Simplified molecular-input line-entry system
A 3D model of a (bio)moelcule represents a physical 3-dimensions. For an experimental structure, each atom has a 3D coordinate (x, y, z) and, if determined by crystallography, an additional isotropic or aniosotropic B-factor (that models atom fluctuations).

A '1D' SMILES is not a physical 1-dimensional representation, and can be converted to a graph (mathematics) representing the chemical structure. The specification of SMILES CAN retain information about structural isomers, stereoisomers (cis/trans; D/L), but not conformers/rotomers, which, unlike smaller chemical structures, IS restricted to certain favorable regions for larger biomolecules.

By "linkage" if you mean chemical linkage such as a disulfide bond, then SMILES can retain such information. By "interactions", if you mean hydrogen-bonding, salt-bridges and even hydrophobic interactions etc., then SMILES does not code in such information, but neither does a 3D model explicitly -- they are implied from the 3D coordinates for each atom.

Thus, converting from a 3D model to SMILES, you would lose


Unusual bond length and bond angle: they are necessarily specified from the 3D coordinates, but in SMILES (or the subsequent graph), they are taken as 'ideal'.
B-factor or temperature factor
Rotomers: e.g. Proteins have favored dihedral angles in both backbone and side chains, which is not specified in SMILES.
"Interactions": certain intramolecular interaction that is inevitable (e.g. salicylaldehyde) is implied in both SMILES and a 3D model. Most others can only be inferred in the 3D model.