An efficient weighted network centrality approach for exploring mechanisms of action of the Ruellia herbal formula for treating rheumatoid arthritis

This study outlines an efficient weighted network centrality measure approach and its application in network pharmacology for exploring mechanisms of action of the Ruellia prostrata (RP) and Ruellia bignoniiflora (RB) herbal formula for treating rheumatoid arthritis. In our proposed method we first calculated interconnectivity scores all the network targets then computed weighted centrality score for all targets to identify of major network targets based on centrality score. We apply our technology to network pharmacology by constructing herb-compound-putative target network; compound-putative targets-RA target network; and imbalance multi-level herb-compound-putative target-RA target-PPI network. We then identify the major targets in the network based on our centrality measure approach. Finally we validated the major identified network targets using the enrichment analysis and a molecular docking simulation. The results reveled our proposed weighted network centrality approach outperform classical centrality measure in identification of influential nodes in four real complex networks based on SI model simulation. Application of our approach to network pharmacology shows that 57 major targets of which 33 targets including 8 compositive compounds, 15 putative target and 10 therapeutic targets played an important role in the network and directly linked to rheumatoid arthritis. Enrichment analysis confirmed that putative targets were frequently involved in TNF, CCR5, IL-17 and G-protein coupled receptors signaling pathways which are critical in the progression of rheumatoid arthritis. The molecular docking simulation indicated four targets had significant binding affinity to major protein targets. Glyceryl diacetate-2-Oleate and Oleoyl chloride showed the best binding affinity to all targets proteins and were within Lipinski limits. ADMET prediction also confirm both compounds had no toxic effect on human hence potential lead drug compounds for treating rheumatoid arthritis. This study developed an efficient weighted network centrality approach as tool for identification of major network targets. Network pharmacology findings provides promising results that could lead us to design and discover of alternative drug compounds. Though our approach is a purely in silico method, clinical experiments are required to test and validate the hypotheses of our computational methods.


Introduction
Rheumatoid arthritis is an autoimmune disease characterized by pain and synovial inflammation that may result in the destruction of cartilage and bone. Recently, a study has reported a rheumatoid arthritis prevalence of 1% and it affects three times more women than men (Anderson et al. 2012;Smolen et al. 2003;Scherer et al. 2020). Understanding the etiology of rheumatoid arthritis remains an active area in medical research. Studies have shown that rheumatoid arthritis is a multi-factorial disease probably caused by genetic predispositions or environmental factors Kour et al. 2022). Developments of alternative drugs to treat and cure rheumatoid arthritis are still out of our reach, and the development of new therapeutic anti-rheumatic drugs with minimal or no side-effects is a great challenge (Koller et al. 2019;Martin et al. 2013;Chakravarty et al. 2008). Although remedies such as nonsteroidal anti-inflammatory drugs (NSAIDs) (Kelleni 2021), corticosteroids (Kapugi and Cunningham 2019;Hodgens and Sharman 2021), disease-modifying anti-rheumatic drugs (DMARDS) (Grove et al. 2001), and biologic response modifiers ('biologicals') (Hazlewood et al. 2016) have been used in the management and treatment of rheumatoid arthritis, some of these remedies have adverse side effects (Tóth et al. 2022;Chakravarty et al. 2008). Therefore, it is necessary to develop alternative drugs with minimal or no side effects for the treatment of rheumatoid arthritis. Recently the use of ayurvedic drugs has gained popularity in clinical research. For instance, a study has shown that Ruellia prostrata (RP) and Ruellia bignoniiflora(RB) herbal medicine and its constituents could have anti-inflammatory and anti-analgesic properties (Dogan et al. 2022(Dogan et al. , 2022Weyand and Goronzy 2021). However, the identification and elucidation of Rueilla active constituent compositive compounds and their molecular mechanism of action in treating of rheumatoid arthritis remain unknown (Smolen et al. 2003;Chothani et al. 2010;Arirudran et al. 2011). To understand the relationship of interacting components such as drugs, genes, proteins, and disease targets computational methods like network biology, system biology, polypharmacology, and network pharmacology have been recently proposed (Yuan et al. 2021;Yu et al. 2018;Zhou et al. 2020). These methods apply omics and system biology strategies to decipher the underlying mechanism of action and synergetic effect of multiple targets and multiple components via a network analysis (Wan et al. 2019;Xin et al. 2021). In general, network pharmacology is widely based on network construction techniques, a network analysis and database quarry techniques which provides a preliminary understanding of the mechanism of action at the system level (Nogales et al. 2021;Niu et al. 2021). Recently, modeling the drug-target interaction in complex biological systems has attracted the attention of medical researchers (Wachi et al. 2005;Zhou et al. 2020;Xin et al. 2021). In network pharmacology these complex biological system are often presented as complex networks with heterogeneous components that are quantified by a network centrality measure approach (Reia et al. 2017). Though several studies in network pharmacology applied traditional centrality measures approaches to investigate the important network components these methods often depend on the network structure and this makes them less efficient when handling with complex dynamic network systems and the area of application (Özgür et al. 2008;Rodrigues et al. 2016;Brandes 2001). Thus,in this study, we developed an efficient weighted network centrality measure approach for exploring mechanisms of action of the Ruellia prostrata and Ruellia bignoniiflora herbal formula for treating rheumatoid arthritis. The rest of this paper is organized as follows. In Section Materials and methods, we describe our new approach for calculating the interconnectivity score and weighted network centrality and its application in network pharmacology. In Section Calculation of the network-based interconnectivity score, we present and interpret our results. In Section Calculation of weighted network centrality, we discuss our findings and then we draw some pertinent conclusions.

Materials and methods
Now, we will describe the our new proposed approach for the calculation of the interconnectivity score and weighted centrality measures for the identification of major network components and its application in network pharmacology.

Calculation of the network-based interconnectivity score
We propose a general approach for the calculation of the interconnectivity score among network components. This approach is a local network-based approach that prioritizes network nodes based on their overall connectivity to other nodes in the network. In our calculations we made the following assumptions: (1) there is a direct interaction between a pair of nodes; (2) there are indirect interactions with a path length of two network nodes which we call the shared neighborhood of the two nodes; (3) the network is a tripartite network consisting of nodes i, j and k. Thus, we can calculate interconnectivity using the following: where I(i, k) is the interconnectivity between nodes i and k, deg(i) and deg(k) is the degrees of node i and k respectively and N is the size of the shared neighborhood connectivity. Here, e(i, k) is the edge between node i and k. Therefore, using Eq. (1) the interconnectivity score of node j directly interacting with node i and k in their shared neighborhood can be calculated using (2) e(i, k) = 1 if an edge exists between i and k 0 otherwise where s j is the interconnectivity score of node j with respect to node k and DEG represents the degree of all set of node k.

Calculation of weighted network centrality
Using the interconnectivity score s j calculated above, we can introduce a new approach for computing the weighted centrality measure based on the traditional centrality measure such as degree centrality, closeness centrality, and betweenness centrality shown in Fig. 1.

Weighted degree centrality
Freeman's (1978) degree centrality is defined as the total number of connections or edges attached to the node with respect to other nodes in the network (Dörpinghaus et al. 2022) and it usually calculated by where C D (i) is the degree centrality of node i, e i, j is the edge connecting nodes i and j is 1 if it exists otherwise it is 0, and N is the total number of nodes in the network. Therefore using Eqs. (2) and (3), the degree weight of node j is given by where w DC j is the degree weight of node j, e j, k represents the edge between nodes j and k whose value is 1 if it exists otherwise it is 0, and n 1 is total number of nodes k in the network. Therefore, using Eq. (4) the weighted degree centrality score of the network node i can be calculated using The darkness and the size of each node is proportional to its centrality measure Here, φ DC (i) is the weighted degree centrality measure of node i with respect to node j, e i, j represents the edge between nodes j and k whose value is 1 if it exists otherwise it is 0 and n 2 is the total number of nodes i.

Weighted closeness centrality
Freeman's (1978) closeness centrality considers a node's importance to be the shortest distance or path or inverse of the sum of the distances between a given node with respect to other nodes in the network. Mathematically, closeness centrality between nodes i and j is calculated by where C C (i) is the closeness centrality, d i, j represents the shortest path or distance between node i and j, while n is the total number of nodes in the network. Here we recalculate the distance by first expressing the sum of the shortest distance between nodes i and j with δ = n ∀j&j� =i d i, j . Therefore, our new closeness centrality measure is calculated using the equality Rearranging Eq. (8) and taking the positive square root where δ is the shortest distance, n−1 δ represents closeness centrality based on the shortest distance and 1 n(n−1) δ represents closeness centrality based on the inverse of the sum of the distances and n is total number of nodes in the network. Hence the shortest distance between nodes i and j is δ i, j . If we take Eqs. (2) and (9), we can calculate a new closeness weight of node j by where w CC j is the closeness centrality weight of node j, δ j, k is the shortest distance or path between nodes j and k and n 1 is the total number of nodes k in the network. Of course, Therefore, using Eq. (10) we can calculate the weighted closeness centrality score of node i by (7) δ j, k = 1 if the shortest path exists between i and k 0 otherwise where φ CC (i) is the weighted closeness centrality measure of node i with respect to node j, δ i, j is the shortest distance or path between nodes j and k whose value is 1 if it exists otherwise it is 0 and n 2 is the total number of nodes j.

Weighted betweenness centrality
Freeman's (1978) betweenness centrality considers that a node's importance is to the number of times that node occurs in the shortest paths between all possible pairs of nodes in a network. Mathematically, betweenness centrality of a node j is calculated by, where σ ik is the total number of shortest paths from node i to node k and σ * ik j is the number of shortest paths between nodes i and k with node j acting as an intermediate/bridge node along the shortest path. If we use the betweenness value i.e. number of shortest paths between node i and k in Eq. (13), then we provide a new formulation for calculation of the betweenness weight of node j by where w BC j is the betweenness centrality weight of node j, σ * ik j represents the intermediary node between nodes i and j, and n 1 is the total number of node k in the network. Also, Thus, with Eq. (15) we can calculate the weighted betweenness centrality score of node i by where φ BC (i) is the weighted betweenness centrality measure of node i, σ * jk (i) represents the intermediary node between nodes j and k whose value is 1 if it exists otherwise it is 0 and n 2 is the total number of nodes j.
σ * ik j = 1 if node j exists between i and k 0 otherwise

Compositive compounds of Ruellia herbs
The chemical compounds of the two Ruellia herbs were retrieved from chemistry database (Allen and Motherwell 2002) and PubChem (Kim et al. 2016). From the database, a total of 103 Ruellia prostrata and 103 Ruellia bignoniiflora active compounds were collected. Using ADMETlab 2.0, an online pharmacokinetics and toxicity prediction program (Xiong et al. 2021), drug-likeness of the active compounds were evaluated. The compounds were subsequently screened for oral bioavailability and drug-likeness by setting filter values at OB ≥ 30% (Xu et al. 2012) and DL ≥ 0.18 (Clark and Pickett 2000) respectively. This enabled the discovery of the active compounds in Ruellia herbs interacting with putative targets proteins (Nickel et al. 2014).

Putative targets for Ruellia herbs
All putative targets related to two Ruellia herbs were retrieved from the STITCH database, an online tool for exploring chemical and protein interactions (Kuhn et al. 2007).
To obtain the putative targets we restricted the search to "Homo sapiens" and confidence score > 0.4 . Only the proteins that directly interacted with Ruellia herbs compositive compounds were selected as putative targets. Hence, we collected distinct putative targets related to compositive compounds of the two Ruellia herbs.

Known RA therapeutic targets
The known RA therapeutic targets were obtained from three sources those include; First source was DrugBank database (Wishart et al. 2018) (http:// www. drugb ank. ca, version 4.3),an online tool that provides comprehensive information on drug target data. In this database the search term was restricted to "rheumatoid arthritis" and only FDA approved gene/protein targets linked to rheumatoid arthritis were selected (Mogul et al. 2019). Second source was Online Mendelian Inheritance in Man (OMIM) (Amberger et al. 2019), (http:// www. omim. org/), an online tool that cataloged all known diseases and link them relevant genes in human genome. From the database we search for the keyword 'rheumatoid arthritis' . Third source was Therapeutic Target Database (Wang et al. 2020), (TTD, http:// db. idrbl ab. net/ ttd/), an online tool that provides information on known and explored therapeutic proteins and nucleic acid targets. The search term was restricted to "rheumatoid arthritis" and only successfully clinically approved therapeutic targets were selected. All the therapeutic targets retrieved from the three source were carefully screened and redundant targets eliminated. A total of 410 important known RA therapeutic were sleeted for the study.

Protein-protein interaction (PPI) data
Eight public database sources were used to retrieved protein-protein interaction data those includes:  (Beuming et al. 2005) and STRING (Szklarczyk et al. 2021). We removed all the retardant entries from the eight sources and merged all the data.

Network construction
The herbs, compositive compounds, putative targets and known RA therapeutic targets data were used to perform network construction as follows: (1) herb-compositive compound-putative target network was built by linking the two Ruellia herbs, compositive compounds and corresponding putative targets; (2) herb-putative target-known RA therapeutic target network was established by linking the two Ruellia herbs, corresponding putative targets, and known RA therapeutic target that interacted with putative targets; and (3) imbalance multi-level network was built by linking herb-compositive compound-putative targets and herb-putative targets-known RA therapeutic targetsother human PPI network built by linking herb-compositive compounds-putative targets network and herb-putative target-known RA therapeutic target-Other human protein's PPI network directly interacting with the two targets. The nodes with high weighted centrality score i.e. "Degree centrality", "Closeness centrality", "Betweenness centrality" were considered as important nodes in the network.

Gene ontology enrichment and KEGG pathway analysis
To perform the Gene Ontology (GO) enrichment and KEGG pathway analysis, DAVID database (https:// david. ncifc rf. gov) (Dennis et al. 2003;Aoki and Kanehisa 2005) were used. To obtain enriched GO terms, functional categories including biological processes and molecular functions were evaluated for the major common putative targets. KEGG pathways analysis was also performed to establish the pathway mechanism of the major common putative targets.

Molecular docking simulation
Molecular docking is a in silico method widely used in drug discovery and design to investigate the inter-molecular interaction and prediction of the binding affinity and conformation (Agarwal and Mehrotra 2016). In this study, AutoDock version 4.2.6 was utilised to perform docking simulation (Cosconati et al. 2010;Morris et al. 2008). The binding affinity was the calculated based on the semi-empirical free energy force field scoring function (Huey et al. 2007) given by equation below where △S conf denotes conformation entropy lost during binding, L and P denotes the ligand and protein respectively. The candidate compounds (ligands) and proteins (receptors) for docking analysis were selected based on the weighted centrality score value calculated from the imbalance multi-level network analysis results. Hydroxychloroquine (Fox 1993) and Methotrexate (Kremer et al. 1994) were chosen as positive control drugs in the treatment of rheumatoid arthritis. The chemical structures of the candidate compounds were obtained in SDF file format from PubChem (Kim et al. 2016) while the crystal structure of the target proteins were retrieved from RCSB database (Deshpande et al. 2005). Open Babel tool et al. 2011) was utilised to convert compounds to PDB file format. AutoDockTools was utilised to import the Candidate ligands and receptors, which were then subjected to the following prepossessing steps: (1) elimination of the all hetero-atoms and water molecules; (2) addition of the polar hydrogens with Gasteiger and Kollman charges to ligands and receptors receptively and (3) conversation of output file into pdbqt. file format. The docking search area was calculated based on (Feinstein and Brylinski 2015), we set grid box dimension of 60 × 60 × 60 Å with a spacing of 0.479 Å for optimal docking results. The 2D and 3D interaction of hydrogen atoms and amino acid residues were visualised using LigPlot+ versions 2.2 (Laskowski andSwindells 2011) andPyMol2.5 (DeLano et al. 2002) software's respectively.

Evaluation of EWNC performance
The performance of our proposed EWNC was evaluated using four real network data obtained from Freeman's electronic information exchange system (EIES) network (Iacobucci et al. 2017), USAir97 network (Zhao et al. 2020;Fei et al. 2017), Groad network (Wang et al. 2017;Zhao et al. 2020), and Newman's scientific collaboration network (Newman 2001(Newman , 2001. We adopt the Susceptible-Infected (SI) Model (Zhou et al. 2006) to assess the spreading influence of the top-L ranked nodes from the networks based on our EWNC method and other existing weighted centrality measures. In this analysis we denote weights of degree centrality (DC),betweenness centrality (BC) and closeness centrality (CC) of the existing centrality measures by DC w , BC w and CC w respectively. To evaluate the performance we compared the cumulative number of infected nodes with the initial nodes appearing at the top of the list for different centrality measures. Figure 2 show the comparison results of our EWNC method and other existing centrality measures applied in the four real networks data. In USAir97 network data, it can be seen that final number of infected nodes for our EWNC approach is higher compared to other centrality measures. In addition, we can note that our approach outperforms other method in the calculation of DC w and BC w . Though after time step 30 the node spread is nearly the identical to CC w , the propagation speed of our proposed EWNC at early stage is rapid. Also it can be observed that our EWNC has minimal error indicating that the method is more effective and accurate in calculation of the influential nodes in the network. In the Groad network, the difference in performance between our EWNC approach and other centrality measures can be noted in DC w and BC w which indicate an increase in number of infected nodes after time-step t ≥ 30 . When t ≤ 30 , the infection process with CC w is nearly identical, and the errors of EWNC are clearly smaller than those of DC w and BC w . In the Newman's network, we observed that when t = 20 , EWNC achieves nearly the same performance of infected nodes as DC w . When t is between 20 and 50, EWNC outperforms BC w for spreading ability and has better infection effect and less error than BC w . The performance of EWNC is slightly identical to DC w . In Freeman's network, EWNC outperforms both DC w and BC w . We noted that our EWNC approach also behaves similarly to or close to CC w , however, with minimal error when when compared to DC w , BC w , and CC w . This means that our proposed EWNC calculation is more precise. Generally, this analysis confirms our EWNC approach to be robust and efficient in the identification of the influential node in the real complex networks. This provides prospect of its application in solving other complex network problems.

Herb-compositive compound-putative target network analysis
To establish the relationship between the two Ruellia herbs and putative targets we built the herb-compositive compound-putative target network as shown in Fig. 3, which includes 634 nodes (2 herbs, 196 compositive compounds, and 436 putative target genes) and 5212 edges. According to the network analysis, all the Ruellia compositive compounds interacted with 436 putative target. Markov cluster (MCL) analysis of the network indicate that from a total of 196 compositive compounds identified from the network, 103 compounds originated from Ruellia prostrata herb and 93 compounds came from Ruellia bignoniiflora herb. Further cluster (MCL) analysis to extract and identify compositive compounds common in both Ruellia herb. According to results in Fig. 4, 22 compositive compounds were common to both Ruellia herbs and had high centrality scores values indicating their importance in the network. For instance high centrality score values of putative targets including CSF2, CXCL1, CCL2, CCR2 and TNF indicated interaction with multiple common compositive compounds such as Glyceryl-2 Palmitate, Glycidyl oleate, Oleoyl chloride, Glyceryl diacetate-2-Oleate and Hexadecanoic acid, methyl ester. This network provided clue on relationship between Ruellia compositive compounds and corresponding putative targets.

Compositive compound-putative target-RA known target network analysis
To establish the relationship between compositive compounds, the putative targets and the known RA therapeutic targets, compositive compound-putative target-known RA therapeutic target network shown in Fig. 5

Imbalance multi-level network analysis
To understand the mechanism of action of two Ruellia herbs in the treatment of rheumatoid arthritis an imbalance multi-level network consisting of herb-compositive compound-putative targets-known RA therapeutic targets-PPI network was built by merging herb-compositive compounds-putative targets network as shown in Fig. 2, compositive compound-putative target-known RA therapeutic target network as shown in Fig. 3 and herb-putative target-known RA therapeutic target-Other human protein's PPI network as shown in Fig. 6A. Figure 6B show an imbalance multi-level network composed of 1519 nodes (2 herbs, 196 compositive compounds, 436 putative targets, 410 known RA therapeutic targets and 475 other human proteins interacting with putative targets or known RA therapeutic targets) and 9375 edges. The significant network components were then identified based on weighted centrality score values. Network analysis revealed a total of 57 nodes (2 herbs, 8 compositive compounds, 15 putative targets, 10 known RA therapeutic targets and 24 other human proteins interacting with putative targets or known RA therapeutic targets) and 417 edges with high centrality score values ('Degree centrality' , 'Betweenness centrality' and 'Closeness centrality') indicating their significance in the network as shown in Table 1. From the network Glycidyl oleate, Glyceryl-2 Palmitate, Oleoyl chloride, 9-Octadecenoic acid (Z)-, methyl ester, Methyl stearate, Hexadecanoic acid, methyl ester, Hexadecanoic acid, 2,3-bis(acetyloxy) propyl ester and Glyceryl diacetate-2-Oleate compounds indicated high interaction with the corresponding putative targets, known RA therapeutic targets and other human proteins. This network provided clue on the relationship between Ruellia herbs, compositive compounds, putative targets, know RA therapeutic targets and other human protein which explains the mechanism of action of the Ruellia herbs in the treatment of rheumatoid arthritis ( Fig. 6A and B).

Gene ontology and pathway enrichment analysis
A total of 39 major targets (15 putative targets and 24 other human proteins) of Ruellia herbs related to rheumatoid arthritis obtained from the imbalance multi-level network were utilised to perform Gene Ontology and Pathway enrichment analysis. Figure 7 show a summary of the significant biological process, molecular function and top-10 KEGG pathway associated with associated with rheumatoid arthritis. According to the analysis top-18 enriched GO terms for biological process Fig. 7A and molecular function Fig. 7B included the were Cytokine-mediated signaling pathway, Inflammatory response, Intracellular signal transduction, Regulation of cell population proliferation, Cytokine receptor binding, Chemokine receptor binding, CXCR chemokine receptor binding,CCR2 chemokine receptor binding and CXCR chemokine receptor binding. In addition, we perform KEGG pathway analysis for the major targets and the top-10 enriched pathways were were IL-17 signaling,IL-10 signaling, TNF signaling, IL-4 and IL-13 signaling, Toll-like receptor signaling signaling pathway, NF-kappa B signaling, CCR interaction, NOD-like receptor signaling pathway, Chemokine signaling pathway, and GPCR ligand binding. The IL-17 signaling pathway promotes neutrophil mobility via T cell activation, which help against inflammatory illnesses such as rheumatoid arthritis (Raucci et al. 2022). TNF signaling is a multifunctional cytokine and plays an important role in pro-inflammatory cytokine (Chen et al. 2022). NF-kappa B signaling pathway play important role in inflammatory and immunological responses, as well as regulating genes involved in cell death, differentiation, and proliferation (Cao et al. 2022). Furthermore, the modulation of chronic inflammatory synovitis by cytokines has been linked in  Chemokines have been linked to a variety of neurological illnesses, mainly via generating inflammation through the chemotactic localization of leukocytes (Skrzypkowska et al. 2022). Chemokine activities mediated by G-protein coupled receptors, play an role in inflammatory reactions (Cheng et al. 2022). Interleukin-10, Interleukin-4 and Interleukin-1β signaling pathways have been implicated in the regulation of the type II inflammatory and anti-inflammatory cytokine which plays a critical role in the regulation of inflammatory processes (de Freitas et al. 2022;Bridgewood et al. 2022).

Molecular docking evaluation
In the compound-target network, the top eight compositive compounds (Glyceryl diacetate-2-Oleate, Glyceryl-2 Palmitate, Hexadecanoic acid, 2,3-bis(acetyloxy)propyl ester, Methyl stearate, Glycidyl oleate, Oleoyl chloride, Hexadecanoic acid, methyl ester, and 9-Octadecenoic acid (Z)-, methyl ester) and the top nine targets (TNF, NOSs, IL-1β , PTGS2, IL-6, PTGS2,DOP, CCR5 and CB2) were selected and molecular docking evaluation was performed. In Table 2 we present top-4 compounds with best binding energy and Lipinski Properties. According to the results, Glyceryl diacetate-2-Oleate and Oleoyl chloride indicated a HIGH binding energy with all target proteins. Though Glyceryl diacetate-2-Oleate had the highest binding energy against TNF ( −10.33 kcal/mol) and CCR5 ( −10.52 kcal/mol). Hexadecanoic acid, methyl ester recorded low binding energy for all other the target proteins except against TNF and L −1β . Compound or ligands with binding energy within the range of −8.0 kcal/mol and −11.0 kcal/mol as well as RMSD ≤ 2.5 Å is clear indication of a good molecular interaction between the compounds and the target receptors.
We evaluate the drug-likeliness of the candidate drug compounds using Molinspiration an online software (Molinspiration 2011) for prediction of molecular properties. We applied Lipinski rule of five which state that "drug-like" molecules have logP≤ 5 , molecular weight ≤ 500 , hydrogen bond acceptors ≤ 10 and hydrogen bond donors ≤ 5 (Zhang and Wilkinson 2007;Chen et al. 2020). The results in Table 2 indicate that the all four candidate drug compounds were within the limits of Lipinski's rule. Also we evaluated the Topological Polar Surface Area (TPSA) (Ertl et al. 2000) to predict the candidate drug compounds permeability. The result indicated that all the compounds had the TPSA in within the set limit of ≤ 140 Å 2 . A clear indication of compounds good drug absorption properties such bioavailability, intestinal absorption, Caco-2 permeability, and blood-brain barrier penetration (Francis and Chakraborty 2022;Ertl et al. 2000). In addition, the number of rotatable bond were within the established limit of 6-170 rotatable bonds (Hamri et al. 2022). A high number of rotatable bonds indicates high molecular flexibility, which acts as an indicator of a good oral bioavailability of the drugs (Veber et al. 2002).
To illustrate the surface interaction and conformation between the candidate compound and the target proteins, it was necessary to visualise the 3D conformations of the andidate compound and the target proteins using Pymol software. Figure 8, show the 3D surface interaction of the Glyceryl diacetate-2-Oleate against selected major target receptors (TNF, NOSs, IL-1β , PTGS1, IL-6, PTGS2,DOP, CCR5 and CB2. We can observe that Glyceryl diacetate-2-Oleate had high hydrogen bond interactions with side chain amino acid and and a slight hydrophobic interaction with the targets proteins.
We also, illustrate the surface interaction and conformation between the Oleoyl chloride (cp6) against the six selected major target receptors (TNF, NOSs, IL-1β , PTGS1, IL-6, PTGS2,DOP, CCR5 and CB2. Again, in Fig. 9 we observe that Oleoyl chloride had high hydrogen bond interactions with side chain amino acid and sa slight hydrophobic interaction with the targets proteins. In drug design, it is critical to understand the interaction of the hydrogen bond of the drug compounds and amino residue of target proteins or receptors. In this study we evaluated the interaction of the hydrogen bonds of the ligand and amino residues of the target protein and visualise 2D interaction using the LigPlot+ Software. Figure 10 show the interaction of the hydrogen bond in Glyceryl diacetate-2-Oleate (cp1) against amino residues of six selected major target proteins (TNF, NOSs, IL-1β , PTGS1, IL-6, PTGS2,DOP, CCR5 and CB2). We can observe that the CB2 and Glyceryl diacetate-2-Oleate had interaction of two hydrogen bonds with Trp1060, and Asp1095. IL-1β with Glyceryl diacetate-2-Oleate formed hydrogen bond interaction with Asn130 and Asn132. IL-6 and Glyceryl diacetate-2-Oleate formed hydrogen bond interaction with Thr156 and Thr161 amino acid residues. PTGS1 with Glyceryl diacetate-2-Oleate formed hydrogen bond interaction with Ser530. TNF with Glyceryl diacetate-2-Oleate formed hydrogen bond interaction with Try151 amino acid residue. DOP with Glyceryl diacetate-2-Oleate had hydrogen bond with Ser100 amino acid residue.
Similarly, we evaluated the interaction of the hydrogen bond in Oleoyl chloride (cp6) against and amino residues of six selected target proteins. From Fig. 11, We observed that CB2 and Oleoyl chloride had three hydrogen bonds with Asn1014, Thr1012 and Gly1013. IL-1β with Oleoyl chloride had hydrogen bonds with Arg102 and His298. IL-6 and Oleoyl chloride formed hydrogen bonds with Ala143, Asn191 and Asn171 amino acid residues. PTGS1 and Oleoyl chloride had hydrogen bond interaction with Ser530. PTGS2 and Oleoyl chloride had hydrogen bond interaction with Trp385. NOSs and Oleoyl chloride had hydrogen bond interaction with Gly371. CCR5 and Oleoyl chloride had hydrogen bond interaction with Thr284. TNF with Oleoyl chloride had hydrogen bonds interaction with Try151 and Gly121. DOP with Glyceryl diacetate-2-Oleate had hydrogen bond interaction with Leu119 and Glu118 amino acid residues.
In our study it was important to evaluate the ADMET properties of the candidate drug compound identified by our proposed weighed network centrality measure and molecular docking simulations. In our scenario we opted to evaluate the absorption, metabolism and toxicity of candidate compounds which play a key role to establish safety of a drug compounds. We import the SMILES chemical structure of the four candidate drug compounds into the ADMETlab 2.0 (Dong et al. 2018), an online software for evaluation and screening the pharmacokinetics and toxicity properties of chemical compounds. According the results in Table 3, all the four candidate drug compounds were within the optimal values for Caco-2 Permeability ( ≥ −5.15 ) and acted as Non-inhibitor and Non-substrate for Pgp. We also observed that cp1 and cp6 had higher HIA value a clear indication of their high absorption to the gastrointestinal system into the bloodstream. Evaluation of metabolism activity indicates cp3, and cp5 high probability of acting as inhibitor of the metabolic enzyme CYP3A4. while cp3, cp5 and cp6 have high probability of acting as substrate to metabolic enzyme CYP2C9. Evaluation of toxicity properties of the candidate drug compounds show that low probability of hERG Blockers indicating low cardiotoxicity that may results to fatal ventricular arrhythmias and sudden death. All the candidate drug compounds were negative to Human Hepatotoxicity (H-HT). Cp3 recorded significantly higher Drug Induced Liver Injury ( DILI = 0.063 ) compared to other drug compounds. we also observed that Cp5 had high AMES Toxicity value a clear indication of mutagenic characteristic and therefore may act as a carcinogen. In addition, all the drug compounds are non-carcinogencity and low Rat Oral Acute Toxicity.

Comparison EWNC to other centrality measures
This study proposed an new efficient weighted network centrality measure by modification classical centrality using node interconnectivity score which consider interaction between pair of nodes and number shared neighborhood in the network. According to simulation results in Fig. 2, SI model was used to evaluate the node spreading process (cumulative number of infected nodes) in four real networks by comparing the influence of the top-ranked nodes using our proposed EWNC approach and other existing weighted centrality measures. Generally, we observed that initial infected nodes are ranked top by our EWNC approach are effectively infected by other nodes in the network when compared to other centralities. In term of identification of the influential nodes in the network, our EWNC approach outperforms others centrality measures. As mentioned above, our EWNC approach is based on modification of traditional centrality measures described in Section Materials and methods, therefore, the nodes are ranked based on the interconnectivity score calculation of each pair of nodes and the number of shared neighbourhood which take into consideration the number edges (node degree) and the shortest paths between pair of nodes in a given network for calculation of weighted centrality score and the definition φ inherit the concept of EWNC, computing the number of shared neighborhood and the number edges associated with to a particular node to calculate the node interconnectivity difference. As shown in our formulation, the centrality scores are based on modification of traditional centrality measures. When ranking nodes, both the degree of the node based on edges and the shortest paths between nodes are taken into account in calculation of weighted centrality score value and the definition of φ inherits the idea of EFCM, removing a node and the edges associated with it to calculate the difference. Based on this our EWNC approach is able to take into account the global structure of the network which make our approach more efficient compared to the classical centrality measures hence suitable for wide application of identification of influential nodes in complex networks.

Network pharmacology simulation
Recently, network science have gained wide application in medical and drug discovery research (Newaz 2022). Network pharmacology and system biology paradigm an application of network science have provided a breakthrough in drug discovery research by establishing the relationship between drug molecules and disease (Zhao et al. 2022). Discovery and development of multi-target therapeutic drug compounds with minimal or no adverse effects is exigent in treatment of complex diseases compared mono-therapeutic drug compounds (Lannes-Vieira 2022). Study has shown herbal medicine to have combinatory drug therapeutic properties hence suitable for developing multi-target therapeutics drug compounds with minimal or no adverse effects (Lannes-Vieira 2022). In this study we develop an efficient weighted network centrality approach to explore the mechanism of Ruellia herbal formula in the treatment of the rheumatoid arthritis. To archive this we built three distinct networks those includes (1) herb-compositive compound-putative target network; (2) herb-putative target-known RA therapeutic target network; and (3) herb-putative targets-known RA therapeutic targets-other human PPI network. All the three networks were merged to built a imbalance multi-level network in odder to identify and explore the mechanism of action of Ruellia herbal compounds and corresponding putative targets. We applied our new weighted centrality approach to identify influential nodes (important components) in the network to establish the mechanism of action in the treatment of the rheumatoid arthritis. According to the network analysis result we discovered a total of 57 influential nodes those includes: 8 compositive compounds, 15 putative targets, 10 RA therapeutic targets and 24 other human proteins interacting with putative targets which had high weighted centrality score values.
To validated the clinical importance of the identified putative targets, an Gene Ontology and Pathway enrichment analysis were performed. From the analysis we discovered that majority of the putative targets were frequently involved in Cytokine receptor binding, Chemokine receptor binding, CXCR chemokine receptor binding,CCR2 chemokine receptor binding, CXCR chemokine receptor binding, IL-17 signaling,IL-10 signaling, TNF signaling, IL-4 and IL-13 signaling, Toll-like receptor signaling signaling pathway, NF-kappa B signaling, NOD-like receptor signaling pathway, Chemokine signaling pathway, and GPCR ligand binding which plays an important role in the progression of rheumatoid arthritis disease. Study has shown that inflammatory cytokines such as IL-6, IL-1β and TNF play a important role in triggering the catabolism and anabolism of the joints (Kato et al. 2014). IL-1β has been reported to activate the inflammatory response by increasing the MMPs expression which play a critical role in the in the degradation of cartilage in rheumatoid arthritis (Dinarello et al. 2002). IL-6 also have been implicated with inflammatory triggered by response by producing the transcription factors such as in inflammation pathways (Kim et al. 2015). TNF is a potent anti-inflammatory cytokines that has been implicated in various autoimmune and inflammatory disease such as rheumatoid arthritis disease (Chen et al. 2022). Study has shown that two risk factors linked arthritis disease are inflammation and pain which are related to PGHS1 which is the main enzyme that regulate PGE2 synthesis that play a critical role in the inflammatory response by stimulation of the inflammatory cytokines like IL-1β and TNF-α (Glauser 1996). In addition, Nitric oxide has also been to impacted to induce mechanical stress and inflammation by modulating cytokine expression that activate MMPs, and suppress proteoglycan synthesis hence leading to pathogeneisis of rheumatoid arthritis (Guilak et al. 2004). In addition, study has also shown that systhesis of nitric oxide by inducible nitric oxide synthase plays an important role in the regulation of rheumatoid arthritis (Abramson 2008). Thus therapeutic intervention such as the use of inhibitors like N6-(1iminoethyl)-L-lysine hydrochloride and Smethylisothiourea has been recommended in the management of rheumatoid arthritis (Balaganur et al. 2014).
To establish the suitable candidate drug compound among the 8 major compounds identified from the multi-level imbalance network, a molecular docking simulation was performed. From the docking analysis, compounds with highest binding affinity were selected (binding energy ≥ −8.0 kcal/mol and RMSD ≤ 2.5 Å). Also we selected six potential major protein targets (TNF, iNOSs, IL-1β , PTGS1, IL-6, PTGS2,DOP, CCR5 and CB2) associated with rheumatoid arthritis. Overally docking results revealed that Glyceryl diacetate-2-Oleate and Oleoyl chloride had highest binding affinity i.e. ≥ −8.0 kcal/mol to all the major protein targets. This implies the two compounds are good inhibitors of the six selected major protein targets associated with rheumatoid arthritis. In addition, Glyceryl diacetate-2-Oleate and Oleoyl chloride showed good H-bond interaction with amino residues of six selected major protein targets validating their inhibitory characteristics. We also observed that Oleoyl chloride and Glyceryl diacetate-2-Oleate were within the Lipinski limits a clear indication that their drug-likeliness properties. ADMET evaluation confirmed that both compounds may be less or not toxic to human and may not trigger DILI, H-HT or act as hERG Blockers. Study has reported drug compounds that trigger DILI and H-HT may cause adverse liver damage to patients (Andrade et al. 2019).

Conclusions
In this study we introduce an efficient weighted network centrality approach by modification of classical centrality measures using node interconnectivity. We then apply our proposed approach to explore the mechanism of action Ruellia herbal formula in the treatment of rheumatoid arthritis. We use the SI model was used to evaluate the node spreading process in four real networks by compared cumulative number of infected nodes using our proposed EWNC approach and other existing weighted centrality measures. The results indicated that initial infected nodes are ranked top by our EWNC approach are effectively infected by other nodes in the network when compared to other centralities. Also our EWNC approach outperforms others centrality measures in terms of identification of the influential nodes in the network. Network pharmacology application reveled that using our approach was efficient in identification of important nodes in the network. From imbalance multi-level network analysis we discovered a total of 57 influential nodes those includes: 8 compositive compounds, 15 putative targets, 10 RA therapeutic targets and 24 other human proteins interacting with putative targets which had high weighted centrality score values. Gene Ontology and Pathway enrichment analysis confirmed that majority of the major identified putative targets were frequently in biological processed, molecular function and pathway system that plays an important role in the progression of rheumatoid arthritis disease. Molecular docking simulations indicate that four major candidate compositive compounds significant binding affinity to the selected major protein targets. Among the four compounds Glyceryl diacetate-2-Oleate and Oleoyl chloride had the highest binding energy and showed good H-bond interaction with amino residues of six selected major protein targets. The two compounds were also within the Lipinski limits a clear indication that their drug-likeliness properties. ADMET evaluation confirmed that both compounds had minimal or no toxic effect human and may not trigger DILI, H-HT or act as hERG Blockers hence indicating their potential as candidate drug compounds for treating rheumatoid arthritis. The our new weighted centrality approach provide an essential tool that may utilised to explore mechanism of action of drug compounds in the treatment of a particular disease. Our network pharmacology findings provide promising results that could lead us to design and discover of alternative drug compounds for the management and treatment of rheumatoid arthritis. Though our approach is a purely in silico method, clinical experiments are required to test and validate the hypotheses of our computational methods.
Additional file 1 This file contains Ruellia Contain all data used for network pharmacology studies.
Additional file 2 Contains network analysis, Gene Ontology and Pathway enrichment analysis, and molecular docking simulationsupplementary results.
Additional file 3 This file contains the all figures used in this article.