Natural logarithmic relationship between brain oscillators

Behaviorally relevant brain oscillations relate to each other in a specific manner to allow neuronal networks of different sizes with wide variety of connections to cooperate in a coordinated manner. For example, thalamo-cortical and hippocampal oscillations form numerous frequency bands, which follow a general rule. Specifically, the center frequencies and frequency ranges of oscillation bands with successively faster frequencies, from ultra-slow to ultra-fast frequency oscillations, form an arithmetic progression on the natural logarithmic scale. Due to mathematical properties of natural logarithm, the cycle lengths (periods) of oscillations, as an inverse of frequency, also form an arithmetic progression after natural logarithmic transformation. As a general rule, the neuronal excitability is larger during a certain phase of the oscillation period. Because the intervals between these activation phases and the temporal window of activation vary in proportion to the length of the oscillation period, lower frequency oscillations allow for an integration of neuronal effects with longer delays and larger variability in delays and larger areas of involvement. Neural representations based on these oscillations could therefore be complex. In contrast, high frequency oscillation bands allow for a more precise and spatially limited representation of information by incorporating synaptic events from closely located regions with short synaptic delays and limited variability. The large family of oscillation frequency bands with a constant relation may serve to overcome the information processing limitations imposed by the synaptic delays.