1. Calcium Dynamics Basic reference: Keener and Sneyd, Mathematical Physiology

2. In the previous talk we concentrated on Na + and K +, as those are the ions that are most important for the control of cell volume and the membrane potential. But Ca 2+ plays an equally important role in practically every cell type. Ca 2+ controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating, and so on. Important in both excitable and non-excitable cells. Calcium is a vital second messenger

3. Calcium in muscle: I

4. Calcium in muscle: II

5. Calcium in phototransduction

7. Calcium in taste receptors

8. Calcium and synapses: I

9. Calcium and synapses: II

10. A: Hepatocytes B: Rat parotid gland C: Gonadotropes D: Hamster eggs (post- fertilization) E, F: Insulinoma cells Typical Calcium Oscillations

11. Inward flux of calcium through voltage-gated calcium channels. Dependent on fluctuations of the membrane potential. Often seen in electrically excitable cells such as neurosecretory cells Not dependent on membrane potential. Oscillations arise from recycling of calcium to and from internal stores (ER and mitochondria) Ryanodine receptors IP 3 receptorsMuscle cells and many neurons Electrically non- excitable cells. Smooth muscle Three principal mechanisms

12. Summary of calcium homeostasis ER Mitochondria Ca 2+ Ca 2+ -B (buffering) serca IPR RyR PM pumps I Ca leak

13. Cardiac cells - EC Coupling ER Ca 2+ serca RyR NCX L-type channel (voltage gated) Na +

14. Calcium excitability Both IPR and RyR release calcium in an excitable manner. They both respond to a calcium challenge by the release of even more calcium. The precise mechanisms are not known for sure (although detailed models can be constructed). An IPR behaves like a Na + channel (in some ways). In response to an increase in [Ca 2+ ] it first activates quickly, and then inactivates slowly, resulting in the short-term release of a large amount of calcium. A lot of attention has been focused on IPR and RyR. Less on pumping. But the dynamics of pumping is equally important.

15. IP 3 Receptor pathway

16. Ryanodine Receptor pathway

17. Generic modelling Set up a typical reaction diffusion equation for calcium: ER fluxesPM fluxes mitochondrial fluxes buffering This reaction-diffusion equation is coupled to a system of o.d.e.s (or p.d.e.s), describing the various receptor states, IP 3, the reaction and diffusion of the buffers, calcium inside the ER or mitochondria, or any other important species. The specifics of the coupled o.d.e.s depend on which particular model is being used. Sometimes the PM fluxes appear only as boundary conditions, sometimes not, depending on the exact assumptions made about the spatial properties of the cell. In general the buffering flux is a sum of terms, describing buffering by multiple diffusing buffers. Total buffer