We report on the size, shape, structure, and interactions of lysozyme in the ternary system lysozyme/DMSO/water at low protein concentrations. Three structural regimes have been identified, which we term the "folded" (0 < phi(DMSO) < 0.7), "unfolded" (0.7 <= phi(DMSO) < 0.9), and "partially collapsed" (0.9 <= phi(DMSO) < 1.0) regime. Lysozyme resides in a folded conformation with an average radius of gyration of 1.3 +/- 0.1 nm for phi(DMSO) < 0.7 and unfolds (average R-g of 2.4 +/- 0.1 nm) above phi(DMSO) > 0.7. This drastic change in the protein's size coincides with a loss of the characteristic tertiary structure. It is preceded by a compaction of the local environment of the tryptophan residues and accompanied by a large increase in the protein's overall flexibility. In terms of secondary structure, there is a gradual loss of alpha-helix and concomitant increase of beta-sheet structural elements toward phi(DMSO) = 0.7, while an increase in phi(DMSO) at even higher DMSO volume fractions reduces the presence of both a-helix and beta-sheet secondary structural elements. Protein-protein interactions remain overall repulsive for all values of phi(DMSO) An attempt is made to relate these structural changes to the three most important physical mechanisms that underlie them: the DMSO/water microstructure is strongly dependent on the DMSO volume fraction, DMSO acts as a strong H-bond acceptor, and DMSO is a bad solvent for the protein backbone and a number of relatively polar side groups, but a good solvent for relatively apolar side groups, such as tryptophan.