conclude, it can be fairly assumed that the molecules SPB07243 and RF03436 could be useful for crop protection and improvement policies. Evenmore, SPB07243 seems to be a better option to start with. As well as, our model extension is a contribution to the field of mathematical modeling of Plant-Insect interaction system and their dependencies on their own molecular counterparts.