A Numerical Model to Study Effect of Potential-Dependent Influx on Calcium Diffusion in Neuron Cells

Abstract

Electrical activity within the brain rapidly encodes information about the world but for these fleeting perceptions to have a lasting impact, long-term changes in the structure and function of neurons must follow. At the synapse, neurotransmitter reception initiates a number of biochemical signaling cascades in the postsynaptic cells, one of the most important of which is the elevation of intracellular calcium. Early events induced by the rise of calcium in dendrites are likely to be local, resulting from posttranslational modifications of the synaptic machinery. However, for long-term structural and functional changes in the neuron, the calcium signal must regulate the expression of new gene products. A mathematical model has been developed for diffusion of Ca²⁺ in the presence of excess buffer approximation in synaptic cleft. This model incorporates the effect of potential activity-dependent influx on calcium diffusion process. The parameters like diffusion rate, dissociation rate, conductance, and membrane potential are incorporated in the above model. Appropriate boundary conditions have been framed using physical processes involved in influx. The finite differences have been employed to obtain numerical solution to the problem. The relationships among various parameters have been studied. The concentration and potential profiles have been obtained with respect to position and time.

Keywords: Calcium concentration, buffers, neurotransmitters, diffusion of calcium, electrical properties, potential activity