1. Quantitative Models of Mammalian Cell Signaling Pathways Ravi Iyengar, Ph.D. Department of Pharmacology and Systems Therapeutics Mount Sinai School of Medicine

2. How do we understand the functions of regulatory configurations ? Integrating experiments and mathematical models What do mathematical models do for us ? Help identify hidden assumptions (Marder 2000) Sort through possible mechanisms Defines limits of generalization (Marder 2000) Quantitative Modeling Mathematical Models of Regulatory Motifs in Signaling Networks

3. Weng, Bhalla and Iyengar, Science. 284, 92 (1999). Why we need mathematical models to understand biological systems

4. Ordinary Differential Equation Models (ODE Models) Partial Differential Equation Models (PDE Models) Stochastic Models Different Types of Models

5. System: A network of interacting adrenergic receptors pathway Key Question: Is there an NE triggered MAPK switch? Modeling Approach: systems of coupled ordinary differential equations (ODEs) … An ODE Model Choosing the right mathematical representation

6. System: A spatial model for Ras activation In different cellular organelles Key Question: What is the temporal characteristic of Ras activation in different cellular compartments? Modeling Approach: Reaction-diffusion model of Ras activation … A PDE Model Choosing the right mathematical representation

7. All signaling reactions can be described in three types of interactions: 1.Ligand-Protein Interactions 2.Protein-Protein Interactions 3.Enzymatic Reactions Modeling Signaling Networks using Ordinary Differential Equations A + B AB kfkf kbkb A+B C+D kfkf kbkb E+S ES k1k1 k2k2 E+P k3k3

8. Model constructed using pair-wise interactions and solving ordinary differential equations (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) Chemical steps

9. Modules of Signaling Pathway

10. Bhalla & Iyengar, Science. 283, 381 (1999). Pathways from EGFR to MAPK and PLC  Simulation closely matched published experimental data Model ComponentsCount Molecules 64 Reactions (Binding and Enzymes) 105 Enzyme activities34 Differential equations 90

11. Emergent Property of MAPK Signaling Network: Bistability (Switching Behavior) Bistable: Two stable states - ON or OFF System exhibits thresholding effect Sharp transition curve between the two states Bhalla & Iyengar, Science. 283, 381 (1999).

12. Basic experimental design Serum starve NIH-3T3 cells 16-20 hrs Stimulate with PDGF for 5 min Wash cells Incubate for desired times Assay for MAPK activity Experimental System Fibroblast (NIH-3T3) cells in culture A well characterized system for studying growth factor regulation of proliferation and oncogene screening model Does a brief pulse of PDGF result in sustained activation of MAPK?

13. Transient response in a linear signaling pathway versus a sustained response in a signaling network Time after wash (min) 0102030 Phospho-MAPK 2 (arbitrary units) 5 1530 Transient MAPK P-MAPK 2 - PLA2 AA PKC Sustained MAPK 5 1015 30 - P-MAPK 2 PDGF-R Grb2 MEK Ras Raf-1 MAPK 1,2 SOS Shc

14. 0 0.05 0.1 0.15 015304560 Activated MAPK (  M) Time (min) Sustained phospho-MAPK levels after brief PDGF stimulus Stim Wash Assay PDGF-R Grb2 MEK Ras Raf-1 MAPK 1,2 SOS Shc PLA2 AA PKC P-MAPK 2 51530406050 Time after wash (min) - Phospho-MAPK 2 (arbitrary units) 0102030405060

15. cPLA2 activity is necessary for sustained MAPK activity Time after wash (min) 0102030 Phospho-MAPK 2 (arbitrary units) Control Time after wash (min) 5 1015 30 - P-MAPK 2 0 50 100 010203040 Time (min) MAPK activity (% max) PLA2 AA PKC 5 1530 AACOF3 50  M Time after wash P-MAPK 2 - PDGF-R Grb2 MEK Ras Raf-1 MAPK 1,2 SOS Shc

16. 0 50 100 010203040 Time (min) MAPK activity (% max) PKC activity is necessary for sustained MAPK activity Time after wash (min) 0102030 Phospho-MAPK 2 (arbitrary units) 5 1530 Control Time after wash (min) P-MAPK 2 - PLA2 AA PKC P-MAPK 2 5 1530 BIM1 10  M Time after wash (min) - PDGF-R Grb2 MEK Ras Raf-1 MAPK 1,2 SOS Shc

17. Murphy et al Nat Cell Biol 4, 556 (2002). Differential biological consequence of sustained versus transient activation of MAPK signaling Transient MAPK activation Sustained MAPK activation

18. A process by which individual neurons change their responses based on prior activity. Many signaling pathways are involved including the four major protein kinases Protein kinase A, Protein kinase C, MAPK, and Calmodulin Dependent Kinase II CaMKII is the signaling protein kinase. Hypothesis: Other protein kinases are regulatory Ca 2+ + CaM K +, Na +, Ca 2+ CaMKII Consequences of Networking: A Gate Long-Term Potentiation at the CA3-CA1 synapse in the hippocampus

20. AC1, 8 cAMP PKA Increased Synaptic Response (LTP) NMDAR Ca 2+ /CaM Gating Pathway Signal Pathway Calcineurin (PP2b) PP1 i  I1- P PP1 a + I-1 CaMKII-P AMPAR

21. Signal Prolongation by Gating

22. Using models to develop experimental hypotheses to understand complex signaling mechanisms

23. MEK 1,2 PLC  IP3 DAG Ca 2+ AA Ca 2+ PKC Ras Raf MAPK 1,2PLA 2 GEF AC2 AC 1/8 CaMCaMKII CaN PP1PKA MKP mGluR NMDAR AMPAR GG cAMP Regulation of Nuclear and Cytoskeletal Events Feedback loop Gating pathway Signal Pathway Glutamate PDE

24. Regulation of a signaling pathway by a gate coupled to a positive feedback loop

25. LTP Induced PHOSPHORYLATION OF CaMKII IS MAPK-DEPENDENT

26. MEK 1,2 PLC  IP3 DAG Ca 2+ AA Ca 2+ PKC Ras Raf MAPK 1,2PLA 2 GEF AC2 AC 1/8 CaMCaMKII CaN PP1PKA MKP mGluR NMDAR AMPAR GG cAMP Regulation of Nuclear and Cytoskeletal Events Feedback loop Gating pathway Signal Pathway Glutamate PDE

27. -20 0 20 40 60 80 TPS + Inhibitor-1 Vehicle PD-98059 EPSP SLOPE (%Baseline) Thio-phosphorylated Inhibitor-1 Protein does not restore the LTP blocked by MEK inhibitor PD-98059

28. Can MAPK prolong the CaMKII signal by some other mechanism? E.g., through transcriptional or translational control

29. TPS-ISO 60 * SH 15 15 60 60 PD TPS-ISO TOTAL CaMKII (% above control) 100 50 0 MAPK-Dependent Expression of CaMKII During TPS-ISO-Induced LTP CaMKII Actin SH +PD S 2 15 60 50 25 0 * TOTAL CaMKII (% above control) TIME (min after TPS)

30. Total CaMKII LTP * * EPSP SLOPE (% baseline) 140 120 100 80 Act-D Aniso TPS-ISO 60 * * 30 10 -10 -30 TOTAL CaMKII (% change from controls) Act-D Aniso TPS-ISO 60 LTP and Increased CaMKII Expression Require Transcription and Translation

31. Phospho-CaMKII Levels Remain Elevated For 60 min After TPS-ISO 50 S 60 0 100 0 PHOSPHO TOTAL * PHOSPHO-CaMKII (% change from controls) Fractional pCaMKII 100 50 25 0 -25 SHAM TPS-ISO 60 CON SH TPS-ISO 60 P-CaMKII Actin

32. MEK 1,2 PLC  IP3 DAG Ca 2+ AA Ca 2+ PKC Ras Raf MAPK 1,2PLA 2 GEF AC 1/8 CaMCaMKII CaN PP1PKA MKP mGluRNMDAR AMPAR GG cAMP Transcriptional and Translational Control Gating pathway Signal Pathway Glutamate PDE Insertion, Phosphorylation

33. Mathematical models can generate hypotheses that can be experimentally tested. Mathematical models can help understand emergent behavior. Conclusions