Event-based integration algorithms for conductance-based integrate and fire networks

Event-driven simulation strategies were proposed recently to simulate integrate-and-fire (IF) type neuronal models. These strategies differ from the classic "clock-driven" integration based on constant or varying time steps. In an event-driven strategy, the neuron model must be analytically solvable, in which case one can predict the time of the next spike in any neuron. The integration is then realized by determining which is the next "event" in the network, and update all the neurons concerned. The great advantage is that such integration may be considerably faster computationally, but most important, it is also exact since the timing of the spike is calculated analytically. The drawback of such event-based strategies is that they are possible only in simple IF models, with current-based synaptic interactions. Unfortunately, they are not possible in more realistic conductance-based models, because the Vm activity cannot be calculated analytically in most of such models.

To address this caveat, with Michelle Rudolph, we have proposed a number of extensions of the classical leaky IF neuron model involving approximations of the membrane equation with conductance-based synaptic current, which lead to simple analytic expressions for the membrane state which, therefore, can be used in the event-driven framework [1]. We have recently proposed an extenstion to this framework, which is still analytic, but gives the full EPSP time course [5]. These conductance-based IF models (gIF models) were compared to commonly used models, such as the leaky IF model or biophysical models in which conductances are explicitly integrated. All models were compared with respect to various spiking response properties in the presence of synaptic activity, such as the spontaneous discharge statistics, the temporal precision in resolving synaptic inputs, and gain modulation under in vivo-like synaptic bombardment. Being based on the passive membrane equation with fixed-threshold spike generation, the proposed gIF models are situated in between leaky IF and biophysical models, but are much closer to the latter with respect to their dynamic behavior and response characteristics, while still being nearly as computationally efficient as simple IF neuron models [1,2,5]. These new conductance-based IF models can also incorporate plasticity [2], and were also compared to other simulation strategies in terms of precision [3,4]. Extension of this approach to network simulations are presently being investigated.

[1] Rudolph, M. and Destexhe, A. Integrate-and-fire neurons with high-conductance state dynamics for event-driven simulation strategies. Neural Computation 18: 2146-2210, 2006 (see abstract)

[2] Rudolph, M. and Destexhe, A. Event-based simulation strategy for conductance-based synaptic interactions and plasticity. Neurocomputing 69: 1130-1133, 2006 (see abstract)

[3] Brette, R., Rudolph, M., Carnevale, T., Hines, M., Beeman, D., Bower, J.M., Diesmann, M., Morrison, A., Goodman, P.H., Harris Jr., F.C., Zirpe, M., Natschlager, T., Pecevski, D., Ermentrout, B., Djurfeldt, M., Lansner, A., Rochel, O., Vieville, T., Muller, E., Davison, A.P., ElBoustani, S. and and Destexhe, A. Simulation of networks of spiking neurons: a review of tools and strategies. J. Computational Neurosci. 23: 349-398, 2007 (see abstract)

[4] Rudolph, M. and Destexhe, A. How much can we trust neural simulation strategies? Neurocomputing 70: 1966-1969, 2007 (see abstract)

[5] Rudolph-Lilith, M., Dubois, M. and Destexhe, A. Analytical integrate-and-fire neuron models with conductance-based dynamics and realistic postsynaptic potential time course for event-driven simulation strategies. Neural Computation 24: 1426-1461, 2012 (see abstract)

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