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Boolean network modeling of β-cell apoptosis and insulin resistance in type 2 diabetes mellitus

Boolean network modeling of β-cell apoptosis and insulin resistance in type 2 diabetes mellitus Background: Major alteration in lifestyle of human population has promoted Type 2 diabetes mellitus (T2DM) to the level of an epidemic. This metabolic disorder is characterized by insulin resistance and pancreatic β-cell dysfunction and apoptosis, triggered by endoplasmic reticulum (ER) stress, oxidative stress and cytokines. Computational modeling is necessary to consolidate information from various sources in order to obtain a comprehensive understanding of the pathogenesis of T2DM and to investigate possible interventions by performing in silico simulations. Results: In this paper, we propose a Boolean network model integrating the insulin resistance pathway with pancreatic β-cell apoptosis pathway which are responsible for T2DM. The model has five input signals, i.e. ER stress, oxidative stress, tumor necrosis factor α (TNFα), Fas ligand (FasL), and interleukin-6 (IL-6). We performed dynamical simulations using random order asynchronous update and with different combinations of the input signals. From the results, we observed that the proposed model made predictions that closely resemble the expression levels of genes in T2DM as reported in the literature. Conclusion: The proposed model can make predictions about expression levels of genes in T2DM that are in concordance with literature. Although experimental validation of the model is beyond the scope of this study, the model can be useful for understanding the aetiology of T2DM and discovery of therapeutic intervention for this prevalent complex disease. The files of our model and results are available at https://github.com/JieZheng- ShanghaiTech/boolean-t2dm. Keywords: Boolean model, Type 2 diabetes mellitus, Insulin resistance, β-cell apoptosis Background excessive nutrients could lead to hyperglycemia, elevated Type 2 diabetes mellitus (T2DM) is characterized by free fatty acids (FFA), and inflammation, which severely insulin resistance at its onset. Persistence of insulin impair β-cell functions, leading to insulin resistance and resistance leads to pancreatic β-cell dysfunction and in β-cell apoptosis. extreme cases to β-cell apoptosis [1–3]. Insulin resistance The ER in the β-cells is responsible for the production increases the load on β-cells to produce more insulin in and secretion of insulin. The increased demand for insulin order to maintain blood glucose at normal levels. This synthesis in the presence of high glucose and FFA lev- homeostasis is maintained as long as β-cells can meet els triggers the accumulation of misfolded proteins in the the increased insulin demand. However, persistence of ER, causing ER stress and the consequent activation of the unfolded protein response (UPR). UPR initially attempts to mitigate ER stress by degrading misfolded proteins and *Correspondence: zhengjie@shanghaitech.edu.cn School of Information Science and Technology, ShanghaiTech University, preventing their further accumulation. However, when ER Shanghai, China stress is not mitigated, UPR activates the apoptosis signals Full list of author information is available at the end of the article [4–6]. 78 kDa glucose regulated protein (GRP78) serves © The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 2 of 12 as a sensor of protein misfolding [7]. Under non-stressed ODE models require detailed kinetic knowledge and conditions, GRP78 binds to three UPR initiator pro- time-series data for accurate parameter estimation. How- teins, i.e. inositol requiring 1 (IRE1), PKR-like ER kinase ever, the size of our proposed network is relatively big (PERK), and activating transcription factor 6 (ATF6), and (consisting of 72 nodes) and hence obtaining time-series maintains them in the inactive state [8]. Under stressed expression data for all the genes would be expensive as conditions, GRP78 dissociates from these three proteins, well as time-consuming. Also, estimating the parameters causing their activation and initiation of UPR. of the ODE model with the time-series expression data When ER stress can be resolved, the UPR assists β of only a small subset of genes would result in erroneous cells in their survival. However, when ER stress cannot be parameter values. Furthermore, in a Boolean network resolved the UPR activates the pro-apoptotic signals [9]. Hyperglycemia causes oxidative stress through the gener- Table 1 The gene interactions incorporated into the model with ation of reactive oxygen species (ROS) [10]. In the absence reference to the existing literature of an appropriate antioxidant response, the system expe- Gene interations Reference riences redox imbalance, leading to the activation of IRE1 ↑→ XBP1 ↑→ β-cell dysfunction [26] oxidative stress-sensitive signaling pathways. Cytokines, (IRE1+TRAF2+ASK1) ↑→ JNK ↑→ BCL2 [28–30] including FasL, TNFα, and IL-6, play important roles in (anti-apoptotic gene)↓ the induction of β-cell apoptosis [11–15]aswellasinsulin BCL2 ↓→ (BAX + BAK) (pro-apoptotic) ↑ [50, 51] resistance [16, 17]. Caspases serve as the final mediators PERK ↑→ EIF2S1 ↓→ ATF4 ↑→ CHOP (pro- [27] of apoptosis. The upstream apoptosis initiator caspases apoptotic) ↑ 8 and 9 are activated on receiving death signal from the ATF6 ↑→ CHOP (pro-apoptotic) ↑→ BCL2 [51, 52] death-inducing signaling complex (DISC) and apopto- (anti-apoptotic gene)↓ some respectively, which in turn activate the downstream Oxidative stress ↑→ ASK1 ↑,JNK ↑,p38 ↑ [31–33] apoptosis effector caspases 3, 6 and 7, which ultimately p38 ↑→ CHOP (pro-apoptotic) ↑ [34] execute apoptosis [18]. FasL ↑→ (FasR + FADD + pro-caspase-8) ↑ [53] Computational modeling is necessary to consolidate → caspase-8 ↑→ caspase-3 ↑→ apoptosis information from various sources, such as listed above, TNFα ↑→ (TNFR1 + TRADD) ↑→ RIPK1 ↑, [54] in order to obtain a comprehensive understanding of the FADD ↑,TRAF2 ↑ pathogenesis of T2DM and investigate possible interven- FADD ↑→ caspase-8 ↑ [54] tionsbyperforming in silico simulations. A few dynamic RIPK1 ↑→ RAIDD ↑→ caspase-8 ↑ [54] models of insulinresistanceinT2DMhavebeenproposed recently. For instance, Brannmark et al. [19]proposedan TNFα ↑→ TNFR2 TNFα ↑→ TRAF2 ↑→ [55–57] ... → JNK ↑,NF-kB ↑ ordinary differential equation (ODE) model of insulin sig- naling in T2DM. Rajan et al. proposed an ODE model (BAX + BAK) (pro-apoptotic) ↑→ [6, 58] Cytochrome c ↑→ (APAF1 + caspase-9) ↑ to study the contribution of Forkhead box protein O1 → caspase-3 ↑ (FOXO1) to insulin resistance in T2DM [20]. Another XIAP ↑→ caspase-3 ↓, caspase-7 ↓, caspase- [35, 36] paper [21] presented an ODE model to simulate the devel- 9 ↓ opment of insulin resistance by hyperglycemia, FFA, ROS, DIABLO ↑,HtrA2 ↑→ XIAP ↓ [37] and inhibition of glucose transporter type 1 (GLUT-1) INSR ↑→ IRS ↑→ PI3K ↑→ ...→ AKT ↑→ [59–61] and glucose transporter type 4 (GLUT-4). However, there FOXO1 ↓,GSK3β ↓,GLUT4 ↑ exists no model of β-cell apoptosis occurring in the T2DM GSK3β ↑→ GS ↓→ glycogen synthesis ↓ [42, 43] condition. Also, there is no existing work that attempts to FOXO1 ↑→ PEPCK ↑,G6PC ↑→ glucose [47, 47–49] integrate the insulin resistance and β-cell apoptosis path- synthesis ↑ ways in order to obtain a comprehensive understanding (mTORC1 + S6K) ↑→ IRS ↓ [44–46] of the molecular mechanisms underlying T2DM. To dis- IKKβ ↑→ TSC1/2 ↓→ mTORC1 ↑ [62] cover potential therapeutic interventions for T2DM, it is essential to have a more comprehensive model for the ER stress ↑→ ...→ IRE1 ↑→ ...→ JNK ↑→ [38, 39, 63] IRS ↓ mechanisms causing T2DM pathogenesis. Therefore, we propose a Boolean network model inte- ER stress ↑→ ...→ IRE1 ↑→ XBP1 ↑→ [64] FOXO1 ↓ grating the insulin resistance pathway and β-cell apoptosis PERK ↑→ FOXO1 ↑ [65] pathway for the purpose of obtaining deeper insights into the mechanisms of development and progression ER stress ↑→ ...→ ATF4 ↑→ CHOP ↑→ [40, 41] TRB3↑→ AKT ↓ of T2DM. The aforementioned existing models are ODE models, whereas we constructed a Boolean net- IL-6 ↑→ JAK ↑→ STAT3 ↑→ SOCS3 ↑→ [66–68] IRS ↓ work model. The reason behind this selection is that Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 3 of 12 model, gene expression is represented by either TRUE (1) Methods or FALSE (0). By simplifying the gene expression levels In this paper, we propose a Boolean network model of into binary states, Boolean networks are feasible for sim- β-cell fate in T2DM. The model was constructed by ulating the behaviour of large regulatory networks in a extracting information from the KEGG pathways [25]and qualitative way. literature. The gene interactions incorporated into the In a Boolean network model the state of each gene is model with reference to the existing literature are listed represented by either 1 (TRUE), indicating the gene is in Table 1. In this model, we integrated the β-cell apopto- highly expressed, or 0 (FALSE) when the gene is lowly sis pathway with the insulin resistance pathway, as shown expressed. An edge in a Boolean network can be either in Fig. 1. The apoptosis pathway consists of the signaling activating or inhibiting [22]. In this paper, we have used pathways triggered by ER stress (UPR pathway), oxida- random asynchronous Boolean simulation [23, 24], which tive stress, and 3 cytokines, i.e. FasL, TNFα,and IL-6. updates genes in a random order in each iteration. This The insulin resistance pathways consist of phosphatidyli- random asynchronous update method is inspired by the nositide 3-kinase (PI3K)-protein kinase B (PKB or AKT) stochastic nature of gene regulatory networks, where gene (KEGG ID: hsa04151), mammalian target of rapamycin expression alteration occurs in a random order rather than (mTOR) (KEGG ID: hsa04150), janus kinase (JAK)- signal simultaneously [24]. transducer and activator of transcription (STAT) (KEGG Due to the lack of experimental gene expression data, ID: hsa04630), and insulin (KEGG ID: hsa04910) signaling we validate our simulation results by comparing pre- pathways. T2DM first causes insulin resistance, i.e. insulin dicted patterns of gene expression levels with experimen- fails to bind to insulin receptors in cells, thereby block- tal observations reported in the literature. We also analyze ing the uptake of blood glucose by cells. Sustained insulin the dynamical behaviors of the model by visualizing the resistance finally leads to β-cell failure and apoptosis. state transition graphs under different combinations of The Boolean update functions, listed in Table 2,for input signals. Our results show that the simple Boolean the target genes in the model are defined by combining network model can capture some qualitative trends of the activating input genes using OR functions and inhibiting genetic circuits regulating the cell fate decision of β-cells, input genes using AND functions. The reason behind this and shed light on the causes and processes of dysfunc- combination strategy is that a target gene will be expressed tional insulin metabolism and loss of β-cell homeostasis when at least one of its activating genes is expressed and that occur in T2DM. all of its inhibiting genes are absent. Fig. 1 Gene Regulatory Network. Insulin resistance and β-cell apoptosis pathways involved in the pathogenesis of Type 2 diabetes mellitus. The red nodes denote the five input signals and the purple node represents β-cell apoptosis. A → B indicates activation of gene B by gene A, and A −| B indicates inhibition of gene B by gene A Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 4 of 12 Table 2 Boolean functions for the Boolean model The proposed Boolean network consists of 72 nodes, of Node Boolean function Node Boolean function which five are input signals, one node represents Apop- tosis, and the remaining 66 nodes represent genes. We ER ER OS OS FasL FasL TNFα TNFα or NFKB employ the random asynchronous Boolean update [23, 24] IL-6 IL-6 or NFKB method to perform the simulations. The random asyn- chronous Boolean method first generates a random per- GRP78 ATF6orXBP1orATF4 ATF6 GRP78 mutation of the nodes at each time step and updates and (not ER) the states of the nodes in the order specified by the PERK GRP78 and (not IRE1 BAX or BAK or GRP78 DNAJC3) permutation. This allows us to capture the stochastic EIF2S1 GADD34 and (not DNAJC3 ATF6 or XBP1 changes in gene expressions that occur in real gene reg- PERK) ulatory networks. The random asynchronous Boolean ATF4 EIF2S1 CHOP ATF6 or ATF4 simulations were performed using the Python code pro- XBP1 IRE1 GADD34 CHOP vided in [23] which is available at https://gitlab.com/ TNFR1 TNFα TNFR2 TNFα stemcellbioengineering/garuda-boolean. TRAF2 IRE1 or TNFR2 or ASK1 OS or TRAF2 or DAXX For example, suppose a gene regulatory network con- TRADD sists of 3 genes, {g , g , g }. The Boolean update functions 1 2 3 JNK OS or ASK1 or p38 OS or ASK1 for the genes are as follows: GADD45 BCL2 (not JNK) and (not BID CASP8 and (not BCL2) g = g 1 3 CHOP) and (not P53) and (not BAD) g = g ∨ g 2 1 3 BAX JNK or P53 and (not BAK BAX and (not BCL2) g = g 3 2 BCL2) DIABLO BAX or BAK or BID HtrA2 BAX or BAK or BID Suppose an iteration randomly generates a permuta- FasR FasL TRADD TNFR1 tion of nodes as {3, 1, 2}. Then the asynchronous Boolean DAXX FasR RIPK1 FasR or TRADD updates will be carried out as follows: RAIDD RIPK1 FADD FasR or TRADD g (t + 1) = g (t) 3 2 CASP8 RAIDD or FADD or CASP9 RAIDD or CASP8 or CASP3 or CASP6 CASP3 or APAF1 or g (t + 1) = g (t + 1) 1 3 CASP12 and (not XIAP) and (not AKT) g (t + 1) = g (t + 1) ∨ g (t + 1) 2 1 3 CASP3 CASP9 or CASP8 and CASP7 CASP9 or CASP8 or From the above equations, we see that the nodes are (not XIAP) CASP3 or CASP6 and updated in a randomly generated order as specified by the (not XIAP) permutation, rather than simultaneously. CASP6 CASP7 or CASP3 After performing the simulations for a fixed number of XIAP (not DIABLO) and (not CytochromeC BAX or BAK or BID HtrA2) (not CASP3) iterations, a directed graph of states is obtained, where APAF1 CytochromeC or P53 Apoptosis CASP3 or CASP6 or each state is a vector representing the expression lev- CASP7 els of all genes at a particular time step. The strategy of INS INS INSR INS strongly connected components (SCCs) is employed on IRS INSR and (not SOCS3) PI3K IRS or JAK this directed graph to capture the dynamic nature of the and (not JNK) (not states [23]. An SCC of a directed graph is a sub-graph IKKβ) and (not S6K) that is strongly connected, i.e., each node is reachable PIP3 PI3K PDK1 PIP3 from every other node in the sub-graph. An illustration AKT PDK1 or mTORC2 and AS160 AKT (not TRB3) of SCC is given in Fig. 2. Each node is a state with the PKCα PDK1 GLUT4 AKT or AS160 or PKCα expression levels of all the genes in the network (for the GSK3β not AKT GS not GSK3β example we assume a network with five genes) and there FOXO1 PERK and (not AKT) PGC1α FOXO1 is a path between each pair of nodes in both directions. and (not XBP1) Let us consider that an SCC consists of a set of N states PEPCK FOXO1 G6PC FOXO1 {S , S , ..., S }. The probability of state S being one of the 1 2 N i PPARα PGC1α TRB3 PPARα or CHOP states of the SCC is given by: TSC1/2 (not AKT) and (not Rheb not TSC1/2 number of occurrences of S IKKβ) i P(S ) = . mTORC1 Rheb S6K mTORC1 number of occurrences of S j=1 mTORC2 not S6K BAD JNK and (not AKT) We calculate the gene expression level of each gene in a JAK IL-6 and (not SOCS3) STAT3 JAK SOCS3 STAT3 IKKβ TRAF2 particular SCC as the sum of probabilities of states where NFκBnotIKBα IKBα not IKKβ the gene is in the ON state. Therefore, the expression level Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 5 of 12 Fig. 2 Strongly Connected Component. An example of a strongly connected component (SCC). Suppose the network consists of five genes. Then each node is a state which contains the expression levels of the five genes. An arrow from state S to state S indicates an update step. In an SCC all 1 2 states can be reached from every other state of a gene, g , with respect to an SCC is determined as Due to the lack of experimental data, we validate our follows: proposed Boolean network model using relevant literature (see Table 1). For each gene g ,weuse thesamesymbol g i i Exp(g ) = P(S ) i j to represent its binary expression level. S ∈OnSt(g ) j i where 1if g is reported as expressed in the literature g = OnSt(g ) ={S ∈ SCC | g (S ) = 1}. 0if g is reported as not expressed in the literature i j i j It is easy to see that In our model, we determine the expression level of each gene with respect to a particular SCC. Thus the gene P(S ) = 1 expression levels are in the range [0, 1]. We assume that j=1 if the expression value of a gene is greater than 0.50, then the gene is expressed, otherwise, it is not expressed. We use ER stress, oxidative stress, TNFα,FasL, andIL- For the purpose of validating our proposed model, we 6 as input signals. Also, based on the literature, some of employ the performance metrics of precision, recall (sen- the nodes are assigned specific values (Table 3)and the sitivity), specificity, and F1 score. The simulation result rest are set to random values as initial conditions. We per- of our proposed model is verified against the literature as formed simulations using different combinations of the input signals, as shown in Table 4. We carried out 1000 simulation runs and 1000 Boolean update steps per simu- lation for each input signal. The results of the simulations Table 4 Different combinations for the input signal nodes are presented and discussed in the following section. ER stress Oxidative stress TNFα FasL IL-6 Case 1 True False False False False Table 3 Initial conditions Case 2 False True False False False Node Initial value Reason Case 3 True True False False False Apoptosis False We set apoptosis to False to see Case 4 False False True False False whether the input signals can cause apoptosis Case 5 False False False True False Caspases 3, 6, 7, 8, 9 False Caspases serve as the final Case 6 False False False False True mediators of apoptosis. So, we set Case 7 False False True True True them to False to see whether the input signals can activate them Case 8 True True True True True Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 6 of 12 Table 5 Gene expressions of the significant genes in the model for input signal cases 1-5 and 7-8 Node Case 1 Case 2 Case 3 Case 4 Case 5 Case 7 Case 8 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 Apoptosis 1 1111111111111 AKT 0.50 0.50 0.49 0.49 0.49 0.49 0.49 0.49 0.50 0.49 0.49 0.50 0.50 0.49 APAF-1 11111111111111 ASK1 11111111111111 ATF4 10101010101010 ATF6 00000000000000 BAK 1 1111111111111 BAX 1 1111111111111 BCL2 00000000000000 Caspase-3 11111111111111 Caspase-6 11111111111111 Caspase-7 11111111111111 Caspase-8 11111111111111 Caspase-9 11111111111111 CHOP 10101010101010 DIABLO 11111111111111 EIF2S1 10101010101010 FADD 11111111111111 FASR 00000000000000 FOXO1 0 0000000000000 G6PC 00000000000000 GADD34 1 0101010101010 GLUT4 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 GRP78 1 1111111111111 GS 0.50 0.50 0.50 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.49 GSK3β 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.50 0.49 0.49 0.49 0.49 0.49 0.50 HtrA2 1 1111111111111 IKBα 00000000000000 IKKβ 11111111111111 INS 1 1111111111111 INSR 11111111111111 IRE1 11111111111111 IRS 0 0000000000000 JAK 0.50 0.49 0.50 0.49 0.49 0.50 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 JNK 1 1111111111111 NFKB 11111111111111 PEPCK 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PERK 0 0000000000000 PI3K 0.50 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.49 0.49 0.50 0.50 0.49 RAIDD 1 1111111111111 RIPK1 1 1111111111111 S6K 1 1111111111111 SOCS3 0.49 0.49 0.50 0.49 0.50 0.50 0.49 0.49 0.50 0.50 0.49 0.49 0.49 0.50 STAT3 0.50 0.49 0.49 0.49 0.49 0.50 0.49 0.49 0.50 0.50 0.49 0.49 0.50 0.50 TNFR1 1 1111111111111 TNFR2 1 1111111111111 Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 7 of 12 Table 5 Gene expressions of the significant genes in the model for input signal cases 1-5 and 7-8 (Continued) Node Case 1 Case 2 Case 3 Case 4 Case 5 Case 7 Case 8 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 TRADD 11111111111111 TRAF2 11111111111111 TRB3 10101010101010 TSC2 00000000000000 XBP1 11111111111111 XIAP 00000000000000 mTORC1 11111111111111 p38 11111111111111 Here A1 and A2 denotes SCC1 and SCC2 follows. For each gene g , ER stress sensor IRE1 and its downstream gene X-box protein binding 1 (XBP1) are TRUE in some attrac- ⎪ True positive, if g = 1 (simulation result) and g = 1 (literature) i i ⎪ tors, and FALSE in others [26]. Another ER stress sen- True negative, if g = 0 (simulation result) and g = 0 (literature) i i sor, PERK is observed to be FALSE in all the attrac- g ∈ False positive, if g = 1 (simulation result) and g = 0 (literature) tors. Also, eukaryotic translation initiation factor 2 sub- ⎪ i i unit 1 (EIF2S1), activating transcription factor 4 (ATF4), False negative, if g = 0 (simulation result) and g = 1 (literature) i i and C/EBP homologous protein (CHOP) are TRUE in The four evaluation metrics are calculated using the some attractors and FALSE in the others. PERK phos- following formulae: phorylates and inactivates EIF2S1, which inhibits protein synthesis. Phosphorylated EIF2S1 increases the transla- True positive Precision = tion of ATF4 [8], which in turn activates pro-apoptotic True positive + False positive CHOP, causing β-cell dysfunction and death [27]. The True positive attractors where IRE1, XBP1, EIF2S1, ATF4, and CHOP Recallorsensitivity = True positive + False negative have expression levels of 0 may denote the transi- True negative tion states when these genes are not contributing to Specificity = True negative + False positive apoptosis. 2 × precision × recall While associating with TNF-receptor-associated fac- F1 score = tor 2 (TRAF2) and apoptosis signal-regulating kinase 1 precision + recall (ASK1), IRE1 activates jun N-terminal kinase (JNK) [28, Results 29], which in turn inhibits the anti-apoptotic protein B- Comparison with the literature cell lymphoma 2 (BCL2) [30]. Oxidative stress activates The expression levels of genes in the SCCs obtained by ASK1 [31, 32], JNK and p38 [33]. Activated p38 phos- phorylates and elevates the expression of pro-apoptotic performing simulations with our proposed Boolean model CHOP [34]. From the simulation results, we observe that are listed in Tables 5 and 6. Simulations performed using the pro-apoptotic genes, TRAF2, ASK1, JNK, p38, BAX, input signal cases 1, 2, 3, 4, 5, 7, and 8 (Table 4) result and BAK are TRUE and the anti-apoptotic gene BCL2 in two attractors (SCCs). Apoptosis is ON in both of the is FALSE in one attractor, while the reverse states are attractors. Simulations performed using input signal case observed in the other. X-linked inhibitor of apoptosis pro- 6(Table 4)result in sixattractors(SCCs). ApoptosisisON tein (XIAP), which inhibits Caspases 3, 7, and 9 [35, 36], in four attractors and OFF in the remaining two attrac- has an expression level of 0, whereas direct IAP-binding tors. These observations are consistent with the literature protein with low pI (DIABLO) and high temperature where ER stress, oxidative stress, and cytokines have been requirement protein A2 (HtrA2), which inhibit XIAP [37], shown to cause apoptosis of β-cells individually as well as have expression levels of 1. together [4–6]. JNK phosphorylates and inhibits insulin receptor sub- From our simulation results, we observe that Caspases strate (IRS) [38, 39]. IRS gene is FALSE in both of the 3, 6, 7, 8, and 9, which serve as the final mediators of attractors. PI3K has an expression level of around 0.50 in apoptosis [18] are TRUE in the attractors, even though all the attractors. Tribbles homolog 3 (TRB3) is induced by in the initial condition they were set to FALSE. The Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 8 of 12 Table 6 Gene expressions of the significant genes in the model Table 6 Gene expressions of the significant genes in the model for input signal case 6. Here A1-A6 denotes SCC1-SCC6 for input signal case 6. Here A1-A6 denotes SCC1-SCC6 (Continued) Node Case 6 Node Case 6 A1 A2 A3 A4 A5 A6 A1 A2 A3 A4 A5 A6 Apoptosis 111100 TRAF2 1 1 0000 AKT 0.49 0.49 0.63 0.55 0.65 0.56 TRB3 1 0 0101 APAF-1 110100 TSC2 0 0 0.37 0.45 0.36 0.44 ASK1 110000 XBP1 1 1 0000 ATF4 100101 ATF6 000000 XIAP 0 0 0011 BAK 110000 mTORC1 1 1 0.63 0.55 0.63 0.57 BAX 110000 p38 1 1 0000 BCL2 001010 Caspase-3 111100 ER stress through the ATF4-CHOP pathway [40]. Over- Caspase-6 111100 expression of TRB3 inhibits AKT and decreases glucose Caspase-7 111100 uptake [41]. TRB3 is TRUE in one attractor and FALSE Caspase-8 111100 in the other. AKT has an expression level of 0.50 in both of the attractors. Thus, from the results, we observe that Caspase-9 111100 ER stress inhibits the PI3K-AKT signaling pathway and CHOP 100101 promotes insulin resistance. DIABLO 110100 Insulin promotes conversion of glucose to glycogen by EIF2S1 100101 inhibiting glycogen synthase kinase-3β (GSK3β)through FADD 110000 the PI3K-AKT signaling pathway, which leads to the acti- FASR 000000 vation of glycogen synthase (GS) [42]. From the simulation FOXO1 000000 results, we observe that the expression level of GSK3β, G6PC 000000 which inhibits glycogen synthesis through inhibition of GADD34 100101 GS [42, 43] is approximately 0.49 and that of GS is approx- GLUT4 0.65 0.65 0.75 0.70 0.78 0.71 imately 0.50. From these simulation results, we can infer GRP78 110101 that glycogen synthesis is reduced which contributes to GS 0.49 0.49 0.62 0.54 0.65 0.55 insulin resistance. GSK3β 0.50 0.50 0.38 0.45 0.36 0.45 In T2DM, the mammalian target of rapamycin com- HtrA2 110100 plex 1 (mTORC1)/ S6 kinase (S6K) signaling is activated IKBα 001111 [44] leading to the inhibition of IRS [45, 46]. We observe IKKβ 110000 from the simulation results that mTORC1 and S6K have INS 111111 expression levels of 1 thus inhibiting IRS which has an INSR 111111 expression of 0. These events cause PI3K and AKT to have IRE1 110000 low expression levels of approximately 0.50, which in turn IRS 0 0 0.19 0.22 0.18 0.22 reducesglucoseuptakethrough GLUT4whose expression JAK 0.49 0.49 0.49 0.49 0.49 0.50 level is around 0.65. JNK 110000 FOXO1 increases the expression of phosphoenolpyru- NFKB 110000 vate carboxykinase (PEPCK) and glucose-6-phosphatase PEPCK 000000 (G6PC) and thus promotes glucose synthesis [47]. Insulin inhibits the expression of FOXO1 through the activa- PERK 000000 tion of the PI3K/AKT signaling pathway, which in turn PI3K 0.49 0.49 0.54 0.55 0.54 0.56 suppresses PEPCK and G6PC, and thereby reduces glu- RAIDD 110000 cose synthesis [47–49]. From our simulation results, we RIPK1 110000 observe that FOXO1, PEPCK, and G6PC are FALSE. This S6K 1 1 0.62 0.55 0.62 0.56 could be due to the fact that PI3K and AKT are not com- SOCS3 0.49 0.50 0.50 0.49 0.49 0.49 pletely inactive, though they may have low expression STAT3 0.49 0.49 0.49 0.49 0.49 0.50 levels, and hence is still able to inhibit the expressions of TNFR1 110000 FOXO1, PEPCK, and G6PC. TNFR2 110000 In Case 6 where only signal IL6 is active, we observe TRADD 110000 six attractors (Table 6), of which four indicate apoptosis Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 9 of 12 and two do not. For the attractors where apoptosis is Figure 4 shows the state transition graph of the state observed, the expression levels of the genes are similar to space generated by simulations conducted using input those mentioned above for the other input signal cases. signal combination given in case 6 (Table 4). The four When apoptosis is not observed, i.e. in the two remaining dense red regions represent the four SCCs where apopto- attractors, the caspases, JNK, BAX, and BAK are FALSE. sis is ON. The two dense blue regions represent the two In one of these two attractors, BCL2 is FALSE and CHOP SCCs where apoptosis is OFF. Thus from the state transi- is TRUE. In the other attractor we observe the reverse tion graph, we observe that, in the presence of only IL-6, expression pattern. Thus, in the presence of only IL-6, apoptosis may or may not be activated. apoptosis may or may not be activated. We further assessed the performance of our proposed Comparison with random Boolean networks Boolean network model by comparing model predictions We also compared our Boolean network model with ran- of gene expressions against the literature. Considering dom Boolean network models using the 8 input signal the simulation results obtained using the 8 input signals combinations given in Table 4.For cases1,2,3,4,5,7, listed in Table 4, the average precision, recall (sensitiv- and 8 we found that the number of attractors obtained ity), specificity, and F1 score obtained for our model are by simulating the random Boolean networks ranges from 0.9524, 0.8, 0.875, and 0.8696, respectively. We observe 28 to 177, whereas for our Boolean network model the that the validation scores for our model are not very high, number of attractors is 2. Similarly, for case 6, the number maybebecause ourmodel is sensitivetosomemissing of attractors obtained by simulating the random Boolean interactions. networks ranges from 25 to 180, whereas for our Boolean network model the number of attractors is 6. Thus, from State transition graphs the results we observe that the random Boolean networks Figure 3 shows the state transition graph of the state space typically have large numbers of attractors. generated by simulations conducted using input signal combination given in case 8 (Table 4). The two dense red Conclusion regions represent the two SCCs where apoptosis is ON. In this paper, we proposed a Boolean network model The blue nodes represent states where apoptosis is OFF. of the integrated insulin resistance and β-cell apoptosis Thus from the state transition graph, we observe that, in pathways. Such a model, which explores the combined the presence of all input signals, apoptosis is eventually mechanism and interplay between insulin resistance and activated, even though in the initial condition it is set to β-cell apoptosis in the pathogenesis of T2DM, has not FALSE. been proposed before. We used the model to simulate the Fig. 3 State Transition Graph 1. State transition graph obtained by simulating our proposed Boolean network model using input signal condition given in Case 8 of Table 4. Simulations generate 2 attractors, both having the Apoptosis node activated. Apoptosis is ON in the red coloured states and OFF in the blue colored states Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 10 of 12 Fig. 4 State Transition Graph 2. State transition graph obtained by simulating our proposed Boolean network model using input signal condition given in Case 6 of Table 4. Simulations generate 6 attractors. In four of the attractors Apoptosis is ON, denoted by red colour, and in the remaining two attractors Apoptosis is OFF, denoted by blue colour dynamics of gene expression induced by different com- play pivotal roles in insulin resistance and/or β-cell apop- binations of the five input signals, i.e. ER stress, oxidativ tosis, and these genes could be further investigated for e stress, and cytokines (TNFα, FasL, IL-6), which serve as possible disease interventions. triggers for insulin resistance and β-cell apoptosis. Abbreviations The random order asynchronous update method was AKT (PKB): Protein kinase B; APAF1: Apoptotic protease-activating factor 1 ; employed to perform the simulations, i.e. all nodes were ASK1: Apoptosis signal-regulating kinase 1; ATF4: Activating transcription factor 4; ATF6: Activating Transcription Factor 6; BCL2: B-cell lymphoma 2; updated in a random order at each update step. We CHOP: C/EBP homologous protein; DIABLO: Direct IAP-binding protein with assessed the performance of our model using the met- low pI; EIF2S1: Eukaryotic translation initiation factor 2 subunit 1; ER: rics of precision, recall (sensitivity), specificity, and F1 Endoplasmic reticulum; FADD: Fas-associated death domain-containing protein; FasL: Fas ligand; FasR: Fas receptor; FFA: Free fatty acids; FOXO1: score, when validating our model against the literature. Forkhead box protein O1; GADD34: Growth arrest and DNA damage-inducible The precision score obtained is high, but sensitivity, speci- protein; G6PC: Glucose-6-phosphatase; GLUT-1: Glucose transporter type 1; ficity, and F1 scores are not so. One possible reason may GLUT-4: Glucose transporter type 4; GRP78: 78 kDa glucose regulated protein; GS: Glycogen synthase; GSK3β: Glycogen synthase kinase-3β; HtrA2: High be that some missing interactions affect the predictions of temperature requirement protein A2; IL-6: Interleukin-6; INSR: Insulin receptor; our model. We also compared our Boolean network model IRE1: Inositol Requiring 1; IRS: Insulin receptor substrate; JAK: Janus kinase; JNK: with random Boolean network models and observed that Jun N-terminal kinase; mTORC1: Mammalian target of rapamycin complex 1; mTORC2: Mammalian target of rapamycin complex 2; ODE: Ordinary random Boolean networks typically have large numbers differential equation; PEPCK: Phosphoenolpyruvate carboxykinase; PERK: of attractors ranging from around 25 to 180, whereas our PKR-like ER kinase; PI3K: Phosphatidylinositide 3-kinase; Rheb: Ras homolog model shows small numbers of attractors ranging from enriched in brain; RIPK1: Receptor-interacting serine/threonine-protein kinase 1; ROS: Reactive oxygen species; S6K: S6 kinase; SCC: Strongly connected 2to6. component; SOCS3: Suppressor of cytokine signaling 3; STAT3: Signal As a future step, we can use this model to perform vir- transducer and activator of transcription 3; T2DM: Type 2 Diabetes Mellitus; tual gene knockout experiments to determine genes that TNFα: Tumor necrosis factor α; TNFR1: Tumor necrosis factor receptor Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 11 of 12 superfamily member 1A; TNFR2: Tumor necrosis factor receptor superfamily 6. Schröder M, Kaufman RJ. The mammalian unfolded protein response. member 1B; TRADD: TNFR1-associated death domain; TRAF2: Annu Rev Biochem. 2005;74:739–89. TNF-receptor-associated factor 2; TRB3: Tribbles homolog 3; TSC: Tuberous 7. Bertolotti A, Zhang Y, Hendershot LM, Harding HP, Ron D. Dynamic sclerosis complex; UPR: Unfolded pro-tein respons; XBP1: X-box protein interaction of bip and er stress transducers in the unfolded-protein binding 1; XIAP: X-linked inhibitor of apoptosis protein response. Nat Cell Biol. 2000;2(6):326. 8. Ron D, Walter P. Signal integration in the endoplasmic reticulum Acknowledgements unfolded protein response. Nat Rev Mol Cell Biol. 2007;8(7):519. We would like to thank Dr. Ket Hing Chong for his valuable discussions. 9. Erguler K, Pieri M, Deltas C. A mathematical model of the unfolded protein stress response reveals the decision mechanism for recovery, Funding adaptation and apoptosis. BMC Syst Biol. 2013;7(1):16. This work was supported by MOE AcRF Tier 1 grant (2015-T1-002-094), Ministry 10. Ihara Y, Toyokuni S, Ichida K, Odaka H, et al. Hyperglycemia causes of Education, Singapore and the Start-Up Grant of ShanghaiTech University, oxidative stress in pancreatic beta-cells of gk rats, a model of type 2 China. Publication of this article was sponsored by the Start-up Grant of diabetes. Diabetes. 1999;48(4):927. ShanghaiTech University, China. 11. Donath MY, Shoelson SE. Type 2 diabetes as an inflammatory disease. Nat Rev Immunol. 2011;11(2):98. Availability of data and materials 12. Maedler K, Spinas GA, Lehmann R, Sergeev P, Weber M, Fontana A, Data sharing is not applicable to this article as no datasets were generated or Kaiser N, Donath MY. 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Authors’ contributions 15. Donath MY. Targeting inflammation in the treatment of type 2 diabetes: JZ initiated the project and idea, PD and LM constructed the model, and PD time to start. Nat Rev Drug Discov. 2014;13(6):465–76. carried out the simulations and analysis; YA provided biological input, PS gave 16. Shoelson SE, Lee J, Goldfine AB. Inflammation and insulin resistance. J suggestions on modeling; PD drafted the manuscript with critical input from Clin Investig. 2006;116(7):1793–801. JZ, and other authors provided comments on the manuscript. All authors have 17. Hameed I, Masoodi SR, Mir SA, Nabi M, Ghazanfar K, Ganai BA. Type 2 read and approved the final manuscript. diabetes mellitus: from a metabolic disorder to an inflammatory condition. World J Diabetes. 2015;6(4):598. Ethics approval and consent to participate 18. Hui H, Dotta F, Mario UD, Perfetti R. Role of caspases in the regulation of Not applicable. apoptotic pancreatic islet beta-cells death. 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Boolean network modeling of β-cell apoptosis and insulin resistance in type 2 diabetes mellitus

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Life Sciences; Bioinformatics; Systems Biology; Simulation and Modeling ; Computational Biology/Bioinformatics; Physiological, Cellular and Medical Topics; Algorithms
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Abstract

Background: Major alteration in lifestyle of human population has promoted Type 2 diabetes mellitus (T2DM) to the level of an epidemic. This metabolic disorder is characterized by insulin resistance and pancreatic β-cell dysfunction and apoptosis, triggered by endoplasmic reticulum (ER) stress, oxidative stress and cytokines. Computational modeling is necessary to consolidate information from various sources in order to obtain a comprehensive understanding of the pathogenesis of T2DM and to investigate possible interventions by performing in silico simulations. Results: In this paper, we propose a Boolean network model integrating the insulin resistance pathway with pancreatic β-cell apoptosis pathway which are responsible for T2DM. The model has five input signals, i.e. ER stress, oxidative stress, tumor necrosis factor α (TNFα), Fas ligand (FasL), and interleukin-6 (IL-6). We performed dynamical simulations using random order asynchronous update and with different combinations of the input signals. From the results, we observed that the proposed model made predictions that closely resemble the expression levels of genes in T2DM as reported in the literature. Conclusion: The proposed model can make predictions about expression levels of genes in T2DM that are in concordance with literature. Although experimental validation of the model is beyond the scope of this study, the model can be useful for understanding the aetiology of T2DM and discovery of therapeutic intervention for this prevalent complex disease. The files of our model and results are available at https://github.com/JieZheng- ShanghaiTech/boolean-t2dm. Keywords: Boolean model, Type 2 diabetes mellitus, Insulin resistance, β-cell apoptosis Background excessive nutrients could lead to hyperglycemia, elevated Type 2 diabetes mellitus (T2DM) is characterized by free fatty acids (FFA), and inflammation, which severely insulin resistance at its onset. Persistence of insulin impair β-cell functions, leading to insulin resistance and resistance leads to pancreatic β-cell dysfunction and in β-cell apoptosis. extreme cases to β-cell apoptosis [1–3]. Insulin resistance The ER in the β-cells is responsible for the production increases the load on β-cells to produce more insulin in and secretion of insulin. The increased demand for insulin order to maintain blood glucose at normal levels. This synthesis in the presence of high glucose and FFA lev- homeostasis is maintained as long as β-cells can meet els triggers the accumulation of misfolded proteins in the the increased insulin demand. However, persistence of ER, causing ER stress and the consequent activation of the unfolded protein response (UPR). UPR initially attempts to mitigate ER stress by degrading misfolded proteins and *Correspondence: zhengjie@shanghaitech.edu.cn School of Information Science and Technology, ShanghaiTech University, preventing their further accumulation. However, when ER Shanghai, China stress is not mitigated, UPR activates the apoptosis signals Full list of author information is available at the end of the article [4–6]. 78 kDa glucose regulated protein (GRP78) serves © The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 2 of 12 as a sensor of protein misfolding [7]. Under non-stressed ODE models require detailed kinetic knowledge and conditions, GRP78 binds to three UPR initiator pro- time-series data for accurate parameter estimation. How- teins, i.e. inositol requiring 1 (IRE1), PKR-like ER kinase ever, the size of our proposed network is relatively big (PERK), and activating transcription factor 6 (ATF6), and (consisting of 72 nodes) and hence obtaining time-series maintains them in the inactive state [8]. Under stressed expression data for all the genes would be expensive as conditions, GRP78 dissociates from these three proteins, well as time-consuming. Also, estimating the parameters causing their activation and initiation of UPR. of the ODE model with the time-series expression data When ER stress can be resolved, the UPR assists β of only a small subset of genes would result in erroneous cells in their survival. However, when ER stress cannot be parameter values. Furthermore, in a Boolean network resolved the UPR activates the pro-apoptotic signals [9]. Hyperglycemia causes oxidative stress through the gener- Table 1 The gene interactions incorporated into the model with ation of reactive oxygen species (ROS) [10]. In the absence reference to the existing literature of an appropriate antioxidant response, the system expe- Gene interations Reference riences redox imbalance, leading to the activation of IRE1 ↑→ XBP1 ↑→ β-cell dysfunction [26] oxidative stress-sensitive signaling pathways. Cytokines, (IRE1+TRAF2+ASK1) ↑→ JNK ↑→ BCL2 [28–30] including FasL, TNFα, and IL-6, play important roles in (anti-apoptotic gene)↓ the induction of β-cell apoptosis [11–15]aswellasinsulin BCL2 ↓→ (BAX + BAK) (pro-apoptotic) ↑ [50, 51] resistance [16, 17]. Caspases serve as the final mediators PERK ↑→ EIF2S1 ↓→ ATF4 ↑→ CHOP (pro- [27] of apoptosis. The upstream apoptosis initiator caspases apoptotic) ↑ 8 and 9 are activated on receiving death signal from the ATF6 ↑→ CHOP (pro-apoptotic) ↑→ BCL2 [51, 52] death-inducing signaling complex (DISC) and apopto- (anti-apoptotic gene)↓ some respectively, which in turn activate the downstream Oxidative stress ↑→ ASK1 ↑,JNK ↑,p38 ↑ [31–33] apoptosis effector caspases 3, 6 and 7, which ultimately p38 ↑→ CHOP (pro-apoptotic) ↑ [34] execute apoptosis [18]. FasL ↑→ (FasR + FADD + pro-caspase-8) ↑ [53] Computational modeling is necessary to consolidate → caspase-8 ↑→ caspase-3 ↑→ apoptosis information from various sources, such as listed above, TNFα ↑→ (TNFR1 + TRADD) ↑→ RIPK1 ↑, [54] in order to obtain a comprehensive understanding of the FADD ↑,TRAF2 ↑ pathogenesis of T2DM and investigate possible interven- FADD ↑→ caspase-8 ↑ [54] tionsbyperforming in silico simulations. A few dynamic RIPK1 ↑→ RAIDD ↑→ caspase-8 ↑ [54] models of insulinresistanceinT2DMhavebeenproposed recently. For instance, Brannmark et al. [19]proposedan TNFα ↑→ TNFR2 TNFα ↑→ TRAF2 ↑→ [55–57] ... → JNK ↑,NF-kB ↑ ordinary differential equation (ODE) model of insulin sig- naling in T2DM. Rajan et al. proposed an ODE model (BAX + BAK) (pro-apoptotic) ↑→ [6, 58] Cytochrome c ↑→ (APAF1 + caspase-9) ↑ to study the contribution of Forkhead box protein O1 → caspase-3 ↑ (FOXO1) to insulin resistance in T2DM [20]. Another XIAP ↑→ caspase-3 ↓, caspase-7 ↓, caspase- [35, 36] paper [21] presented an ODE model to simulate the devel- 9 ↓ opment of insulin resistance by hyperglycemia, FFA, ROS, DIABLO ↑,HtrA2 ↑→ XIAP ↓ [37] and inhibition of glucose transporter type 1 (GLUT-1) INSR ↑→ IRS ↑→ PI3K ↑→ ...→ AKT ↑→ [59–61] and glucose transporter type 4 (GLUT-4). However, there FOXO1 ↓,GSK3β ↓,GLUT4 ↑ exists no model of β-cell apoptosis occurring in the T2DM GSK3β ↑→ GS ↓→ glycogen synthesis ↓ [42, 43] condition. Also, there is no existing work that attempts to FOXO1 ↑→ PEPCK ↑,G6PC ↑→ glucose [47, 47–49] integrate the insulin resistance and β-cell apoptosis path- synthesis ↑ ways in order to obtain a comprehensive understanding (mTORC1 + S6K) ↑→ IRS ↓ [44–46] of the molecular mechanisms underlying T2DM. To dis- IKKβ ↑→ TSC1/2 ↓→ mTORC1 ↑ [62] cover potential therapeutic interventions for T2DM, it is essential to have a more comprehensive model for the ER stress ↑→ ...→ IRE1 ↑→ ...→ JNK ↑→ [38, 39, 63] IRS ↓ mechanisms causing T2DM pathogenesis. Therefore, we propose a Boolean network model inte- ER stress ↑→ ...→ IRE1 ↑→ XBP1 ↑→ [64] FOXO1 ↓ grating the insulin resistance pathway and β-cell apoptosis PERK ↑→ FOXO1 ↑ [65] pathway for the purpose of obtaining deeper insights into the mechanisms of development and progression ER stress ↑→ ...→ ATF4 ↑→ CHOP ↑→ [40, 41] TRB3↑→ AKT ↓ of T2DM. The aforementioned existing models are ODE models, whereas we constructed a Boolean net- IL-6 ↑→ JAK ↑→ STAT3 ↑→ SOCS3 ↑→ [66–68] IRS ↓ work model. The reason behind this selection is that Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 3 of 12 model, gene expression is represented by either TRUE (1) Methods or FALSE (0). By simplifying the gene expression levels In this paper, we propose a Boolean network model of into binary states, Boolean networks are feasible for sim- β-cell fate in T2DM. The model was constructed by ulating the behaviour of large regulatory networks in a extracting information from the KEGG pathways [25]and qualitative way. literature. The gene interactions incorporated into the In a Boolean network model the state of each gene is model with reference to the existing literature are listed represented by either 1 (TRUE), indicating the gene is in Table 1. In this model, we integrated the β-cell apopto- highly expressed, or 0 (FALSE) when the gene is lowly sis pathway with the insulin resistance pathway, as shown expressed. An edge in a Boolean network can be either in Fig. 1. The apoptosis pathway consists of the signaling activating or inhibiting [22]. In this paper, we have used pathways triggered by ER stress (UPR pathway), oxida- random asynchronous Boolean simulation [23, 24], which tive stress, and 3 cytokines, i.e. FasL, TNFα,and IL-6. updates genes in a random order in each iteration. This The insulin resistance pathways consist of phosphatidyli- random asynchronous update method is inspired by the nositide 3-kinase (PI3K)-protein kinase B (PKB or AKT) stochastic nature of gene regulatory networks, where gene (KEGG ID: hsa04151), mammalian target of rapamycin expression alteration occurs in a random order rather than (mTOR) (KEGG ID: hsa04150), janus kinase (JAK)- signal simultaneously [24]. transducer and activator of transcription (STAT) (KEGG Due to the lack of experimental gene expression data, ID: hsa04630), and insulin (KEGG ID: hsa04910) signaling we validate our simulation results by comparing pre- pathways. T2DM first causes insulin resistance, i.e. insulin dicted patterns of gene expression levels with experimen- fails to bind to insulin receptors in cells, thereby block- tal observations reported in the literature. We also analyze ing the uptake of blood glucose by cells. Sustained insulin the dynamical behaviors of the model by visualizing the resistance finally leads to β-cell failure and apoptosis. state transition graphs under different combinations of The Boolean update functions, listed in Table 2,for input signals. Our results show that the simple Boolean the target genes in the model are defined by combining network model can capture some qualitative trends of the activating input genes using OR functions and inhibiting genetic circuits regulating the cell fate decision of β-cells, input genes using AND functions. The reason behind this and shed light on the causes and processes of dysfunc- combination strategy is that a target gene will be expressed tional insulin metabolism and loss of β-cell homeostasis when at least one of its activating genes is expressed and that occur in T2DM. all of its inhibiting genes are absent. Fig. 1 Gene Regulatory Network. Insulin resistance and β-cell apoptosis pathways involved in the pathogenesis of Type 2 diabetes mellitus. The red nodes denote the five input signals and the purple node represents β-cell apoptosis. A → B indicates activation of gene B by gene A, and A −| B indicates inhibition of gene B by gene A Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 4 of 12 Table 2 Boolean functions for the Boolean model The proposed Boolean network consists of 72 nodes, of Node Boolean function Node Boolean function which five are input signals, one node represents Apop- tosis, and the remaining 66 nodes represent genes. We ER ER OS OS FasL FasL TNFα TNFα or NFKB employ the random asynchronous Boolean update [23, 24] IL-6 IL-6 or NFKB method to perform the simulations. The random asyn- chronous Boolean method first generates a random per- GRP78 ATF6orXBP1orATF4 ATF6 GRP78 mutation of the nodes at each time step and updates and (not ER) the states of the nodes in the order specified by the PERK GRP78 and (not IRE1 BAX or BAK or GRP78 DNAJC3) permutation. This allows us to capture the stochastic EIF2S1 GADD34 and (not DNAJC3 ATF6 or XBP1 changes in gene expressions that occur in real gene reg- PERK) ulatory networks. The random asynchronous Boolean ATF4 EIF2S1 CHOP ATF6 or ATF4 simulations were performed using the Python code pro- XBP1 IRE1 GADD34 CHOP vided in [23] which is available at https://gitlab.com/ TNFR1 TNFα TNFR2 TNFα stemcellbioengineering/garuda-boolean. TRAF2 IRE1 or TNFR2 or ASK1 OS or TRAF2 or DAXX For example, suppose a gene regulatory network con- TRADD sists of 3 genes, {g , g , g }. The Boolean update functions 1 2 3 JNK OS or ASK1 or p38 OS or ASK1 for the genes are as follows: GADD45 BCL2 (not JNK) and (not BID CASP8 and (not BCL2) g = g 1 3 CHOP) and (not P53) and (not BAD) g = g ∨ g 2 1 3 BAX JNK or P53 and (not BAK BAX and (not BCL2) g = g 3 2 BCL2) DIABLO BAX or BAK or BID HtrA2 BAX or BAK or BID Suppose an iteration randomly generates a permuta- FasR FasL TRADD TNFR1 tion of nodes as {3, 1, 2}. Then the asynchronous Boolean DAXX FasR RIPK1 FasR or TRADD updates will be carried out as follows: RAIDD RIPK1 FADD FasR or TRADD g (t + 1) = g (t) 3 2 CASP8 RAIDD or FADD or CASP9 RAIDD or CASP8 or CASP3 or CASP6 CASP3 or APAF1 or g (t + 1) = g (t + 1) 1 3 CASP12 and (not XIAP) and (not AKT) g (t + 1) = g (t + 1) ∨ g (t + 1) 2 1 3 CASP3 CASP9 or CASP8 and CASP7 CASP9 or CASP8 or From the above equations, we see that the nodes are (not XIAP) CASP3 or CASP6 and updated in a randomly generated order as specified by the (not XIAP) permutation, rather than simultaneously. CASP6 CASP7 or CASP3 After performing the simulations for a fixed number of XIAP (not DIABLO) and (not CytochromeC BAX or BAK or BID HtrA2) (not CASP3) iterations, a directed graph of states is obtained, where APAF1 CytochromeC or P53 Apoptosis CASP3 or CASP6 or each state is a vector representing the expression lev- CASP7 els of all genes at a particular time step. The strategy of INS INS INSR INS strongly connected components (SCCs) is employed on IRS INSR and (not SOCS3) PI3K IRS or JAK this directed graph to capture the dynamic nature of the and (not JNK) (not states [23]. An SCC of a directed graph is a sub-graph IKKβ) and (not S6K) that is strongly connected, i.e., each node is reachable PIP3 PI3K PDK1 PIP3 from every other node in the sub-graph. An illustration AKT PDK1 or mTORC2 and AS160 AKT (not TRB3) of SCC is given in Fig. 2. Each node is a state with the PKCα PDK1 GLUT4 AKT or AS160 or PKCα expression levels of all the genes in the network (for the GSK3β not AKT GS not GSK3β example we assume a network with five genes) and there FOXO1 PERK and (not AKT) PGC1α FOXO1 is a path between each pair of nodes in both directions. and (not XBP1) Let us consider that an SCC consists of a set of N states PEPCK FOXO1 G6PC FOXO1 {S , S , ..., S }. The probability of state S being one of the 1 2 N i PPARα PGC1α TRB3 PPARα or CHOP states of the SCC is given by: TSC1/2 (not AKT) and (not Rheb not TSC1/2 number of occurrences of S IKKβ) i P(S ) = . mTORC1 Rheb S6K mTORC1 number of occurrences of S j=1 mTORC2 not S6K BAD JNK and (not AKT) We calculate the gene expression level of each gene in a JAK IL-6 and (not SOCS3) STAT3 JAK SOCS3 STAT3 IKKβ TRAF2 particular SCC as the sum of probabilities of states where NFκBnotIKBα IKBα not IKKβ the gene is in the ON state. Therefore, the expression level Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 5 of 12 Fig. 2 Strongly Connected Component. An example of a strongly connected component (SCC). Suppose the network consists of five genes. Then each node is a state which contains the expression levels of the five genes. An arrow from state S to state S indicates an update step. In an SCC all 1 2 states can be reached from every other state of a gene, g , with respect to an SCC is determined as Due to the lack of experimental data, we validate our follows: proposed Boolean network model using relevant literature (see Table 1). For each gene g ,weuse thesamesymbol g i i Exp(g ) = P(S ) i j to represent its binary expression level. S ∈OnSt(g ) j i where 1if g is reported as expressed in the literature g = OnSt(g ) ={S ∈ SCC | g (S ) = 1}. 0if g is reported as not expressed in the literature i j i j It is easy to see that In our model, we determine the expression level of each gene with respect to a particular SCC. Thus the gene P(S ) = 1 expression levels are in the range [0, 1]. We assume that j=1 if the expression value of a gene is greater than 0.50, then the gene is expressed, otherwise, it is not expressed. We use ER stress, oxidative stress, TNFα,FasL, andIL- For the purpose of validating our proposed model, we 6 as input signals. Also, based on the literature, some of employ the performance metrics of precision, recall (sen- the nodes are assigned specific values (Table 3)and the sitivity), specificity, and F1 score. The simulation result rest are set to random values as initial conditions. We per- of our proposed model is verified against the literature as formed simulations using different combinations of the input signals, as shown in Table 4. We carried out 1000 simulation runs and 1000 Boolean update steps per simu- lation for each input signal. The results of the simulations Table 4 Different combinations for the input signal nodes are presented and discussed in the following section. ER stress Oxidative stress TNFα FasL IL-6 Case 1 True False False False False Table 3 Initial conditions Case 2 False True False False False Node Initial value Reason Case 3 True True False False False Apoptosis False We set apoptosis to False to see Case 4 False False True False False whether the input signals can cause apoptosis Case 5 False False False True False Caspases 3, 6, 7, 8, 9 False Caspases serve as the final Case 6 False False False False True mediators of apoptosis. So, we set Case 7 False False True True True them to False to see whether the input signals can activate them Case 8 True True True True True Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 6 of 12 Table 5 Gene expressions of the significant genes in the model for input signal cases 1-5 and 7-8 Node Case 1 Case 2 Case 3 Case 4 Case 5 Case 7 Case 8 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 Apoptosis 1 1111111111111 AKT 0.50 0.50 0.49 0.49 0.49 0.49 0.49 0.49 0.50 0.49 0.49 0.50 0.50 0.49 APAF-1 11111111111111 ASK1 11111111111111 ATF4 10101010101010 ATF6 00000000000000 BAK 1 1111111111111 BAX 1 1111111111111 BCL2 00000000000000 Caspase-3 11111111111111 Caspase-6 11111111111111 Caspase-7 11111111111111 Caspase-8 11111111111111 Caspase-9 11111111111111 CHOP 10101010101010 DIABLO 11111111111111 EIF2S1 10101010101010 FADD 11111111111111 FASR 00000000000000 FOXO1 0 0000000000000 G6PC 00000000000000 GADD34 1 0101010101010 GLUT4 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 GRP78 1 1111111111111 GS 0.50 0.50 0.50 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.49 GSK3β 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.50 0.49 0.49 0.49 0.49 0.49 0.50 HtrA2 1 1111111111111 IKBα 00000000000000 IKKβ 11111111111111 INS 1 1111111111111 INSR 11111111111111 IRE1 11111111111111 IRS 0 0000000000000 JAK 0.50 0.49 0.50 0.49 0.49 0.50 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 JNK 1 1111111111111 NFKB 11111111111111 PEPCK 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PERK 0 0000000000000 PI3K 0.50 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.49 0.49 0.50 0.50 0.49 RAIDD 1 1111111111111 RIPK1 1 1111111111111 S6K 1 1111111111111 SOCS3 0.49 0.49 0.50 0.49 0.50 0.50 0.49 0.49 0.50 0.50 0.49 0.49 0.49 0.50 STAT3 0.50 0.49 0.49 0.49 0.49 0.50 0.49 0.49 0.50 0.50 0.49 0.49 0.50 0.50 TNFR1 1 1111111111111 TNFR2 1 1111111111111 Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 7 of 12 Table 5 Gene expressions of the significant genes in the model for input signal cases 1-5 and 7-8 (Continued) Node Case 1 Case 2 Case 3 Case 4 Case 5 Case 7 Case 8 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 A1 A2 TRADD 11111111111111 TRAF2 11111111111111 TRB3 10101010101010 TSC2 00000000000000 XBP1 11111111111111 XIAP 00000000000000 mTORC1 11111111111111 p38 11111111111111 Here A1 and A2 denotes SCC1 and SCC2 follows. For each gene g , ER stress sensor IRE1 and its downstream gene X-box protein binding 1 (XBP1) are TRUE in some attrac- ⎪ True positive, if g = 1 (simulation result) and g = 1 (literature) i i ⎪ tors, and FALSE in others [26]. Another ER stress sen- True negative, if g = 0 (simulation result) and g = 0 (literature) i i sor, PERK is observed to be FALSE in all the attrac- g ∈ False positive, if g = 1 (simulation result) and g = 0 (literature) tors. Also, eukaryotic translation initiation factor 2 sub- ⎪ i i unit 1 (EIF2S1), activating transcription factor 4 (ATF4), False negative, if g = 0 (simulation result) and g = 1 (literature) i i and C/EBP homologous protein (CHOP) are TRUE in The four evaluation metrics are calculated using the some attractors and FALSE in the others. PERK phos- following formulae: phorylates and inactivates EIF2S1, which inhibits protein synthesis. Phosphorylated EIF2S1 increases the transla- True positive Precision = tion of ATF4 [8], which in turn activates pro-apoptotic True positive + False positive CHOP, causing β-cell dysfunction and death [27]. The True positive attractors where IRE1, XBP1, EIF2S1, ATF4, and CHOP Recallorsensitivity = True positive + False negative have expression levels of 0 may denote the transi- True negative tion states when these genes are not contributing to Specificity = True negative + False positive apoptosis. 2 × precision × recall While associating with TNF-receptor-associated fac- F1 score = tor 2 (TRAF2) and apoptosis signal-regulating kinase 1 precision + recall (ASK1), IRE1 activates jun N-terminal kinase (JNK) [28, Results 29], which in turn inhibits the anti-apoptotic protein B- Comparison with the literature cell lymphoma 2 (BCL2) [30]. Oxidative stress activates The expression levels of genes in the SCCs obtained by ASK1 [31, 32], JNK and p38 [33]. Activated p38 phos- phorylates and elevates the expression of pro-apoptotic performing simulations with our proposed Boolean model CHOP [34]. From the simulation results, we observe that are listed in Tables 5 and 6. Simulations performed using the pro-apoptotic genes, TRAF2, ASK1, JNK, p38, BAX, input signal cases 1, 2, 3, 4, 5, 7, and 8 (Table 4) result and BAK are TRUE and the anti-apoptotic gene BCL2 in two attractors (SCCs). Apoptosis is ON in both of the is FALSE in one attractor, while the reverse states are attractors. Simulations performed using input signal case observed in the other. X-linked inhibitor of apoptosis pro- 6(Table 4)result in sixattractors(SCCs). ApoptosisisON tein (XIAP), which inhibits Caspases 3, 7, and 9 [35, 36], in four attractors and OFF in the remaining two attrac- has an expression level of 0, whereas direct IAP-binding tors. These observations are consistent with the literature protein with low pI (DIABLO) and high temperature where ER stress, oxidative stress, and cytokines have been requirement protein A2 (HtrA2), which inhibit XIAP [37], shown to cause apoptosis of β-cells individually as well as have expression levels of 1. together [4–6]. JNK phosphorylates and inhibits insulin receptor sub- From our simulation results, we observe that Caspases strate (IRS) [38, 39]. IRS gene is FALSE in both of the 3, 6, 7, 8, and 9, which serve as the final mediators of attractors. PI3K has an expression level of around 0.50 in apoptosis [18] are TRUE in the attractors, even though all the attractors. Tribbles homolog 3 (TRB3) is induced by in the initial condition they were set to FALSE. The Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 8 of 12 Table 6 Gene expressions of the significant genes in the model Table 6 Gene expressions of the significant genes in the model for input signal case 6. Here A1-A6 denotes SCC1-SCC6 for input signal case 6. Here A1-A6 denotes SCC1-SCC6 (Continued) Node Case 6 Node Case 6 A1 A2 A3 A4 A5 A6 A1 A2 A3 A4 A5 A6 Apoptosis 111100 TRAF2 1 1 0000 AKT 0.49 0.49 0.63 0.55 0.65 0.56 TRB3 1 0 0101 APAF-1 110100 TSC2 0 0 0.37 0.45 0.36 0.44 ASK1 110000 XBP1 1 1 0000 ATF4 100101 ATF6 000000 XIAP 0 0 0011 BAK 110000 mTORC1 1 1 0.63 0.55 0.63 0.57 BAX 110000 p38 1 1 0000 BCL2 001010 Caspase-3 111100 ER stress through the ATF4-CHOP pathway [40]. Over- Caspase-6 111100 expression of TRB3 inhibits AKT and decreases glucose Caspase-7 111100 uptake [41]. TRB3 is TRUE in one attractor and FALSE Caspase-8 111100 in the other. AKT has an expression level of 0.50 in both of the attractors. Thus, from the results, we observe that Caspase-9 111100 ER stress inhibits the PI3K-AKT signaling pathway and CHOP 100101 promotes insulin resistance. DIABLO 110100 Insulin promotes conversion of glucose to glycogen by EIF2S1 100101 inhibiting glycogen synthase kinase-3β (GSK3β)through FADD 110000 the PI3K-AKT signaling pathway, which leads to the acti- FASR 000000 vation of glycogen synthase (GS) [42]. From the simulation FOXO1 000000 results, we observe that the expression level of GSK3β, G6PC 000000 which inhibits glycogen synthesis through inhibition of GADD34 100101 GS [42, 43] is approximately 0.49 and that of GS is approx- GLUT4 0.65 0.65 0.75 0.70 0.78 0.71 imately 0.50. From these simulation results, we can infer GRP78 110101 that glycogen synthesis is reduced which contributes to GS 0.49 0.49 0.62 0.54 0.65 0.55 insulin resistance. GSK3β 0.50 0.50 0.38 0.45 0.36 0.45 In T2DM, the mammalian target of rapamycin com- HtrA2 110100 plex 1 (mTORC1)/ S6 kinase (S6K) signaling is activated IKBα 001111 [44] leading to the inhibition of IRS [45, 46]. We observe IKKβ 110000 from the simulation results that mTORC1 and S6K have INS 111111 expression levels of 1 thus inhibiting IRS which has an INSR 111111 expression of 0. These events cause PI3K and AKT to have IRE1 110000 low expression levels of approximately 0.50, which in turn IRS 0 0 0.19 0.22 0.18 0.22 reducesglucoseuptakethrough GLUT4whose expression JAK 0.49 0.49 0.49 0.49 0.49 0.50 level is around 0.65. JNK 110000 FOXO1 increases the expression of phosphoenolpyru- NFKB 110000 vate carboxykinase (PEPCK) and glucose-6-phosphatase PEPCK 000000 (G6PC) and thus promotes glucose synthesis [47]. Insulin inhibits the expression of FOXO1 through the activa- PERK 000000 tion of the PI3K/AKT signaling pathway, which in turn PI3K 0.49 0.49 0.54 0.55 0.54 0.56 suppresses PEPCK and G6PC, and thereby reduces glu- RAIDD 110000 cose synthesis [47–49]. From our simulation results, we RIPK1 110000 observe that FOXO1, PEPCK, and G6PC are FALSE. This S6K 1 1 0.62 0.55 0.62 0.56 could be due to the fact that PI3K and AKT are not com- SOCS3 0.49 0.50 0.50 0.49 0.49 0.49 pletely inactive, though they may have low expression STAT3 0.49 0.49 0.49 0.49 0.49 0.50 levels, and hence is still able to inhibit the expressions of TNFR1 110000 FOXO1, PEPCK, and G6PC. TNFR2 110000 In Case 6 where only signal IL6 is active, we observe TRADD 110000 six attractors (Table 6), of which four indicate apoptosis Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 9 of 12 and two do not. For the attractors where apoptosis is Figure 4 shows the state transition graph of the state observed, the expression levels of the genes are similar to space generated by simulations conducted using input those mentioned above for the other input signal cases. signal combination given in case 6 (Table 4). The four When apoptosis is not observed, i.e. in the two remaining dense red regions represent the four SCCs where apopto- attractors, the caspases, JNK, BAX, and BAK are FALSE. sis is ON. The two dense blue regions represent the two In one of these two attractors, BCL2 is FALSE and CHOP SCCs where apoptosis is OFF. Thus from the state transi- is TRUE. In the other attractor we observe the reverse tion graph, we observe that, in the presence of only IL-6, expression pattern. Thus, in the presence of only IL-6, apoptosis may or may not be activated. apoptosis may or may not be activated. We further assessed the performance of our proposed Comparison with random Boolean networks Boolean network model by comparing model predictions We also compared our Boolean network model with ran- of gene expressions against the literature. Considering dom Boolean network models using the 8 input signal the simulation results obtained using the 8 input signals combinations given in Table 4.For cases1,2,3,4,5,7, listed in Table 4, the average precision, recall (sensitiv- and 8 we found that the number of attractors obtained ity), specificity, and F1 score obtained for our model are by simulating the random Boolean networks ranges from 0.9524, 0.8, 0.875, and 0.8696, respectively. We observe 28 to 177, whereas for our Boolean network model the that the validation scores for our model are not very high, number of attractors is 2. Similarly, for case 6, the number maybebecause ourmodel is sensitivetosomemissing of attractors obtained by simulating the random Boolean interactions. networks ranges from 25 to 180, whereas for our Boolean network model the number of attractors is 6. Thus, from State transition graphs the results we observe that the random Boolean networks Figure 3 shows the state transition graph of the state space typically have large numbers of attractors. generated by simulations conducted using input signal combination given in case 8 (Table 4). The two dense red Conclusion regions represent the two SCCs where apoptosis is ON. In this paper, we proposed a Boolean network model The blue nodes represent states where apoptosis is OFF. of the integrated insulin resistance and β-cell apoptosis Thus from the state transition graph, we observe that, in pathways. Such a model, which explores the combined the presence of all input signals, apoptosis is eventually mechanism and interplay between insulin resistance and activated, even though in the initial condition it is set to β-cell apoptosis in the pathogenesis of T2DM, has not FALSE. been proposed before. We used the model to simulate the Fig. 3 State Transition Graph 1. State transition graph obtained by simulating our proposed Boolean network model using input signal condition given in Case 8 of Table 4. Simulations generate 2 attractors, both having the Apoptosis node activated. Apoptosis is ON in the red coloured states and OFF in the blue colored states Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 10 of 12 Fig. 4 State Transition Graph 2. State transition graph obtained by simulating our proposed Boolean network model using input signal condition given in Case 6 of Table 4. Simulations generate 6 attractors. In four of the attractors Apoptosis is ON, denoted by red colour, and in the remaining two attractors Apoptosis is OFF, denoted by blue colour dynamics of gene expression induced by different com- play pivotal roles in insulin resistance and/or β-cell apop- binations of the five input signals, i.e. ER stress, oxidativ tosis, and these genes could be further investigated for e stress, and cytokines (TNFα, FasL, IL-6), which serve as possible disease interventions. triggers for insulin resistance and β-cell apoptosis. Abbreviations The random order asynchronous update method was AKT (PKB): Protein kinase B; APAF1: Apoptotic protease-activating factor 1 ; employed to perform the simulations, i.e. all nodes were ASK1: Apoptosis signal-regulating kinase 1; ATF4: Activating transcription factor 4; ATF6: Activating Transcription Factor 6; BCL2: B-cell lymphoma 2; updated in a random order at each update step. We CHOP: C/EBP homologous protein; DIABLO: Direct IAP-binding protein with assessed the performance of our model using the met- low pI; EIF2S1: Eukaryotic translation initiation factor 2 subunit 1; ER: rics of precision, recall (sensitivity), specificity, and F1 Endoplasmic reticulum; FADD: Fas-associated death domain-containing protein; FasL: Fas ligand; FasR: Fas receptor; FFA: Free fatty acids; FOXO1: score, when validating our model against the literature. Forkhead box protein O1; GADD34: Growth arrest and DNA damage-inducible The precision score obtained is high, but sensitivity, speci- protein; G6PC: Glucose-6-phosphatase; GLUT-1: Glucose transporter type 1; ficity, and F1 scores are not so. One possible reason may GLUT-4: Glucose transporter type 4; GRP78: 78 kDa glucose regulated protein; GS: Glycogen synthase; GSK3β: Glycogen synthase kinase-3β; HtrA2: High be that some missing interactions affect the predictions of temperature requirement protein A2; IL-6: Interleukin-6; INSR: Insulin receptor; our model. We also compared our Boolean network model IRE1: Inositol Requiring 1; IRS: Insulin receptor substrate; JAK: Janus kinase; JNK: with random Boolean network models and observed that Jun N-terminal kinase; mTORC1: Mammalian target of rapamycin complex 1; mTORC2: Mammalian target of rapamycin complex 2; ODE: Ordinary random Boolean networks typically have large numbers differential equation; PEPCK: Phosphoenolpyruvate carboxykinase; PERK: of attractors ranging from around 25 to 180, whereas our PKR-like ER kinase; PI3K: Phosphatidylinositide 3-kinase; Rheb: Ras homolog model shows small numbers of attractors ranging from enriched in brain; RIPK1: Receptor-interacting serine/threonine-protein kinase 1; ROS: Reactive oxygen species; S6K: S6 kinase; SCC: Strongly connected 2to6. component; SOCS3: Suppressor of cytokine signaling 3; STAT3: Signal As a future step, we can use this model to perform vir- transducer and activator of transcription 3; T2DM: Type 2 Diabetes Mellitus; tual gene knockout experiments to determine genes that TNFα: Tumor necrosis factor α; TNFR1: Tumor necrosis factor receptor Dutta et al. BMC Systems Biology 2019, 13(Suppl 2):36 Page 11 of 12 superfamily member 1A; TNFR2: Tumor necrosis factor receptor superfamily 6. Schröder M, Kaufman RJ. The mammalian unfolded protein response. member 1B; TRADD: TNFR1-associated death domain; TRAF2: Annu Rev Biochem. 2005;74:739–89. TNF-receptor-associated factor 2; TRB3: Tribbles homolog 3; TSC: Tuberous 7. Bertolotti A, Zhang Y, Hendershot LM, Harding HP, Ron D. Dynamic sclerosis complex; UPR: Unfolded pro-tein respons; XBP1: X-box protein interaction of bip and er stress transducers in the unfolded-protein binding 1; XIAP: X-linked inhibitor of apoptosis protein response. Nat Cell Biol. 2000;2(6):326. 8. Ron D, Walter P. Signal integration in the endoplasmic reticulum Acknowledgements unfolded protein response. Nat Rev Mol Cell Biol. 2007;8(7):519. We would like to thank Dr. Ket Hing Chong for his valuable discussions. 9. Erguler K, Pieri M, Deltas C. A mathematical model of the unfolded protein stress response reveals the decision mechanism for recovery, Funding adaptation and apoptosis. BMC Syst Biol. 2013;7(1):16. This work was supported by MOE AcRF Tier 1 grant (2015-T1-002-094), Ministry 10. Ihara Y, Toyokuni S, Ichida K, Odaka H, et al. Hyperglycemia causes of Education, Singapore and the Start-Up Grant of ShanghaiTech University, oxidative stress in pancreatic beta-cells of gk rats, a model of type 2 China. Publication of this article was sponsored by the Start-up Grant of diabetes. Diabetes. 1999;48(4):927. ShanghaiTech University, China. 11. Donath MY, Shoelson SE. Type 2 diabetes as an inflammatory disease. Nat Rev Immunol. 2011;11(2):98. Availability of data and materials 12. Maedler K, Spinas GA, Lehmann R, Sergeev P, Weber M, Fontana A, Data sharing is not applicable to this article as no datasets were generated or Kaiser N, Donath MY. Glucose induces β-cell apoptosis via upregulation analysed during the current study. of the fas receptor in human islets. Diabetes. 2001;50(8):1683–90. 13. Spranger J, Kroke A, Möhlig M, Hoffmann K, Bergmann MM, Ristow M, About this supplement Boeing H, Pfeiffer AF. Inflammatory cytokines and the risk to develop This article has been published as part of BMC Systems Biology Volume 13 type 2 diabetes: results of the prospective population-based european Supplement 2, 2019: Selected articles from the 17th Asia Pacific Bioinformatics prospective investigation into cancer and nutrition (epic)-potsdam study. Conference (APBC 2019): systems biology. The full contents of the supplement Diabetes. 2003;52(3):812–7. are available online at https://bmcsystbiol.biomedcentral.com/articles/ 14. Eizirik DL, Mandrup-Poulsen T. A choice of death–the signal-transduction supplements/volume-13-supplement-2. of immune-mediated beta-cell apoptosis. Diabetologia. 2001;44(12): 2115–33. Authors’ contributions 15. Donath MY. Targeting inflammation in the treatment of type 2 diabetes: JZ initiated the project and idea, PD and LM constructed the model, and PD time to start. Nat Rev Drug Discov. 2014;13(6):465–76. carried out the simulations and analysis; YA provided biological input, PS gave 16. Shoelson SE, Lee J, Goldfine AB. Inflammation and insulin resistance. J suggestions on modeling; PD drafted the manuscript with critical input from Clin Investig. 2006;116(7):1793–801. JZ, and other authors provided comments on the manuscript. All authors have 17. Hameed I, Masoodi SR, Mir SA, Nabi M, Ghazanfar K, Ganai BA. Type 2 read and approved the final manuscript. diabetes mellitus: from a metabolic disorder to an inflammatory condition. World J Diabetes. 2015;6(4):598. Ethics approval and consent to participate 18. Hui H, Dotta F, Mario UD, Perfetti R. Role of caspases in the regulation of Not applicable. apoptotic pancreatic islet beta-cells death. J Cell Physiol. 2004;200(2): 177–200. Consent for publication 19. Brannmark C, Nyman E, Fagerholm S, Bergenholm L, Ekstrand E-M, Not applicable. Cedersund G, Stralfors P. Insulin signaling in type 2 diabetes-experimental and modeling analyses reveal mechanisms of insulin resistance in human Competing interests adipocytes. J Biol Chem. 2013;288(14):9867–80. The authors declare that they have no competing interests. 20. Rajan MR, Nyman E, Brännmark C, Olofsson CS, Strålfors P. Inhibition of foxo1 transcription factor in primary human adipocytes mimics the Publisher’s Note insulin resistant state of type 2 diabetes. Biochem J. 2018;475:1807–20. Springer Nature remains neutral with regard to jurisdictional claims in 21. Sarkar J, Dwivedi G, Chen Q, Sheu IE, Paich M, Chelini CM, D’Alessandro PM, published maps and institutional affiliations. Burns SP. A long-term mechanistic computational model of physiological factors driving the onset of type 2 diabetes in an individual. PLoS ONE. 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