Brain function, nonlinear coupling, and neuronal transients

The brain can be regarded as an ensemble of connected dynamical systems and as such conforms to some simple principles relating the inputs and outputs of its constituent parts. The ensuing implications, for the way we think about, and measure, neuronal interactions, can be quite profound. These range from 1) implications for which aspects of neuronal activity are important to measure and how to characterize coupling among neuronal populations; 2) implication for understanding the emergence of dynamic receptive fields and functionally specialized brain architectures; and 3) teleological implications pertaining to the genesis of dynamic instability and complexity, which is necessary for adaptive self-organization. This review focuses on the first set of implications by looking at neuronal interactions, coupling, and implicit neuronal codes from a dynamical perspective. By considering the brain in this light, one can show that a sufficient description of neuronal activity must comprise activity at the current time and its recent history. This history constitutes a neuronal transient. Such transients represent an essential metric of neuronal interactions and, implicitly, a code employed in the functional integration of brain systems. The nature of transients, expressed conjointly in different neuronal populations, reflects the underlying coupling among brain systems. A complete description of this coupling, or effective connectivity, can be expressed in terms of generalized convolution kernels (Volterra kernels) that embody high-order or nonlinear interactions. This coupling may be synchronous, and possibly oscillatory, or asynchronous. A critical distinction between synchronous and asynchronous coupling is that the former is essentially linear and the latter is nonlinear. The nonlinear nature of asynchronous coupling enables the rich, context-sensitive interactions that characterize real brain dynamics, suggesting that it plays an important role in functional integration.