James R. Knox Biological Sciences Group University of Connecticut Storrs, 06268
Protein Molecular Weight by X-ray Diffraction
To keep the crystal moist during the X-ray experiment, one The use of X-ray crystallography to must seal it in a widemouth glass or quarts capillary tube (Unidetermine three-dimensional structure of molecules mex-Caine Corp., Gary, Ind.) about 1 mm in diameter. This has remained of primary importance for 40 years, and step requires some dexterity, but is easily accomplished by the its foundations have been reviewed in THIS JOURNAL following procedure. The capillary, cut t o alength of 20 mm and sealed a t the narrow end, is filled with the buffered salt solution by (1). Only within the last decade have the structures means of long hypodermic needle. A 3 mm space is left for the of proteins been established by the method (Z), and crystd a t the closed end. The crystal is carefully picked or now the chemical and biochemical implications are scooped from the depression slide and quickly immersed in the gradually appearing in textbooks. Because the first solution a t the wide mouth of the capillary. After allowing the step in an X-ray study is the determination of the shape crvstal to sink to the meniscus near the closed end.,one uses a elass .. Kbrr to push the cryatnl ju-t I,ry almu 21 hr oratory sessions are needed to complete the project. . tlwreforr i n w h coooer radlnriou. nirkel fil~cr.18 m.\. 35 k \ ~ snd ~
of the data recordine must he done hetween sessions. I n eeneral.
Procedure Tetragonal lysozyme chloride crystsls are grown a t room temperature from a solution of equal parts A and B, where A is 0.4 g dry lysoeyme in 1 ml 0.2 M acetate buffer, pH 4.7, well stirred with4 ml water; B i s a 10% NaClsolution. If the mixtureis first passed through a Millipore filter, fewer nuclei will form, resulting in larger crystals. Crystals are conveniently grown in microscope depression slides sealed with a greased cover slip. I n about one week crystals about 0.75 mm should appear, but t o allow for difficulties the instructor should begin the crystallization several weeks before the first laboratory meeting. Trigonal RNaseS crystds are grown by mixing the protein solution (75 mg in 1ml 6 M CsCI, 0.1 M acetate buffer, pH 6.0) with an equal volume of 80% saturated ammonium sulfate also buffered a t pH 6.0. The crystals are transferred t o 75% saturated ammonium sulfate a t pH 5.5 to remove CsCl(7). Table 1.
the diffraction spots will he very close or even overlapping when molybdenum radiation is used. I t is therefore preferable t o use copper or cobalt radiation and a camera with a large crystal-tofilm distanceof 75 or 100 mm rather than the conventional 60 mm linkaee. Irradiation of urotein crvstals uusallv causes sienifieant shsenoe of film shrinkage corrections. Of the many methods for measurement of crystal density (16), the density gradient method is preferred for protein crystals. I n 1 or 2 hr the students can prepare a hromobenzene-xylene gradient column about 10 om long and 2.5 om wide (Fig. 1). Six or seven mixtures of hromohenzene (1.5 g/cma) and xylene (0.86
Some Cryrtallizoble Proteins Commercially Available'
Protein
Source
Molecular weieht
Lysoeyme Ribonuclease-A Rihanuclease-Sh Papain a-Chymotr.msin Chymotrypsinogen-A Triose phosphate isomerase Carhoxypeptidase-A 8-Lacta~lohulin Aldolase
Egg white Bovine Bovine Papaya Bovine Bovine Rahbit Bovme Milk Rabbit
14,700 13,700 13,700 23,000 25.000 25;000 26,000 34,600 36.000 160:000
In. ,"L".
~
Cell tvoe
a
Tetragond Manoclinic Trigonal Orthorhomhic Monoclinic Orthorhomhic Hexagonal Monoclinic Variou~ Hexaeonal
79 30 44 45 49 52 99 51 96
Crystdlagntph~cdata Parameters (A, deg.) b c snele 79 38 104 67 64 99 60
38 53 97 51 66 77 106 47
90 106 120 90 102 90 120 98
96
168
120
44
Reference
Worthington Biochemical Corp., Freehold, N. J.; Nutritions1 Biochemicdls Corp., Cleveland, Ohio; Sigma Chemical Co., Prepared from RNsse-A (3).
476 / Journal of Chemical Educafian
Flgure 1. Bromobenrene-xylene grmdient celumn for meorurement of crysto1 density. Crystals of lyroryrne and ribonucleare ore seen near the two lower drops of potosium carbonate solution.
g/emJ), covering the density range 1.1-1.4 g/cm8, are carefully pipetted sequentially with a, slight cross-wise stirring near the interface after each addition. The gradient will remain stable for about 12 hr. It is calibrated by a. series of drops of aqueous s d t solutions, the density of each solution having been determined with a pycnometer or Westphal balance. Before the crystal is dropped into the tube, i t must be quickly touched with blotting paper t o remove adhering liquor. Two minutes are allowed for the erystd t o reach its buoyant position, after which time i t will slowly sink. By marking the positions of erystd and calibration drops a n a strip of graph paper behind the column, one can obtain the crystal density by interpolation. The error involved depends on the sharpness of the column gradient and on the number of calibration drops, but one should be able t o measure the density within 2% of published values. Alternatively, the density may be calculated by microscopically determining the volume of a well-farmed preweighed crystal.
Analysis of Data
Before measuring spacings on the X-ray films, students should first examine the spot pattern and (1) derive the shape of the crystallographic unit cell giving rise to the pattern, (2) establish the orientation of the unit cell with respect to the directions of the incident X-ray beam and horizontal spindle axis of the camera, and (3) assign Miller indices to spots on the basis of the unit cell chosen. The diffraction patterns for the trigonal cell of RNase-S (Fig. 2) are very good for this instruction because not all angles of the cell are 90'. The two rows of spots with the smallest interval are chosen as two of the three major reciprocal cell axes and are designated a* and b* (Appendix). The interval along a* is found to equal the interval along b*, while the observed angle between them, y*, is 60". These observations show that one face of the unit cell has equal sides a and b; the included angle y is equal 120" because the hOO and OkO Bragg planes are perpendicular to a* and b*. Since the cell edges a and b are inclined to the directions of dm and dolo, the length of each edge is dloo/sin60'. The length of the c edge is now determined. During the photography of the hkO level, the c* axis precessed around the incident beam direction. To see spacings along the c* direction we must rotate the crystal about the horizontal spindle axis. For RNase-S a 90" rotation brings either the h01 or hhl level parallel to the film, depending on
Figure 2. X-ray photographs of ribonucleose-5. (A1 hkC level, b * axis 60' from horizontola* axis. 1%)hCl level,cY oxit vertical.
whether the a* axis or the a*b* diagonal is horizontal. I n either instance the d spacing corresponding to the vertical interval on the film is do,,, the distance between the 001 planes. Since c is also perpendicular to these planes, c = dm,. A similar analysis of the two lysozyme patterns (Fig. 3) shows that the unit cell has a = b Z c with all angles equal 90°, and the instructor may wish to use the reciprocal lattice concept to show how the four-fold symmetry of the diffraction arises from a tetragonal unit cell. After these qualitative observations have been made, the film is placed over a light box, and the intervals between spots or r o w of spots are measured to the nearest 0.025 mm using a sliding hairline scale. Better reproducibility is achieved if equivalent points above and below the center are measured and the distance between them is halved and then divided by n, the order of the spot. Five or six pairs of spots far from the center are usually measured. The average intervals are converted to d spacings by the relationship d = XF/y (Appendix). If the photograph of the hkO level of RNase-S is positioned so the hairline is kept parallel to the a* axis, the vertical y interval being measured is inversely proportional to dolo/sin 60°, which provides b directly. The protein molecular weight is X D p V N / Z ,where X, is the weight fraction of protein in the crystal, p is the densitypf the wet crystal (g/cm3), V is the unit cell volume (A3 X N is Avogadro's number, and Z is the number of molecules in the cell, as given Volume 49, Number 7 , July 1972
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477
X., we now have X , = 1 - X , - X,x.. It has been found that a small quantity of water remains in the crystal after heating, amounting to 5 1 0 % of the dry crystal weight (17). This hound water is thought to be in the form of a monolayer around the protein molecule and is probably involved in stabilizing the tertiary protein structure by forming hydrogen bonds between the surface folds of the polypeptide chain. I n calculating molecular reights from the data in Table 2 1r.e have assumed that all the water is lost from the crystal during heating, and that a11 this water is permeable to salt ions. A more accurate \ray for finding X,directly is to use the Lowry method (18) or a suitable assay to determine the protein content of a single crystal of knonm weight. Appendix.
The Reciprocal Lattice
E H I ~*PII BTHSL: p l u n ~ van i bcdelmed by r t m i e ~ t a t i o ni n the unit cell nnrl by i l . inrcrplamr :pnrit.g, d Fig.1 . \Veshnll show
lel,\e can define both the orientation and d spacing of the fund* mental set and its higher orders by a row of points falling on the normal to all the planes and with an interval between points equal l l d ~ . The point for the n t h order planes is then n times farther from the origin than the point for the first-order planes. For example, let the Bragg planes 100, 200, . . . be inclined r degrees t o the 010, 020, . . planes, and let these planes he perpendicular t o the page. We can draw two rows of points along the normals a*
Figure 3. X-ray photographs of lysoryme chloride. vertical. 181 h01 level,c* oxis vertical.
IA Il hkO level, b* oxis
in the original reference (see Tables 1 and 2). The fraction of protein X , (weight protein/weight crystal) is always quite less than 1.0 because the crystal contains a considcrablc amount of water and salt. Therefore, students should measure by weight difference the natcr lost at 110°C from a collection of wet crystals togcther wighing at least 1 mg. A fractional water contcnt X, (wight water/weight crystal) from 0.25 to 0.35 will be observed for both RiYase-S and lysozyme. Thc fractional amount of salt X . (weight salt/weight crystal) is determined indirectly. One finds the ratio of salt to water x, by weighing a sample of salt solution (containing no protein) before and after heating to dryness. Since the protein fraction is 1 - X, Table 2.
Representative Data for Molecular Weight Calculation
(Published values are shown in parentheses) RNase-Sa Lysoeyme Cell dimension, a (A) b C
Cell type Cell volome, T'(Xa) Molecules per cell, Z Crystal density, p(g/cm8) Water content, X, Salt/water ratio, r. I\lalecular weight
44.5 (44.5) 44.5 (44.5) 97.3 (97.3) Tligonal 167,000 6 1.282 0.178(0.312) 0.574 15,500 (13,700)
79.1 (79.1) 79.1 (79.1) 37.9 (37.9) Tetragonal 237,100 8 1.235 (1.242) 0.319(0.335) 0.0613 14,600 (14,700)
" If the pH of the mother liquor is not carefully checked, a second trigonal form will readily grow near pH 6.6. I t has cell dimensions a = b = 64.4 and c = 64.4 A (7). 478
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Journal o f Chemical Education
Figure 4. Relationship between Bragg plmer and reciprocal lanice points. (A) The ob face of o unit cell with a few Bragg spocingr indicated. (BIA portion of thecorresponding hkO level of the reciprasml lonice. Theo* and b* axes are normal to the hOO and 0k0 planes, m d the interval dong the oier B proportional to 1 Id.
Figure 5. Triangular representation of Bragg'r law for lhrse orders of diffraction. In each triangle tho hypotenuse is 2/A, but the ride opposite 8 increases with n.
and b*, which are inclined to each other 180' - 7 , or r*. The point for the 110 planeis added by moving oneunit in the positive direktion along hotha* and b*. Other points are drawnfor planes with negative indices. The 001 planes need not be parallel to the page, so the positive direction of e* is generally oblique to and out of the page. Then the point 111 is constructed by stepping one unit along all three axes. The resulting three-dimensional grid is the reciprocal lattice, and the points in it are reciprocal lattice points, each one labeled with the Miller indices of the corresponding Bragg plane. To relate the reciprocal lattice to Bragg diffraction, let us rewrite B r a d s law in the form sin em& nt = (nld~)l(Z/A). We see that di8rsction from n orders can be repr&ent& by n right trirtngles, each with a hypotenuse of length 2/A and with the side , distance of the nth reciproopposite enh%X of length n l d ~ rthe cal lattice point from the origin point 0 (Fig. 5). If the hypotenuses of aU triangles are superposed, the locus of all right-angle verticesis a circleof diameter Z/A (Fig. 6). Avector from the center C to sright-angle vertex can he shown to form an angle 28 with the diameter. We now have a convenient geometrical representation of Bragg diffraction at an angle 28 with the incident X-my. For if a crystal is placed at C and the incident X-ray direction defined dong the diameter through the crystal to point 0, we see that as the crystal rotates around C, the imaginary row of reciprocal lattice points rotates around 0, bringing each reciprocd lattice point in turn onto the circumference of the circle. At the instant the nth point reaches the circle the Bragg equation is satisfied for planes with spacing d,n .x nr which are perpendicular to the reciprocal lattice row. If during the rotation a. photographic film is maintained parallel to the reciprocal lattice row a t a distance F from the crystal, the diffraction spot appearing a distance y. from the center of the film is inversely related to the first order Braggspacing by theequation d m = nAF/y..
,
Figure 6. As cryst01 plane at C rotates into diffracting paition, its reciprocal lonice point rotates o.to circle, forming Brogg'r low triangle (Fig. 5 ) with diameter of circle.
Literature Cited (1) WAaEn, J.. J . cam^ Eono., 45,446 (1968). (2) DICIERBON.R . E., A N D GEIB,I.. "The Structure and Action of Proteins," Harper and Row, Ne%vYork,1%9, p. 67. F. M., A N D VITHATATHLL, P. J., J. B i d . Chem., 243, 1459 (3) RIOHARDB, ,,O=.OI \.""",.
(4) M.. A N D GALYIN,J. A,, 3. Amcr. Chsm. . . P*Lxen. K . J.. BALLANTPNE. soc.. 70,906 Soc.. 70, s o e '(1948); ( 1 ~ 4 8 ) S~eranAus, s; ~ e r a k * u d L. , K.. K.: Acto ~ c t Cryst.. crvst.. o ii,77 (1959). 12.77 (19Jsj. D. C..Pm.Nat. Aeod. Sci. U . S . A , ,. 57,484 (51 57.484 (1967). (5) PXLLLIPB. J . . A N D HARKER, D., Nature, 213,862 (1967). (6) K*nl'xn, G., BELLO, (7) Wuoaor*. H. \V.. T s m n ~ o o ~ oD., u . H w s o n , A. W.. KNOX.J. R., LEE, LEE, R . , AND RIONARDB, F . M . , J . BiDZ. Chem.. 245.305 (1970). TOL. . J~~ONIU . I . B N.., KOEROEY. R., SIYEN.H. M.. AND WOL(8) D n e n ~ n J., m e n & B . G . , N ~ t w e . 2 1 8 . 8 2 9(1968). (91 S ~ L E BP.. B., B.,'BLow. D. hi.. B . W., AND HENDERSON. BLOW.D. M.. M*THE&, MATHEWB, R., R.. J . Mol. Biol., 35,143 (1968). N a f . &cod. s Sci. (10) KBAUT.J.. H ~ R D, . P.. AND SIEIER, L. C.,PTDC. U.S.A.. 51,839 (1964). (11) J O H N ~ O N N . L. . A N D W & m . S . G.. J. M d . B i d . , 29,321 (1967). , . N.. In., R ~ m s u o aJ. . A,. Luowm. M . L.. Quracm. F. A,. (12) R ~ e x eG STEITZ.T. A.. STEITZ. A,. LIPBOOMB, W. N . , PIOC.Not. Acad. Sci. U.S. A , , 58,
---" iroa7, \."".,. 99""
(18) A s c ~ ~ ~ a ~ ~R.. s uGREEN. n a . D. W.,AND S I X X O N8. ~ . M,, 3. M d . Biol., 13, 194 (1965). E. GI. WEVER,B. H., A N D EIBSNBERQ. D . , Science, 171, 677 (14) HELDNER, (~....,. 1911>~
(151 STOUT.G. H.. A N D JENBEN,L. H.. "X-ray Structure Determination." The Maomillan Co.. New York. 1968, p. 122: Bu~nomn,M . J.. "The Precession Method." John Wiley & Sons. Ino.. New York, 1964, p.
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