Simulation and Model Checking of HMGB1 Signaling Pathway in Cancer

Haijun Gong1*, Paolo Zuliani1, Qinsi Wang1, Anvesh Komuravelli1, James Faeder2, Michael Lotze2, Edmund Clarke1 1Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213 2University of Pittsburgh, Pittsburgh, PA 15260 *Email: [email protected] Boolean Network Model [4] Abstract Statistical Model Checking Require: Property P (Φ), Threshold T ≥ 1, Prior g HMGB1 Statistical Model Checking of biochemical models: ╞═ P (Φ)? ≥θ High-mobility group box-1 (HMGB1) has been recently shown to be associated with the cell M ≥θ n := 0 {number of traces drawn so far} proliferation of various types of cancers. The protein HMGB1 can activate a number of signaling Statistical Model Checker x := 0 {number of traces satisfying Φ so far} TLR2/4 RAGE BioNetGen networks – , NFkB, Ras and Rb pathways – which control many physiological processes of the repeat A Boolean network is composed of a graph cell. We propose a rule-based model and a Boolean model of the HMGB1-p53-NFkB-Ras-Rb σ := draw a sample trace from BioNetGen (iid) MYD88 RAS Model M M╞═ P≥θ (Φ) G and a Boolean transfer function for each network to investigate how these couplings influence proliferation and of cancer cells. The n := n + 1 Stochastic Statistical RAC1 IRAKs RAF MEK node. The state of each node could be either rule-based model was implemented using the BioNetGen language which can simulate both ordinary if σ Φ then simulation Test ╞═ P (Φ) x := x + 1 ON (1) or OFF (0) at any time step. differential equations and Gillespie's stochastic simulation algorithm. Then, we analyzed and verified M ≥θ PI3K endif ERK AP1 qualitative properties of the model by means of simulations and statistical model checking. For TAB1 := BayesFactor(n, x, θ,g) INK4a The Boolean transfer function describes the Boolean network model, Symbolic Model Checking (SMV) is applied to query and verify some Error B probability until (B > T v B < 1/T ) PIP3 AKT Myc transformation of the state of node from time temporal logic properties of HMGB1 model. if ( > T ) then IKK Formula B CyclinD t to t + 1, which depends on its current state Temporal return “H accepted” monitor 0 PTEN MDM2 and that of its parents, which can be parental Our simulations show that, if HMGB1 is overexpressed, the expression level of oncoproteins property Φ else A20 IkB activators or parental inhibitors, that is, CyclinD/E, which regulate cell proliferation, are upregulated, while tumor suppressor which return “H0 rejected” RB regulate cell apoptosis, such as p53, are repressed. The discrete, stochastic simulations show that endif P53 ARF NFkB HMGB1-activated receptors can generate sustained oscillations of irregular amplitude for the p53, Figure 2. Flow chart and Pseudocode for Statistical Model Checking P21 MDM2 and NFkB proteins. Moreover, the models predict that or overexpression of RAS, Bcl-XL ARF,ARF, p21p21 andand IkB kinasekinase couldcould influenceinfluence thethe cancercancer cellcell' s fatefate -- apoptosisapoptosis oror survivalsurvival – throughthrough thethe Simulation Results [[,]1,2] BAX CyclinE

4 4 crosstalk of different pathways. Our work shows that computational modeling and model checking x 10 A:SSA x 10 B:SSA C:SSA Proliferate 12000 4 A: SSA 4 B: SSA Apoptosis p53 p53 x 10 x 10 can be effectively combined in the study of biological signaling pathways. 15 15 1.1 MDM2p MDM2p 10000 NF B Knockout 9 κ 8000 10 10 p53 6000 8 NFκ B Symbolic Model Checking (SMV) CyclinE HMGB1 Signaling Pathway [1,2] CyclinE 4000 5 5 CyclinE(No NFκ B) 1.05 7 Number of Molecules of Number 2000 HMGB1 0 0 0 6 0 500 1000 SMV code can be divided into three parts: 0 4 500 1000 0 4 500 1000 x 10 D:ODE x 10 E:ODE F:ODE

12000 variable declarations (“boolean”); 5 15 p53 15 p53 TLRa TLR RAGE RAGEa MDM2p MDM2p 10000 ofNumber Molecules 1 NFκ B Knockout 4 8000 initialization of the states for each 10 10 Molecules ff 6000 variable with init; PI3K RASa RAS 3 CyclinE 5 5 4000 0.95 2 Number o CyclinE(No NFκ B) IKK IKKa 2000 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Implementation – updating the state of RAF RAFa log HMGB1 log HMGB1 10 10 PIP2 PIP3 0 0 0 each node in the state transition diagram 0 500 1000 0 500 1000 0 500 1000 MEKp MEK Time (min) Time (min) Time (min) Figure 4. Overexpression of HMGB1 leads to the increase of DNA with next IkBp NFkB Figure 3. Baseline simulation results for the SSA (A-C) and ODE (D-F) replication proteins Cyclin E and NFkB, decrease of p53. deg models. AKT AKTp A20 ERK ERKp INK4A The verification of CTL properties is [1,2] encoded using the SPEC statement. deg IkB-NFkB Verification of Rule-based HMGB1 Model MDM2 MDM2p CyclinD PTEN A20t IkB Property 1: PI3K will be activated in order of minutes after HMGB1 binds to RAGE. deg RBp RB E2F deg IkBt SMV Applications [4] MDM2t deg Table 1 validates that half of PI3K will be activated within 20 minutes with different values of HMGB1. Verification of five types of properties occurrence, consequence, steady states, oscillation, and pathway. Property 1: If HMGB1 is overexpressed, cancer cell will necessarily activate Proliferate at some time in deg ARF RB-E2F NFkBn Table 1 the future. The CTL property is verified:

CyclinE deg P53 P21 Property 2: If RAS is continuously activated, the cell will eventually satisfy ( !Apoptosis & Proliferate )

Apoptosis deg S Phase Property 3: Are the states ( !P53 & !Apoptosis & CyclinE & Proliferate ) steady? Figure 1. Schematic view of HMGB1 . Blue nodes represent tumor suppressor proteins, red nodes Property 2: NFkB’s expression level oscillates due to the negative feedback loops activated by IkB and A20 which are represents oncoproteins/lipids. Solid lines with arrows denote protein transcription, degradation or changes of molecular NFkB’s transcription targets. species; dashed line with arrows denote activation processes. Property 4: The release of HMGB1 will oscillations of NFkB’s expression level in the nucleus.

Rule-based Simulation Method Property 5: Is NFkB's activation a necessary checkpoint that the cancer cell should go through before it Table 2 We formulated a reaction model corresponding to the reactions illustrated in Fig.1 in the reaches ( !Apoptosis & Proliferate )? form of rules specified in the BioNetGen language, The ordinary differential equation Conclusions (ODE) method and stochastic simulation algorithm (SSA) are used to simulate the 1. Overexpression of HMGB1 will promote the expression level of cell cycle regulatory protein model. Example ODE and BioNetGen rules: Cyclin E and NFkB, inhibit the pro-apoptotic protein p53. •MDM2 phosphorylation: MDM2(a~U) + AKTp Æ MDM2(a~p) + AKTp k1 Property 3: A large proportion of PI3K, RAS and IKK will be activated and stay at a high expression level all the time 2. Statistical Model Checking and Symbolic Model Checking techniques can be effectively combined in the signaling pathway and verify some important temporal properties. •MDM2p dephosphorylation: MDM2(a~p) Æ MDM2(a~U) d1 when HMGB1 is overexpressed: •MDM2p degradation: MDM2(a~p) Æ Trash() d2 Acknowledgement •MDM2p degradation : MDM2(a~p) + ARF Æ ARF d3 This work was supported b y a g rant from the U.S. national Science Foundation’s Exp editions in Property 4: The overexpression of IKK will promote the translocation of NFkB into nucleus, inducing the Computing Program (award ID 0926181). Linear Temporal Logic & Computation Tree Logic transcription of Cyclin E: References LTL formula describes the properties of an infinite sequence of states. LTL temporal operators describe Table 3 shows the verifications of the property 3 and 4 with various values of t and IKK expression level. [1] H. Gong, P. Zuliani, A. Komuravelli, J. Faeder, E. Clarke, Analysis and Verification of the HMGB1 Signaling the properties of a path: Xp – p holds in the second state of the path; Fp – p holds at some state in the Pathway, BMC Bioinformatics 2010 Table 3 [2] H. Gong, P. Zuliani, A. Komuravelli, J. Faeder, E. Clarke, Computational Modeling and Verification of future on the path; Gp – p holds globally (always) at every state on the path; pUq – p holds until q holds. Signaling Pathways in Cancer, Proceedings of Algebraic and Numeric Biology 2010 A CTL temporal logic formula is constructed from path quantifiers and temporal operators. Two path [3] P. Zuliani, A. Platzer, E. Clarke, Bayesian statistical model checking with application to Simulink/Stateflow quantifiers describe the branching structure in the computation tree: A – for all paths, and E – there verification, HSCC 2010 exists a path. [4] H. Gong, Q. Wang, P. Zuliani, J. Faeder, M. Lotze, E. Clarke, Symbolic Model Checking of Signaling Pathways in Pancreatic Cancer, Proceeding of International Conference on Bioinformatics and Computational Biology 2011