Is the integrate-and-fire model good enough?--a review

We review some recent results on the behaviour of the integrate-and-fire (IF) model, the FitzHugh-Nagumo (FHN) model, a simplified version of the FHN (IF-FHN) model and the Hodgkin-Huxley (HH) model with correlated inputs. The effect of inhibitory inputs on the model behaviour is also taken into account. Here, inputs exclusively take the form of diffusion approximation and correlated inputs mean correlated synaptic inputs (Sections 2 and 3). It is found that the IF and HH models respond to correlated inputs in totally opposite ways, but the IF-FHN model shows similar behaviour to the HH model. Increasing inhibitory input to single neuronal models, such as the FHN model and the HH model can sometimes increase their firing rates, which we termed inhibition-boosted firing (IBF). Using the IF model and the IF-FHN model, we theoretically explore how and when IBF can happen. The computational complexity of the IF-FHN model is very similar to the conventional IF model, but the former captures some interesting and essential features of biophysical models and could serve as a better model for spiking neuron computation.