Protein Structure Parameters
It depends on how accurate you want the description to be. Ideal bond lengths are normally assumed, so the structure can be described using φ, ψ, ω (for the backbone) and χ1-χ5 (for the sidechain) angles. This is what is used in most cases. However, the positions of the hydrogens in the sidechains are not uniquely defined by this description. This also does not describe hydrogen bonds and disulfide bridges, but those could be deduced from the relative positions.

You can get more information here: http://kinemage.biochem.duke.edu/teaching/anatax/html/anatax.1b.html

This description should be enough for most applications, though.