Van Goor, LeBeau, Krsmanovic, Sherman, Catt, Stojilkovic, 2000

Model Structure

During an action potential, depolarisation of the plasma membrane causes voltage-gated Ca²⁺ channels to open, allowing Ca²⁺ to diffuse into the cell. The subsequent increase in cytosolic calcium concentration ([Ca²⁺]_i) triggers a number of biochemical events involved in the control of cell function. The frequency, amplitude and duration of the Ca²⁺ signals determine the specificity of the cellular response. However, the exact relationship between the action potential waveform, the gating properties of the voltage-gated Ca²⁺ channels, the pattern of Ca²⁺ influx and the ionic mechanisms underlying the the agonist-induced Ca²⁺ spike broadening has not been characterised.

In their 2000 paper, Fredrick Van Goor, Andrew P. LeBeau, Lazar Z. Krsmanovic, Arthur Sherman, Kevin J. Catt and Stanko S. Stojikovic examine the ionic mechanism mediating depolarisation-induced Ca²⁺ spike broadening in GnRH-secreting (GT1) neurons. The validity of their experimental results were tested by comparing them with a computational model. They also used this mathematical model to examine the influence of voltage-gated Ca²⁺ channel gating properties on the ability of action potential broadening to enhance the I_Ca.

Their mathematical model is based exclusively on the on the properties of the individual ionic currents characterised in GT1 neurons. The ionic currents used were a TTX-sensitive I_Na, L- and T-type I_Ca, a voltage sensitive (delayed-rectifying) I_K(dr), an M-like I_K (I_M), an inward rectifier I_K (I_ir), and a Ca²⁺ permeable, voltage-insensitive inward leak, I_d (see figure 1 below).

In their original model, Van Goor et al. used a Hodgkin-Huxley type equation to represent the sodium current. However, in this description, I_Na exhibited a large surge of activation during the spike repolarisation, and it also did not spike during broadening, suggesting that the model gating kinetics didn't accurately represent those in GTI neurons. Consequently, they replaced the Hodgkin-Huxley-like description with Kuo and Bean's 1994 model of I_Na (see figure 2 below). In this description the Na+ channel is composed of subunits with four possible states: deactivated (D), activated (A), deactivated-inhibited (D*), and activated-inhibited (A*). The open, conducting state (O) is given by A3 in the reaction scheme.

The complete original paper reference is cited below:

Amplitude-Dependent Spike-Broadening and Enhanced Ca²⁺ Signaling in GnRH-Secreting Neurons, Fredrick Van Goor, Andrew P. LeBeau, Lazar Z. Krsmanovic, Arthur Sherman, Kevin J. Catt and Stanko S. Stojikovic, 2000, Biophysical Journal , 79, 1310-1323. (Full text and PDF versions of the article are available for Journal Members on the BJ website.) PubMed ID: 10968994