The dynamics of calcium ion in FCM model

Calcium ion plays a critical role in the neurons and has been the subject of numerous experimental measurements and mechanism studies. The dynamics of calcium ion, especially the computation models, will provide quantitative insights into the neuron signaling. FCM model is a widely used retinal ganglion cells model with five channels including sodium channels, calcium channels, and three types of potassium channels namely the A type, Ca-activated potassium, and the delayed rectifier. Aimed to make retinal prostheses which can help the blind man to recover sight, the effects of calcium ion in FCM model on the calcium channel potential and on the calcium-activated potassium potential were studied. With MATLAB software, calcium current of FCM model was numerically computed with backward Euler methods, and FCM model was simulated in absence of either Ca-current(I_Ca) or Ca-activated potassium current(I_K,Ca). The model was also analyzed with phase plane method. The results indicated that the relationship curve between the peak calcium current and clamped potentials was an inverted bell shape, and both calcium current and Ca-activated potassium current increased the frequency of firing and the peak of membrane potential. Calcium concentration played an important role in control the frequency of the ganglion cell spikes and the magnitude of peak membrane voltage.