The last time I read into this subject, there were neural network models that achieved around 80% accuracy. There's a research group at my uni dedicated to this research area.
I think you're referring to the prediction of "secondary structure" of proteins, which was attempted using neural network models as early as 1989. [1] Predicting secondary structure is child's play compared to predicting the folded tertiary structure of a protein, hence the continued use of insanely computationally expensive ab initio folding efforts like Folding@Home.
[1] http://www.ncbi.nlm.nih.gov/pmc/articles/PMC286422/