The structure of haemoglobin Sir Lawrence Bragg, F.R.S., Cavendish , University of Cambridge and M. F. Perutz, Medical Research Council Unit for the Study of the Molecular Structure of Biological , Cavendish , University of Cambridge ( Received02 February 1952) The paper describes the first steps in an attempt to solve the structure of a haemoglobin molecule by X-ray analysis, using a direct method. It is based on an extensive series of absolute measurements of the diffraction by various shrinkage stages of a haemoglobin crystal, and estimates based on many crystalline forms of the general dimensions of the haemoglobin molecule. The methods used are described here and applied to a direct deter mination of the electron density in one particular direction in the molecule. The extension of the methods to the subsequent problem of obtaining a picture of the molecule as projected on a plane will, it is hoped, form the subject of a subsequent paper.
426 Sir Lawrence Bragg and M. F. Perutz transform unambiguously. We have carried out this analysis over the transform which corresponds to the projection of the monoclinic crystal structure on a plane perpendicular to its b axis, where the phases of the values are represented by positive and negative signs. The present paper describes the principle and its application to the F(OOZ) values; it is intended in a further paper to describe its extension to the whole transform.
The structure of haemoglobin 427 a simple close-packed hexagonal lattice with an a axis of 56 A, so that each molecule has six neighbours at this distance around its equatorial plane. In met-, oxy- and carboxy-haemoglobin of man the molecules are very nearly on a simple tetragonal body-centred lattice with an a axis of 54 A. One section of the molecule must therefore be approximately circular with a diameter of about 55 A (Bragg & Perutz 19526).
428 Sir Lawrence Bragg and M. F. Perutz a row of a given overall length. In order to ensure a random distribution of ‘incident’ in a definite confine, with at the same time an avoidance of marked concentration in any particular part, we have plotted in figure 2 (a) the times of arrival of Cambridge trains at Liverpool Street Station on Sundays between 8 a.m. and midnight. This gives fifteen points, and to make the group sym metrical we have supposed it to be repeated by a centre of symmetry at A (group BAB) and alternatively by one at B (group ABA). A weight of \ has been given to each point, so that F(000) is 15. The two corresponding transforms or diffrac tion patterns are plotted in figure 2 (6) and (c).
The structure of haemoglobin 429 dimensions of the molecule in a corresponding direction. The transform is due to the superposition of sets of fringes due to pairs of diffracting points such as AA or BB in figure 1. The fringes of least spacing are produced by pairs of points at the outer confines of the molecule, and since the addition of two cosine curves cannot produce one of higher wave number than either constituent there is a definite limit to the rapidity with which the transform can alternate between positive and negative values in going outwards from the origin. This feature is clearly illustrated in figure 2. The lower curve (d) shows the positions only (not the amplitudes) of the maxima and minima due to a uniform region of length 2AB; it will be noted how closely the oscillations of the transform correspond in spacing though so irregular in amplitude. The spacing of the fringes for two points such as AA in figure 1, it will be remembered, is the same as that for a uniform line though shifted outwards by one-quarter of a wave-length.
430 Sir Lawrence Bragg and M. F. Perutz and orientations of the molecules. The changes take place by a shearing and approximation towards each other of successive sheets as the angle /? varies.
The structure of haemoglobin 431 sponding points along the c*-axis; the corrections for salt-containing crystals giving F values at intermediate points have been estimated by interpolation.
432 Sir Lawrence Bragg and M. F. Perutz As has been indicated above, the curve is the transform for a body which has the outer shape of the hydrated molecule, but no internal structure. The form must be rounded since the first minimum is so small and the succeeding ones die away so quickly. The salt must be excluded from a region larger than the protein molecule itself, as is shown by the closing in of the nodes and loops.
Thes tructure of haemoglobin 433 7. Distribution of electrons in sheets parallel to the afe-plane The curves in figure 5 make it possible to form a Fourier summation which represents the electron density projected on a normal to the a6-plane. Since the complete molecular transform is known, an arbitrary value for the c spacing may be taken. Values of F corresponding to a cspacing of 150 A have been used in the curves shown in figure 6. With this spacing, F(001) and F(002) are closer to the origin than the first measured point on the curve, and values for them must be assumed. The central maximum has a somewhat different form depending on whether it is the Fraunhofer pattern of a slit, a circular aperture, or a sphere. However, if the curves are adjusted to correspond at the origin and at the first node, the estimates of F(001) are closely the same and those of F(002) only vary by 10%.
434 Sir Lawrence Bragg and M. F. Perutz analysis, the availability of absolute values enables conclusions to be drawn with much greater certainty. Secondly, the estimates of intensities have been checked and should be more accurate than those in the previous papers; their range has been extended by a more thorough comparison of diffraction by crystals with different salt contents, and one more shrinkage stage is available. The main basis of our present conclusions, however, is our interpretation of the form of the transform. We have given our reasons for concluding that the regions of the molecule responsible for the intramolecular diffraction effects does not extend at the most to more than 50 A in the c*direction, and probably only to 40 A. We conclude that the transform has a corresponding minimal distance between the loops, and that the form for the transform which we have deduced is the only one compatible with this principle. We do not regard the positive sign which we have given to Eni figure 4 to be conclusively proved, but we think the evidence points very strongly to its being correct.