Computer Simulation of Biological Pathways and Network Crosstalk based on Mass Action Laws Y.Z. Chen, C.Y. Ung, H. Li, and Julian H.E. Lee Department of Pharmacy National University of Singapore Tel: ; ; Web: Biological pathways and crosstalkBiological pathways and crosstalk Simulation model developmentSimulation model development Simulation model of RhoA crosstalk to EGFR-ERK/MAPK pathwaysSimulation model of RhoA crosstalk to EGFR-ERK/MAPK pathways

Generic Signaling Pathway Signal Receptor (sensor) Transduction Cascade Targets Response Altered Metabolism Metabolic Enzyme Gene Regulator Cytoskeletal Protein Altered Gene Expression Altered Cell Shape or Motility

Integrated circuit of the cell

EGFR- ERK/MAPK Signaling Pathways

Crosstalk of Rho and Ras

The Multiple Functions of Rho Aznar & Lacal Cancer Lett 165, 1 (2001) Hall Biochem Society Transactions 33, 891 (2005)

Actin Cytoskeleton Regulation Pathways

Crosstalk between RhoA and EGFR- ERK/MAPK via MEKK1 and PTEN RhoA promotes ERK activation by its interaction with Rho kinase, an effector of RhoA, which helps to delay EGF receptor endocytosis by phosphorylating endophilin A1 and to prevent Akt inhibition of Raf by activating phosphatase PTEN that hydrolyzes Akt second messenger PIP3. RhoA binds to MEKK1 and activate its kinase activity which subsequently phosphorylates and activates MEK1 As activated MEK1 promotes ERK activation, it is of interest to examine to what extent RhoA can prolong ERK/MAPK activity via this MEKK1-mediated crosstalk between RhoA and EGFR-ERK signaling networks Gallagher et al. J Biol Chem 2004: 279, 1872

RhoA's crosstalk to EGFR-mediated Ras/MAPK activation via MEKK1

RhoA's crosstalk to EGFR-mediated Ras/MAPK activation via PTEN

Pathway Mathematical Model Biochemical kinetics based on mass action law (Guldberg and Waage 1864) Fussenegger et al Nature Biotech 18, 768 (2000) Schoeberl et al Nature Biotech 20, 370 (2002) Sasagawa et al Nature Cell Biol 7, 365 (2005) Kiyatkin et al J Biol Chem 281, (2006)

Pathway Mathematical Model Biochemical kinetics based on mass action law (Guldberg and Waage 1864) Fussenegger et al Nature Biotech 18, 768 (2000) Schoeberl et al Nature Biotech 20, 370 (2002) Sasagawa et al Nature Cell Biol 7, 365 (2005) Kiyatkin et al J Biol Chem 281, (2006)

Pathway Mathematical Model Michaelis-Menton Kinetics (Leonor Michaelis ; Maud Menton ) The rate of the reaction is equal to the negative rate of decay of the substate as well as the rate of product formation Initial concentration of the substrate is much larger than the concentration of the enzyme Leading to:

Solving the Pathway Equations Runge-Kutta method Our task is to solve the differential equation: dx/dt = f(t, y), x(t0)= x0 Clearly, the most obvious scheme to solve the above equation is to replace the differentials by finite differences: dt = h dx = x(t+h) - x(t) One can then apply the Euler method or first-order Runge-Kutta formula: x(t+h) = x(t) + h f(t, x(t)) + O(h 2 ) The term first order refers to the fact that the equation is accurate to first order in the small step size h, thus the (local) truncation error is of order h 2. The Euler method is not recommended for practical use, because it is less accurate in comparison to other methods and it is not very stable.

Solving the Pathway Equations Runge-Kutta method The accuracy of the approximation can be improved by evaluating the function f at two points, once at the starting point, and once at the midpoint. This lead to the second-order Runge-Kutta or midpoint method: k1 = h f(t, x(t)) k2 = h f(t+h/2, x(t)+k1/2) x(t + h) = x(t) + k2 + O(h 3 ) The most popular Runge-Kutta formula is the fourth-order one: k1 = h f(t, x(t)) k2 = h f(t+h/2, x(t)+k1/2) k3 = h f(t+h/2, x(t)+k2/2) k4 = h f(t+h, x(t)+k3) x(t + h) = x(t) + k1/6 + k2/3 + k3/3 + k4/6 + O(h 5 )

Solving the Pathway Equations Cash-Karp embedded Runge-Kutta algorithm

Mathematical Model of EGFR-ERK/MAPK Pathway Interaction equations and kinetic parameters

Mathematical Model of EGFR-ERK/MAPK Pathway Interaction equations and kinetic parameters

Mathematical Model of EGFR-ERK/MAPK Pathway Analysis of kinetic parameters

Mathematical Model of EGFR-ERK/MAPK Pathway Analysis of kinetic parameters

Mathematical Model of EGFR-ERK/MAPK Pathway Analysis of kinetic parameters

Validation of RhoA EGFR-ERK/MAPK Crosstalk Model Time-dependent behavior of EGF activation of ERK in PC12 cells Our model predicted that ERK activation peaks at ~300s (5 minutes) and decays within 3000s (~50 minutes), in good agreement with observation

Validation of RhoA EGFR-ERK/MAPK Crosstalk Model EGF variation on duration of ERK activation in PC12 cells Our model predicted that further increase of EGF levels leads to sustained ERK activation, in good agreement with observation and previous simulation results

Validation of RhoA EGFR-ERK/MAPK Crosstalk Model Time-dependent behavior of active RasGTP and their effects on ERK activation in PC12 cells Our model predicted that RasGTP peaks at ~2.5 minutes (250s) and quickly decays to its basal levels within 20 minutes (1200s), in good agreement with observation and previous simulation results

Validation of RhoA EGFR-ERK/MAPK Crosstalk Model Time-dependent behavior of active RasGTP and their effects on ERK activation in PC12 cells Our model predicted that Ras over-expression prolongs ERK activation by delaying its decay rate without altering the time cause for reaching the peak of activation, in good agreement with observation and previous simulation results

Validation of RhoA EGFR-ERK/MAPK Crosstalk Model Effect of scaffold protein MEKK1 on ERK activities Our model predicted that Increased MEKK1 concentration helps to increase the level of active ERK, delay its peak time, and slightly prolong the duration of ERK activation, in good agreement with observation

Validation of RhoA EGFR-ERK/MAPK Crosstalk Model Effects of Ras over-expression on RhoA and ERK activities Our model predicted that Ras over-expression increases the amount of active GTP-bound RhoA and prolongs the duration of its activation, leads to sustained ERK activation, in good agreement with observation and previous simulation results

Effects of RhoA over-expression on ERK activation When Ras expression is at the normal level, RhoA over- expression was found to prolong ERK activation in a dose- dependent manner

Effects of RhoA over-expression on ERK activation Effect of scaffold

Effects of RhoA over-expression on ERK activation When Ras is over-expressed, RhoA over-expression significantly reduces the number of active ERK while further prolonging its activation

Future work: Crosstalk via RTK - PI3K – AKT pathways P

Conclusions Mass action law –based simulation models are capable of simulating the dynamic behavior and crosstalk of biological network MEKK1 mediated RohA EGFR-ERK/MAPK crosstalk model suggests possible roles of RhoA in regulating the activities of Ras/MAPK/ERK pathway via MEKK1, which may have implication in cell cycle control

Acknowledgement Current Group Members: Computer-Aided Drug Design: CW Yap, H Li, CY Ung, XH Ma, XH Liu, Pankaj Kumar Protein Function, Interaction and Network: J Cui, HL Zhang, H. Li, CY Ung, XH Ma Databases and Servers: J Cui, ZQ Tang, J Jia, H Zhou, L Jiang Medicinal Herb: CY Ung, H Li, H Zhou Microarray and biomarkers : ZQ Tang, J Jia Former Members: PhD: ZW Cao (SCBIT), ZL Ji (Xiamen U), X Chen (Zhejiang U), CW Yap (NUS), LY Han (NIH), CJ Zheng (delayed employment), HH Lin (Harvard) Research Fellow/Assistant: ZR Li (SiChuan U), Y Xue (SiChuan U), W Liu (DUT), D Mi (DUT), CZ Cai (CongQing U) DG Zhi (UCSD, Berkeley), MSc: Y.J. Guo (GWU), L.Z. Sun (U Tenn.), J. F. Wang (MSU), L.X. Yao (Columbia), X.L. Gu (?) BSc: W.K. Yeo (IMCB, Novartis)