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Study of calcium profile in neuronal cells with respect to temperature and influx due to potential activity

Calcium is a critically important second messenger in the nervous system. It enters through voltage-gated Ca2+ channels and regulates the release of the synaptic transmitter. This mechanism is monitored by calcium diffusion, buffering mechanism and calcium influx into the cytoplasm. The study of Ca2+ dynamics is interesting because the concentration of Ca2+ shows highly complex spatial-temporal behavior. There are many controls on the cytoplasmic Ca2+ concentration. First, it is heavily buffered (i.e., bound) by large proteins and second control is that of the variable diffusion coefficient. The diffusion coefficient is directly proportional to the temperature and inversely proportional to the viscosity. In this paper, the one-dimensional steady-state case with boundary conditions has been studied to understand the Ca2+ distribution in neuronal cells incorporating diffusion of calcium, point source, excess buffer approximation (EBA), an influx due to the calcium current. Moreover, the dependency of Ca2+ concentration based on the variable diffusion coefficient is studied. The finite element method (FEM) has been employed to obtain the solutions.