Protein Structure and Information Content 109 



Kauzmann (9) has given an excellent discussion of the known types of 

 intramolecular bonds which are responsible for protein folding and which should 

 therefore affect 7^. The most common type is the H— bond, especially those 

 formed between the carboxyl O and the amide H. These are essentially non- 

 specific bonds which can form between any pair of amino acid residues in 

 which the C — O and N — H bonds are oriented at the proper angle. A stronger, 

 more specific, but less common H^ — bond can form between the phenolic 

 OH groups of tyrosine and the carboxyl group of glutamic or aspartic acid 

 (9, 10). Another common type of bond stems from the van der Waals forces, 

 which can exist between the atoms in different portions of the same or neigh- 

 boring chains. The third type discussed by Kauzmann is the so-called hydro- 

 phobic bond, which is distinct from the more commonly discussed van der 

 Waals bonds. This results from the tendency of the more hydrophobic amino 

 acid residues to avoid the aqueous phase and adhere together to form a sort of 

 intramolecular micelle. These bonds, although they possess a low order 

 of specificity, may contribute a good deal of stability since they arise as a 

 result of the fact that the more hydrophobic amino acids cannot participate 

 in the strong H-bonding with the solvent water molecules. Salt bridges, which 

 are the ionic bonds formed between the negatively charged (glutamic and 

 aspartic) and positively charged (lysine and argenine) residues, are another 

 type. However, Jacobsen and Linderstrgm-Lang (11) have presented evidence 

 which indicates that these bonds are of negligible importance as intramolecular 

 protein bonds. One of the most important types of intramolecular bond (at 

 least according to current theories (12)) is the highly specific S — S bond formed 

 between cysteine residues in different portions of the same or neighboring 

 chains. The formation of disulfide bonds as well as the 'strong' H-bonds greatly 

 reduces the number of physical states available to the molecule since they can 

 only be formed at a very few sites in the molecule. Since these two types of bond 

 are the most specific of the intramolecular bonds, they are undoubtedly the 

 most effective in determining variations in structure between different kinds of 

 proteins. 



Repetitions Structures: Intramolecular bonds fonned in such a fashion 

 as to produce repetitious structures reduce 4 tremendously. In the helical or 

 pleated sheet structures proposed by Pauling, Corey and Branson (8) (and 

 illustrated in (13)) the number of free parameters necessary to describe the 

 configuration completely is extremely low and therefore the information content, 

 /f, is also very lov/. In the helices it is only necessary to specify the length 

 (that is, the total number of residues R), the pitch (3.7 or 5.1 residues per turn) 

 and the exact orientation of the helix with respect to a reference point in the protein. 



An estimate of the lower bound of /^ can be obtained from these factors 

 as follows: 1) To find the exact number of residues, /?, in a helix requires about 

 2 log2 R bits.* 2) The pitch requires 1 bit (3.7 or 5.1 residues/turn of the helix). 



* It is rather interesting that the determination of the value of any integer, either + or — 

 (other than zero), requires exactly In bits, where 2"~^ < i? < 2" (which is close to 2 logs R): 

 II bits are necessary to find that |^| is in the range indicated, // — 1 bits to find \R\ and 1 bit to 

 determine R, i.e. the sign. For example, let R = —48: six questions which can be answered 

 by yes or no will show that \R\ is 33-64; five more questions will determine that of the 32 

 possible values \R\ = 48 and one yes or no question determines R = —48. Thus, 2* < i? < 2« 

 and 111 = 12 bits. 



