How does trimethylamine N-oxide counteract the denaturing activity of urea?

Trimethylamine N-oxide, TMAO, stabilizes globular proteins and is able to counteract the denaturing activity of urea. The mechanism of this counteraction has remained elusive up to now. A rationalization is proposed grounded on the same theoretical model used to clarify the origin of cold denaturation, and the denaturing activity of GdmCl versus the stabilizing one of Gdm(2)SO(4) [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252; G. Graziano, Phys. Chem. Chem. Phys., 2011, 13, 12008-12014]. The fundamental quantities are: (a) the difference in the solvent-excluded volume on passing from the N-state to the D-state, calculated in water and in aqueous osmolyte solution; (b) the difference in energetic attractions of the N-state and the D-state with the surrounding solvent molecules, calculated in water and in aqueous osmolyte solution. In aqueous 8 M urea + 4 M TMAO solution, the first quantity is so large and positive to counteract the second one that is large and negative due to preferential binding of urea molecules to the protein surface. This happens because aqueous 8 M urea + 4 M TMAO solution has a volume packing density markedly larger than that of water, rendering the cavity creation process much more costly. The volume packing density increase reflects the strength of the attractions of water molecules with both urea and TMAO molecules. This mechanism readily explains why TMAO counteraction is operative even though urea molecules are preferentially located on the protein surface.