  Non-coding RNA molecules fold into precise base pairing patterns to carry out
critical roles in genetic regulation and protein synthesis. We show here that
coupling systematic mutagenesis with high-throughput SHAPE chemical mapping
enables accurate base pair inference of domains from ribosomal RNA, ribozymes,
and riboswitches. For a six-RNA benchmark that challenged prior
chemical/computational methods, this mutate-and-map strategy gives secondary
structures in agreement with crystallographic data (2 % error rates), including
a blind test on a double-glycine riboswitch. Through modeling of partially
ordered RNA states, the method enables the first test of an 'interdomain
helix-swap' hypothesis for ligand-binding cooperativity in a glycine
riboswitch. Finally, the mutate-and-map data report on tertiary contacts within
non-coding RNAs; coupled with the Rosetta/FARFAR algorithm, these data give
nucleotide-resolution three-dimensional models (5.7 {\AA} helix RMSD) of an
adenine riboswitch. These results highlight the promise of a two-dimensional
chemical strategy for inferring the secondary and tertiary structures that
underlie non-coding RNA behavior.
