Intracellular Calcium dynamics

The calcium dynamics are usually modeled in the following simple fashion.  

$$\frac{d[Ca]_{in}}{dt} = -\frac{k}{2Fd}I_{Ca} -\frac{K_T[Ca]_{in}}{[Ca]_{in} + K_d}$$ (6)

or with just a linear term. Here F is the Faraday constant, d is the depth of the shell between the membrane (usually, e.g., $0.1\mu$), k=0.1 for I in $\mu A/cm^2$, [Ca] in millimolar, K_T=10^-4 mM/ms and K_d=10^-4 mM. Note that as the calcium current increases in an inward direction, -I_Ca becomes positive and thus intracellular calcium increases. The uptake of calcium is modeled here as a Michaelis-Menten type reaction. An even simpler uptake would be simply linear. These constants are for thalamic neurons but are in the right ballpark for most models. Finally, in general, extracellular calcium is about 2 mM and intracellular tends to be around 2.4 10^-4 mM.