John McCrone wrote a brief essay on this topic several years ago in the now-defunct Science and Consciousness Review (or, can anyone point me to a newer URL that works??). I thought that it is worth repeating and abstracting here:
Our entire brain is recycled about every two months, and different components of the synapses that transmit information between nerve cells replace themselves, molecular for molecule, on a time scale of hours to days. All of these synapses and the intricate network of trillions of connections that they form have been crafted by our experience to make us who we are. How can all this remain stable when the large molecules that make synapses seem to be boiling, falling apart nearly as soon as they are made?
Synapses turn out to be reflecting a living confluence of top-down and bottom-up pressures.. (Bottom up: gene or RNA expression patterns remembering what the state of a synapse should be; top down: a constant replaying, or jangling trace, that helps keep labile synapses stabilized). The information is out there in the whole system and it is making the synaptic patterns we observe.
"This kind of topsy-turvey picture can only be resolved by taking a more holistic view of the
brain as the organ of consciousness. The whole shapes the parts as much as the parts shape
the whole. No component of the system is itself stable but the entire production locks together
to have stable existence. This is how you can manage to persist even though much of you is
being recycled by day if not the hour."