Effects of synaptic noise and filtering on the frequency response of spiking neurons.

Noise can have a significant impact on the response dynamics of a nonlinear system. For neurons, the primary source of noise comes from background synaptic input activity. If this is approximated as white noise, the amplitude of the modulation of the firing rate in response to an input current oscillating at frequency omega decreases as 1/square root[omega] and lags the input by 45 degrees in phase. However, if filtering due to realistic synaptic dynamics is included, the firing rate is modulated by a finite amount even in the limit omega-->infinity and the phase lag is eliminated. Thus, through its effect on noise inputs, realistic synaptic dynamics can ensure unlagged neuronal responses to high-frequency inputs.

[1]  C. E. Adams.  Tables of mathematical functions , 2022 .

[2]  H. Davis.  Tables of mathematical functions , 1965 .

[3]  Bruce W. Knight,et al.  Dynamics of Encoding in a Population of Neurons , 1972, The Journal of general physiology.

[4]  J. Hammersley,et al.  Diffusion Processes and Related Topics in Biology , 1977 .

[5]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .

[6]  H. Tuckwell.  Introduction to Theoretical Neurobiology: Linear Cable Theory and Dendritic Structure , 1988 .

[7]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[8]  Idan Segev,et al.  Methods in Neuronal Modeling , 1988 .

[9]  C. Doering,et al.  Mean exit times for particles driven by weakly colored noise , 1989 .

[10]  B. M. Fulk.  MATH , 1992 .

[11]  J. Movshon,et al.  Spike train encoding by regular-spiking cells of the visual cortex. , 1996, Journal of neurophysiology.

[12]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[13]  Kenneth D. Miller,et al.  Physiological Gain Leads to High ISI Variability in a Simple Model of a Cortical Regular Spiking Cell , 1997, Neural Computation.

[14]  P. Hagan,et al.  Colored noise and a characteristic level crossing problem , 1998 .

[15]  N. Brunel,et al.  Firing frequency of leaky intergrate-and-fire neurons with synaptic current dynamics. , 1998, Journal of theoretical biology.

[16]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[17]  Wulfram Gerstner,et al.  Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking , 2000, Neural Computation.