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

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

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

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

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

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

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

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

Modules of Signaling Pathway

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

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).

Basic experimental design Serum starve NIH-3T3 cells 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?

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

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 Time after wash (min) - Phospho-MAPK 2 (arbitrary units)

cPLA2 activity is necessary for sustained MAPK activity Time after wash (min) Phospho-MAPK 2 (arbitrary units) Control Time after wash (min) P-MAPK Time (min) MAPK activity (% max) PLA2 AA PKC AACOF3 50  M Time after wash P-MAPK 2 - PDGF-R Grb2 MEK Ras Raf-1 MAPK 1,2 SOS Shc

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

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

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

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

Signal Prolongation by Gating

Using models to develop experimental hypotheses to understand complex signaling mechanisms

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

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

LTP Induced PHOSPHORYLATION OF CaMKII IS MAPK-DEPENDENT

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

TPS + Inhibitor-1 Vehicle PD EPSP SLOPE (%Baseline) Thio-phosphorylated Inhibitor-1 Protein does not restore the LTP blocked by MEK inhibitor PD-98059

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

TPS-ISO 60 * SH PD TPS-ISO TOTAL CaMKII (% above control) MAPK-Dependent Expression of CaMKII During TPS-ISO-Induced LTP CaMKII Actin SH +PD S * TOTAL CaMKII (% above control) TIME (min after TPS)

Total CaMKII LTP * * EPSP SLOPE (% baseline) Act-D Aniso TPS-ISO 60 * * TOTAL CaMKII (% change from controls) Act-D Aniso TPS-ISO 60 LTP and Increased CaMKII Expression Require Transcription and Translation

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

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

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