From spiking neurons to rate models: A cascade model as an approximation to spiking neuron models with refractoriness

被引:17
作者
Aviel, Yuval [1 ]
Gerstner, Wulfram
机构
[1] Ecole Polytech Fed Lausanne, Sch Comp & Commun Sci, CH-1015 Lausanne, Switzerland
[2] Ecole Polytech Fed Lausanne, Brain Mind Inst, CH-1015 Lausanne, Switzerland
来源
PHYSICAL REVIEW E | 2006年 / 73卷 / 05期
关键词
D O I
10.1103/PhysRevE.73.051908
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
A neuron that is stimulated repeatedly by the same time-dependent stimulus exhibits slightly different spike timing at each trial. We compared the exact solution of the time-dependent firing rate for a stochastically spiking neuron model with refractoriness (spike response model) with that of an inhomogeneous Poisson process subject to the same stimulus. To arrive at a mapping between the two models we used alternatively (i) a systematic parameter-free Volterra expansion of the exact solution or (ii) a linear filter combined with nonlinear Poisson rate model (linear-nonlinear Poisson cascade model) with a single free parameter. Both the cascade model and the second-order Volterra model showed excellent agreement with the exact rate dynamics of the spiking neuron model with refractoriness even for strong and rapidly changing input. Cascade rate models are widely used in systems neuroscience. Our method could help to connect experimental rate measurements to the theory of spiking neurons.
引用
收藏
页数:10
相关论文
共 35 条
[1]   Computation in a single neuron: Hodgkin and Huxley revisited [J].
Arcas, BAY ;
Fairhall, AL ;
Bialek, W .
NEURAL COMPUTATION, 2003, 15 (08) :1715-1749
[2]   What causes a neuron to spike? [J].
Arcas, BAY ;
Fairhall, AL .
NEURAL COMPUTATION, 2003, 15 (08) :1789-1807
[3]  
Berry MJ, 1998, J NEUROSCI, V18, P2200
[4]   Fast global oscillations in networks of integrate-and-fire neurons with low firing rates [J].
Brunel, N ;
Hakim, V .
NEURAL COMPUTATION, 1999, 11 (07) :1621-1671
[5]   Effects of synaptic noise and filtering on the frequency response of spiking neurons [J].
Brunel, N ;
Chance, FS ;
Fourcaud, N ;
Abbott, LF .
PHYSICAL REVIEW LETTERS, 2001, 86 (10) :2186-2189
[6]  
Chichilnisky EJ, 2001, NETWORK-COMP NEURAL, V12, P199, DOI 10.1088/0954-898X/12/2/306
[7]  
Cox D. R., 1962, Renewal theory
[8]   The high-conductance state of neocortical neurons in vivo [J].
Destexhe, A ;
Rudolph, M ;
Paré, D .
NATURE REVIEWS NEUROSCIENCE, 2003, 4 (09) :739-751
[9]   Collective behavior of networks with linear (VLSI) integrate-and-fire neurons [J].
Fusi, S ;
Mattia, M .
NEURAL COMPUTATION, 1999, 11 (03) :633-652
[10]   Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking [J].
Gerstner, W .
NEURAL COMPUTATION, 2000, 12 (01) :43-89