M. F. Perutz

The Structure of Haemoglobin. IV. Sign Determination by the Isomorphous Replacement Method

Native horse haemoglobin contains free sulphydryl groups and forms crystalline compounds with para-mercuribenzoate groups and with silver ions. Crystals in which two of the four available SH groups are so combined are exactly isomorphous with normal monoclinic methaemoglobin, but exhibit significant changes in the intensities of many reflexions. The changes in F(h0l) were used to determine the x and z parameters of the pair of heavy atoms attached to each haemoglobin molecule; this was done both for the normal wet lattice and for one of the acid-expanded lattices. The positions of the heavy atoms proved to be slightly different in each case, giving rise to three sets of diffraction fringes, each set making measurable contributions in different areas of the reciprocal net. In each case the isomorphous substitution allowed the signs of just over two-thirds of the reflexions to be found with certainty. Between them the three sets of diffraction fringes determined the signs over the entire area of the h0l plane so far investigated. These signs were then superimposed on the waves of the transform described in previous papers of this series. All the sign relations established by the transform method were confirmed and the remaining uncertainties cleared up. Comparison of the transform with the three sets of isomorphous replacement results allowed the consistency of the signs to be rigorously checked; not a single inconsistent sign was found. In the normal wet lattice the mercury and the silver compounds between them allowed the signs of 87 out of 94 reflexions to be found with certainty. This suggests that the isomorphous replacement method may offer a way of finding the phases in protein crystals even when practical difficulties preclude the use of the transform method.

The structure of haemoglobin. IX. A three-dimensional Fourier synthesis at 5.5 Å resolution: description of the structure

The electron density distribution in the unit cell is calculated at intervals of approximately 2Å and plotted in a series of sections parallel to (010). The contour maps show that haemoglobin consists of four subunits in a tetrahedral array. The subunits are identical in pairs in accordance with the twofold symmetry of the molecule. The two pairs are very similar in structure, and the members of each pair closely resemble the molecule of sperm-whale myoglobin. The four haem groups lie in separate pockets at the surface of the molecule. The positions of the iron atoms are confirmed by comparison of observed and calculated anomalous scattering effects, which also serve to determine the absolute configuration of the molecule. The four subunits found by X-ray analysis correspond to the four polypeptide chains into which haemoglobin can be divided by chemical methods. In horse haemoglobin the amino acid sequence within these chains is still partly unknown, but in human haemoglobin it has already been determined. Comparison of this sequence with the tertiary structure of the chains as now revealed in horse haemoglobin and with the atomic model of sperm-whale myoglobin recently obtained by Kendrew and his collaborators shows many interesting relations. Prolines appear to come where the chains turn corners or where their configuration is known to be non-helical. On the other hand, the chains also have corners which contain no proline. Certain residues appear to be structurally vital, because they appear in identical positions in myoglobin and in the two chains of haemoglobin, while in other parts of the molecule a wide variety of different side-chains appears to be allowed.

The structure of haemoglobin III. Direct determination of the molecular transform

Horse methaemoglobin crystallizes with two molecules in a face-centred monoclinic unit cell (space group C2), in which rigid layers of molecules parallel to (001) alternate with layers of liquid. The crystals can be made to swell and shrink in a series of steps involving changes in d(001) and in the angle β. It appears that only the distances between the molecular layers change, but not their internal structure. The lattice changes allow the modulus of the molecular Fourier transform to be sampled along lines of constant h and k. When k = 0 the transform is real and the sampled values of |F| describe a series of loops and nodes. Part I of this series dealt with the principles of deciphering these and established the absolute signs of the 00l reflexions. In part II the absolute signs of certain 20l reflexions were derived from the changes in intensity produced by the substitution of salt solution for water as the liquid of crystallization. In this paper the transform is measured for all values of h and l up to λ/d = 0·24, comprising nine layer lines in all. The absolute signs of layer lines with h > 2 are left in doubt, but many sign relations are established within each of them. It is difficult to assess exactly the number of sign relations found by the transform method, but it is estimated that the number of alternative sign combinations is reduced from 296 to 218. The remaining uncertain ties are cleared up by the isomorphous replacement method described in part IV .

The Structure of Haemoglobin. VIII. A Three-Dimensional Fourier Synthesis at 5.5

Determination of the phase angles of a crystalline protein requires a series of isomorphous heavy-atom compounds, with heavy atoms attached to different sites on the protein molecule. The asymmetric unit of horse oxyhaem oglobin was found to combine with heavy atoms at two different sites which are now known to be sulphydryl groups. Altogether six different heavy - atom com pounds of haemoglobin were made which proved isomorphous on X -ray analysis. The positions of the heavy atoms were determined first by difference Patterson and Fourier projections on the centrosym metric plane of the monoclinic crystals, and later by three-dimensional correlation functions, (FH1 — FH2)2 being used as coefficients, where FH1 and FH2 are the structure factors of the two different heavy-atom compounds. The parameters and anisotropic shape factors of the heavy atoms were refined by a three-dimensional least-squares method. For each of the 1200 reflexions in the limiting sphere of (5.5 Å)-1 the structure amplitudes of all seven compounds were combined in an Argand diagram and the probability of the phase angle having a value a was calculated for oc = 0, 5, 10, ..., 355°. The coefficients for the final Fourier summation were then calculated in two different ways. In one method the vector from the origin to the centroid of the probability distribution, plotted around a circle of radius |F|, was chosen as the ‘best F’. The alternative set of coefficients was calculated, using the full, observed, value of F and the most probable value of the phase angle a. The most probable error in phase angle was found to be 23°, and the standard error in electron density to be expected in the final results 0.12 e/Å3.

\overset{\circ}{\mathrm A}

The crystals are apparently orthorhombic; their unit-cell dimensions and the intensities of the 00l reflexions suggest a structure closely related to monoclinic methaemoglobin. Each structure appears to contain the same molecular layers parallel to (001), but in the monoclinic form the molecules are tilted the same way in each layer, while in the new form the tilt is alternately left and right in successive layers. Precession pictures show an interesting sequence of sharp and diffuse layer lines, those with certain indices h containing streaks parallel to c*. In other layer lines the spots are broadened in varying degrees. The amplitudes of the h0l reflexions are related to the molecular Fourier transform described in previous papers of this series. Each value of F(h0l) is compounded from the sum or the difference of the amplitude at two points on the transform having the co-ordinates ha* 0 Ic* and ha* 0 l̄c*. The rules for addition and subtraction of amplitudes follow a simple scheme which is related to the sequence of sharp and diffuse layers. The scheme accounts for all observed values of F(h0l), a reliability factor of 0. 21 being obtained. This correlation provides an independent check for the sequence of signs along certain layer lines of the transform. A preliminary analysis of the structure is made, and molecules in neighbouring layers are shown to be displaced by 11. 2 Å in the a direction.