Here are some links about the effects of salt on protein (from a chemistry/physics perspective).
How Does Salt Affect Protein? | LIVESTRONG.COM
The basics of it though are that salt draws out the water in muscle cells so it's possible that some water soluble nutrients might be lost during a salting process, however water is lost during the cooking process also (incidentally, this is why raw veggies contain more nutrients than cooked) so the same can be said of cooking meat. In the case of brining meat, the salt is already bonded with water at a higher concentration than is contained in the meat. The water in the meat will try to balance itself with the water outside the meat and therefore draw the salt into it. This also means it may lose some water soluble nutrients as the concentration of nutrients dissolved in the water in the muscle tissue tries to balance with the concentration of those nutrients outside the muscle tissue. However the increased salt in the muscle tissue will help hold in extra water during the cooking process (extra heat is required to cause the water to turn to steam since the bond between it and the salt must first be broken) thus helping preserve any remaining water soluble nutrients during the cooking process (although some may still be lost).
As for the proteins themselves, they are denatured, not destroyed. Denaturation is when the tertiary and possibly secondary structure of the protein is destroyed. However, this only affects the shape of the protein molecule. The primary structure, created by petide bonds, remains in tact, so the particular amino acid composition remains in tact. In order to actually destroy the protein and lose part of the protein nutrients (amino acids), you'd have to break the peptide bonds, and salt doesn't create a strong enough chemical reaction to do that.
So, bottom line, brining:
Some water soluble nutrients (minerals such as iron, magnesium) might be lost during the process.
Meat will have a higher salt content (obviously).
Meat will have a higher water content (makes it juicier).
Protein nutrients will remain in tact.