Does Life Use a Non-Random Set of Amino Acids?

An interesting research paper was recently published in the Journal Astrobiology by Gayle K. Philip and Stephen J. Freeland, which asks, "Did Evolution Select a Nonrandom Alphabet of Amino Acids?"

The article notes that there exists no strict limitation on the character or type of amino acids which can be used in living systems. Indeed, biology could conceivably have used a different amino acid alphabet, and there appears to be a fairly wide range from which it could have chosen. But is there ...