2004/03/25 by A. Lerchner, Alexander Lerchner, Gustaf Sterner +9
Biochemistry, Genetics and Molecular Biology · Neuroscience · #FOS: Biological sciences #Neural dynamics and brain function #Neurobiology and Insect Physiology Research #Neurons and Cognition (q-bio.NC) #Visual perception and processing mechanisms #q-bio.NC
paper · pdf · doi:10.48550/arxiv.q-bio/0403037
20 pages, 9 figures
arxiv created 2004/03/25 · openalex publication_date 2004/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stimulus orientations that elicit firing. We also find that the tuning of the noise in the input current is the same as the tuning of the external input, while that for the mean input current depends on both the external input and the intracortical connectivity.