Analytical Integrate-and-Fire Neuron Models with Conductance-Based Dynamics and Realistic Postsynaptic Potential Time Course for Event-Driven Simulation Strategies

In a previous paper (Rudolph & Destexhe, 2006), we proposed various models, the gIF neuron models, of analytical integrate-and-fire (IF) neurons with conductance-based (COBA) dynamics for use in event-driven simulations. These models are based on an analytical approximation of the differential equation describing the IF neuron with exponential synaptic conductances and were successfully tested with respect to their response to random and oscillating inputs. Because they are analytical and mathematically simple, the gIF models are best suited for fast event-driven simulation strategies. However, the drawback of such models is they rely on a nonrealistic postsynaptic potential (PSP) time course, consisting of a discontinuous jump followed by a decay governed by the membrane time constant. Here, we address this limitation by conceiving an analytical approximation of the COBA IF neuron model with the full PSP time course. The subthreshold and suprathreshold response of this gIF4 model reproduces remarkably well the postsynaptic responses of the numerically solved passive membrane equation subject to conductance noise, while gaining at least two orders of magnitude in computational performance. Although the analytical structure of the gIF4 model is more complex than that of its predecessors due to the necessity of calculating future spike times, a simple and fast algorithmic implementation for use in large-scale neural network simulations is proposed.