Petri net-based prediction of therapeutic targets that recover abnormally phosphorylated proteins in muscle atrophy
© The Author(s). 2018
Received: 3 August 2017
Accepted: 21 February 2018
Published: 5 March 2018
Muscle atrophy, an involuntary loss of muscle mass, is involved in various diseases and sometimes leads to mortality. However, therapeutics for muscle atrophy thus far have had limited effects. Here, we present a new approach for therapeutic target prediction using Petri net simulation of the status of phosphorylation, with a reasonable assumption that the recovery of abnormally phosphorylated proteins can be a treatment for muscle atrophy.
The Petri net model was employed to simulate phosphorylation status in three states, i.e. reference, atrophic and each gene-inhibited state based on the myocyte-specific phosphorylation network. Here, we newly devised a phosphorylation specific Petri net that involves two types of transitions (phosphorylation or de-phosphorylation) and two types of places (activation with or without phosphorylation). Before predicting therapeutic targets, the simulation results in reference and atrophic states were validated by Western blotting experiments detecting five marker proteins, i.e. RELA, SMAD2, SMAD3, FOXO1 and FOXO3. Finally, we determined 37 potential therapeutic targets whose inhibition recovers the phosphorylation status from an atrophic state as indicated by the five validated marker proteins. In the evaluation, we confirmed that the 37 potential targets were enriched for muscle atrophy-related terms such as actin and muscle contraction processes, and they were also significantly overlapping with the genes associated with muscle atrophy reported in the Comparative Toxicogenomics Database (p-value < 0.05). Furthermore, we noticed that they included several proteins that could not be characterized by the shortest path analysis. The three potential targets, i.e. BMPR1B, ROCK, and LEPR, were manually validated with the literature.
In this study, we suggest a new approach to predict potential therapeutic targets of muscle atrophy with an analysis of phosphorylation status simulated by Petri net. We generated a list of the potential therapeutic targets whose inhibition recovers abnormally phosphorylated proteins in an atrophic state. They were evaluated by various approaches, such as Western blotting, GO terms, literature, known muscle atrophy-related genes and shortest path analysis. We expect the new proposed strategy to provide an understanding of phosphorylation status in muscle atrophy and to provide assistance towards identifying new therapies.
Muscle atrophy is defined as the involuntary loss of muscle mass, resulting in low quality of life, morbidity and mortality . It is associated with various diseases, such as heart failure , chronic kidney disease (CKD)  and cancer-cachexia , that occur in 80% of patients with advanced cancer . In recent years, many researchers have been devoted to discovering drugs for muscle atrophy. For example, Enobosarm, launched by the biotech firm GTx in 2011, is a molecule that binds to the testosterone receptor in the muscle in order to stimulate muscle build-up . Bimagrumab is an anti-myostatin antibody developed by Novartis that prevents myostatin (one of the main factors inducing muscle atrophy) from activating the ACTRIIB receptor . Unfortunately, these drugs have shown limited effects on muscle atrophy [5, 6], and therefore new therapeutic strategies are required for treating muscle atrophy. Here, we present a new systematic approach to predict therapeutic targets for muscle atrophy.
For therapeutic target prediction, the effects of gene inhibition (knock-down) are necessarily analyzed with a general assumption that most drugs inhibit their targets. shRNA knockdown, one of the in-vitro experiments, is a popular and typical tool for the purpose. However, it is time-consuming and labor-intensive to perform the experiments in genome-scale, especially with a specific disease condition (e.g. atrophic state in this case). Thus, in this study, we employed the Petri net, an in-silico method, which enables dynamic simulations on a large-scale network with incomplete kinetic parameters . The Petri net facilitates genome scale analysis with low cost and short time. Due to this beneficial characteristic, Petri net has been frequently used to model and simulate perturbations of biological signaling networks in previous studies. For example, the Lee D group applied efficient dynamic simulation of EGF-induced signal transduction pathways with colored Petri net . In Derek Ruths’ work, the signaling Petri net-based simulator was employed for the MAPK and AKT signaling network in breast cancer cell lines for computing the response to TSC2 and mTOR inhibitions . In addition, the Jin group proposed an enhanced Petri net model to predict the synergistic effects of drug combinations, which was simulated for signaling pathways and protein-protein interactions related to EGFR and BCL2 .
We predicted therapeutic targets for muscle atrophy by analyzing phosphorylation status among reference, atrophic and each gene-inhibited state, which were computed by Petri net simulations on large-scale phosphorylation network. Here, we developed a phosphorylation-specific Petri net model whose token represents the amount of phosphate and that involves two types of transitions (phosphorylation or de-phosphorylation) and two types of places (activation with or without phosphorylation). The difference between the phosphorylation status of reference and atrophic states were validated by Western blotting experiments detecting five marker proteins, i.e. RELA, SMAD2, SMAD3, FOXO1 and FOXO3. Among 331 kinases and phosphatases, all of which link to the five validated marker proteins in the integrated network, we generated 37 potential therapeutic targets whose inhibition recovers the five abnormally phosphorylated proteins in atrophic states. The predicted therapeutic targets were validated by the genes associated to muscle atrophy reported in the Comparative Toxicogenomics Database (CTD) , and they were compared with that of the shortest path analysis. Furthermore, they were evaluated by the enriched gene ontology terms and KEGG pathways, and three of them (i.e. BMPR1B, ROCK, and LEPR) were verified by literature evidence.
Phosphorylation network construction
We constructed an integrated phosphorylation network, whose nodes represent proteins and whose edges represent either phosphorylation or de-phosphorylation. To this end, we retrieved phosphorylation and de-phosphorylation interactions from three databases, the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway , the Dephosphorylation Database (DEPOD)  and PhosphoNetworks . KEGG pathway is a collection of manually drawn pathways representing various molecular interaction and reactions, where 3529 phosphorylation and 1140 de-phosphorylation interactions were extracted. DEPOD is a manually curated de-phosphorylation database collecting interactions between human phosphatases and their substrates, where 888 de-phosphorylation interactions were extracted. PhosphoNetworks contains kinase-substrate relationships retrieved from recent high-throughput protein microarrays as well as manually curated literature, where 4337 phosphorylation interactions were extracted.
A phosphorylation or de-phosphorylation event occurs when the enzyme, such as kinase or phosphatase, is activated. We needed to determine the activation condition of the 409 kinases and 117 phosphatases in terms of their phosphorylation status because we utilize phosphorylation status, instead of activity status, in the Petri net model. We basically assume that most kinases and phosphatases are activated with phosphorylation. This is based on several reports in the literature showing that phosphorylation leads to an activation of the substrate [21, 22] and an external stimuli leads to the consecutive activation of several down-stream kinases with phosphorylation (phosphorylation cascade) . However, we do not believe that all kinases and phosphatases are activated with phosphorylation. Among the 409 kinases and 117 phosphatases, we characterized 19 kinases and 6 phosphatases that are activated without phosphorylation (i.e. inhibited with phosphorylation) based on the information in KEGG pathways. Here, we determined that an enzyme K is activated without phosphorylation if both activation and de-phosphorylation or both inhibition and phosphorylation are concurrently assigned for a certain enzyme Q to K in KEGG pathways. The other 390 kinases and 111 phosphatases were regarded to be activated with phosphorylation based on the assumption (Fig. 3b).
Petri net configuration
In the Petri net model used in this study, the proteins are represented by places (1985 places), and phosphorylation and de-phosphorylation interactions are represented by transitions (7283 transitions), and the amount of phosphates is represented by the number of tokens, an integer. The amount of phosphates in a specific protein (the phosphorylation status) is represented by the number of tokens in the corresponding place, whose value is an integer that is equal to or greater than zero. For the purpose of the study, we developed a phosphorylation-specific Petri net configuration that involves two types of transitions and two types of places, which is quite different from a typical Petri net model.
We also presented the two types of places as introduced in the above section. It should be noted that the criteria for the two types of places is an activation condition of the enzymes, such as activation with phosphorylation or without phosphorylation, and not a function of the enzymes, such as kinase or phosphatase that has been already considered in transitions. For an input place that is activated with phosphorylation (309 kinases and 111 phosphatases), its transition is enabled when the number of tokens in the input place is greater than the enabling condition, 35. On the other hand, for an input place that is activated without phosphorylation (19 kinases and 6 phosphatases), its transition is enabled when the number of tokens in the input place is less than 35 (Fig. 4b).
Petri net simulation
In state-specific perturbations, there is no perturbation for the reference state. On the other hand, for atrophic state, high activity is assigned to myostatin that is a protein inhibiting muscle cell growth and inducing muscle atrophy . This perturbation is consistent with the Western blotting condition that continuously treats the myostatin to normal muscle for its transition to atrophic muscle. Due to the absence of myostatin from the network, we assigned high activity to its direct targets instead of myostatin itself. In each gene-inhibited state, we set zero activity to each place on the atrophic state (Fig. 5b). Here, among 526 phosphorylation-related enzymes (409 kinases and 117 phosphatases), we only performed 331 gene-inhibited state simulations for 256 kinases and 72 phosphatases that are linked to the five validated markers in wet experiments (see Intermediate validation of the Petri net model in Methods). After performing all transitions in the shuffled transition list, we executed a biological degradation process by reducing 10% of the tokens in every place and write the resulting marking to a file.
Due to randomness in assigning the initial marking and shuffling transition list, 10 Petri net simulations were performed for the reference, atrophic and each gene-inhibited state, respectively (10 iterations). We noticed that tokens were saturated at the final block (the 100th block) for most places in all three states, and for each state we computed the phosphorylation status of 1985 proteins by averaging the final markings (the marking of 100th block) of the 10 iterations. As a result, we obtained the phosphorylation status of 1985 proteins in one reference, one atrophic, and 331 gene inhibited states (Fig. 5c). All of the Petri net simulations were performed by Python codes developed in this study.
Intermediate validation of the petri net model
For the six marker proteins, the differences in the simulation results between reference and atrophic state were compared to those of the Western blotting experiments in Fig. 6a. Here, we did not focus on the amount of changes, but rather the directions of the changes. As a result, we observed the same directions of changes in the five proteins (RELA, SMAD2, SMAD3, FOXO1, and FOXO3) except for the AKT1 protein (Fig. 6b). An imperfection in the phosphorylation network might be one of the reasons for the inconsistency with AKT1 protein. With these coincident directions in the five proteins, we decided to use the five validated proteins as the marker proteins to predict potential of therapeutic targets. As mentioned in the above section, Petri net simulations in the gene-inhibited state were only performed for 331 genes that link to these five validated markers.
Enabling threshold of the petri net model
The Petri net simulation results highly depend on the enabling threshold we selected. Thus, we selected the most robust threshold, i.e. 35, among the eleven enabling thresholds (1, 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50). To do this, for each enabling threshold, ten simulations were performed in reference and atrophic states, respectively, with consideration of randomness in assigning initial marking and shuffling transition list. Then, for each simulation, we generated a list of the ranked places by their final marking (the marking of 100th block), which describes the saturated phosphorylation status. Among the ten list of the ranked places in an enabling threshold, we calculated rank correlations in a pair-wise manner with the spearman rank correlation, which results in 45 rank correlations (except for the correlation of itself). When averaging the 45 rank correlations, the enabling threshold of 35 yields the highest rank correlation (0.791), which indicates that the threshold of 35 is the most robust among the eleven thresholds. Thus, we decided to use 35 as the enabling threshold (Additional file 1: Figure S1).
Therapeutic target prediction
Characterized therapeutic targets
Enrichment analysis to GO terms and KEGG pathways
Functional enrichment tests were performed on the 37 potential therapeutic targets against Gene Ontology (GO) terms and KEGG pathways [17, 28], and their enriched terms (adjust p-value < 0.001) were specified in Additional file 2: Table S2. We noticed that the enriched GO terms include several actin-related terms such as regulation of actin cytoskeleton organization, regulation of actin filament bundle assembly, and regulation of actin filament-based processes. Actin is one of the main structural proteins in muscle, and it switches on the serum-response factor (SRF) pathway that has a role in muscle development and maintenance. Therefore, mutations in the actin protein lead to alterations in the SRF pathway that could promote muscle cell degeneration and cause myopathy or muscular dystrophy . The enriched KEGG pathways also include one actin-related pathway, i.e., regulation of actin cytoskeleton, and one muscle contraction pathway, i.e., vascular smooth muscle contraction.
Evaluation with genes associated with muscle atrophy in the CTD
Results of the hypergeometric test compared to muscle atrophy-associated genes from the CTD
# of muscle atrophy associated genes from CTD
p-value of hypergeometric test
20 (z-score > 1.43)
25 (z-score > 1.15)
30 (z-score > 0.89)
35 (z-score > 0.83)
40 (z-score > 0.78)
Here, the inferred genes in CTD are genes associated with muscle atrophy, which include not only genes curing the disease (therapeutic targets) but also genes causing the disease (causing genes) as well as genes effected by the disease (effected genes). It can be a reason for not very high predictive power. In addition, an imperfect network model also can be an explanation of this low performance because there are still unknown phosphorylation reactions in a cell.
Comparison to the shortest path analysis
Various types of proximity measures in biological networks have been developed to elucidate drug efficacies or mechanisms . Among them, the shortest path analysis is typical and most widely used measure. For example, recently, the shortest path analysis has been applied on multi-level biological networks for an inference of unknown drug-disease relationship . In this section, we compared the potential targets by Petri net simulation to those inferred by the shortest path analysis (SPA). To this end, we computed the average shortest path length from each of the 331 candidate proteins to the five marker proteins, and then, we selected the top 55 genes resulting in the shortest length, which are determined as atrophy-related genes by the SPA. We tried to get 37 genes, which is the same number of genes selected in this study, for a fair comparison; however, 44 genes from 12th to 55th ranked genes have the same shortest path length. A hypergeometric test between the two sets of genes (the 37 genes by Petri net and 55 genes by SPA) showed a non-significant result with p-value 0.136. This indicates that the Petri net-based potential targets are not connected to the marker proteins within a short length. We noticed that their shortest path lengths yield a range from 2 to 5 and their average is 3.07, which is larger than the average shortest path length of all 331 candidate proteins, 3.06. Among the 37 Petri net-based targets, 15 proteins are longer in length than the overall average, 3.06. It could be frustrating because our results are not reproduced in a shortest path analysis, which is one of the most popular static network analysis. However, on the other hand, we think that Petri net simulation can characterizes atrophy-related gene sets, which cannot be predicted by the shortest measure.
We validated several predicted therapeutic target genes by literature searches. BMPR1B is a member of the bone morphogenetic protein (BMP) receptor family, which is reported as a positive regulator of muscle mass in Winbanks’ work . Rho-associated kinase (ROCK) is a regulator of the actomyosin cytoskeleton that induces contractile force generation. Hudson’s group identified that ROCK is highly correlated with the phosphorylation level of myosin phosphatase that regulates myosin light chains . Moreover, in Li’s experiments, an inhibitor of ROCK2 attenuated the Angiotensin II induced contraction in human airway smooth muscle cells . LEPR is a receptor of leptin hormone that regulates adipose-tissue mass, and its expression is highly up-regulated in the condition of skeletal muscle disuse atrophy in humans .
Among several well-known simulation tools including Petri net, Random walk and ordinary differential equation (ODE), we consider that Petri net is the most appropriate tool for this work. The size of the constructed phosphorylation network is so large (7283 interactions) that we cannot employ ODE, whose kinetic parameters are incomplete. Additionally, it is not possible to employ Random walk for this study that particularly focuses on phosphorylation status, which involves two types of interactions and two types of nodes.
We expected that myostatin direct targets, such as ACVR1 and ACVR1B, would be included in the predicted therapeutic targets because their inhibition produces almost the same effect as the inhibition of myostatin, which should recover the phosphorylation status from an atrophic state for the all five marker proteins; however, ACVR1 and ACVR1B are excluded. When they were inhibited, the numbers of markers recovered are 5, 5, 3 for ACVR1 and 4, 5, 3 for ACVR1B for the three simulations in the gene-inhibited state, which does not satisfy the selection criteria for potential therapeutic targets. We recognize that the criteria should be modified so as not to miss such obvious targets, and this will be carried out in further work.
In this study, we suggested a new approach to predict potential therapeutic targets for muscle atrophy based on the phosphorylation status of the reference, atrophic and gene-inhibited states, which were simulated by Petri net. The simulation results between the reference and atrophic states were validated with Western blotting experiments detecting five marker proteins. We generated a list of the potential therapeutic targets whose inhibition recovers the five abnormally phosphorylated proteins in the atrophic state, and they were evaluated by various approaches, such as GO terms, the literature, and genes associated with muscle atrophy. We expect the new proposed strategy can provide an understanding of phosphorylation status in muscle atrophy and provide assistance towards identifying its therapeutics.
This work was supported by the Bio-Synergy Research Project (NRF-2012M3A9C4048758) of the Ministry of Science, ICT and Future Planning through the National Research Foundation.
Availability of data and materials
The datasets and Python codes generated and/or analyzed during the current study are available in the Github repository, https://github.com/jmjung83/PetriNet_for_therapeuticTarget_of_muscleAtrophy.
JJ and DL designed the overall method, and JJ performed Petri net simulation. MK performed data-preprocessing used in the simulation. SB helped to write the main manuscript text and provided comments that improved the introduction and methods sections. JJ performed the evaluation process. SY gathered and processed the data used in the evaluation part. DL supervised this work. All authors read, wrote and approved the manuscript.
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