Modeling Effect of Sodium Pump on Calcium Oscillations in Neuron Cells

Calcium plays a significant role in a number of processes like muscle contraction, gene expression, synaptic plasticity, signal transduction etc. but the significance of calcium oscillation is not yet completely understood in most of the cell types. A number of investigators have reported the oscillatory behavior of calcium due to intracellular concentration of inositol 1,4,5-trisphosphate (IP3). In this paper, an attempt has been made to study the oscillations induced in calcium due to dynamically changing membrane potential with special relevance to sodium pump. A mathematical model is developed which incorporates nearly all important and necessary biophysical components like L-type calcium channel, sodium channel, potassium channel, cytosolic buffers, calcium pump, sodium–calcium exchanger (NCX), sodium–potassium ATPase (sodium pump), and dynamic membrane potential. These channels have realistic gating mechanism and emulate the gating mechanism proposed in the famous paper of Hodgkin and Huxley.1 The model leads to an initial value problem involving system of non-linear ordinary differential equations. A numerical solution has been obtained using Gear's method. The numerical results have been used to study the effect of sodium pump over the frequency of Ca 2+ oscillation. At lower and higher sodium pump current densities the Ca 2+ oscillation frequency is observed to be 278 Hz and 225 Hz respectively.