An analytical approximation to the AdEx neuron allows fast fitting to physiological data
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Bernstein-Center for Computational Neuroscience Heidelberg-Mannheim, Central Institute of Mental Health, Heidelberg University, Computational Neuroscience, Germany
Fitting spiking neuron models to physiological data sets is often a demanding and time-consuming task. For large-scale network simulations with many different neuron types, it is therefore important to have mathematically tractable, yet in a defined sense still physiologically realistic neuron models that allow for a fast fitting process. Recent extensions of the basic LIF model [1,2,3] enable to reproduce voltage traces and spiking dynamics of real neurons to a reasonable degree. Most of these previous studies used voltage traces to fit the model which are obtained by injecting a fluctuating current into neurons recorded from acute brain slices. Some of the models [1,3] also perform quite well on 'test' sections of these recordings that were not explicitly used for training the model. However, since both training and test data consist of voltage traces generated by input currents with the same statistical distribution, it could be that the model performs well only within the limited input regime used for fitting and would not generalize well to different input regimes.
Here, rather than fitting model parameters to fluctuating voltage traces, we use standard f/I (firing rate over current) curves from cortical pyramidal cells recorded in vitro. These curves cover the whole range of spike rates up to the point of the depolarization block. For this purpose we derive an approximation to the adaptive exponential Integrate-and-Fire model (AdEx) [4] which yields a closed-form expression for the f/I curves. This approach is based on a separation of time scales [5], assuming that the time constant of the adaptive current is much slower than the membrane time constant. The model is fitted to almost perfectly match the training set consisting of initial and steady state f/I curves. It is then, however, tested on recordings of voltage traces upon fluctuating input currents as in previous approaches [1,3]. The approximated model allows a fitting process that is about one order of magnitude faster than fits via numerical integration, and it still produces a remarkably low prediction error on the qualitatively different test set. We used established performance measures to assess the prediction capabilities of the model and to compare the results with previously published work [3]. Thus, we have created a neuron model which can be adjusted to physiological f/I curves very quickly, which is physiologically realistic in the sense that it generalizes to independent test sets, and is also mathematically tractable.
Acknowledgements
This work was funded by grants from the German ministry for education and research (BMBF, 01GQ1003B) and the Deutsche Forschungsgemeinschaft to D.D. (Du 354/5-1 & 6-1).
References
1. Gerstner, W., and Naud, R. (2009). How good are neuron models? Science 326, 379-380.
2. Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons? IEEE Trans Neural Networks 15(5), 1063-1070.
3. Badel, L., and Lefort, S., and Berger, T. K., and Petersen, C. C. H., and Gerstner, W., and Richardson, M. J. E. (2008). Extracting non-linear integrate-and-fire models from experimental data using dynamic I-V curves. Biol Cybern 99, 361-370.
4. Brette, R., and Gerstner, W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neurophysiol 94, 3637-3642.
5. Naud, R., and Marcille, N., and Clopath, C., and Gerstner, W. (2008). Firing patterns in the adaptive exponential integrate-and-fire model. Biol Cybern 99, 335-347.
Keywords:
dynamical sytsems,
networks,
neuron model,
Neurons
Conference:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.
Presentation Type:
Poster
Topic:
neurons, networks and dynamical systems (please use "neurons, networks and dynamical systems" as keywords)
Citation:
Hertäg
L,
Hass
J,
Golovko
T and
Durstewitz
D
(2011). An analytical approximation to the AdEx neuron allows fast fitting to physiological data.
Front. Comput. Neurosci.
Conference Abstract:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011.
doi: 10.3389/conf.fncom.2011.53.00206
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Received:
22 Aug 2011;
Published Online:
04 Oct 2011.
*
Correspondence:
Ms. Loreen Hertäg, Bernstein-Center for Computational Neuroscience Heidelberg-Mannheim, Central Institute of Mental Health, Heidelberg University, Computational Neuroscience, Mannheim, 68159, Germany, loreen.hertaeg@zi-mannheim.de