Summations Only

I should say that there have been some studies done on the quantum mechanical effects in the brain. On the biological side, the "typical" time scale for a process in the brain is around 1 millisecond. In concrete terms, the electric signals in the brain only contain information down to the millisecond level. Any detail in the signal on smaller scales has no meaning to the rest of the brain. (I'm sure there are others here much more well-versed in these things than me)However the brain is a nightmare when it comes to trying to create quantum mechanical superposition. Superposition is the common microscopic effect where an object has a probability of possessing several different values of a quantity, rather than a 100% probability of possessing one value. For example, a regular spinning top is either spinning left or right, not 40% chance of spinning left and 60% chance of spinning right. Such states are the basis of quantum mechanics, however the brain is not very conducive to these states.First of all, it's a very warm place in absolute terms (310 Kelvin). Secondly there is constant collisions between the neural material and ions such as Cl-, the ions themselves having thermal fluctuations due to the heat. Collisions with these ions external to the cell will count as a measurement that collapses the wavefunctions of the neurons to single definite values. Secondly there are water molecule collisions, as well as interactions with distant molecules.All together these mean that the average wavefunction in the brain collapses within:
0.00000000000000000001 seconds / 10^(-20) seconds*
compared with
0.001 seconds, which is the lowest meaningful timescale for the information processing in the brain.*This is not guess work, the original paper is:
Tegmark, M. (2000). Importance of quantum decoherence in brain processes. Physical Review E 61, 4194—4206.Available for free here: http://arxiv.org/abs/quant-ph/9907009A more readable account by A. Litt et al for a talk at the university of Waterloo:
http://cogsci.uwaterloo.ca/Articles/quantum.pdfDecoherence is basically the process where quantum superpositions die off.

If I'm reading you correctly, you're stating that the brain might have effects due to chaos theory. I would say this is definitely true, I'd be shocked if the brain had no chaos theory like effects considering it's such a complicated system. All I'm saying is that there is absolutely no way quantum effects can particpate, they occur at timescales far smaller than timescales of the dynamics of the brain and any chaos theoretic effects would work on those dynamics.

It doesn't really work like this. Quantum effects don't really feed into classical chaos in the way you're imagining because of an effect known as decoherence and the linearity of quantum mechanics. Quantum Dynamics is completely linear, so small changes in the initial state never cause large changes in the evolution. Quantum Mechanics suppresses classical chaos for this reason. So rather than feed on Quantum Mechanical fluctuations, chaos is driven away by them.This is where decoherence comes in. In the brain, for example, the atomic systems are constantly interacting with other atomic systems. These interactions count as a measurement which kills off the quantum effects and this is what actually allows classical chaos to appear. The classical chaos will then act on the time scales of whatever the classical dynamics of the brain are. It isn't effected by the quantum fluctuations because any time it tries to "reach that far down" quantum linearity kills it.Quantum fluctuations have no more of an effect on the evolution of a chaotic classical system than they do on a non-chaotic one.

That's basically the answer, as you've said the region could be very small. If you do the calculations it turns out to be very small indeed, atomic scale. So the quantum effects don't really show up outside the atoms and molecules themselves. Which is basically no different to what goes on when you drop a stone. There are quadrillions of quantum entanglements inside a stone, but due to interaction with the environment they never grow larger than the individual atoms and molecules. So quantum mechanics is necessary for the chemistry of atoms in the stone but not for the evolution of the stone as an object itself. It's the same with the brain.