Viscoelasticity of protein crystal as a probe of the mechanical properties of a protein molecule

J. Mol. Biol. (1982) 157, 173-179

Viscoelasticity of Protein Crystal as a Probe of the Mechanical Properties of a Protein Molecule Hen Egg-white Lysozyme Here we present a new approach of a protein globule based on

to studying

the anisotropy

of the elastic

properties

an analysis of the elastic properties of a protein monocrystal. The anisotropy of the elasticity of hen egg-white lysozyme triclinic crystals, as well as its changes because of the formation of a lysozyme-N-acetyl-aon the glucosamine complex, were investigated. The data can be explained assumption that the lysozyme molecule consists of two rigid domains connected by a flexible

link. The binding

of the inhibitor

in the active-site

an increase of about 40:/o in the interdomain

cleft is accompanied

by

rigidity.

From the mechanical viewpoint a protein crystal is a molecular construction in which the only interaction is between nearest neighbours (Perutz, 1965), and this interaction is comparatively small so that the molecules in the crystal retain their general properties (Rupley, 1969). The problem consists of deducing the properties of t,he individual elements of the construction from those of the whole assembly. We illustrate below the close relationship between the properties of the protein molecule and the mechanical properties of the monocrystal on triclinic crystals of lysozyme and its complex with inhibitor. The method for measuring the dynamic Young’s modulus, E, and the logarithmic decrement, 9, of protein monocrystals consists of analysing the resonance vibrations of a cantilever made of the crystalline plate, as described earlier (Morozov & Morozova, 1981). We have shown that the elasticity of the crystal is non-entropic as long as the globules retain their integrity, and is determined by deformation of both the globules and the intermolecular contact areas. Analysis of the mode of packing of lysozyme molecules in triclinic crystals enables us to advance several hypotheses about the mechanical properties of the monocrystals that can be tested experimentally. In sections (100) and (001). presented in Figure l(a) and (c), two domains separated by the active-site cleft can be seen clearly. If the domains are rigid bodies (Young’s modulus for protein along the material E, - 6GNme2; Morozov & Morozova. 1981), the deformation direction [OlO] will lead to displacement of the domains with respect to each other and thus t’o a change in the width of the active-site cleft. As a consequence, the crystallographic direction [ 0101 would possess a relatively higher compliance, S = E - ‘, than [ 1001 and [OOl] due to a greater softness of the globule along this direction. The binding of the competitive inhibitor in the activesite cleft is accompanied by the formation of numerous van der Waals’ and a few hydrogen bonds with both the domains (Imoto et ~1.. 1972: Kurachi et al.. 1976). 002&2836/w/130173-07

$03.00/O

‘i” I982

Acadrmic

Press Inc.

(I~mdon)

Ltd.

T. Y. MOROZOVA

174

ANI)

\‘. S.

XJOMOZOT’

FIG. 1. Sections of the triclinic crystal parallel to the main crystallographic planes and going through contact sites : (a) parallel (100); (b) p arallel (010); (0) parallel (001). Sections were performed in accordance with the set of co-ordinates (Imoto el rcl.. 1972), orientation of the molecules was performed according to Moult et al. (1976). Numbers on the left between cross-sections show the distance in A from the section that goes through the centre of the contact, area.

The decrease in the compliance of the domains pronounced We

for the direction

analyse

crystallographic directions are crystallographic molecules

of the globule due to t)he restriction

must cause a decrease in the crystal compliance the

because

properties the

of

the

intermolecular

Iysozyme contact’

the most extended and are nearly axes. This eliminates t,o some extent

and facilitates

The experimental above hypothesis

lOlO].

viscoelastic

axes

of the mobility

that’ would be most’

the interpretation

data presented

about the mechanical

crystal areas

along

along

perpendicuIar the “slipping”

its

these to of

the the

of the results.

in Table 1 are in good properties

agreement

of t’he triclinic lysozyme

with the crystal.

As was expected, at high humidities the compliance of the [OlO] direction reliably exceeds those of the [loo] and [OOl] directions. The [OlO] direction remains more compliant up to 45”/b humidity. There is no difference in the compliance of the directions at lower humidities. The same is true for different protein crystals

LETTERS

TO THE TABLE

Average

compliances

directions

S = E-l

EDITOR

175

1

(E is Young’s modulus)

for the main crystallographic A9 and their change.s. AS, and the changea in the logarithmic decrement, 9, after soaking

in 0.5 .wGlcNAc

2 Crystal

direction

[10(4 IO101

I(@11

S(98) (GN-’

m*)

S’(98) x ; (N-l

x 10’ m)

Q734f0.016 w 0822 + 0.023 25t

21.3 f046

0.739

33.1+ 1.3

+ 0029

8t

31.7 kO.88

AS(82) (GN-’

II?)

@125+0+-107 3tlt @166+0906 58t @120f0010

AS(82) x @f/V) x 10’

A9 s

(R-1 In)

(%)

3.62 + 0.20

5f5

6.40 k 022

7*5

5.38 + 0.50

7*5

m

The measurements were done on crystals equilibrated at relative humidities (in %) shown in parenthesis. S’Q~/~~are the values related to a single molecule in the triclinic crystal ; cl1is the unit cell dimension (a. b or c in Fig. 1) for the corresponding direction: B is the unit cell volume. Experimental conditions: temperature, 25°C; the solution of GlcNAc (Sigma) was prepared using the buffer the crystals were grown from. The time of soaking was not less than 2 h. t Number of experiments from which the average values are calculated.

(Morozov & Morozova, 1981). It is more reasonable to consider the compliance of the crystal at low humidity as that of protein material rather than that of a construction consisting of individual protein globules. Soaking the crystals in O-5 M-N-acetyl-n-glucosamine (GlcNAc) considerabl) decreases the compliance; the effect along the [OlO] direction being about 1.3 times the effect along the other directions. As seen from Figure 2, in a humidity range from 98 to 70% the effect remains practically unaltered in spite of a twofold variation in the compliance. At humidities lower than 70% the effect of the inhibitor rapidly decreases. Presumably. this may be the result of the immobilization of the domains due to adhesion of the molecules. The change in compliance upon inhibitor binding. AS, for the series-connected globules must be proportional to that of a single globule and to the fraction of proteirlGlhibitor complex present in the crystal. The Scatchard plot presented in Figure 3(a) appears to be biphasic, with different limiting slopes at low and high fractional saturation. Such a complex concentration dependence may be equally well described, assuming both the heterogeneity of the binding sites (at least two of (as them with K, = 70 to 90 M-’ and Kz = 6 to 9 M-I) and negative co-operativity it is seen from Fig. 3(b), with Hill’s coefficient n = 0.84, Kapp = 23 M-l). These two possible explanations cannot be distinguished between by binding measurements alone. Irrespective of this, the binding constants are high enough to be comparable with those obtained in solutions (Imoto et al., 1972) and in tetragonal crystals (Butler & Rupley, 1967). We consider this fact as evidence that the mechanical effects of inhibitor binding are due to binding in the active-sit,e

T. Y. MOROZOVA

176

I

ANT)

V. X. MOROZO\

1

I

I

1

80

60

40

20

Relative

humidity

1

1 0

(%)

FK. 2. Effect of GlcNAc on compliance, S = E-‘. of lysozyme triclinic crystals at different humidities: ( - 0 - 0 - ) crystals soaked in a buffer (50 mM-acetate, 2% NaNO,. pH 4.5); (- l - 0 - ) the same crystals after soaking in 0.5 M-GlcNAc in the same buffer for more than 2 to 3 h. Direction [OlO].

8.0

(a)

cog CGLCNACI

4

8

12

16

AS x IO2 (GN-‘m”) FIG. 3. (a) A Scatchard plot of the data of the binding of GlcXAc with Iysozyme triclinic crystals. dS is the decrease in the crystal compliance for the [OlO] direction induced by binding with the inhibitor. The curve is calculated for the scheme with two independent sites, with parameters: K, = 81 M- ‘, AS;“” = 0968 GN-’ m2, K, = 7+X M-I, AS’T = 0.119 GN-’ m’. (b) A Hill plot for the same data: Hill constant n = 0.84; the apparent binding constant K,,, = 23 M- ’

LETTERS

TO THE

EDITOR

177

cleft, as was revealed by X-ray analysis (Kurachi et al., 1976). These data can also be applied to the glutaraldehyde-treated crystals, as glutaraldehyde does not change the mode of inhibitor binding (Yonath et al., 1977; Sielecki & Yonath, 1978). Both the compliance of the protein molecule and the packing of the globules in the crystal determine the measured compliance, S. Therefore, the decrease in the compliance caused by inhibitor binding may be the result of both the decrease in the compliance of the globules and some disturbances in intermolecular contacts. Though X-ray analysis does not show any significant changes in the lysozyme conformation, apart from the vicinity of the inhibitor binding site (Kurachi et al., 1976), some slight disturbances in the contacts might take place. There are two ways to check the contribution of intermolecular contacts to the generation of the inhibitor-induced effect: either by changing the structure of the contacts in the same crystal, or by studying the effect in different forms of lysozyme crystals. The similarity of the signs and values of the effect in all these experiments would be sufficient evidence that the contacts do not contribute essentially to the effect. The evidence obtained in our experiments on the alteration of the contacts in triclinic crystals is presented in Figure 2. Our measurements show that a decrease in humidity from 98 to 70yb is accompanied by - l-2:/, decrease in the length of the crystal sample. Therefore the protein molecules must tend to come closer together (the displacement - @4 A) and hence to increase the area of contact between adjacent molecules. In spite of this considerable disturbance of the contacts, which causes an increase of more than lOOo/o in the rigidity of the crystal, the inhibitorinduced change in the compliance of the crystal remains remarkably constant in the humidity range from 98 to 70%, for each crystal direction that was investigated. The data lead to the conclusion that some other elastic element. different, from the contacts but series-connected with them is responsible for the effect of the inhibitor. Recently, we found that. like triclinic crystals, tetragonal P432, 2, crystals and amorphous lysozyme films showed about the same decrease in compliance after soaking in acetyl glucosamine solution (unpublished data). This is sufficient evidence in favour of the idea that the change in the compliance of the globule is responsi.ble for the effect. All the data presented above can be easily understood if the crystal is thought of as being constructed of two series-connected elastic elements; namely. globules, the elasticity of which depends slightly on humidity but is responsible for the effect. and intermolecular contact areas, which are not affected by inhibitor binding but are strongly dependent on humidity. From this point of view there is no essential difference in the effect for all the crystal forms in which binding of the inhibitor is compatible with the crystal structure. So far we have discussed the compliance of the crystal as a whole. To take account, of the number of molecules along the main crystallographic direction in triclinic crystals as well as the number of molecules per unit area of a perpendicular cross-section. the measured compliance of the crystal, S, must be multiplied by a fact,or (az/V). where ai is the unit cell dimension (a, b or c in Fig. 1) for the corresponding direction and V is the volume of the cell. The value obtained in this way may be used as roughly characteristic of “molecular compliance”. It includes

T. Y. MOROZOVA

178

AND V. 5. MOROZOL

both the sum of the compliances of the globule and the intermolecular contact areas and a portion of the compliance along other directions due to Poisson’s ratio. As seen in Table 1. the anisotropy of the effect of inhibitor in terms of molecular compliance is more pronounced than that of the crystal. The compliance of intermolecular contacts decreases rapidly with the dehydration of the crystal. As seen in Figure 2; at humidities below 70($, it reaches a plateau value. Assuming the compliance of the crystal in the range of humidity from 70 to 600/, to be due mainly to the deformation of the globules, the ratio of the maximum change in the compliance in the [OlO] direction to the compliance at 700,;. dS~~~,/S,O,o, (70%) = O-4, gives a rough approximation of the relative change in the elasticity of the interdomain link in the lysozyme molecule resulting from inhibitor binding. It is interesting to note that the maximum effect’ of inhibitor binding in terms of hinge-bending rigidity corresponds to the disappearance of the “spring” with the This value can be calculated (at least b? rigidity k, - 2 x 1Ol3 erg.mo-‘.rad-2. the order of magnitude) assuming that the axis of rotation of t’he t,wo domains passes through the point 0 in Figure l(c) perpendicular to the plane (OOl), and the forces to be applied at points P and Q along the [OIO] direction. The value is very close to k, = 3.3 x lOI erg.mol-’ .rade2 as calculated by McCammon et al. (1977) for the hinge-bending mode of deformation of the lysozymr molecule. There are clearly a number of problems to be solved to complete a more accurate analysis of the internal anisotropy of the protein globule using t,he mechanical properties of the crystal. Nevertheless, the present study shows that there is a strong correlation between the mechanical properties of the prot,ein molecule and those of the protein crystal. Should t,he packing of the molecules be known from Xrav analysis. the mechanical properties of the crystal may be interpreted in terms of the molecular mechanics. Institute

of’ Biological

Physics

of the U.S.S.R. $cademy of Sciences Pushchino. 3Ioscow Region, 142292. I’.S.S.R. Received

!> December

198 I

REFERENCES Butler. L. G. & Rupley, ,J. 8. (1967). J. Biol. Chem. 242, 1077.-1078. Imoto, T.. Johnson. L. N.. North, A. C. T., Phillips, D. C. & Rupley, J. ,4. (1972). In Thr Enzymes (Boyer, P. D., ed.), vol. 7, pp. 665-868, Academic Press, London. Kurachi, K., Sicker, L. C. & Jensen, L. H. (1976). J. Mol. Biol. 101. 1 I-24. McCammon, J. A.. Gelin, B. R.. Karplus, M. & Wolynes, P. Q. (1977). Natwe (London), 262, 585-590. Morozov, V. N. & Morozova, T. Ya. (1981). Biopolymers, 20, 451--467. Moult. J., Yonath, A., Traub, W., Smilansky, A., Podjarny. A.. Rabinovich. D. $ Saya, A. (1976). J. Mol. Riol. loo, 179-195. Perutz, M. F. (1965). J. Mol. Biol. 13, 64tS-668. Rupley, J. A. (1969). In Structure and 8tnbility of Biologimi M(lcronLolrculrs (Timashrff. S. N, & Fastnan, G. I).. eds). pp. 291-353. Marcel Dekker. New York.

LETTERS

TO THE

EDITOR

179

Sielecki, A. & Yonath, A. (1978). In Biomoleculnr W-ucture Conform&ion, Function trod holution. Proc. In,t. Symp.. Madras, January, 1978 (Srinivasan, R., ed.), vol. I. pp. 201-204. Pergamon Press, Oxford. New York. Toronto. Sydney. Paris and Frankfurt. Yonath, A., Sielecki, A., Moult, J., Podjarny, A. & Traub, W. (1977). Biochemistry, 16, 1413-1417. Edited by A. Klug