Woud NMR be a reasonable assay? What is the feasibility to detect 13C-methane binding or consumption in whole cells or extracts using appropriate NMR technologies.

Depending on how big your protein is, I think the technique you may be looking for is saturation transfer difference (STD) NMR. In STD, the broad underlying signal of the protein is saturated. During the formation of a transient (KD=10-2 to 10-8) complex with methane some of this saturation is transferred to the methane, which is carried away when the methane dissociates. The result is a decrease in the sharp methane signal which is proportional to the amount of ligand bound at a given moment.

http://pubs.rsc.org/en/content/articlehtml/2013/mb/c2mb25395j

http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1521-3773(19990614)38:12%3C1784::AID-ANIE1784%3E3.0.CO;2-Q/abstract

http://pubs.acs.org/doi/full/10.1021/ed101169t

general reference for nmr techniques of ligand binding

http://facilities-dc.unh.edu/TRC/REFERENCES/NMR/Fielding2007.pdf

Unlike most NMR techniques this actually works better for large proteins than small ones. It can even be perform directly in cells. In more complex molecules than methane it also provides epitope mapping in that the signal from the binding parts of the ligand is decreased more than the non-binding parts.