The Two-Pool Model for Ca2+ Dynamics in the Cell
by Mike Martin

On this page, you can vary the parameters in the two-pool model for calcium dynamics in a cell.   Let c (t) be the calcium ion concentration in the cell's cytoplasm at time t and cs (t) be the calcium ion concentration in the Ca2+-sensitive pool.   The model equations are given by

f (c, cs) is the flux of Ca2+ from the cytoplasm into the Ca2+-sensitive pool.   Juptake is the rate at which Ca2+ is pumped from the cytosol into the Ca2+-sensitive pool.   Jrelease is the rate at which Ca2+ is released from the Ca2+-sensitive pool.

Submit real, non-negative values for all of the parameters to obtain graphical solutions of the system as functions of time and in the phase plane.   A numeric solution on the interval [0, T] is produced using Mathematica's numerical ODE solver, NDSolve.   Initial values must be input.   The first graph below is that of the calcium concentration in the cytoplasm, c (in red), the second graph is that of the calcium concentration in the Ca2+-sensitive pool, cs (in purple).   The last graph is that of the phaseplane with the solution (in black) and streamlines.

Enter in the value of the parameters and select the plotting bounds, then press the "Plot" button.

r =  

k =  

K1 =  

K2 =  

K3 =  

V1 =  

V2 =  

kf =  

m =  

n =  

p =  


c(0) =  

cs(0) =  


T =  


  ≤   c   ≤  

  ≤   cs   ≤  


References:

Goldbeter, A, G Dupont, MJ Berridge (1990). Minimal Model for Signal-Induced Ca2+ Oscillations and for Their Frequency Encoding Through Protein Phosphorylation. Proc. Natl. Acad. Sci. USA, 87: 1461-1465.

Keener, J, J Sneyd Mathematical Physiology. Springer, Berlin, Germany, 1998.