19 January 1954
Memo from LP from Himself
Third Report on Collagen
Linus Pauling 11 January 1954.
During the past year I have been trying to find a structure for collagen to replace the 3-chain structure originally proposed.
All of the work has been based on the assumption that the collagen molecule consists of a single polypeptide chain, and also the assumption that the amide groups all have the trans configuration.
A thorough study was made of helical structures involving a repeating unit of three trans amide group, forming two hydrogen bonds. Over a dozen possible structures were found, of which two or three seemed to merit detailed consideration. No structure was found, however, which accounts satisfactorily for the observed negative infrared dichroism, which indicates that the hydrogen bonds make an angle of about 65° with the fiber axis (this is, rather, the angle made by the carbonyl groups and the NH groups). One promising structure is (10, 10, a). (In this nomenclature the numbers of atoms in hydrogen-bonded rings are given, in a sequence in the direction in which the N-H groups point; a signifies that no hydrogen bond is formed by the nitrogen atom.) This structure makes about three turns of the large helix for ten units, and can be made to have axial length 2.86 A per unit. There seem to be somewhat too small van der Waals contacts, however; moreover, the structure gives about zero dichroism, and cannot be made to give negative dichroism. Another interesting structure is (14, 14, a), a gamma-type structure. Interatomic distances in general seem satisfactory. The structure has one three-residue unit in axial length 2.86 A, and is hence satisfactory in this respect. The structure does not account for the layer-line intensities, inasmuch as it has five units in three turns (ten in six turns, rather than ten in seven turns, as indicated by the layer lines); moreover, it gives positive rather than negative infrared dichroism.
It is, in fact, very hard to find structures which give negative infrared dichroism. The three-chain structure with two cis groups and one trans group per unit, is satisfactory in this respect. Crick’s new structure, with the chains, each having two residues in 2.86 A, is also satisfactory – there are four residues per unit, and two hydrogen bonds, in this structure. It is, however, ruled out by some very bad contacts.
I have found a gamma-type structure with a two-residue unit, its symbol being (11, a). Half the residues form hydrogen bonds. The identity distance is about 1.6 A – perhaps it can be made as large as 1.8 A. The infrared dichroism is negative. It does not seem to be compatible with x-ray data.
I have now made a search for structures which have a repeating unit of either three residues or four residues in 2.86 A, and which form a compound helix with ten units in three turns (or seven turns), giving up, however, the requirement of N-H• • •O-C hydrogen bonds be formed in number one less than the number of residues per unit. This search has been thorough but not exhaustive. No promising structure of the gamma type has been found. No structure of the alpha type with one N-H• • •O-C hydrogen bond per three residue unit has been found – it is not possible to achieve three turns in ten units, even with only one hydrogen bond per unit. Moreover, in a structure of the alpha type the hydrogen bonds are nearly parallel to the axis of the helix, and a three-residue structure with length 2.86 A cannot give negative dichroism. A four-residue structure is satisfactory in this respect. The length of four residues along the axis of the alpha helix is 5.9 A. If this is reduced to 2.86 A, the square of the direction cosine becomes (2.86/5.9)2 = 0.235. The square along each of the directions in the basal plane is then 0.383, the direction cosine being 0.619, as compared with 0.485 along the fiber axis. This gives a negative dichroic ration of 1.28.
I have assumed that van der Waals contacts eliminate structures with a ten-membered hydrogen-bonded ring. I have not found any satisfactory structure based on the sixteen-membered ring. A structure has been found, however, based on the alpha helix, with four residues per repeating unit, and ten units in three turns of the compound helix. In this structure two N-H• • •O-C hydrogen bonds are formed per unit, and a third nitrogen atom forms a twelve-membered ring involving a water molecule. The symbol can be written (13, 13, a, 12*). The water molecule can, in fact, also be hydrogen bonded to the fourth carbonyl oxygen, by way of an additional water molecule. The angles of the two water molecules are tetrahedral. All van der Waals contacts seem to be satisfactory. The predicted length per unit is close to 2.86 A. The average basal-plane component for the three N-H groups, which make angles of 15°, 15°, and 20° with the basal plane is 0.95, and the axial component is 0.29 – a predicted negative dichroic ratio of about three. For the four carbonyl groups the values are 0.86 and 0.39, respectively, giving a negative ratio of 1.6. These values are in approximate agreement with experiment. Badger has reported that the ratio is about 1.6 for carbonyl and only 1.2 for N-H.
There seems to be only one serious difficulty with this structure. Using the value 1.34 for the density and 95 for the average residue weight, the spacing for the plane 10.0 is calculated to be 12 A, whereas the value 10.4 A has been reported by Astbury for dehydrated collagen, and about 11 or 11.5 for collagen in equilibrium with the atmosphere at ordinary humidity. The difference between 12 A and 10.4 A corresponds to the ratio of four residues to three residues.
The molecules are predicted to be about 12 A in diameter, if the larger side chains are packed into the cavity down the center.
Bear has suggested that the well crystallized parts of collagen have four residues in the length 2.86 A, and perhaps consist mainly of the smaller residues. The presence of what seems to be a meridional reflection with spacing about 4.1 A suggests that there may be two kinds of molecules present in collagen. Further evidence is needed to settle the question.
cc: RB Corey