You are mixing two things together. There are no proteins on a fatty acid molecule. Proteins are made up of polymer chains of amino acids. Fatty acids are a totally different type of chemical. A fatty acid is a long hydrocarbon chain that is capped with a carboxylic acid. The fatty acids in lipids are bound to a glycerol molecule via an ester linkage. Unsaturated fatty acids have no carbon carbon double bonds on their hydrocarbon chains. You may be confusing the terms amino acid and fatty acid in this case.