×

zbMATH — the first resource for mathematics

Theory of input spike auto- and cross-correlations and their effect on the response of spiking neurons. (English) Zbl 1138.92014
Summary: Spike correlations between neurons are ubiquitous in the cortex, but their role is not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients, and correlation time scale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. In fact, the total input current has a nontrivial two-point correlation function described by two main parameters: the correlation time scale (how precise the input correlations are in time) and the correlation magnitude (how strong they are). Therefore, the total current generated by the input spike trains is not well described by a white noise Gaussian process. Instead, we model the total current as a colored Gaussian process with the same mean and two-point correlation function, leading to the formulation of the problem in terms of a Fokker-Planck equation.
Solutions of the output firing rate are found in the limit of short and long correlation time scales. The solutions described here expand and improve on our previous results [R. Moreno-Bote et al., Phys. Rev. Lett. 89, No. 28, 288101 ff (2002)] by presenting new analytical expressions for the output firing rate for general IF neurons, extending the validity of the results for arbitrarily large correlation magnitude, and by describing the differential effect of correlations on the mean-driven or noise-dominated firing regimes. Also the details of this novel formalism are given here for the first time. We employ numerical simulations to confirm the analytical solutions and study the firing response to sudden changes in the input correlations. We expect this formalism to be useful for the study of correlations in neuronal networks and their role in neural processing and information transmission.

MSC:
92C20 Neural biology
92C05 Biophysics
60G35 Signal detection and filtering (aspects of stochastic processes)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abeles M., Isr. J. Med. Sci. 18 pp 83– (1982)
[2] Aersten A., J. Neurophysiol. 61 pp 900– (1989)
[3] DOI: 10.1523/JNEUROSCI.2948-05.2006
[4] DOI: 10.1088/0954-898X/8/4/003 · Zbl 0904.92013
[5] DOI: 10.1093/cercor/7.3.237
[6] DOI: 10.1016/j.tins.2004.02.006
[7] Bair W., J. Neurosci. 21 pp 1676– (2001)
[8] DOI: 10.1073/pnas.88.24.11569
[9] DOI: 10.1006/jtbi.1998.0782
[10] DOI: 10.1162/089976699300016485
[11] DOI: 10.1103/PhysRevLett.96.058101
[12] DOI: 10.1152/jn.00949.2002
[13] Cragg B. G., J. Anat. 101 pp 639– (1967)
[14] DOI: 10.1007/BF00238837
[15] DOI: 10.1038/381610a0
[16] DOI: 10.1016/0301-0082(92)90015-7
[17] DOI: 10.1103/PhysRevLett.59.2129
[18] DOI: 10.1103/PhysRevE.74.030903
[19] DOI: 10.1162/089976600300015745
[20] DOI: 10.1126/science.1055465
[21] DOI: 10.1073/pnas.94.23.12699
[22] DOI: 10.1007/BF00230962
[23] DOI: 10.1162/089976603321043702 · Zbl 1026.92011
[24] DOI: 10.1162/0899766041732468 · Zbl 1055.92011
[25] DOI: 10.1146/annurev.neuro.24.1.263
[26] Lee D., Journal of Neuroscience 18 (3) pp 1161– (1998)
[27] DOI: 10.1162/neco.2006.18.3.634 · Zbl 1087.92008
[28] DOI: 10.1103/PhysRevE.73.022901
[29] DOI: 10.1103/PhysRevE.72.061919
[30] DOI: 10.1162/089976606774841521 · Zbl 1079.92015
[31] DOI: 10.1103/PhysRevLett.92.028102
[32] DOI: 10.1103/PhysRevLett.94.088103
[33] DOI: 10.1103/PhysRevLett.96.028101
[34] DOI: 10.1103/PhysRevLett.89.288101
[35] Nowak L. G., J. Neurophysiol. 81 pp 1057– (1999)
[36] DOI: 10.1162/089976601300014448 · Zbl 1052.92016
[37] DOI: 10.1016/S0006-3495(67)86597-4
[38] DOI: 10.1162/neco.2007.19.1.1 · Zbl 1116.92018
[39] DOI: 10.1016/S0925-2312(01)00548-3
[40] DOI: 10.1162/0899766053429444 · Zbl 1076.92014
[41] DOI: 10.1126/science.278.5345.1950
[42] DOI: 10.1103/PhysRevLett.86.3662
[43] Salinas E., J. Neurosci. 20 pp 6193– (2000)
[44] DOI: 10.1038/35086012
[45] Shadlen M. N., J. Neurosci. 18 pp 3870– (1998)
[46] DOI: 10.1152/jn.00415.2003
[47] DOI: 10.1016/0306-4522(94)90154-6
[48] Softky W., J. Neurosci. 13 pp 334– (1993)
[49] DOI: 10.1038/35004588
[50] Ts’o D. Y., J. Neuroscie. 6 pp 1160– (1986)
[51] DOI: 10.1146/annurev.physiol.61.1.435
[52] DOI: 10.1038/373515a0
[53] Wehr M., J. Neurosci. 19 pp 381– (1999)
[54] DOI: 10.1038/370140a0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.