Calcium Dynamics

Basic reference: Keener and Sneyd, Mathematical Physiology

• 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 Ca2+ plays an equally important role in practically every cell type.

• Ca2+ 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

Calcium in muscle: I

Calcium in muscle: II

Calcium in phototransduction

Calcium in phototransduction

Calcium in taste receptors

Calcium and synapses: I

Calcium and synapses: II

A: Hepatocytes

B: Rat parotid gland

C: Gonadotropes

D: Hamster eggs (post-fertilization)

E, F: Insulinoma cells

Typical Calcium Oscillations

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)

Ryanodinereceptors

IP3 receptors

Muscle cells and many neurons

Electrically non-excitable cells. Smooth muscle

Three principal mechanisms

Summary of calcium homeostasis

ER

Mitochondria

Ca2+

Ca2+

Ca2+-B(buffering)serca

IPR

RyR

PM pumps

ICa

leak

Cardiac cells - EC Coupling

ER

Ca2+

Ca2+

serca

RyR

NCX

L-type channel(voltage gated)

Na+

Na+

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 [Ca2+] 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.

IP3 Receptor pathway

Ryanodine Receptor pathway

Generic modellingSet up a typical reaction diffusion equation for calcium:

€

∂c∂t

= D∇ 2c + (JIPR + JRyR − Jserca ) + (Jleak − JPM + JI ) + (Jm,out − Jm,in ) − k1c(bt −b) + k2b

ER fluxes PM fluxesmitochondrial

fluxesbuffering

• This reaction-diffusion equation is coupled to a system of o.d.e.s (or p.d.e.s), describing the various receptor states, IP3, 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