CRYSTAL STRUCTURE OF “GLOBULAR” PROTEINS

A. I. Kitaigorodsky

It has long been known that a number of proteins form good single crystals, the dimensions of which are quite sufficient for carrying out a complete X-ray structural investigation. This task, however, is a very difficult one. It is hard to maintain single crystals in an unchanged state throughout the entire investigation. Special difficulties also arise because the unit cells of the crystals are exceptionally large, and therefore the interference spots on the X-ray photograph, under ordinary exposure conditions, would be situated extremely close together and near the primary spot.

Despite these difficulties, the number of proteins investigated is fairly large, as is shown by the table. Among these objects, insulin, lactoglobulin, and hemoglobin have been studied in especially great detail. For these compounds, in addition to measurements of the unit cell and space group, an analysis of the intensities of the X-ray reflections has been carried out.

As can be seen from the table (see next page), for most substances measurements have been made for wet and dry crystals. The existence of protein crystals in these two forms—with crystallization liquid and without it—is an interesting peculiarity of these substances. This same circumstance, as will be seen below, renders an important service in solving the fundamental problems of protein structure.

The investigation of wet crystals is carried out in special capillary tubes made of borosilicate glass, permeable to X-rays. The thickness of the capillary walls should be about 0.01 mm, the cross section 1 mm, and the length 30 mm. The protein crystal is introduced into the capillary together with a drop of the mother liquor. By means of a thin woolen thread, liquid is introduced into both ends of the capillary. The crystal remains midway between two 10-millimeter columns of liquid and, since it is wet, adheres to the wall. Both ends of the capillary are sealed with sealing wax. In this way, the crystal remains in equilibrium with its

Crystalline Structure of “Globular” Proteins

Table

with liquid and at the same time the X-rays pass only through the crystal. If these precautions are not taken, the crystal will be destroyed during the exposure.

It is much more difficult to prepare dry crystals. They crack because salt crystallizes out between the mosaic blocks. Good specimens were obtained by immersing wet crystals, freed of salt, in pure xylene, which is hygroscopic, absorbs the water of crystallization, and itself does not penetrate into the crystal.

Fig. 1.

Dry crystals are considerably worse objects for physical investigation. Whereas wet crystals make it possible to carry out a complete optical study, to measure their birefringence and pleochroism, dry crystals always have cracks and are opaque. The X-ray scattering of dry crystals is very weak in intensity, so that even the scattering of air interferes with obtaining good radiographs.

Satisfactory results were obtained only when exposures were made in vacuum.

To obtain a radiograph, the capillary with the crystal was mounted on a goniometer head and placed in the rocking camera. The exposure was made on a flat plate located at a distance of 50–60 mm from the object. Exposure on a cylindrical camera is not meaningful, since the observed interferences are situated near the primary spot. The radiographs were taken mostly with filtered copper radiation: a series of rocking radiographs was taken about the principal axes of the crystal, with the rocking interval being 3–5°. Typical radiographs are shown in Fig. 1. In order to judge the maximum deviations of the interference rays from

CRYSTALLINE STRUCTURE OF “GLOBULAR” PROTEINS

of the primary direction, data are given on the smallest observed interplanar spacings:

In the radiographs presented, we see the positions of spots along the usual layer lines. The peculiar arrangement of the reflections in rings is noteworthy. This arrangement becomes understandable from consideration of Fig. 2. In the upper part of the figure a series of planes of the reciprocal lattice of the crystal, perpendicular to the primary beam, is shown. In view of the closeness of these planes to one another, and also because of the density of the reciprocal-lattice nodes on these planes, the regions effective for reflection in the reciprocal lattice will be rings (composed of two crescents), shown in the lower part of the figure. These rings are the sections of the reflecting region, i.e. of the region between the two positions of the Ewald spheres at the beginning and at the end of the rocking interval, by reciprocal-lattice planes perpendicular to the beam. This circumstance facilitates the indexing of the radiographs—the spots lying in one region have one common interference index. The second index is determined by the number of the layer line of the given spot. Consequently, the indexing is reduced to finding only one third index.

It should be borne in mind that the distance between the layer lines is, for the most part, 0.5–1.0 mm. This imposes the requirement of very accurate adjustment of the crystal; it is also necessary to use sufficiently narrow diaphragms.

We shall dwell in particular detail on the last investigation in the series of works devoted to proteins, namely, on the study of the structure of hemoglobin1. The object of the investigation was horse hemoglobin. Crystals of this substance were obtained with dimensions of 1–1.5 mm. Wet hemoglobin gives reflections down to interplanar spacings of 2.4 angstroms—this is the limiting value for all proteins studied up to the present. Finally, especially important for accurate analysis is the circumstance that the hemoglobin molecule occupies in the crystal a special, not a general, position, namely, it lies on a simple twofold axis. This follows quite strictly from the following considerations. All 62,700 reflections that could be observed at the above-mentioned limiting value of the Bragg angle (corresponding to an interplanar spacing of 2.8 angstroms—from 2.8 to 2.4 angstroms only weak individual reflections were observed) indicate equality of the intensities of \(hkl\) and \(\bar{h}\bar{k}l\), and also the absence of all indices \(hkl\) for which \(h + k\)

odd. Thus, the crystals under investigation belong to the monoclinic system and form an elementary cell centered on the face \(a, b\). Three space groups satisfy this condition: \(C2\), \(Cm\), and \(C2/m\). However, it has been established that hemoglobin possesses optical activity; therefore, of the three groups indicated, only the group containing axes of symmetry is possible, i.e. \(C2\). In this group there are four general positions. By chemical means one can obtain data on the molecular weight of hemoglobin: on the assumption that one molecule contains 4 iron atoms, the figure 67,000 is obtained with an accuracy of about 5%. On the basis of the dimensions of the unit cell of dry crystals, we find that the number of molecules in the cell is equal to two (it should be emphasized here that

Fig. 2.

symmetry of the wet and dry crystals is the same). Thus, the hemoglobin molecules occupy a special position in the crystal, namely, they lie on the twofold axis which, in the unit cell shown in the table, runs along the \(b\) axis of the crystal.

On the basis of the data on the symmetry and dimensions of the unit cell, a number of conclusions about the shape and volume of the molecule can be drawn from purely geometrical considerations. Considering the form of the cell of dry crystals, we note that the centers of the molecules in the \(ab\) plane form an almost ideal hexagonal pattern. In Fig. 3, circles of three types show the positions of the centers of the molecules in three successive layers. The \(ab\) plane could be densely packed with spheres of diameter \(b\), i.e., of radius approximately equal to 30 angstroms. However, in that case the next layer cannot approach the first layer to a distance smaller than \(d \cos 30^\circ\). This gives a value of about 50 angstroms, whereas the observed interplanar distance is 36 angstroms. It follows from this that a spherical shape can by no means be assigned to hemoglobin molecules.

Fig. 3.

The authors of the work cited raise objections to the assumption of an ellipsoidal form of the molecule and settle on a cylindrical form. This part of the work is, unfortunately, the weakest and quite unconvincing. In arguing against the ellipsoidal form of the molecule, the authors suppose that the density of the molecule itself (i.e., the ratio of the weight of the molecule to its own volume) is equal to the density of the crystal—an entirely incorrect assertion. By the method we have developed\(^{4}\), we shall find without difficulty that, from geometrical considerations based on the dimensions of the unit cell, the hemoglobin molecule can be approximated by an ellipsoid close to an ellipsoid of revolution, with semiaxes \(30 \times 30 \times 16\) angstroms. The volume corresponding to two molecules, from our point of view, should amount to \(73\%\) of the volume of the unit cell, and not \(91\%\), as the authors quite erroneously suppose. It seems to us that the ellipsoidal model of the molecule was rejected by the authors for the reason that they did not consider the possibility of ellipsoids whose axes are inclined in the \(ab\) plane. The necessity of such an inclination is quite obvious in Fig. 3. We see that the hexagon of centers of each subsequent layer is displaced relative to the preceding one along the \(a\) axis by a small ...

a quantity from the symmetrical arrangement. This quantity, indicated by us with arrows in the authors’ figure, determines the inclination of the ellipsoid axis from the normal to the plane \(ab\). Thus, from our point of view, contrary to the authors’ point of view, all the experimental data are well explained by approximating hemoglobin molecules by triaxial ellipsoids of size \(30 \times 30 \times 16\) angstroms, inclined with their minor axis to the plane \(ab\) at a small angle. The authors believe that the molecules should be approximated by cylinders 34 angstroms high and with a base diameter of 56 angstroms.

One should not think that the difference between these two models is so great. The authors point out that their data claim only to give a “vague outline” of the molecule; they also point out that the base of the cylinder is somewhat convex, which brings the two models cited above still closer together. It should also be taken into account that linear dimensions cannot be specified with an accuracy greater than 5%. We wished only to note that the authors should not have contrasted so sharply, as they do in their conclusion, the ellipsoidal model (which had been proposed more than once previously) with the cylindrical one.

Be that as it may, the approximate volume and shape of the hemoglobin molecule are quite evident. On them is based the further investigation— from our point of view, the most interesting part of the work—concerning wet crystals. The experimental material for this part of the work consists of the intensities of 7840 reflections estimated on oscillation X-ray photographs. On the basis of these measurements, for all the crystals studied one can construct a Patterson series of interatomic vectors. In this work the authors consider two-dimensional projections of the series onto the principal planes of the crystal. In the future they intend to carry out an analysis of the three-dimensional series.

At first glance the meaning of constructing the Patterson series may seem unclear. Let us recall that the Patterson series is a Fourier series constructed on the basis of experimental data: all the coefficients of this series are positive and are equal to the structure factors of the X-ray reflections. As Patterson showed, the maxima of this series indicate the existence in the crystal of one or another interatomic vector. It is quite understandable that, with the number of atoms in a hemoglobin molecule being of the order of 5000 and with a corresponding number of peaks in the Patterson series of the order of \(10^8\), there is no point in dreaming of deciphering the series, i.e. of assigning one or another peak to a particular interatomic distance. Moreover, one might think that with such a large number of maxima the series would be smeared out and would not in general possess characteristic features. The latter, however, is incorrect. Indeed, if there is a definite regularity in the structure of the molecule itself, and if there is the undoubtedly existing regularity in the arrangement of molecules with respect to one another, then there must exist interatomic vectors that will occur especially often. In this case we are entitled to suppose that in the series there will appear

interatomic vectors of two types—intramolecular (their peaks should be near the origin of the series of coordinates—small distances) and intermolecular, corresponding to considerably larger distances. The overlap of the maxima of the two types should be small, since the distance between molecules is large in comparison with the important interatomic vectors.

It is quite clear that consideration of a single Patterson series cannot be of any benefit, and the analysis of intensities acquires meaning thanks to the exceptional property of crystals of globular proteins to provide a series of objects containing different percentages of water. Particularly interesting and ingenious are the experiments involving replacement of the crystallization liquid. Ions diffuse into the protein crystal. It has therefore been possible to obtain objects in which the electron density of the crystallization liquid varied from 0.33 to 0.45 electron per cubic ångström. The study of two objects differing only in the concentration of electrons in the crystallization liquid has the following meaning. The protein molecule may be spongy and absorb the crystallization liquid into itself; another possibility is that the crystallization liquid is located in the gaps between the molecules. If heavy ions penetrate inside the molecules, then the entire scattering pattern should change. If, on the contrary, the molecule does not allow the crystallization liquid to penetrate inside, then the heavy ions merely border the molecule. In this case the pattern of intramolecular scattering should remain unchanged, and this means that the introduction of heavy ions can change the intensity of low-order reflections. The general character of the intensity distribution should remain unchanged. A careful investigation, carried out for hemoglobin by the three authors cited, proves in this way that the crystallization liquid is located between the molecules. It is also interesting that there are low-order reflexes—some few, others especially sensitive to the replacement of the light crystallization liquid by a heavy one. For example, the intensity of the 110 reflection changes sharply, while that of 200 changes hardly at all. These data can be used in order to localize the crystallization liquid in the crystal and, consequently, to refine the contours of the molecules. This fruitful idea was not carried through to the end by the authors and was only partially used by them in discussing questions of the shape of the molecule.

An excellent proof of the structure of wet crystals as a system consisting of “solid” molecules surrounded by crystallization liquid is the comparison of analogous Patterson series for crystals at different degrees of swelling or contraction.

Swelling of the crystals was induced by suspending them in a certain defined medium (for example, an unneutralized solution of ammonium sulfate). Contraction was induced by artificial drying of the solution with which the crystal was in equilibrium. The simplest way to do this ...

is achieved if, in the capillary tube described above and sealed with Picein, a small opening is made.

In hemoglobin it proved possible to observe five different cells at different stages of contraction of the crystal. It may be regarded as established that the processes of swelling and contraction proceed stepwise, since upon repeated observations only these five quite definite cells are obtained. The process is reversible, so that these five cells can be made to appear in order from larger to smaller and conversely. If one does not consider the completely dried crystal, it turns out that all changes reduce to a variation of the monoclinic angle from \(127.5^\circ\) to \(84.5^\circ\). The magnitude of the period \(c\), within the limits of error, remains unchanged. The values of the periods \(a\) and \(b\) remain very strictly constant. Thus the change of the lattice occurring upon swelling of the crystal reduces to an increase in the interplanar spacing 001 from 42 to 55 angstroms. Thus the character of the distribution of liquid in the crystal becomes obvious: the liquid must be distributed as a layer along the plane \(ab\); only a very small amount of it can participate in the formation of the layer \(ab\). Consequently, the layer \(ab\) is a layer of protein molecules. Still more definite judgments in the same direction may be drawn from consideration of Patterson series constructed for crystals at different degrees of swelling. Strictly speaking, only this consideration should be regarded as direct proof of the existence, at different stages of contraction or swelling, of protein molecules that remain unchanged. In the Patterson projections, for both wet and dry insulin, there was found a group of 18 maxima situated near the origin of the projection coordinates and having the same arrangement relative to one another in both projections. Figure 4 shows these two Patterson projections for insulin; for clarity, their schematic representations are given beneath these projections. The difference in the two projections is reduced mainly to the orientation of the entire group of 18 maxima—it differs by 6 degrees. The same effect was shown by a series of Patterson maps for hemoglobin (unfortunately, the drawings are very poor and not reproducible) and for lactoglobulin. Figure 5 shows two projections of this latter substance at two stages of contraction. In all cases it is possible to note the constancy of a group of peaks clustering near the origin of the projection coordinates (i.e., the constancy of a certain system of small interatomic distances). This is precisely how a Patterson projection should behave if the process of swelling or contraction is imagined as a process of mutual displacement of “rigid” molecules.

As we have said, for hemoglobin the cell changes at different degrees of contraction make probable the arrangement of molecules in layers \(ab\). The Patterson maps for hemoglobin make it possible to confirm and refine this picture. Upon swelling and contraction the layer \(ab\) pro-

protein molecules approach and move away from one another, and also shift. Observing those peaks which change from projection to projection, we find peaks corresponding to important intermolecular distances. In hemoglobin such peaks correspond to a distance of 18–20 angstroms. In this way the distance between the “surfaces” of the molecules is determined, i.e. the thickness of the layer of liquid (the authors interpret this result not quite in this way, and, as it seems to us, unnecessarily

Fig. 4.

complicate the picture). On the basis of what has been said, the crystalline structure of hemoglobin may be illustrated by Fig. 6.

X-ray investigation makes it possible to solve the interesting question of protein hydration. It is known that the concentration of mobile ions in the crystallization liquid is always lower than in the medium with which the crystal is in equilibrium. Thus, the crystal contains an excess of water, which within broad limits does not depend on the salt concentration. Two hypotheses may be put forward concerning the location of this “additional” water. First, one may suppose that the water should be divided into two kinds: “bound,” directly connected with the protein molecule, and “free,” which permits the diffusion of ions and is in dynamic equilibrium with the medium. Of course, the composition of the “free” liquid will be the same as that of the surrounding medium. Another assumption would be

converse of the first: we may assume that the “additional” water is distributed uniformly throughout the entire crystallization liquid.

In a normal moist crystal the distance between layers is equal to 50.7 angstroms. If the second assumption is correct, then the crystal under study must be regarded as a protein layer 34 angstroms thick and a layer of liquid of uniform concentration 16.7 angstroms thick. If the first assumption is correct, then we have a layer of hydrated protein 40.1 angstroms thick and a layer of free liquid 10.6 angstroms thick. The latter figure is ex-

Fig. 5.

numerically multiplied by 16.7 by the ratio of “free” water to its total amount. In the presence of heavy ions in the liquid, the mean electron concentration of the layer of crystallization liquid is considerably greater than this value for water. For both of the indicated models one can calculate the intensities of reflections from the plane \(ab\). Comparison with experiment leads to proof of the hydration of the protein. Each protein molecule is hydrated, i.e. surrounded by a layer of water.

Fig. 6.

Unfortunately, only very scant information can be obtained about the structure of the protein molecule itself. The high regularity of the structure of the molecules of moist crystals seems to be beyond doubt—this is indicated by the observability of interferences down to \(2.5\) angstroms, i.e. almost to interatomic distances. This, however, is not entirely consistent with the observability of reflexes only down to \(10\) angstroms in dry crystals. We find Bernal and Fankuchen’s conclusion about the complete regularity of the structure of the protein molecule somewhat premature.

A more detailed investigation of the structure of the molecule has been carried out with respect to hemoglobin. A whole series of indirect considerations helped the authors establish the signs of the structural amplitudes of reflections from the principal plane \(ab\) of the crystal (the plane of the molecular layer). Thus it proved possible to construct a one-dimensional series of electron density. Since there is one layer of molecules in the cell, the resulting series makes it possible directly to determine the general character of the distribution of electron density along the short axis (the one equal to \(32\)—\(36\) angstroms) of the molecule. Four maxima of electron density were found at distances of about \(9\) angstroms from one another. The meaning of these accumulations of density remains unclear. Experiment cannot at present test such theories of protein structure as the cyc-

hypothesis of Rinch. Her attempts to substantiate her theory by analysis of Patterson series have no foundation.

Remaining within the framework of X-ray structural analysis, we can hope to obtain new results only by applying three-dimensional Patterson synthesis. This exceptionally cumbersome work will evidently soon be carried out and, it is to be hoped, will provide new data on the structure of globular proteins.

Cited Literature

1. J. Boyes-Watson, E. Davidson and M. F. Perutz, Proc. Roy. Soc. A 191, 83 (1947).
2. D. Crowfoot, Chem. Rev. 28, 215 (1941).
3. T. Fankuchen, Ann. Rev. Biochem. 14, 213 (1945).
4. A. I. Kitaigorodskii, Izvestiya Khim. Otd. AN SSSR, 587 (1946).