J. Mol. Biol. (1971) 66, 163-168

Symmetry, Molecular Weight and Crystallographic Data for Sweet Potato fl-Amylase

P. M. COLMAN AND B. W. MATTHEWS

Institute of MoZecuZar Biology University of Oregon, Eugene, Ore. 97403, U.X.A.

(Received 25 March 19i’l)

Sweet potato /3-amylase has been crystallized in the tetragonal space group P4,22 (or enantiomorph) with unit cell dimensions a = b = 210.7 A, c = 157.0 A.

A new method has been developed by which accurate molecular weight values can be obtained from protein crystals grown from concentrated salt solutions. The method also gives the hydration of the protein in the crystal. Using this new technique the molecular weight of @nnylase was found to be 206,000 + 10,000. The enzyme is tetrameric with molecular symmetry which includes, at least to low resolution, a diad axis.

1. Introduction

Sweet potato /3-amylase (EC 3.2.1.1, a-1,4 glucan maltohydrolase, sweet potato) was one of the f&t enzymes to be crystallized (Balls, Walden t Thompson, 1948). The reasons which led us to consider this enzyme as a potential candidate for an X-ray diffraction analysis include the fact that /3-amylase is a subunit enzyme; it produces an inversion of configuration upon hydrolysis ; the morphology of the crystals (Balls et al., 1948) is ideal for X-ray photography, and the sulphydryl sensitivity of the enzyme might be utilized to obtain isomorphous heavy atom derivatives,

2. Crystallization and X-ray Data

Crystalline /?-amylase was purchased from Worthington Biochemical Corporation, and crystals suitable for X-ray study were obtained by a method based on that of Balls et al. (1948). Best crystals were obtained by the following procedure. The suspension of /3-amylase was centrifuged and the supernatant discarded. Sufficient water was added to obtain a solution of about 8 mg of enzyme/ml. After recentri- fugation the clear solution was divided into vials. An equal volume of 60% saturated ammonium sulphate, pH 4.0, was added and the vials left in the cold room. After several weeks, tetragonal bipyramids up to O-8 mm x 0.7 mm x 0.5 mm were obtained, accompanied by a slight amorphous precipitate also observed by Balls et al. (1948).

Before X-ray photography the crystals were slowly equilibrated with 45% saturated ammonium sulphate, pH 4-O. In spite of their large size the crystals gave rather weak X-ray diffraction patterns. Individual reflections could be seen corresponding to Bragg spacings d = 2.6 A, but precession photography yielded measurable intensities to spacings of about d = 5 A. To low resolution (d > 13 A) the unit cell

163

164 P. M. COLMAN AND B. W. MATTHEWS

of /3-amylase appears to be tetragonal, space group P4,22 (or P4,22) with a = 6 = 149-O & 05 A, c = 157.0 f- 0.5 A. At higher resolution, additional weak X-ray reflections begin to occur (Plate I) and when these are taken into account it follows that the true unit cell has space group P4,22 (or P4,22) with cell dimensions a = b = 210.7 A (i.e. 149-O& A), c = 157-O A. The correct unit cell is related to the pseudo cell by a rotation of 45” about c, and a translation along x of c/S. Consideration of the space group symmetry shows that the crystallographic symmetry elements of the crystal would be identical for the true unit cell and for the pseudo unit cell, except that the pseudo cell would imply an additional two-fold axis.

To determine the number of /3-amylase molecules in the unit cell it is necessary to know the molecular weight (or more precisely, the weight of protein in the asym- metric unit), and also the solvent content of the crystals. In view of the widely different published values given for the molecular weight of /?-amylase, ranging from 152,000 (England & Singer, 1950) to 215,000 (Thoma, Koshland, Rusica & Baldwin, 1963), we have determined the molecular weight independently.

3. Determination of Molecular Weight It is well known that if “salt free” crystals of a protein are avilable, the molecular

weight can be determined with an accuracy of about f5% from measurement of the unit cell dimensions and the density of single crystals of the protein (e.g. Crick, 1957). However, in most oases protein crystals are grown from concentrated salt solutions, and in such oases, the molecular weight cannot be determined without l&t establishing the volume fractions in the crystal of the protein, the “bound water”, and the “free liquid” (Peru@ 1946; Adair & Adair, 1936). Such estimates are difllcult to make, and for this reason accurate determinations of the molecular weight from protein crystals containing a large amount of salt are usually not attempted (Crick, 1957).

For ,%amylase we have determined the molecular weight by a new method in which the crystal density is measured at a number of solvent densities. The resultant graph is linear and can be extrapolated back to obtain a “salt free density” and hence the molecular weight of the protein. From the same graph accurate values may be obtained for the protein, solvent and bound water content of the crystals.

We do not suggest that the method for molecular weight determination proposed here should necessarily be preferred when accurate determinations can be made by conventional methods, but in oases where an unequivocal result is not obtained, for example due to partial aggregation of subunits, the crystallographic method can often provide a reliable value for the molecular weight.

The density of a protein crystal is a function of the “apparent specific volume” and the “apparent density” (Cohen & Edsall, 1943) of its constituents. Following Adair & Adair (1936) we denote the crystal density by D,, and the apparent density of the anhydrous protein, the bound water and the free solvent by D,, D, and D,, respectively. The apparent specific volume of the protein Gp = l/D,. Let V be the volume of one unit cell and let the fractional volumes occupied by protein, bound water and solvent be (I’,/?‘), (VW/V) and ( VJV).

The crystal density D, may be written

De = 4. (VP’) + D, U’w/V) + D, (Vs/V). (1)

If the solvent density D, is varied, then the crystal density will change. If none of the

PLATE I. X-ray diffraction precession photograph (7”) showing the (h01) reflections of tetra- gonal j3-amylase. Weak reflections with h odd begin to occur about halfway between the center and the outer edge of the photograph. The h axis runs from bottom right to top left.

[ facinrr p. 164

CRYSTALLOGRAPHIC DATA OF ,8-AMYLASE 165

other quantities vary then a plot of crystal density against solvent density would be a straight line of slope VJV. Furthermore, such a straight line could be extrapolated back to obtain a salt free crystal density, denoted D,, for which we assume D, = D, = 1-O g/ml. It is easy to show that kf,, the molecular weight of the protein in daltons, can then be obtained from the relation

MD = N V (D, - l*O)/n(l - Q, (2)

where N is Avogadro’s number and n is the number of protein molecules per unit cell. The method does not yield a value for T& the apparent partial specific volume of the protein, which must be obtained independently.

It is possible to use the determined values of (V,.V) and the molecular weight to find the fraction of bound water in the crystal. However, an equivalent answer can be obtained more quickly by determining from the D, versus D, plot the point at which D, = D, = D,, the equilibrium density at which the crystals neither float nor sink. The ratio of the volumes of bound water to protein is then

VwP’, = P, - QWe - 1). (3)

The bound water or protein hydration is usually expressed as grams water per gram protein, and denoted w (Perutz, 1946; Adair & Adair, 1936). In this case the formula of Adair & Adair may be used directly, i.e.

w = (D, - WD, (De - 11,

where we have substituted D, for D,, and assumed that D, = 1-O g/ml.

(4)

To check the feasibility of the proposed method for determining the molecular weight of ,%amylase, experiments were first performed with y-chymotrypsin crystals grown from 50% saturated ammonium sulfate solutions (D. R. Davies, personal communication). For both these proteins it was possible to diffuse caesium sulfate into the crystals without measurably changing the unit cell dimensions, and thereby investigate a range of solvent densities from 1-l to 2-9 g/ml. The crystals were slowly brought to the desired solvent concentration, and then left to equilibrate for at least 24 hours. Densities were measured in a calibrated density gradient (Low & Richards, 1952) consisting of water-saturated iodobenzene, carbon tetrachloride and xylene. Attempts to remove excess liquid from the crystals before introducing them to the gradient tube were not very successful. Instead, we found it preferable to introduce the crystals to the gradient in a droplet of the mother liquor. The mother liquor was then drawn off with a micro-syringe, and if necessary the crystal freed from the syringe tip by using a fine dry glass rod previously treated with a dilute silicone solution.

4. Results and Discussion The results for y-chymotrypsin and /3-amylase are shown in Figure 1. In both cases

the points fall on straight lines. The equation of the line of best fit was obtained by least-squares, assuming the solvent densities to be more accurate than the crystal densities.

For y-chymotrypsin we obtain

D, = 0.345 D, + 0.833,

from which Do = 1.178 f 0904 g/ml. and D, = l-272 f. 0903 g/ml. No value has

166 P. M. COLMAN AND B. W. MATTHEWS

f I.2

I I I I I.4 I.6 I.8 2.0

Solvent density, D, ( g/ml. 1

FIQ. 1. Density of j3-amylake and y-ohymotrypsin crystals plotted as a function of supernatant density. (0) y-ohymotrypsin; (0) /3-amylase. The supernatant density was varied by adding increasing amounts of a saturated solution of oaesium sulfate to the ammonium sulfate solution used for crystallization, and allowing the system to equilibrate (see text).

been published for the partial specific volume of y-ohymotrypsin, but it has been shown that y-chymotrypsin and cu-ohymotrypsin are virtually identical molecules (Cohen, Matthews & Davies, 1970; D. R. Davies, personal communication). We have therefore assumed that the apparent partial specific volume of crystalline y-chymo- trypsin is 0.736 ml./g, the partial specific volume of monomeric ar-chymotrypsin (Schwert & Kaufman, 1951). Using (2) we obtain 24,060 i 700 for the molecular weight of y-chymotrypsin, which is in acceptable agreement with the value of 25,260 calculated from the amino-acid sequence of or-chymotrypsin (Hartley, 1964,197O). The quoted standard deviation in the molecular weight was calculated from the uncertainty in the density measurements end in the unit cell volume and assumes no error in the partial specific volume. For y-chymotrypsin the fractional volumes of the unit cell occupied by protein, solvent and bound water are 50%, 34% and 16%, respectively.

For /?-amylase the best fit straight line (Fig. 1) is

Do = 0.611 D, + O-491,

giving D, = I.102 + 0904 g/ml. and D, = 1,262 f 0903 g/ml. Assuming that the apparent partial specific volume of /I-amylese is 0.74 ml./g (Spradlin t Thoma, 1970) the molecular weight of protein in one asymmetric unit is 206,000 f 10,000. To satisfy the crystallographic date the molecular weight of one j?-amylsse molecule must equal 206,000, or some integral fraction of this value, but sny fractional value would be in disagreement with all the published molecular weight values for /3-amylase, and may therefore be ignored. The value we have obtained for the molecular weight is in good agreement with the value of 197,000 f 6000 recently obtained by Spradlin & Thorn& (1970). Also our result confirms the conclusion of Spradlin & Thorn& that /3-amylese is a tetrameric enzyme.

The accurrtcy quoted here for the molecular weights of y-chymotrypsin and

CRYSTALLOGRAPHIC DATA OF fl-AMYLASE 167

jl-amylase give an estimate of the precision which can be expected for molecular weight determinations of other proteins which can be obtained as reasonably large single crystals. From (2) it can be seen that the accuracy of a given molecular weight determination will be limited in practice by the respective uncertainties in (D,, - l), (1 - CP), and V. The /?-amylase crystals described here have a protein content of about 29% by volume, which is abnormally low (see below). As a consequence D, is closer to unity than would be expected for most crystalline proteins, and in this respect the @mylase crystals happen to be less favourable for an accurate molecular weight determination than would be the case for most other protein crystals. It is for this reason that the standard deviation in the molecular weight of 8.amylase is about S%, whereas for y-chymotrypsin it is about 3%. The second source of error, from the partial specific volume term (1 - Q,), is common to many of the methods of determining molecular weight, and need not be discussed here. Finally, errors may occur in the determination of the unit cell volume, although for most protein crystals the uncertainty would be less than about 1%.

A check on the unit cell dimensions of the y-chymotrypsin and j?-amylase crystals at the upper limit of the solvent concentrations revealed no changes. This observa- tion, together with the linearity of the D, verse D, plots, shows that under the conditions used, penetration of the bound water by the solute ions does not sig- niticantly change as a function of the solute concentration. The experiments des- cribed here do not rule out the possibility that the volume of bound water associated with a given protein might change for different solutes, or be a function of pH, although it may be noted that such variations, if they do occur, would not invalidate the determination of the molecular weight by the proposed method.

The density measurements for 8.amylase indicate that in the crystals the respective volume fractions occupied by protein, solvent, and bound water are 29%, 61%, and 10% respectively. The fact that only 29% of the total crystal volume is occupied by protein suggests that the molecular packing must be very tenuous. The solvent content parameter V, (Matthews, 1968) is 4-2 A3 per dalton which is outside the range normally observed for smaller proteins, and tends to con&m the suggestion made earlier (Matthews, 1968) that higher molecular weight proteins tend to form crystals containing a relatively higher fractional volume of solvent.

In the low resolution pseudo unit cell of the ,%amylase crystals discussed above there are four molecules but eight equivalent positions. If the pseudo cell were the true unit cell it would follow that the j?-amylase molecule had at least one two-fold axis of symmetry. Because the symmetry of the pseudo cell holds only to low resolu- tion the interpretation becomes ambiguous. Either the /3-amylase molecule has at least one exact two-fold axis of symmetry which almost coincides with a crystallo- graphic two-fold axis, or the p-amylase molecule has only approximately two-fold symmetry. These two possibilities cannot be distinguished from the present X-ray data.

We would like to include here reference to an independent study of /3-amylase by D. R. Davies (personal communication) in which similar crystallizing conditions were used, but a hexagonal crystal form was obtained. The hexagonal crystal form may be more suitable for a detailed structural analysis than the tetragonal form described here.

This work WISS supported by the Public Health Service Grant GM 15423 and by the Office of Scientific and Scholarly Research of the University of Oregon.

108 P. M. COLMAN AND B. W. MATTHEWS

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