Conductancebased integrate and fire modelsThe simplest mechanism to model neuronal spiking is the integrate and fire (IF) model, in which spike occurs when the membrane potential (Vm) crosses a given threshold, and is then instantaneously reset to a given reset value. This model does not take into account the large increase of conductance associated to the spike, and in particular, does not correctly model the following afterhyperpolarization due to the activation of K+ conductances. Because many neuronal properties may depend on these conductances, we have conceived a more sophisticated IF model derived from the quantitative model of Hodgkin and Huxley (HH) [1]. The simplification derives from the observation that during a spike in the HH model, the rate constants vary abruptly. If these time courses are approximated by square pulses, HH equations can be solved analytically. If the pulses are triggered when the voltage crosses a given threshold, then the simplified model generate action potentials very similar to the HH model, and with almost identical conductance characteristics [1]. The simplified pulsebased model also produces similar repetitive firing activity, and similar response to noisy inputs, compared to the HH model. It also performs much better than the IF model in situations involving complex intrinsic properties, as illustrated in circuits of thalamic bursting neurons [1]. A last advantage is that, because it is analytic, the pulsebased IF model is computationally much faster than the HH model, and is therefore a good candidate for largescale network models. In a recent study, the pulsebased IF model was among the most performant models to fit experimental data [2]. Another approach is to attempt to obtain integrate and fire models which are analytically solvable, enabling eventbased simulation strategies. However, the membrane equation is not solvable with the full dynamics of conductances. We have proposed socalled "gIF models" (for gbased IF models) [3,4]. These models are analytic and enables the eventbased simulation of networks of conductancebased IF neurons (see Section 6.2). [1] Destexhe, A. Conductancebased integrate and fire models. Neural Computation 9: 503514, 1997 (see abstract) [2] Pospischil M, Piwkowska Z, Bal T and Destexhe A. Comparison of different neuron models to conductancebased poststimulus time histograms obtained in cortical pyramidal cells using dynamicclamp in vitro. Biological Cybernetics 105: 167180, 2011 (see abstract) [3] Rudolph, M. and Destexhe, A. Integrateandfire neurons with highconductance state dynamics for eventdriven simulation strategies. Neural Computation 18: 21462210, 2006 (see abstract) [4] RudolphLilith, M., Dubois, M. and Destexhe, A. Analytical integrateandfire neuron models with conductancebased dynamics and realistic postsynaptic potential time course for eventdriven simulation strategies. Neural Computation 24: 14261461, 2012 (see abstract)
Department of Integrative and Computational Neuroscience (ICN),
