Stuart Hameroff seems to think so. Here's his paper from the latest issue of Cognitive Science. Prepare to be stunned by the copious truckloads of woo-woo.

In the Orch OR model, quantum computations are proposed to occur in microtubules in cytoplasm within gap junction-linked dendrites (dendritic webs; see Fig. 1) of these same brain neurons in cortex and other regions (i.e. embedded in integration phases of integrate-and-fire cycles). The proposed quantum computations/integrations are discrete events of roughly 25 msec duration (coupled to gamma synchrony EEG) with each quantum computation culminating in a conscious moment (e.g., at 40 Hz).

Get all that? Now one of the ironies here is that the model was cooked up by Hameroff and Roger Penrose, who wrote The Emperor's New Mind, a diatribe against the ability to create AI.

And yet if any Emperor were stark naked, it would be Orch OR, with consciousness arising from quantum computations in the microtubules of dendrites. Hameroff's article is a response to Litt et al.'s 2006 article "Is the brain a quantum computer?", which they resoundingly answer "no" based on three reasons:

We present three classes of reason why it is implausible that quantum mechanical processes are relevant to explaining how brains operate. Our first argument is computational: that quantum mechanisms are unlikely to play a role in information processing in the brain. Our second argument is biological: that there are several reasons why the essential functionality of an organic system such as the brain should not require quantum mechanical explanation. Finally, our third argument is psychological: that there is no reason to believe that quantum computing contributes to mental phenomena.

They do a fine job of pointing at the Emperor and loudly yelling, "Look, he's nekkid!" Orch OR is a pile of nonsense masquerading as a viable theory. As Patricia Churchland is quoted in the Hameroff article:

...the explanatory vacuum is catastrophic. Pixie dust in the synapses is about as explanatorily powerful as quantum coherence in the microtubules.

Yep.

I especially admire Litt et al. because it takes a huge amount of patience and effort to wade through unfounded, jargon-riddled theorizing and lay out the reasons why it shouldn't be taken seriously. It's hard work, and they deserve kudos. It's easier to take apart work that's not theoretical, that actually makes testable scientific claims. It's a lot more difficult to go after theorizing, especially theorizing that posits interactions at the quantum level that are virtually impossible to measure.

In other news, I'm submitting my theory of consciousness based on integer spin dynamics in the Bosons of the neurotransmitters gamma-aminobutyric acid (GABA) and glutamic acid (glutamate). Wish me luck!