Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations.

Alpha functions are commonly used to describe different receptor channel kinetics (non-NMDA, GABAA and GABAB). In this paper we show that they may be represented as solutions to simple ordinary differential equations. This alternative method is compared with the commonly used direct summation of the alpha function conductances in a high-level neuronal circuit model. A parametric study shows that the differential equation method greatly speeds up the previous summation method. The forward Euler method used to solve this differential equation is shown to be accurate for this type of simulation. The modelling of NMDA receptor channel kinetics is also discussed.