Of course we know that the brain of every animal contains cells--nerve cells, support cells and more--and that cells are made up mainly of organic molecules. Their membranes and contents are built from lipids, proteins, nucleic acids, sugars, etcetera, all of which are built with a carbon-based chemistry.

But, must it be this way? Let's approach this with a thought experiment.

Here is a very typical nerve cell with its dendrites sprouting from the cell body and its axon leaving the cell body on its way to communicate with other neurons:

Neuroscientists have learned a great deal about how an axon functions to carry a neuron's signal--the action potential--from the cell body to the synapses at the axonal tip, however far away that is. In fact we know so much, and in such great detail that it is conceivable to imagine a procedure in which we take out the axon itself and replace it with a self-powered integrated circuit (sort of like a computer chip) designed based on the exact functioning of an axon.

Yes, we still have a bit of work to do on how to interface the cell edges with the silicon of the chip, but even that's under study and in any case is not a theoretical problem.

So, here we are with what might we might describe as a 'prosthetic' axon in our thought-experimental neuron, with the result that the whole thing functions exactly as it did naturally.