1. Mathematical Modeling and Analysis of Intracellular Signaling Pathways Paul D. Smolen, Douglas A. Baxter, and John H. Byrne http://nba.uth.tmc.edu/homepage/jbyrne/ University of Texas, Houston Medical School Chapter 14: Björn Brembs

2. Why prefer mathematical or computer models over word models? The main feature of science is the ability to predict future events (e.g. Laplace) Emperor Napoleon Bonaparte inquired of Laplace after reading his theory – „Where does God fit into your system?“ Laplace replied: “Sire, I have no need for that hypothesis”.

3. Why prefer mathematical or computer models over word models? Often complexity or nonlinearity preclude intuitive prediction Claude Monet b. Nov. 14, 1840, Paris d. Dec. 5, 1926, Giverny

4. Why prefer mathematical or computer models over word models? → mathematical models and simulations have the power to predict unexpected features of the system in question Many examples in physics…  Bending of light at the sun, slowing down of time at high velocities, speed of light is upper limit (Relativity).  Huge number of subatomic particles, antimatter, black hole radiation, wave- properties of particles (Quantum Physics) …but only few biological examples: Development: Gierer-Meinhard models of Hydra regeneration predict activator and inhibitor substances Psychology: Rescorla-Wagner model predicts overexpectation Neuroscience: Simulations using Hodgkin-Huxley equations predict action potentials

5. The “information” in Bioinformatics

6. How do we capture information flow?

7. Methods for modeling intracellular signaling pathways 1. Diffusion for ions and small molecules Calcium imaging Calcium current: H&H! Rate of change of cytoplasmic calcium Calcium from ER Calcium leaving the cell

8. Methods for modeling intracellular signaling pathways 2. Standard equations (enzymatic reactions)

9. Methods for modeling intracellular signaling pathways 2. Standard equations (enzymatic reactions) Michaelis-Menten

10. Methods for modeling intracellular signaling pathways 2. Standard equations (allosteric reactions)

11. activator inhibitor Methods for modeling intracellular signaling pathways 2. Standard equations (allosteric reactions) Michaelis-Menten with Hill function...activating effectors …inhibitory effectors Hill functions for… Hill coefficient

12. Combining equations to a simulation

14. Why prefer mathematical or computer models over word models?

15. Predictability and indeterminism