Signaling in the Brain: In Search of Functional Units

What are the functional units of the brain? If the function of the brain is to process information-carrying signals, then the functional units will be the senders and receivers of those signals. Neurons have been the default candidate, with action potentials as the signals. But there are alternatives: synapses fit the action potential picture more cleanly, and glial activities (e.g., in astrocytes) might also be characterized as signaling. Are synapses or nonneuronal cells better candidates to play the role of functional units? Will informational signaling still be the best model for brain function if we move beyond the neuron doctrine?