Turing Machines and the Brain

I was listening to NPR this morning.  A surgeon was describing his impression of the operation he was performing on a girl's brain.  He commented that this was the most amazing part of the operation... we can see where Maribel thinks and feels - this is Maribel.  My first thought was, no Maribel is a program running on this hardware.  Part of Maribel, how she identifies herself as Maribel, would be the consistent input of sensations from her body, so Maribel isn't located here in the brain exactly at all.  Then I started thinking about what sort of computer the brain was.  Every sort of computer we have built ourselves is a Turing machine in effect.  The Instruction Pointer trundles up and down a strip (code segment) reading instructions, calculating, and writing out results.  Meanwhile the brain is not built anything like this.  Neurons individually are sum and difference calculators.  They take inputs from many other neurons, sum the excitatory inputs, sum the inhibitory inputs, subtract one from the other, and then fire or not depending on whether the result is greater than some threshold.  The nets of neurons form feedback loops which generate quasi-periodic waves of excitation with some of the information being encoded by the amplitude of the waves across the surface of the cortex.  Meanwhile, there is yet another level of calculation going on.  The glial cells support the individual synapses and share information regionally, this determines which synapses are strengthened and which are removed.  The pruning and augmentation of synapses could be considered part of the long term calculation which the brain is performing as well, and the glial cells mediate this, so there is another level of cells involved in the calculations the brain is making apart from the neurons.  I wondered if this structure could be modeled by a Turing machine.  Supposedly, everything that is calculable can be reproduced by a Universal Turing Machine, which is basically what a computer is at the machine language level, but can the brain's calculating architecture by modeled by this structure?  If the brain is not representable as a Turing machine, then some of its operation would not representable as calculation, at least according to the Church-Turing theorem, and to this degree, it could not be captured by a computer program.