Are you suggesting there is no room for quantum effects in the brain? Honest question because I thought determinism is out of fashion now-a-days for that reason.
No one in "mainstream" neuroscience or cell biology takes these proposals seriously. Hameroff and Penrose have proposed some possible mechanisms (e.g., dendritic lamellar bodies), but none of these have panned out experimentally; for example, the DLBs are in the wrong place. They keep revising the theory around these data, but I think a lot of experimentalists have lost interest. I gather there are other more philosophical/first principles arguments against this too.
It would be neat if it were true though....
The deterministic effects in the brain must be negligible, as you can't reasonably reproduce the internal and external state of 100 billion neurons, swimming in a incomprehensibly complex chemical soup that is altered by the brain itself, at the same time experiencing the changing reality.