Cool! I'd like to believe that there's way more complexity stashed away in the brain than is readily apparent, perhaps in those microtubule structures.
But after seeing some of the presentations from Mark Tilden (the engineer behind some of the RoboSapiens toys and a few other DIY BEAM robotics kits) on how sophisticated behaviors can emerge from some of the dirt-simple neural networks cobbled together from a handful of transistors, sensors, and motors in a feedback loop, it's pretty clear that there's a lot about neural networks that we just don't understand.
His simplest BEAM bots would just have maybe 9 transistors hooked up to a light sensor and one or two step motors. Depending on whether you hooked up the light sensor for positive feedback or negative feedback, the thing would eventually start twitching itself towards or away from a light source. They were trying to characterize the system behavior somehow by watching the electrical signals at various points in the network, but it still kinda defied reason. The various voltages would flop around randomly at first, but eventually all of them would start oscillating regularly in a pattern that would vibrate the bot in a particular direction using its two rudimentary "appendages". They kinda attributed it to "chaos systems theory" for emergent behavior of asynchronous neural networks, since chaos was like the handwavy buzzword of the 90s that would solve all of our large intractable problems. And of course one of the fundamental characteristics of these neural networks is that they're pretty hard to program "by hand" , you pretty much can only train them and let them adapt themselves, and there's not really all that much you can discern about how they actually work by watching parts of them or prodding them with electrodes (or tweaking their weighting values) from the sidelines.
So given that and the fact that brain networks appear to always be reconfiguring themselves to become more compact and efficient with each night's sleep, I think a lot of that can account for a lot of the "complexity gap" based on neuron counts in the brain vs. estimates of how difficult it would be to program a computer to perform common tasks like vision processing, memory recall, and speech. I think a lot of behavior is encoded in various complex rhythms of neuron groups firing in chaotic feedback loops, which would also give us our sense of time, and perhaps help explain why we can't maintain consciousness indefinitely.
I'm sure quantum physics plays some part in optimizing parts of the process because biochemistry, but I doubt it does anything critical, like hiding tons of information in other "dimensions" through quantum superposition or somesuch... though it ought to be a neat way to compress data, like holographic storage. I don't see a lot of crystal-like structures in the brain, though. That said, there's gotta be something at that scale, since even single-celled organisms have some ability to react to stimuli by waving their flagella and stuff appropriately.
Anyway, enough handwaving for today :P