BIOPOLY MERS VOL. 9, PI’. 113-115 (1970)

COMMUNICATIONS TO THE EDITOR

A Physical Model for the Structure of Glutamate Dehydrogenase

The molecular weight of the active oligomer of bovine liver glutamate dehydrogenase, GDH, has been variously reported between 250,000 and 400,000; i t has been claimed that the enzyme is composed of four to eight subunits and associates further to molecular weights as high as 1-2 x 106.1

Subunits are used by nature as a device towards the solution of complicated regulatory biological processes. It is therefore of utmost importance that, once the correct number of subunits has been determined, this information be used towards the establishment of a physical model of enzyme structure, in which the spatial relationship of these subunits is well defined. This then is only a preliminary step towards the complete description of the location of each individual atom, a goal recently achieved in some selected cases by x-ray crystallography.

We believe, on the basis of a recent study,2 that the active oligomer of GDH has a molecular weight of 312,000 and is composed of six identical subunits of 52,000 molecular weight each. Our molecular weight determinations have recently received support from other physical studies, both with respect to the oligomer3e4 and the subunits.5 Also, although Sund and Burchard6 recently report a molecular weight of 280,000 for the active oligomer, a value slightly lower than our own value of 312,000, we find by plotting their molecular weight values (from light scattering) a t low enzyme concentration, that extrapolation may well lead to a value close to our own.

Support for our belief that the active oligomer is a hexamer comes from a comp!etely independent source. Valentine’ recently reported some pictures taken of this elusive enzyme; he confirms earlier observationss that the molecule has a triangular profile : “This suggests two layers with 3 units in each (symmetry 322).”

The physical model of GDH which we would like to explore further is illustrated schematically in Figure 1. In this tentative model the oligomer is formed by two layers, each composed of three elongated subunits approximated by prolate ellipsoids of rotation, arranged in triangular fashion. In the individual layers the major axes 2a of the ellipsoids point in the same direction. Two layers, stacked on top of each other, form an elongated oligomer, which can further polymerize, to polymers of indefinite length,2 in the direction of the major axes of the prolate ellipsoids. (On the basis of studies performed to date, it is not possible to distinguish whether the three-subunit layers in the oligomer are arranged in a staggered or eclipsed configuration with respect to each other.) This polymerization is affected by enzyme concentration and by a large number of reagents, but it is interesting to note that dissociation into active half- oligomers, containing three subunits each, has not been achieved.

In evaluating the quantitative aspects of the proposed model we are greatly helped by a recent low angle x-ray scattering study of Sund et aL9 They find, by a careful study over a wide range of concentrations, that the mass per unit length .Of GDH is 2340 Dalton/& and the radius of gyration ro of the cross section, rg = 30.3 A, independent of the state of association of the enzyme. Clearly, this confirms the linear association of the enzyme.

The following quantitative deductions can now be made in conjunction with the model propoosed. The major axis 2a of the ellipsoidal subunits equals ,,3 X 52,000/2340 = 66.5 A. The volume V of the subunits V = (4/3) Tab2 equals 52,000 ~ / N A (in ml), where 6, = 0.75 is the partial specific volume (in ml/g) of the enzyme and N A is Avogadro’s number. With a = 33.25 A we evaluate b = 21.5 A. The value of r p with respect to the long axis of the

The length of the oligomer is therefore 2 X 66.5 = 133 A.

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114 l3IOI’OLYMEHY VOL. ‘3 (1970)

I

Fig. 1. Schematic drawing of niodel of UDH olig2rner. Arrotws indicate dircetion of polymerization; 2a = 66.5 A; 2b = 13 A.

structure of Figure 1 is given by

To2 = (2/5) b” + d2 = (26/15) b2 (1)

where d = (4/3)l/z b is the distance fromothe central axis to the axes 20 of theoellipsoids. With b = 21.5 .&we calculate r , = 28.3 A. This is rather close to r0 = 30.3 A reported by Sund et al.,Q and the slightly lower value given by the model may be due to vooids, loose arrangements of the subunits, or hydration. Valentinelo reports about 80 A for the triangular “edge” of the oligomer, we find (Fig. I) a value 4b = 86 A from the model. The overall agreement may be regarded as satisfactory.

We find that addition of small amounts of toluene to GDH solutions greatly increases the linear association and leads to well defined structures similar to the structures obtained in phosphate buffer (but at twentyfold lower concentrations), with molecular weights in excess of 3 X 106. A unique linear relationship was found between molecular weight and radius of gyration of the particles (Fig. 2). Therefore only one, linear association, model appears feasible. Let us consider an aggregate containing 10 oligomers, molecu- lar weight 3.12 X 106; the length of this titructure, according to the model is 10 X 133 = 1330 A. We find, from light scattering studies (Fig. 2), a radius of gyration R, with respect to the cent,er of the molecule, ZZ, = 430 A. We calculate for R, on the basis of the model

(2)

where P is the number of oligomera per polymer; L = 4uP is the length of the polymer. For I’ >> 1, the first two terms are negligible, and eq. (2) reduces to fig2 i= L2/12, which

It is now possible to test the dimensions of the long linear aggregates.

Roz = (26/15) b2 + (1/5) a2 + L2[(4P2 - 1)/48P2]

m 0q400 m t 2ool

I I I I I I I 5 10 15 20 25 30 35

M , ~ ~ X I O - 5

Fig. 2. Radius of gyration It?, from light scattering of GDH solutions vs. apparent molecular weight, Mspp; (0) sodium phosphate buffer 0.261, pH 7, l0-4M EDTA, 25"C, enzyme concentration range 0.5-1 1 mg/ml; (A) same butrer, various temperatures (10-3O0C), same range of enzyme concentrations; (+) same buffer, saturated with respect to toluene, enzyme concentration range 0.034.5 mg/nil; (0) calculated value for the oligomer, P = 1.

is the relationship valid for long rigid rods. For u = 333.25 A, 6 = 21.5 A, and 1' = 10, we calculate 12, ; 385 A. This is only slightly smaller than the value experimentally determined (430 A), and the discrepancy may be due to polydispersity in the associated enzyme. The value of R , obtained from light scattering is a higher average than the weight-average molecular weight.

With P = 1, and the values for u and b as above, we find R, = 46 A. This value is consistent with the extrapolation of IZ, values (Fig. 2) from Iiigher niolecular weights to MW = 312,000 of the oligomer. I t is suggested that this can be experimentally verified (by low-angle x-ray scattering, for instance), in systems in which association does not occur.*

We hope to confirm by angular dependence of scattering, viscosity, and velocity sedinientation that both the dimen- sions of the oligomer and of the proposed linear aggregates are consistent with a struc- ture similar to the one documented in the present work.

It is of interest to calculate R , for the oligomer unit kMW = 312,000).

Scattering and hydrodynamic work is in progress.

References 1. H. Sund, In Biological Oxidations, T. P. Singer, Ed., Interscience, New York,

2. H. Eisenberg and G. Tonikins, J . Mol. Hiol., 31, 37 (1968). 3. 1M. Cassman, private communication, 1968. 4. P. Uessen and L). Pantaloni, European J . Uiochem., 8, 292 (1969). 5. A. Ullman, M. E. Goldberg, L). Perrin, and J. Monod, Biochemistrg, 7,261 (1968). 6. H. Sund and W. Burchard, European J . Bioclieim., 6, 202 (1968). 7. It. C. Valentine, paper presented a t Fourth European Regional Conference OIJ

8. It. W. Horne and G. L). Greville, J . M o l . Biol., 6, 506 (1963). 9. H. Sund, I. Pilz, and M. Herbst, European J. Hiochem., 7, 517 (1969).

1968, p. 658.

Electron Microscopy, Rome, 1968; dbstrucls, 2, 3 (1968).

10. It. C. Valentine, private conimunication, 1968.

HENRYK EISENBERG EMIL REELER

Polymer Department The Weizmann Institute of Science Rehovot, Israel

Received May 28, 1969 Revised September 8, 1969