A Mathematical Model of CA1 Hippocampal Neurons with Astrocytic Input

Abstract

Over time astrocytes have been thought to function in an auxiliary manner, providing neurons with metabolic and structural support. However, recent research suggests they may play a fundamental role in the generation and propagation of focal epileptic seizures by causing synchronized electrical bursts in neurons. It would be helpful to have a simple mathematical model that represents this dynamic and incorporates these updated experimental results. We have created a two-compartment model of a typical neuron found in the hippocampal CA1 region, an area often thought to be the origin of these seizures. The focus is on properly modeling the astrocytic input to examine the pathological excitation of these neurons and subsequent transmission of the signals. In particular, we consider the intracellular astrocytic calcium fluctuations which are associated with slow inward currents in neighbouring neurons. Using our model, a variety of experimental results are reproduced, and comments are made about the potential differences between graded and “all-or-none” astrocytes.