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BIOCATALYSIS-2000: FUNDAMENTALS & APPLICATIONS

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MECHANISM OF THE THERMOINACTIVATION OF THE -GALACTOSIDASE FROM ESCHERICHIA COLI
L. F. Atiaksheva, O. S. Pilip enko, and O. M. Poltorak

The activity of oligomeric enzymes is sensitive to the formation of interprotein contact that make up the conformational lo ck. The mechanism for this is discussed in this article concerning the -galactosidase from Escherichia coli. The thermoinactivation curve, obtained at 40 C, has induction p erio d that may b e ascrib ed to latent structural changes in conformational lo ck. The analysis of the kinetic curve has allowed us to calculate the minimum numb er of denaturation stages in the conformational lo ck ( n 3 ), i. e. tetramer = b ecomes labile and capable of disso ciation into two active dimers. These data supp ort the kinetic scheme used to describ e the disso ciative inactivation of dimeric enzymes. The inactivation rate decreases in the presence of Mg 2+ . As metal binding sequences are placed in domains 1 and 3, therefore, tetramer interglobular contacts stabilize each subunit. Formation of tetramer influences the activity of each subunit.

-Galactosidase is the example of glycosidases. Galactosidase participates in lactose degradation. The enzyme catalyses lactose transformation into -galactose and glucose. -Galactosidase is metalloenzyme exhibiting broad substrate specificity [1]. The enzyme is a tetramer of four identical subunits. Within each subunit the 1023-amino acid polypeptide chain folds into five sequential domains plus an extended segment at the amino terminus. Each of the four active sites in the tetramer is formed by elements from two different subunits. The -galactosidase from Escherichia coli is a large homotetrameric enzyme (MW = 465 412 Da). The active site of the molecule is possibly formed by the Mg ions therefore conformation changes in residues binding the ions would influence the enzyme activity. The three types of interglobular tetramer contacts were studied according to procedure, proposed in [2]. The summary information concerning interactions between interglobular contacts and active site for each globule is presented in Table 1. In interglobular interactions domains mainly involved domains 1, 3 and 5. As metal binding sequences are placed in domains 1 and 3, therefore, tetramer interglobular contacts stabilise each subunit and one way of activity regulation during some modification of interglobular regions is through domains' displacements. This way of regulation

is characteristic for all three interglobular contact types. The other way, activity influence through displacement of adjacent to active site interglobular sequences is specific for AD-tetramer contact. Thus, formation of tetramer influences the activity of each subunit. In accordance with this primary dissociation active tetramers on two active (and less stable) dimers must be connected with the relationship break-up AB and DC. A @D B @ C AD + BC A + B + C + D.
catalytic active catalytic inactive

From kinetic data follows that dimers of -galactosidase are catalytic active, but structural Data speak of greater toughness of contacts AD and BC, near which are located important for the act of catalysis ions Mg 2+ . The complex multipoint structure of contacts AB (and CD) allows multistage their destroying without the observable influence upon space removed active centres, situated near contacts AD and BC. This is according with the kinetic scheme (1), used for the thermodegradation description of -galactosidase. It is less probable, but is principle possible the process of dissociation with primary break-up AD and BC contacts

Table 1 Active site and interglobular contact interactions in Escherichia coli -galactosidase. A, B, C and D-globules [1]. Protein molecule site Mg 2002 binding Mg 2012 binding Intg AB Intg AC Intg AD Domain(s) involved 1, 3 1 3, 5 1, 2 1, (2), 3 Overlap with metal binding sequence -- -- No No Yes Metal binding interdomain stabilisation -- -- Yes Yes Yes

Department of Physical Chemistry, Faculty of Chemistry, Moscow State University.

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VESTNIK MOSKOVSKOGO UNIVERSITETA. KHIMIYA. 2000. Vol. 41, No. 6. Supplement

A @D B @ C

AB + CD A + B + C + D.
catalytic active catalytic inactive

An example of such inactivation of -galactosidase is given in [3]. Study of processes of thermoinactivation under more low temperatures (5561 C) is more informative. In this interval of temperature thermal inactivation may occur via dissociative inactivation according to the kinetic scheme: E4 E4 . . . 2E2 4E1 4Ed , (1)
Fig. at pH (1, 3) Mg 2+ 2. Kinetic of thermoinactivation of -galactosidase 7.5 and 48 C and various concentrations of enzyme: 36.55 mg/l and (2, 4) 7.3 mg/l; (1, 2) in absence of ions and (3, 4) in the presence 0.01 M of Mg 2+ .

where E 4 is stable tetramer, E 4 and E 2 are active intermediate forms (labile tetramer and active dimer), E 1 is inactive monomer, and E d is a denatured monomer. Presence of dimer and labile tetramers in the process of thermoinactivation of -galactosidase is discovered in work [3]. When raising a temperature to separate stages of scheme (1) become kinetic indistinguishable, but kinetic process is described by first-order equation. Kinetic study of scheme (1) enables to define from experimental data efficient constants of velocity of inactivation. It is clear, that the real mechanism of dissosiative inactivation have turned out to be complex. The inactivation curves shown in Figs. 1 and 2 are observed for oligomeric enzyme-- -galactosidase. For this enzyme at 40 C some induction period is observed during thermal inactivation. This is illustrated in Fig. 1 by kinetic curve 1. It is important that in this case only one quantity is to be additionally determined from experiment--the induction period (latency period) and in scheme (1) there is unknown number of conversion steps with unknown number of rate constants for reciprocal transitions. Thus, this problem has no conclusive solution, and it cannot be solved only by the methods of chemical kinetics. In this case, other information must be added to kinetic analysis of inactivation, for example the X-ray data on the spatial structure of dimeric enzymes, which give additional information on the state of protein before its dissociation.

The kinetic problem has also turned out to be more definitive. It has been found that a limiting value of the number of possible intermediate steps of protein conversion can be determined. A simple approximate relation for practical calculations has the form [4]: n = (0.13 + )/(0.13 - 0.05 ), where n is a certain quantity that describes the irreversible transitions of n enzyme oligomeric forms with similar rate constants (equal to k1 ), R = (1 + ) is the ordinate intercept produced by a tangent to the inflection point of the kinetic curve in Fig. 1, and is a dimensionless parameter used to calculate a minimal number of active intermediate enzyme forms. This makes it possible to estimate the minimal number of step protein conversion for dissociation into catalytically inactive monomers. It has been found n = 2.9 , as illustrated in Fig. 1. Within the error of calculation it means, that it may be three active forms in scheme (1) E4 E4 E2 or E4 E2 E2 . Here E 4 is stable tetramer, E' 4 is labile tetramer ABCD and E 2 and E 2 is stable and labile any active dimers AD or BC. Based on kinetic data, it is impossible to judge either the real number of intermediate active forms of an enzyme or of the nature of organisation of the conformational lock. Here, an alternative arises that cannot be understood without appealing to the data on a real spatial structure of -galactosidase. This alternative is the following: whether the conformational lock opens through two steps within one spatial site of interprotein contact ADBC, or there are two such sites within interprotein contact AD (or BC). Thermal inactivation of -galactosidase at 45 C, 48 C, 50 C, and 52 Cas have shown in Fig. 1 curves 25 does not proceed through an induction period. A specific feature of these kinetic curves plotted in co-ordinates of first-order equation is the presence of inflection points. As seen from Fig. 2, in fact these inflection points I and II are the intercepts of asymptotes to a continuous straight line. It is not difficult to determine the inflection points in experiments. Position of inflection points and the slopes

Fig. 1. Kinetics of thermal inactivation of -galactosidase for different temp eratures at pH 7.5: 1, 40 C; 2, 45 C; 3, 48 C; 4, 50 C, and 5, 52 C.

BIOCATALYSIS-2000: FUNDAMENTALS & APPLICATIONS

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of curves in coordinates of first-order kinetic curve allow us to determine three elementary constants of kinetic scheme (2)--degradation of dimeric protein E 2 , E2 Kdis 2E1 --kd 2Ed . (2)

rate constant kd that characterises of native monomeric protein as follows: kd = kd (v0 + v )/2(v0 - v ), where kd is the effective rate constant determined by slope of the straight line at t > : (Fig. 2) 1.3 в 10-4 s -1 (36.5 mg/l protein) and 1.5 в 10-4 s -1 (7.3 mg/l protein). In the presence of Mg 2+ ions kd is 3.8 в 10-5 M and does not depend on the protein concentration (Fig. 2, curves 3 and 4). The inactivation rate decreases in the presence of Mg 2+ . In interglobular interactions domains mainly involved domain 1, 3 and 5. As metal binding sequences are placed in domains 1 and 3, therefore, tetramer interglobular contacts stabilise each subunit. Formation of tetramer influences the activity of each subunit.
References 1. Jacobson R.H., Zhany X.J., Dubose R.F., and Matthews B.W. Nature. 1994. 369. P. 761. 2. Poltorak O.M., Chukhray E.S., Atiaksheva L.F., and Torshin I.Y. Zh. Fiz. Khim. 2000. 74. 3. Chang B.S. and Mahcney R.R. Biothechnol. Appl. Biochem. 1994. 15. P. 169. 4. Poltorak O.M., Chukhray E.S., and Torshin I.Y. Biochemistry (Moscow). 1998. 63. P. 360.

Here E 1 is a monomeric protein capable of a reversible restoration of initial structure and E d is the product of an irreversible changing of E 1 . Kinetic scheme (2) has no explicit analytical solution, because in addition to two monomolecular processes, it involves a bimolecular stage ( k-1 ). However, chemical kinetics has available approximation methods develop to describe complex reactions. For a zero approximation, the description of one process is used. At the initial moment of time ( t = 0 ) the single occurring process is dissociation with the rate constant k1 . It is described by first-order equation. The slope of the straight line plotted in linear co-ordinates of first-order equation ( ln[E2 ] against t ) gives value of constant k1 : 3.6в10-5 s -1 (45 C); 1.3в10-4 s -1 (48 C and 50 C) and 3.3в10-4 s -1 (52 C). An approximate determination of kd , the constant for inactivation of native monomer capable of reversible association may be carried out for quasi-equilibrium concentrations of intermediate form E 1 . The rate constant determined by the slope of the straight line at t > , in the point t = (inflection point) is related to the elementary