  In the brain, cross-frequency coupling has been hypothesized to result from
the activity of specialized microcircuits. For example, theta-gamma coupling is
assumed to be generated by specialized cell pairs (PING and ING mechanisms), or
special cells (e.g., fast bursting neurons). However, this implies that the
generating mechanisms is uniquely specific to the brain. In fact, cross-scale
coupling is a phenomenon encountered in the physics of all large, multi-scale
systems: phase and amplitude correlations between components of different
scales arise as a result of nonlinear interaction. Because the brain is a
multi-scale system too, a similar mechanism must be active in the brain. Here,
we represent brain activity as a superposition of nonlinearly interacting
patterns of spatio-temporal activity (collective activity), supported by
populations of neurons. Cross-frequency coupling is a direct consequence of the
nonlinear interactions, and does not require specialized cells or cell pairs.
It is therefore universal, and must be active in neural fields of any
composition. To emphasize this, we demonstrate the phenomenon in excitatory
fields. While there is no doubt that specialized cells play a role in
theta-gamma coupling, our results suggest that the coupling mechanism is at the
same time simpler and richer: simpler because it involves the universal
principle of nonlinearity; richer, because nonlinearity of collective activity
is likely modulated by specialized-cell populations in ways to be yet
understood.
