- Poster presentation
- Open Access
Analytical results for integrate-and-fire neurons driven by dichotomous noise
© Droste and Lindner; licensee BioMed Central Ltd. 2013
- Published: 8 July 2013
- White Noise
- Voltage Threshold
- Synaptic Input
- Shot Noise
- Diffusion Approximation
Models of the integrate-and-fire type have been widely used in the study of neural systems . Usually, they consist of an evolution equation for the neuron's membrane voltage, complemented by a fire-and-reset rule that is applied once a voltage threshold is crossed. This minimalist description has allowed impressive analytical insights, for instance into neuronal information transmission properties , the effect of input correlations , or the dynamics of whole networks . Further, it can be readily extended to include more complex behavior, such as spike-frequency-adaptation , which can then be studied in a well-understood setting.
The synaptic input to the neuron is usually modeled as a sequence of spikes with stochastic arrival times; mathematically speaking, it is a Poisson process where each event is a delta spike (shot noise). As such discrete input is notoriously difficult to treat analytically (but see ), many studies have employed the so called diffusion approximation, modeling the massive synaptic bombardment as Gaussian white noise.
We derive analytical expressions for firing-rate, CV and the steady-state voltage distribution of this system and verify them by numerical simulation. Furthermore, we study the transmission of a weak signal through such a neuron.
This work was supported by Bundesministerium fuer Bildung und Forschung grant 01GQ1001A and the research training group GRK 1589 "Sensory Computation in Neural Systems".
- Burkitt AN: A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol Cybern. 2006, 95 (1): 1-19. 10.1007/s00422-006-0068-6.View ArticlePubMedGoogle Scholar
- Lindner B, Schimansky-Geier L: Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett. 2001, 86 (14): 2934-2937. 10.1103/PhysRevLett.86.2934.View ArticlePubMedGoogle Scholar
- De La Rocha J, et al: Correlation between neural spike trains increases with firing rate. Nature. 2007, 448 (7155): 802-806. 10.1038/nature06028.View ArticlePubMedGoogle Scholar
- Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comp Neurosci. 2000, 8 (3): 183-208. 10.1023/A:1008925309027.View ArticleGoogle Scholar
- Liu , Ying-Hui , Xiao-Jing Wang: Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron. J Comp Neurosci. 2001, 10 (1): 25-45. 10.1023/A:1008916026143.View ArticleGoogle Scholar
- Richardson MJE, Swarbrick R: Firing-rate response of a neuron receiving excitatory and inhibitory synaptic shot noise. Phys Rev Lett. 2010, 105 (17): 178102-View ArticlePubMedGoogle Scholar
- Salinas E, Sejnowski TJ: Integrate-and-fire neurons driven by correlated stochastic input. Neural Comput. 2002, 14 (9): 2111-2155. 10.1162/089976602320264024.PubMed CentralView ArticlePubMedGoogle Scholar
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