I think that the time has now come for us to finish up the job on collagen.
I have finally become convinced that there is no reasonable alternative to the (10,10,a)
structure for collagen, and that our job now is to refine the structure somewhat (this
involves moving the atoms only a few hundredths of an Angstrom), and gathering and
presenting the evidence about it.
I have just carried out another effort to find an alternative structure to (10,10,a),
without success.
I think that it is very unlikely that I have overlooked the correct structure in my
search. Moreover, the fact that three structures for collagen have been published
in the last few months, by Crick, by Huggins, and by Ramachandran and his coworkers,
shows that other investigators have been searching, too, and it is of some significance
that they have not proposed a structure that is acceptable. It is, of course, true
that they have apparently not discovered the (10,10,a) structure, and that accordingly
they might have overlooked the correct structure, if it is a different one.
I shall summarize the present situation in the following paragraphs.
1. It is likely that the amide groups are all in the trans configuration, although
possible that the proline amide group has the cis configuration. (I shall use proline
in this discussion to refer to both proline and hydroxyproline, when discussing the
main chain.) There is evidence, in the papers of Mizushima and Simanouti, that the
trans configuration is more stable than the cis configuration, by significant amount.
I think that the argument would, however the proline and hydroxyproline groups, because
for them the nitrogen atom forms two single bonds to carbon atoms, which would behave
in a nearly equivalent manner. Professor Badger says that the spectroscopic data pretty
well show that the amide groups have the trans configuration. It is, I think, likely
that the spectroscopic argument involves the N-H vibration, and that his conclusion
accordingly applies only to the non-proline groups.
Our original structure was of the type cis-cis-trans. It does not agree with the x-ray
data. I have not been able to formulate a cis-cis-trans structure that is acceptable.
The Huggins structure, which is of this type, is probably unsatisfactory because of
a non-coplanarity of the bonds formed by the nitrogen atom. I have not made a further
detailed study of it.
I have not been able to find any satisfactory structure of the type cis-trans-trans.
I think that all structures of this type can be ruled out if the assumptions are made
that two hydrogen bonds must be formed for every three residues, the repeating unit
being a three-residue unit, and that the orientation of the hydrogen bonds must conform
roughly to the limitation set by the infrared dichroism.
The following detailed discussion relates accordingly to trans-trans-trans structures,
involving a repeating unit of three residues.
2. Elimination of structures involving three chains twisted about one another. On
5 March 1954 Professor Badger told me that in glycylglycine the N-H vibration, 3300
cm-1, lies about 10º from the N-H axis, in the N•••O direction, and that the amide II
vibration (which is probably to be attributed largely to the wagging of N-H) is very
nearly perpendicular to it, and in the plane of the group.
The direction assigned to the amide II vibration by Badger is within 2 degrees of
the line stretching across the amide group between the two α-carbon atoms at its ends.
Accordingly the observed dichroism of the amide II vibration, which occurs at about
1550 cm-1, provides a very simple way of drawing conclusions about the folding of the polypeptide
chain.
Let us assume that the amide II vibration lies within 10 degrees of the αC-αC axis,
and draw conclusions from this.
If there are three chains, each amide group must stretch 2.86 A along the fiber axis.
The distance between α-carbon atoms is 3.83 A. Hence the angle is 48º between the/axis
and the basal plane. This corresponds to a positive dichroism of 2.54, which is far
greater than the observed 1.22 (Badger). The observed dichroism corresponds to an
angle of 38º, which is 10º less than calculated, and accordingly possible. However,
there is no acceptable way of arranging three chains, with suitable hydrogen bonds.
3. Structures involving a single chain.
I have made an exhaustive analysis of structures involving a single chain, with a
repeating unit of three trans groups, forming two hydrogen bonds.
Several of these structures have an axial length per unit of 2.86 A. The include (10,10,a),
(14,14,a), (16,16,a), and (10,16,a). The last three of these four are easily eliminated
by the observed infrared dichroism.
First let us consider the amide II vibration. The observed dichroism is positive,
with value 1.22. If we assume that this vibration is along the α-carbon axis of the
amide group, then the positive dichroism eliminates all structures of the single-chain
all-trans type in which the x coordinates of the α-carbon atoms show only increase
in value along the chain. The chain must progress the distance 2.86 A along the z
axis, in the unit of three residues. If each residue is occupies one third of this
distance, 0.95 A, the axis is at the angle 14.4º with the basal plane, and the dichroism
is negative, the ratio being 17.6. The closest approximation to positive dichroism
occurs when two of the residues have zero component along the figure axis, and the
third the full component 2.86. The dichroism is still then negative, with ratio 1/2.2.
This is so far from the observed 1.22/1 that we conclude that any three-chain all-trans
structure must be a retrograde structure, with one residue having a negative component
of its α-carbon axis along the fiber axis. (Or perhaps two residues having negative
components.)
The structures (14,14,a), (16.16,a), and (10,16,a) are all non-retrograde in character.
All have calculated dichroisms for amide II that are strongly negative, approximately
1/7 in each case. These structures may accordingly be ruled out.
All three structures may also be ruled out by consideration of the infrared dichroism
for the N-H stretching vibration and for the amide I vibration (which is largely the
C=O stretching vibration). These vibrations both show negative dichroism. The calculated
dichroisms for the three structures just discussed are strongly positive, and the
structures are hence eliminated.
4. The (10,10a) structure and the observed infrared dichroisms.
The calculated dichroism for the amide II vibration is 1.23 for the (10,10,a) structure
when all three amide groups are counted, and 1.16 when 70 percent of one amide group
is occupied by proline and hydroxyproline, and considered not to contribute to this
vibration; these values correspond to positive dichroism, and are acceptable.
The calculated dichoirc ratios for the N-H and amide I vibrations, assuming them to
be along the N-H axis or C=O axis, are approximately 1, whereas these vibrations are
observed to show negative dichroism, 1/1.8 and 1/1.2, respectively. There is enough
uncertainty about the effective directions of the dipole moments for these vibrations
in the complex structure of the coupled hydrogen bonds that, however, the lack of
complete agreement cannot be used to rule out the structure. The structure may be
considered to be composed of three amide groups (alternating in the polypeptide chain)
that are coupled together by two hydrogen bonds, and that may form a unit responsible
for the infrared absorption. (The interaction is probably large for these vibrations,
and small for the amide II vibration.) The configuration of this unit in space is
such as to indicate that the effective dipole moments form a smaller angle with the
basal plane than that formed by the N-H and C=O axes. This is presumably the explanation
of the observed negative dichroisms. It may be desirable to carry out a somewhat detailed
theroretical discussion of this question.
5. Dimensions of the structure.
The x-ray data indicate that there are three residues for collagen in the axial length
2.86 A, and that there probably is a repeating unit of three residues forming a helix
with ten units in three turns or in seven turns. The (10,10,a) structure with planar
amide groups and 110º bond angles gives 2.75 A per unit and 4.5 units per turn, rather
than 3.3. If two of the residues in a unit are twisted about the C'N axis, through
about 6º, the structure can be deformed to 2.86 A per unit and 3.3 units per turn.
This corresponds to a strain energy of about 0.3 kcal/mole for each of the two residues.
The same result can be achieved by distributing the deformation over several features
of the structure – changing several bond angles by about 1 degree apiece, bending
the double C'-N bond a little, and rotating about it through a smaller angle, perhaps
three degrees. A total strain distributed over n features rather than one decrease
the strain energy to 1/n of its value. It is accordingly probable that the amount
of deformation involved here is not more than a few tenths of a kcal/mole per unit.
The deformation is presumably the result of steric repulsion between the δ-carbon
atom of the proline ring and the adjacent (once removed) amide group, and perhaps
also between the carbonyl oxygens and the adjacent amide groups.
The orientation of the α-carbon atom adjacent to the proline nitrogen is a satisfactory/for
formation of the proline ring.
6. Side chains.
The structure provides satisfactory positions for side chains. Of the two non-proline
α-carbon atoms, one projects toward the axis of the compound helix, and one is on
the outside. It cannot be concluded, however, that the former must represent only
glycine residues, because there seems to be room enough for a larger side chain.
7. Radial distribution curve.
An experimental radial distribution curve published by Riley and Arndt has now been
replaced by another one, sent to me by Dr. Riley. In the region from 6 A to 12 A the
new curve shows acceptable agreement with the calculated radial distribution curve,
made by Dr. Pasternak. There is a pronounced difference between the two curves, in
that the experimental curve has a larger peak at 5 A, which is not shown on the theoretical
curve.
It seems to me likely that the large peak at 5 A is to be attributed to the effect
of atoms of side chains, not taken into consideration in the theoretical calculation.
The (10,10,a) structure is in the form of a compound helix, which may be described
as a rod with the 310 structure in which every third hydrogen bond is broken, permitting the rod to be
twisted into a helix. The rod is about 6 A in diameter, including the Van der Waals
radii of the atoms, and it is twisted into a helix with average radius about 3.5 A
and pitch about 9.5 A. There is accordingly a helical cavity about 4 A in diameter,
which must be filled up with side-chain atoms. Consideration of the model shows that
an atom in this helical cavity will have some neighbors at about 3 A distance, and
a number of neighbors at about 5 A distance.
I think that it would be wise to have Dr. Pasternak carry out, without delay, a determination
of the radial distribution function for collagen. Possibly this should be done by
Dr. Marsh, using the spectrometer and a disoriented sample of collagen or of gelatin,
or perhaps both.
It might be worth while to repeat this work with a hydrated specimen, to see whether
or not the same radial distribution curve is obtained.
8. The distribution of intensities along the equator.
I think that it would be worth while to make a comparison of observed and calculated
intensities along the equator of a fiber diagram.
As for the calculated intensities, it would, I think, be enough to use the Bessel-function
formula, which is given in our paper on Atomic Coordinates and Structure Factors for
Two Helical Configurations of Polypeptide Chains. I think that you have a record of
the atomic coordinates for the structure – the atomic coordinates were used by Dr.
Pasternak in his radial distribution calculation. They may have to be refined somewhat
later on, but I do not think that any changes that will be made are significant for
this calculation. Could you have Mrs. Oberhettinger carry it out?
It might be worth while also to have Dr. Marsh make a spectrometer study of the equatorial
intensities for kangaroo-tail tendon, both in the dried state and hydrated.
9. I feel that it would be well worth while to make some new collagen photographs,
In particular, I think that we should examine the large-angle region along the meridian,
to see whether reflections that at 1.43 A, 0.95 A, and 0.72 A can be picked up – perhaps
even at 0.57 A. If the orders from 1 to 5 of the 2.86-A meridional reflection could
be observed, and if their relative intensities were found to correspond to the proposed
structure, we would have a pretty strong argument in favor of the structure. There
will no doubt be a very heavy general background in this region, but I feel that it
would be wise to make a vigorous effort to obtain experimental values of the intensities
of these reflections. You remember how much more could be seen on the silk photographs
than had been reported in the literature.
10. Ramachandran has stated that the 2.86-A reflection is not a meridional reflection.
Perhaps a Weissenberg photograph could be made to check this point.
11. I think that it might be worth while to evaluate the complete form factor for
the structure. I think that it should be done for only one azimuthal orientation of
the helix. It is true that there are only ten orientations of different units, rather
than eighteen in the α helix, but the result obtained by Dr. Yakel for the α helix,
that the form factor varies only slightly with change in azimuthal orientation of
the fiber relative to the x-ray beam, probably would apply pretty well to this structure
also. The calculation would be made by use of the formula of Cochran, Crick, and Vand.
12. A simple calculation might be made to explain the observed meridional reflections
on the third and seventh layer lines – perhaps also on the sixth layer line (I had
thought that I could see such a reflection).
The chemical analyses of collagen indicate that in 30 residues there are about three
hydroxyproline residues and four proline residues, a total of seven Pro + Hypro. There
are, however, ten positions which might be occupied by these seven residues. Presumably
three of the positions are occupied by some other amino acid.
I have assumed the sequence x, pro, hypro, x, pro, hypro, pro, x, pro, hypro, as a
repeating sequence, in the identity distance 28.6 A.
I have assumed a scattering center with scattering power unity at each of the pro
+ hypro positions, and have calculated the following values of the structure factor
for the first ten orders of reflection (00l): 0.4, 0.6, 2.6, 1.6, 1.0, 1.6, 2.6, 0.6,
0.4, 7.
We see that there should be a very strong tenth order, the observed 2.86 A meridional
reflection. The two next longest reflections are the third and seventh; these are
observed. Next are the fourth and sixth; of these the fourth is not present, but I
have thought that I could see the sixth. It is calculated to be about 40 percent as
intense as the third or seventh.
Perhaps the calculation should be carried out with use of the z coordinates of the
atoms gamma-C and δ-C for the proline and hydroxyproline ring, and perhaps also for
the oxygen atom of hydroxyproline. The β-carbon atom of the ring probably should not
be included, because presumably there is a β-carbon atom in the residue taking the
place of the ring. It might turn out that interference of the gamma-C, δ-C, and O
would cause the intensity of 004 to be decreased, and perhaps that of 006 to be increased.
