Biochimica et Biophysica Acta, 495 (1977) 195-202 © Elsevier/North-Holland Biomedical Press BBA 37791
T H E P O L Y M E R I Z A T I O N P A T T E R N OF ZINC(II)-INSULIN AT pH 7.0
BRUCE K. MILTHORPE, LAWRENCE W. NICHOL and PETER D. JEFFREY
Department of Physical Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T. 2601 (Australia) (Received April 22nd, 1977)
SUMMARY
Sedimentation equilibrium experiments were conducted at pH 7.0 using solutions of bovine insulin containing 2 mol of zinc(II) ions per six base-mol of insulin. A detailed analysis of these results revealed the existence of a stable zinc-insulin hexamer together with linked polymerization reactions. Specifically these are a background polymerization of zinc-free insulin as previously described by Jeffrey et al. ((1976) Biochemistry 15, 4660-4665) and a slight tendency for the zinc-insulin hexamer to undergo indefinite self-association. Equilibrium constants governing these reactions are reported together with equations which permit calculation of the composition of the solution at any given total concentration. Comment is made on the possible biological significance of this linked polymerization pattern, and on the likely identity o f the structure of the stable zinc-insulin hexamer with that pceviously reported from X-ray crystallographic studies.
INTRODUCTION
In a previous communication [1] it was established that the polymerization pattern of bovine insulin, freed of proinsulin and zinc, at pH 7.0 comprised an equilibrium mixture of monomer (molecular weight 5734), dimer, and a series of higher polyr0ers formed by isodesmic indefinite self-association of the dimer. Thus, the systel~ was described by two equilibrium constants, a dimerization constant, K2, of 1.1. l0 s M -~ and an isodesmic equilibrium constant, KI.2, of 1.7- 104 M -1. The latter isodesmic constant requires that each successive addition of a dimer unit to form higher polymers be governed by the same standard free energy change, a postulate consistent with linear or branched chain growth [2, 3]. In this connection, it is noteworthy that hexamer is postulated as one polymer in chain formation but is given no particular prominence; whereas X-ray crystallographic studies [4] emphasize the importance of a hexamer of closed structure. The basic difference between the studies is that while those in solution were conducted in the absence of zinc(II), the structure indicated in the crystallographic studies refers to a hexamer with two zinc(II) ions coordinated to histidines on the three-fold axis. The major purpose of this work is to explore a possible correlation between these findings by conducting sedimentation equilibrium experiments on a system to which the stoichiometric amount of zinc(II)
196 has been added to the self-associating apoprotein. Although zinc(II)-insulin has been extensively studied [5-9] no detailed thermodynamic analysis of the results in terms of possible linked polymerization patterns has been performed. MATERIALS AND METHODS Bovine insulin containing 0.78 g zinc/g anhydrous protein, 3-4 ~ proinsulin and approximately 5 ~ monodesamido insulin was obtained from Australian Commonwealth Serum Laboratories. The sample was freed of zinc ions by extensive dialysis against 0.01 M HC1 as previously described [1]. This material was freed of proinsulin by gel chromatography on a Sephadex G-50 column (55 × 1.7 cm), subsequent analysis by polyacrylamide disc-gel electrophoresis, conducted as previously reported [1], revealing the absence of proinsulin but retention of a small amount of the monodesamido component. The sample, termed fractionated insulin, was therefore identical with that used in the previous study [1]. The introduction of zinc(II) in the form of zinc nitrate was effected as follows: fractionated insulin was dialysed to pH 7.0 (buffer 0.1 M Tris/HC1, 0.1 M NaC1 at 25 °C), the protein concentration was determined spectrophotometrically at 276 nm employing an extinction coefficient of 1.05 A units/cm (mg/ml) [10], and the requisite amount of standard zinc nitrate solution was added by weight to achieve a final stoichiometry of 2 mol of zinc(II) ions/six base-mol of insulin. It was found that the solubility limit of zinc-insulin so prepared was 0.9 g/1. It is required to precede each sedimentation equilibrium experiment by dialysis [11] and this was performed in pre-washed Visking 18/32 tubing against twenty times the volume of the pH 7.0 buffer containing no zinc ions for a period of 12 h. In a control experiment the zinc(II) content was checked after dialysis by atomic absorption spectroscopy and within experimental error it was shown that the bound zinc(II) maintained the cited stoichiometry. This does not imply that the binding of zinc(II) is an irreversible process, for indeed binding constants have been estimated [8, 12] and it is known that the bound zinc(II) may be removed by addition of the chelating agent EDTA [13]. It does imply that, within the 12 h equilibrium dialysis used to equilibrate buffer ions, the extent of dissociation of bound zinc(II) was not detectable within the precision of the analysis technique. Sedimentation equilibrium experiments were conducted at 25 °C using a Spinco model E analytical ultracentrifuge equipped with electronic speed control and a Rayleigh interference optical system. The protocol of the experiments, which used the inert fluorocarbon FC43 as an inert base fluid and were of the Chervenka meniscusdepletion design [14], has been given previously [1]. The experiments were run for 24 h and the attainment of equilibrium was checked by measuring penultimate and final interferograms, all measurements being made on a Nikon microcomparator. The low solubility limit of zinc(II)-insulin at pH 7.0 (0.9 g/l) precludes a series of sedimentation equilibrium experiments conducted with a wide range of initial loading concentrations and angular velocities. Accordingly, a single set of conditions (angular velocity of 36 000 rev./min and initial loading concentration of 0.060 g/l) was employed, although the loading volume3 differed slightly in each experiment. The experimental sedimentation equilibrium distributions, with meniscus concentration essentially zero, were converted into plots of total concentration vs. radial distance using the determined relationship, 3.93 Rayleigh interference fringes is equivalent to 1.00 g/l. The
197 monomer molecular weight of bovine insulin was taken as 5734 [14], a value of 0.73 ml/g was used for the partial specific volume [10] and solution densities were measured with an Anton Paar DMA-02C precision density meter. RESULTS The experimental records of total concentration, O(r), vs. radial distance, r, at sedimentation equilibrium reflect only the contribution of the protein constituent since the unbound zinc ion concentration, of estimated magnitude less than 10-6 M [8 ], cannot contribute significantly to the interferogram. It was accordingly possible to use the f2(r) method [15] to determine the concentration distribution of the insulin monomer. Specifically the f2(r) function is defined as .(2(r) = ((r) exp {qOlM,(rvz -- rZ)}/((rv)
(1)
where ~t equals (1 -- ~19)co2/2RT (with the conventional notation) and (?(rF),rF) is a reference point selected from within each experimental distribution. Provided a common ((rv) is selected, data from both experiments exhibiting different equilibrium distributions may be correlated [15]. The plots of.Q(r) vs. ((r) for both experiments, using ~ M t referring to the monomer, are shown in Fig. la. Except for minor deviations at low ((r), it is evident that the results from both experiments fall on the same curve and that there is little difficulty in extrapolating the averaged results to yield a value of-Q°(r) of 0.05 -4- 0.01 at infinite dilution. The estimated error was obtained as extremes of extrapolated values for the two experiments considered separately. It follows directly from the previous theoretical treatment [15] that
al(r) ---- ((r)f2°(r)/g2(r)
(2)
where at(r) is the thermodynamic activity of monomer. It has also been shown previously for the insulin system [1] that in the total concentration range spanned in Fig. la non-ideality effects are of negligible magnitude and thus at(r) may be identified with the weight concentration o f monomer, el(r). Fig. lb presents a plot of c~(r) vs. the corresponding ((r) derived from Eqn. 2 with I2°(r) equal to 0.05 and the data presented in Fig. l a. These results clearly demonstrate that even in the presence of the stoichiometric amount of zinc(lI), appreciable quantities of insulin monomer continue to exist at all points in the cell at sedimentation equilibrium. The finding is in agreement with other sedimentation equilibrium studies on zinc(II)-insulin at pH 7.0 where a less refined analysis based on weight-average molecular weights also indicated the existence of monomer [9]. If the assumption, reasonable on stoichiometric grounds, is made that this monomeric form is free of bound zinc ions, it follows as a necessary thermodynamic consequence that the complete zinc-flee insulin polymerization pattern described in the introduction must also be operative. The contribution, ¢~(r), to the total observed concentration, ((r), of this set of equilibria may be calculated using the equation el (r) =
2
M1 ml (r) {(1 -- K2 KI.2 ma (r)) 2 + 2K2 ml (r)} {1 -- 1(2 K~.z m~ (r)} 2
(3)
198
1.0
.4¢"°
Q (r) 0.5
fo* .,Z f
2" o11
0:2
o13
oi,
~(r)
(g/l)
o16
0.03
cl(r) (g/l) 0.02
o
~o
0.01
I
072
o"
o!s
0!6
o,
Fig. 1. Plots relating to the 12(r) analysis of two sedimentation equilibrium exlzeriments with insulin in buffer (0.1 M Tris.HC1, 0.1 M NaCI) at pH 7.0, 25 °C containing 2 mol of zinc(II)/six base-tool of insulin. (a) O(r) vs. ~(r) as specified in Eqn. 1 ; O, exl~eriment 1 ; ?(rv) = 0.50 g/l, rv = 7.1084 cm; 0 , experiment 2, ~(rv) = 0.50 g/l, rF = 7.1101 cm. The dotted line represents an attempt to average the data points in the extrapolation to find g2°(r) at infinite dilution. (b) The insulin monomer concentration, ca(r),vs. the total insulin concentration, E(r), derived from Eqn. 2 and the data presented in Fig. 1 (a). where mx(r) equals cx(r)/M1. Eqn. 3 is a closed solution derived previously [15] for regions, as presently apply, where non-ideality effects may be neglected. Values o f ml(r) appropriate to Eqn. (3) m a y be derived f r o m Fig. lb, while the values o f K2 and K],2 have been reported in the introduction. Table I summarizes such results for one o f the sedimentation equilibrium experiments (Expt. 1). Columns 1 and 2 show the experimentally obtained total concentration distribution, column 3 the corresponding concentration o f m o n o m e r and column 4 the values o f 6~(r) calculated from Eqn. 3. It is immediately apparent that the addition o f zinc ions has profoundly affected the experimental distribution which can no longer be described solely on the basis o f the zinc-free polymerization pattern. Indeed the last column in Table I emphasizes this point by presenting the difference, ?(r) -- ~(r), at each radial distance. This residual must represent the summed sedimentation equilibrium distributions o f new species
199 TABLE I SEDIMENTATION EQUILIBRIUM DISTRIBUTIONS OF VARIOUS SPECIES IN THE Z I N C - I N S U L I N SYSTEM The experimental environment was 0.1 M Tris.HCl. 0.1 M NaC1, pH 7.0 at 25 °C. All concentrations are in g/1. Radius (cm)
Total concn, ~(r)
Monomer conch, cl(r)
Zinc-free insulin concn. &(r)
Zinc-insulin concn. ~(r) -- ~l(r)
7.0081 7.0297 7.0532 7.0719 7.0849 7.0952 7.1031 7.1100 7.1141
0.047 0.054 0.082 0.137 0.206 0.299 0.395 0.538 0.629
0.014 0.015 0.018 0.020 0.022 0.023 0.024 0.025 0.026
0.022 0.024 0.031 0.036 0.042 0.045 0.048 0.051 0.054
0.025 0.030 0.051 0.101 0.164 0.254 0.347 0.487 0.575
4- 0.006 ± 0.006 ± 0.010 ± 0.010 ± 0.011 -4- 0.015 -4- 0.015 -4- 0.016 -4- 0.017
i n t r o d u c e d o n the a d d i t i o n o f the zinc ions. The errors o f the residuals, also reported in the last c o l u m n o f Table I, were o b t a i n e d by repeating all calculations using the extreme values o f ~Q°(r) o f 0.04 a n d 0.06. T h e first a t t e m p t to analyze this residual d i s t r i b u t i o n is shown in Fig. 2 where the n a t u r a l logarithms o f the average values are plotted against the squares o f the c o r r e s p o n d i n g radial distances: the indicated error bars follow directly from the errors shown in the last c o l u m n o f Table I a n d are clearly representative o f the range o f results examined. The solid line represents a n a t t e m p t to average the data, treated as linear, by least-squares regression a n d indicates, from the slope, the p r e d o m i n a n c e o f a new species o f molecular weight 39 000, close to that o f the zinc-insulin hexamer +
-1
_2 ¸ IO
-3 .49.8
..50.0
50.2 r2
50.4
50.6
{cm')
Fig. 2. Plot of the natural logarith of the residual zinc-insulinconcentration, ~(r) -- ~(r), as a function ofr 2for sedimentation equilibrium experiment 1. The line representing a least-squares fit to the experimental points (A), on the assumption of linearity, has a slope corresponding to a molecular weight of 39 000. Typical error bars for average experimental points are denoted by vertical lines.
200 (35 000). Indeed, little error would be made if the residual concentration, ((r) -- (~(r), were viewed as the sum of the concentrations of hexameric insulin with stoichiometry of Zn(II):hexamer of 1:1 and 2:1, species both of molecular weight 35 000 within error of ultracentrifuge measurement. In this connection, it is of interest that the ratio {((r) -- (q(r)}/c61(r)obtained from Table I is 2.0.109 lS.g -5 (standard deviation, 0.6. 109); since this value could be regarded as the pseudo overall equilibrium constant for the formation of the zinc-hexamer constituent. Such a constant is independent of the pathway of formation of the constituent; but is pseudo in the sense that the assumption is implicitly made that the equilibrium concentration of unbound zinc ions is essentially invariant with total protein concentration in the range investigated. This direct interpretation then leads to a description of the dependence of solution composition on total protein concentration in terms of Eqn. 3 (with/£2 and KI.2 known) to which is added the term 2.109 ¢61(r). This interpretation, however, neglects two relatively minor points evident in Fig. 2. First, there is a 1 0 ~ discrepancy between the molecular weight of the zincinsulin hexamer constituent and that predicted by the solid line (39 000). Secondly, there is a deviation of points from linearity evident at higher concentrations outside the error bars indicated. These observations suggest the presence of small amounts of polymeric forms (larger than the hexamer) involving bound zinc(II) formed by the self-association of either or both the 1 : 1 and 2:1 zinc-hexameric species. In order to attempt a more refined analysis to account for this possibility, without invoking an unreasonable number of parameters, it seems realistic to suggest that the 2:1 species predominates (since such a stoichiometry is always observed) and is involved in a weak isodesmic self-association. On this basis, the total protein concentration is given by, M~ m, (r) {(1 -e (r) =
K2 KL2 rn~ (r)) 2 -+- 2 K2 ml (r)}
{1 - - K 2 KI, 2 m z (r)} 2
+
Mz.-6 ~pm6 (r) {1 -- K,,z,_67~m~(r)} 2 (4)
where m z n _ 6 ( r ) denotes the molar equilibrium concentration of the 2:1 zinc-hexamer species of molecular weight Mz,-6; KI,zn-6 is the isodesmic self-association constant and % a pseudo constant on the basis ofinvariance of unbound zinc(lI) concentration, is given by mz,_6(r)/m6(r). Eqn. 4 is seen to be the sum of Eqn. 3 and the conventional term [1, 3] for the total weight concentration of an isodesmically self-associating system. Least-squares regression analysis of (?(r), ml(r)) points (Table I and additional points not shown) using Eqn. 4 led to the following best-fit values: KI, zn-6 = 4" 103 M and ~p = 1.7" ]027 M -5. In a final test of this refined polymerization pattern, the latter values and those reported for//2 and K~,2were used in Eqn. 4 to calculate d(r) values. It was found that these calculated values differed from the experimental ~7(r) found in the two sedimentation equilibrium experiments with standard deviations (50 comparisons) of ~ 10/~m and ± 20/Jm, respectively, within experimental precision of e(r) determinations. It is now possible to calculate on the basis of the above postulated schemes the composition, at any given total protein concentration, of solutions containing either no zinc(II) or those containing the stoichiometric amount. In the former case, Eqn. 3 is applicable and leads to the solid lines shown in Fig. 3, which depict for the purpose of illustration, the concentration-dependence of the weight fractions of
201 1.0
~ 0.5
,.:
,,..,,.......... b~ ~
o o
........ T
.........
o.4
Fig. 3. A comparison of the weight-fractions of monomer (a) and hexamer (b) as a function of total weight concentration for the zinc-free insulin ( ) and zinc-insulin ( - -- --) systems in Tris. HCI/ NaCI buffer at pH 7.0, 1 -- 0.2 and 25 °C. In the case of zinc(II) being present, the weight fraction of zinc-free hexamer is indistinguishable from the abscissa and - - - , (b) refers to the 2:1 zincinsulin hexamer. zinc-free monomer and hexamer. In the latter case, Eqn. 4 applies and was used to compute the broken lines in Fig. 3, where now curve (a) refers to the zinc-free monomer and curve (b) to the 2:1 zinc-hexamer species: in this case, the curves are less certain at low ¢(r) due to the pseudo-constant nature of V). It is also of interest to note that, if the last term in Eqn. 4 is replaced by 2.109 c6(r), thereby neglecting the weak self-association of zinc-hexamer species, there is no pronounced shift (less than 5 ~ for both curves over the entire ¢(r) range) of the broken curves in Fig. 3, where curve (b) is now visualized as referring to the total zinc-hexamer constituent. DISCUSSION The results summarized in Table I and Fig. 3 show that the introduction o f zinc(II) (2 mol per six base-mol of insulin) has a profound effect on the polymerization pattern observed for zinc-free insulin in solution. In the presence of Zn(II), the zinc-free pattern persists as a background but new species are introduced. Of these, the zinc-insulin hexamer constituent predominates, as was initially indicated by Fig. 2. Indeed, this result is in basic accord with the more refined analysis based on Eqn. 4 which led to a relatively small value of K~.zn-6 and to a value of ~0, which when expressed on a weight concentration scale becomes 1.7.10 9 lS.g -s which compares favourably with the value of 2.0.109 1s. g-S found on the basis that K~,zn-6 equals zero. The tendency of the zinc-hexamer constituent to self-associate, therefore, while definitely indicated by Fig. 2 and the fit of results to Eqn. 4, is undoubtedly a relatively small effect, too small indeed to permit more detailed analysis in terms of a possible involvement of the partly saturated 1 :l zinc-hexamer species. The important point is, however, that regardless of the details of its pathway of formation or self-association, the zinc-hexamer itself comprises 75 ~ or more of the total protein at total concentrations above 0.1 g/1 (Fig. 3). Comment is required on the correlation o f this zinc-insulin hexamer observed in solution with that observed in X-ray crystallographic studies [4]. The present work has established identity with respect to molecular
202 weight and ascertained that the zinc-hexamer in solution is certainly stable. This indicated stability, itself, is evidence for a cyclic structure [16] and, in addition, it has been shown that the sedimentation coefficient of the zinc-insulin hexamer in solution of 3.2 S [7] is consistent with that predicted for a closed structure of six monomer units of overall shape that of an oblate ellipsoid of revolution with dimensions comparable with that found by X-ray crystallography [17]. This evidence taken together strongly suggests that the two entities are the same or very similar. As is seen by Fig. 3, the fundamental use of values of the equilibrium constants, K2, KI.2 and Kl,zn_ 6 and of W, is in the determination of solution compositions. These parameters being thermodynamic in character cannot aid in the specification of the detailed pathway by which zinc-insulin hexamer species may be formed. A direct pathway consistent with the results involves successive addition of two zinc(II) ions directly to the zinc-free hexamer, which, albeit an open chain, may adopt a configuration particularly suited for zinc(I1)-histidine coordination with accompanying ring closure; but this is not the only possibility. In terms of the thermodynamic description of the system, it remains valid of course that at the extreme dilutions of insulin encountered in serum ( ~ 3 ng/ml) linkage of the polymerization patterns will ensure, at equilibrium, virtually complete dissociation to the zinc-free monomer [18] with the consequent release of zinc(ll). This point is illustrated in Fig. 3 where the weightfraction of insulin monomer is seen to approach unity as the total concentration approaches zero. It seems therefore that the formation of the zinc-insulin hexamer (and possibly that of the indicated higher polymers) at high concentrations is of biological importance in relation to its storage in the/3-cell [8], while the linked nature of the polymerization pattern provides a means, effected by dilution, of forming insulin monomer, even in the presence of Zn(II): it is thought that it is the monomeric form that binds to insulin-receptors on membranes [4, 19].
REFERENCES 1 Jeffrey, P. D., Milthorpe, B. K. and Nichol, L. W. (1976) Biochemistry 15, 4660-4665 2 Steiner, R. F. (1952) Arch. Biochem. Biophys. 39, 333-354 3 Van Holde, K. E. and Rossetti, G. P. (1967) Biochemistry 6, 2189-2194 4 Blundell, T., Dodson, G., Hodgkin, D. and Mercola, D. (1972) Adv. Protein Chem. 26, 280-402 5 Cunningham, L. W., Fischer, R. L. and Vestling, C. S. (1955) J. Am. Chem. Soc. 77, 5703-5707 6 Fredericq, E. (1956) Arch. Biochem. Biophys. 65, 218-228 7 Creeth, J. M. (1953) Biochem. J. 53, 41-47 8 Grant, P. T., Coombs, T. L. and Frank, B. H. (1972) Biochem. J. 126, 433-440 9 Jeffrey, P. D. (1974) Biochemistry 13, 4441-4447 10 Frank, B. H. and Veros, A. J. (1968) Biochem. Biophys. Res. Commun. 32, 155-160 11 Casassa, E. F. and Eisenberg, H. (1964) Adv. Protein Chem. 19, 287-395 12 Sumerell, J. M., Osmond, A. and Howard, G. (1965) Biochem. J. 95, Proceedings 31 13 Adams, M. J., Dodson, G., Dodson, E. and Hodgkin, D. C. (1967) Conformation of Biopolymers, Vol. 1, p. 9, Academic Press, New York 14 Ryle, A. P., Sanger, F., Smith, L. F. and Kitai, R. (1955) Biochem. J. 60, 541-556 15 Milthorpe, B. K., Jeffrey, P. D. and Nichol, L. W. (1975) Biophys. Chem. 3, 169-176 16 Gilbert, G. A. (1959) Proc. Roy. Soc. A 250, 377-388 17 Andrews, P. R. and Jeffrey, P. D. (1976) Biophys. Chem. 4, 93-102 18 Pekar, A. H. and Frank, B. H. (1972) Biochemistry 11, 4013-4016 19 Pullen, R. A., Lindsay, D. G., Wood, S. P., Tickle, I. J., Blundell, T. L., Wollmer, A., Krail, G., Brandenburg, D., Zahn, H., Gliemann, J. and Gammeltoft, S. (1976) Nature 259, 369-373
T H E P O L Y M E R I Z A T I O N P A T T E R N OF ZINC(II)-INSULIN AT pH 7.0
BRUCE K. MILTHORPE, LAWRENCE W. NICHOL and PETER D. JEFFREY
Department of Physical Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T. 2601 (Australia) (Received April 22nd, 1977)
SUMMARY
Sedimentation equilibrium experiments were conducted at pH 7.0 using solutions of bovine insulin containing 2 mol of zinc(II) ions per six base-mol of insulin. A detailed analysis of these results revealed the existence of a stable zinc-insulin hexamer together with linked polymerization reactions. Specifically these are a background polymerization of zinc-free insulin as previously described by Jeffrey et al. ((1976) Biochemistry 15, 4660-4665) and a slight tendency for the zinc-insulin hexamer to undergo indefinite self-association. Equilibrium constants governing these reactions are reported together with equations which permit calculation of the composition of the solution at any given total concentration. Comment is made on the possible biological significance of this linked polymerization pattern, and on the likely identity o f the structure of the stable zinc-insulin hexamer with that pceviously reported from X-ray crystallographic studies.
INTRODUCTION
In a previous communication [1] it was established that the polymerization pattern of bovine insulin, freed of proinsulin and zinc, at pH 7.0 comprised an equilibrium mixture of monomer (molecular weight 5734), dimer, and a series of higher polyr0ers formed by isodesmic indefinite self-association of the dimer. Thus, the systel~ was described by two equilibrium constants, a dimerization constant, K2, of 1.1. l0 s M -~ and an isodesmic equilibrium constant, KI.2, of 1.7- 104 M -1. The latter isodesmic constant requires that each successive addition of a dimer unit to form higher polymers be governed by the same standard free energy change, a postulate consistent with linear or branched chain growth [2, 3]. In this connection, it is noteworthy that hexamer is postulated as one polymer in chain formation but is given no particular prominence; whereas X-ray crystallographic studies [4] emphasize the importance of a hexamer of closed structure. The basic difference between the studies is that while those in solution were conducted in the absence of zinc(II), the structure indicated in the crystallographic studies refers to a hexamer with two zinc(II) ions coordinated to histidines on the three-fold axis. The major purpose of this work is to explore a possible correlation between these findings by conducting sedimentation equilibrium experiments on a system to which the stoichiometric amount of zinc(II)
196 has been added to the self-associating apoprotein. Although zinc(II)-insulin has been extensively studied [5-9] no detailed thermodynamic analysis of the results in terms of possible linked polymerization patterns has been performed. MATERIALS AND METHODS Bovine insulin containing 0.78 g zinc/g anhydrous protein, 3-4 ~ proinsulin and approximately 5 ~ monodesamido insulin was obtained from Australian Commonwealth Serum Laboratories. The sample was freed of zinc ions by extensive dialysis against 0.01 M HC1 as previously described [1]. This material was freed of proinsulin by gel chromatography on a Sephadex G-50 column (55 × 1.7 cm), subsequent analysis by polyacrylamide disc-gel electrophoresis, conducted as previously reported [1], revealing the absence of proinsulin but retention of a small amount of the monodesamido component. The sample, termed fractionated insulin, was therefore identical with that used in the previous study [1]. The introduction of zinc(II) in the form of zinc nitrate was effected as follows: fractionated insulin was dialysed to pH 7.0 (buffer 0.1 M Tris/HC1, 0.1 M NaC1 at 25 °C), the protein concentration was determined spectrophotometrically at 276 nm employing an extinction coefficient of 1.05 A units/cm (mg/ml) [10], and the requisite amount of standard zinc nitrate solution was added by weight to achieve a final stoichiometry of 2 mol of zinc(II) ions/six base-mol of insulin. It was found that the solubility limit of zinc-insulin so prepared was 0.9 g/1. It is required to precede each sedimentation equilibrium experiment by dialysis [11] and this was performed in pre-washed Visking 18/32 tubing against twenty times the volume of the pH 7.0 buffer containing no zinc ions for a period of 12 h. In a control experiment the zinc(II) content was checked after dialysis by atomic absorption spectroscopy and within experimental error it was shown that the bound zinc(II) maintained the cited stoichiometry. This does not imply that the binding of zinc(II) is an irreversible process, for indeed binding constants have been estimated [8, 12] and it is known that the bound zinc(II) may be removed by addition of the chelating agent EDTA [13]. It does imply that, within the 12 h equilibrium dialysis used to equilibrate buffer ions, the extent of dissociation of bound zinc(II) was not detectable within the precision of the analysis technique. Sedimentation equilibrium experiments were conducted at 25 °C using a Spinco model E analytical ultracentrifuge equipped with electronic speed control and a Rayleigh interference optical system. The protocol of the experiments, which used the inert fluorocarbon FC43 as an inert base fluid and were of the Chervenka meniscusdepletion design [14], has been given previously [1]. The experiments were run for 24 h and the attainment of equilibrium was checked by measuring penultimate and final interferograms, all measurements being made on a Nikon microcomparator. The low solubility limit of zinc(II)-insulin at pH 7.0 (0.9 g/l) precludes a series of sedimentation equilibrium experiments conducted with a wide range of initial loading concentrations and angular velocities. Accordingly, a single set of conditions (angular velocity of 36 000 rev./min and initial loading concentration of 0.060 g/l) was employed, although the loading volume3 differed slightly in each experiment. The experimental sedimentation equilibrium distributions, with meniscus concentration essentially zero, were converted into plots of total concentration vs. radial distance using the determined relationship, 3.93 Rayleigh interference fringes is equivalent to 1.00 g/l. The
197 monomer molecular weight of bovine insulin was taken as 5734 [14], a value of 0.73 ml/g was used for the partial specific volume [10] and solution densities were measured with an Anton Paar DMA-02C precision density meter. RESULTS The experimental records of total concentration, O(r), vs. radial distance, r, at sedimentation equilibrium reflect only the contribution of the protein constituent since the unbound zinc ion concentration, of estimated magnitude less than 10-6 M [8 ], cannot contribute significantly to the interferogram. It was accordingly possible to use the f2(r) method [15] to determine the concentration distribution of the insulin monomer. Specifically the f2(r) function is defined as .(2(r) = ((r) exp {qOlM,(rvz -- rZ)}/((rv)
(1)
where ~t equals (1 -- ~19)co2/2RT (with the conventional notation) and (?(rF),rF) is a reference point selected from within each experimental distribution. Provided a common ((rv) is selected, data from both experiments exhibiting different equilibrium distributions may be correlated [15]. The plots of.Q(r) vs. ((r) for both experiments, using ~ M t referring to the monomer, are shown in Fig. la. Except for minor deviations at low ((r), it is evident that the results from both experiments fall on the same curve and that there is little difficulty in extrapolating the averaged results to yield a value of-Q°(r) of 0.05 -4- 0.01 at infinite dilution. The estimated error was obtained as extremes of extrapolated values for the two experiments considered separately. It follows directly from the previous theoretical treatment [15] that
al(r) ---- ((r)f2°(r)/g2(r)
(2)
where at(r) is the thermodynamic activity of monomer. It has also been shown previously for the insulin system [1] that in the total concentration range spanned in Fig. la non-ideality effects are of negligible magnitude and thus at(r) may be identified with the weight concentration o f monomer, el(r). Fig. lb presents a plot of c~(r) vs. the corresponding ((r) derived from Eqn. 2 with I2°(r) equal to 0.05 and the data presented in Fig. l a. These results clearly demonstrate that even in the presence of the stoichiometric amount of zinc(lI), appreciable quantities of insulin monomer continue to exist at all points in the cell at sedimentation equilibrium. The finding is in agreement with other sedimentation equilibrium studies on zinc(II)-insulin at pH 7.0 where a less refined analysis based on weight-average molecular weights also indicated the existence of monomer [9]. If the assumption, reasonable on stoichiometric grounds, is made that this monomeric form is free of bound zinc ions, it follows as a necessary thermodynamic consequence that the complete zinc-flee insulin polymerization pattern described in the introduction must also be operative. The contribution, ¢~(r), to the total observed concentration, ((r), of this set of equilibria may be calculated using the equation el (r) =
2
M1 ml (r) {(1 -- K2 KI.2 ma (r)) 2 + 2K2 ml (r)} {1 -- 1(2 K~.z m~ (r)} 2
(3)
198
1.0
.4¢"°
Q (r) 0.5
fo* .,Z f
2" o11
0:2
o13
oi,
~(r)
(g/l)
o16
0.03
cl(r) (g/l) 0.02
o
~o
0.01
I
072
o"
o!s
0!6
o,
Fig. 1. Plots relating to the 12(r) analysis of two sedimentation equilibrium exlzeriments with insulin in buffer (0.1 M Tris.HC1, 0.1 M NaCI) at pH 7.0, 25 °C containing 2 mol of zinc(II)/six base-tool of insulin. (a) O(r) vs. ~(r) as specified in Eqn. 1 ; O, exl~eriment 1 ; ?(rv) = 0.50 g/l, rv = 7.1084 cm; 0 , experiment 2, ~(rv) = 0.50 g/l, rF = 7.1101 cm. The dotted line represents an attempt to average the data points in the extrapolation to find g2°(r) at infinite dilution. (b) The insulin monomer concentration, ca(r),vs. the total insulin concentration, E(r), derived from Eqn. 2 and the data presented in Fig. 1 (a). where mx(r) equals cx(r)/M1. Eqn. 3 is a closed solution derived previously [15] for regions, as presently apply, where non-ideality effects may be neglected. Values o f ml(r) appropriate to Eqn. (3) m a y be derived f r o m Fig. lb, while the values o f K2 and K],2 have been reported in the introduction. Table I summarizes such results for one o f the sedimentation equilibrium experiments (Expt. 1). Columns 1 and 2 show the experimentally obtained total concentration distribution, column 3 the corresponding concentration o f m o n o m e r and column 4 the values o f 6~(r) calculated from Eqn. 3. It is immediately apparent that the addition o f zinc ions has profoundly affected the experimental distribution which can no longer be described solely on the basis o f the zinc-free polymerization pattern. Indeed the last column in Table I emphasizes this point by presenting the difference, ?(r) -- ~(r), at each radial distance. This residual must represent the summed sedimentation equilibrium distributions o f new species
199 TABLE I SEDIMENTATION EQUILIBRIUM DISTRIBUTIONS OF VARIOUS SPECIES IN THE Z I N C - I N S U L I N SYSTEM The experimental environment was 0.1 M Tris.HCl. 0.1 M NaC1, pH 7.0 at 25 °C. All concentrations are in g/1. Radius (cm)
Total concn, ~(r)
Monomer conch, cl(r)
Zinc-free insulin concn. &(r)
Zinc-insulin concn. ~(r) -- ~l(r)
7.0081 7.0297 7.0532 7.0719 7.0849 7.0952 7.1031 7.1100 7.1141
0.047 0.054 0.082 0.137 0.206 0.299 0.395 0.538 0.629
0.014 0.015 0.018 0.020 0.022 0.023 0.024 0.025 0.026
0.022 0.024 0.031 0.036 0.042 0.045 0.048 0.051 0.054
0.025 0.030 0.051 0.101 0.164 0.254 0.347 0.487 0.575
4- 0.006 ± 0.006 ± 0.010 ± 0.010 ± 0.011 -4- 0.015 -4- 0.015 -4- 0.016 -4- 0.017
i n t r o d u c e d o n the a d d i t i o n o f the zinc ions. The errors o f the residuals, also reported in the last c o l u m n o f Table I, were o b t a i n e d by repeating all calculations using the extreme values o f ~Q°(r) o f 0.04 a n d 0.06. T h e first a t t e m p t to analyze this residual d i s t r i b u t i o n is shown in Fig. 2 where the n a t u r a l logarithms o f the average values are plotted against the squares o f the c o r r e s p o n d i n g radial distances: the indicated error bars follow directly from the errors shown in the last c o l u m n o f Table I a n d are clearly representative o f the range o f results examined. The solid line represents a n a t t e m p t to average the data, treated as linear, by least-squares regression a n d indicates, from the slope, the p r e d o m i n a n c e o f a new species o f molecular weight 39 000, close to that o f the zinc-insulin hexamer +
-1
_2 ¸ IO
-3 .49.8
..50.0
50.2 r2
50.4
50.6
{cm')
Fig. 2. Plot of the natural logarith of the residual zinc-insulinconcentration, ~(r) -- ~(r), as a function ofr 2for sedimentation equilibrium experiment 1. The line representing a least-squares fit to the experimental points (A), on the assumption of linearity, has a slope corresponding to a molecular weight of 39 000. Typical error bars for average experimental points are denoted by vertical lines.
200 (35 000). Indeed, little error would be made if the residual concentration, ((r) -- (~(r), were viewed as the sum of the concentrations of hexameric insulin with stoichiometry of Zn(II):hexamer of 1:1 and 2:1, species both of molecular weight 35 000 within error of ultracentrifuge measurement. In this connection, it is of interest that the ratio {((r) -- (q(r)}/c61(r)obtained from Table I is 2.0.109 lS.g -5 (standard deviation, 0.6. 109); since this value could be regarded as the pseudo overall equilibrium constant for the formation of the zinc-hexamer constituent. Such a constant is independent of the pathway of formation of the constituent; but is pseudo in the sense that the assumption is implicitly made that the equilibrium concentration of unbound zinc ions is essentially invariant with total protein concentration in the range investigated. This direct interpretation then leads to a description of the dependence of solution composition on total protein concentration in terms of Eqn. 3 (with/£2 and KI.2 known) to which is added the term 2.109 ¢61(r). This interpretation, however, neglects two relatively minor points evident in Fig. 2. First, there is a 1 0 ~ discrepancy between the molecular weight of the zincinsulin hexamer constituent and that predicted by the solid line (39 000). Secondly, there is a deviation of points from linearity evident at higher concentrations outside the error bars indicated. These observations suggest the presence of small amounts of polymeric forms (larger than the hexamer) involving bound zinc(II) formed by the self-association of either or both the 1 : 1 and 2:1 zinc-hexameric species. In order to attempt a more refined analysis to account for this possibility, without invoking an unreasonable number of parameters, it seems realistic to suggest that the 2:1 species predominates (since such a stoichiometry is always observed) and is involved in a weak isodesmic self-association. On this basis, the total protein concentration is given by, M~ m, (r) {(1 -e (r) =
K2 KL2 rn~ (r)) 2 -+- 2 K2 ml (r)}
{1 - - K 2 KI, 2 m z (r)} 2
+
Mz.-6 ~pm6 (r) {1 -- K,,z,_67~m~(r)} 2 (4)
where m z n _ 6 ( r ) denotes the molar equilibrium concentration of the 2:1 zinc-hexamer species of molecular weight Mz,-6; KI,zn-6 is the isodesmic self-association constant and % a pseudo constant on the basis ofinvariance of unbound zinc(lI) concentration, is given by mz,_6(r)/m6(r). Eqn. 4 is seen to be the sum of Eqn. 3 and the conventional term [1, 3] for the total weight concentration of an isodesmically self-associating system. Least-squares regression analysis of (?(r), ml(r)) points (Table I and additional points not shown) using Eqn. 4 led to the following best-fit values: KI, zn-6 = 4" 103 M and ~p = 1.7" ]027 M -5. In a final test of this refined polymerization pattern, the latter values and those reported for//2 and K~,2were used in Eqn. 4 to calculate d(r) values. It was found that these calculated values differed from the experimental ~7(r) found in the two sedimentation equilibrium experiments with standard deviations (50 comparisons) of ~ 10/~m and ± 20/Jm, respectively, within experimental precision of e(r) determinations. It is now possible to calculate on the basis of the above postulated schemes the composition, at any given total protein concentration, of solutions containing either no zinc(II) or those containing the stoichiometric amount. In the former case, Eqn. 3 is applicable and leads to the solid lines shown in Fig. 3, which depict for the purpose of illustration, the concentration-dependence of the weight fractions of
201 1.0
~ 0.5
,.:
,,..,,.......... b~ ~
o o
........ T
.........
o.4
Fig. 3. A comparison of the weight-fractions of monomer (a) and hexamer (b) as a function of total weight concentration for the zinc-free insulin ( ) and zinc-insulin ( - -- --) systems in Tris. HCI/ NaCI buffer at pH 7.0, 1 -- 0.2 and 25 °C. In the case of zinc(II) being present, the weight fraction of zinc-free hexamer is indistinguishable from the abscissa and - - - , (b) refers to the 2:1 zincinsulin hexamer. zinc-free monomer and hexamer. In the latter case, Eqn. 4 applies and was used to compute the broken lines in Fig. 3, where now curve (a) refers to the zinc-free monomer and curve (b) to the 2:1 zinc-hexamer species: in this case, the curves are less certain at low ¢(r) due to the pseudo-constant nature of V). It is also of interest to note that, if the last term in Eqn. 4 is replaced by 2.109 c6(r), thereby neglecting the weak self-association of zinc-hexamer species, there is no pronounced shift (less than 5 ~ for both curves over the entire ¢(r) range) of the broken curves in Fig. 3, where curve (b) is now visualized as referring to the total zinc-hexamer constituent. DISCUSSION The results summarized in Table I and Fig. 3 show that the introduction o f zinc(II) (2 mol per six base-mol of insulin) has a profound effect on the polymerization pattern observed for zinc-free insulin in solution. In the presence of Zn(II), the zinc-free pattern persists as a background but new species are introduced. Of these, the zinc-insulin hexamer constituent predominates, as was initially indicated by Fig. 2. Indeed, this result is in basic accord with the more refined analysis based on Eqn. 4 which led to a relatively small value of K~.zn-6 and to a value of ~0, which when expressed on a weight concentration scale becomes 1.7.10 9 lS.g -s which compares favourably with the value of 2.0.109 1s. g-S found on the basis that K~,zn-6 equals zero. The tendency of the zinc-hexamer constituent to self-associate, therefore, while definitely indicated by Fig. 2 and the fit of results to Eqn. 4, is undoubtedly a relatively small effect, too small indeed to permit more detailed analysis in terms of a possible involvement of the partly saturated 1 :l zinc-hexamer species. The important point is, however, that regardless of the details of its pathway of formation or self-association, the zinc-hexamer itself comprises 75 ~ or more of the total protein at total concentrations above 0.1 g/1 (Fig. 3). Comment is required on the correlation o f this zinc-insulin hexamer observed in solution with that observed in X-ray crystallographic studies [4]. The present work has established identity with respect to molecular
202 weight and ascertained that the zinc-hexamer in solution is certainly stable. This indicated stability, itself, is evidence for a cyclic structure [16] and, in addition, it has been shown that the sedimentation coefficient of the zinc-insulin hexamer in solution of 3.2 S [7] is consistent with that predicted for a closed structure of six monomer units of overall shape that of an oblate ellipsoid of revolution with dimensions comparable with that found by X-ray crystallography [17]. This evidence taken together strongly suggests that the two entities are the same or very similar. As is seen by Fig. 3, the fundamental use of values of the equilibrium constants, K2, KI.2 and Kl,zn_ 6 and of W, is in the determination of solution compositions. These parameters being thermodynamic in character cannot aid in the specification of the detailed pathway by which zinc-insulin hexamer species may be formed. A direct pathway consistent with the results involves successive addition of two zinc(II) ions directly to the zinc-free hexamer, which, albeit an open chain, may adopt a configuration particularly suited for zinc(I1)-histidine coordination with accompanying ring closure; but this is not the only possibility. In terms of the thermodynamic description of the system, it remains valid of course that at the extreme dilutions of insulin encountered in serum ( ~ 3 ng/ml) linkage of the polymerization patterns will ensure, at equilibrium, virtually complete dissociation to the zinc-free monomer [18] with the consequent release of zinc(ll). This point is illustrated in Fig. 3 where the weightfraction of insulin monomer is seen to approach unity as the total concentration approaches zero. It seems therefore that the formation of the zinc-insulin hexamer (and possibly that of the indicated higher polymers) at high concentrations is of biological importance in relation to its storage in the/3-cell [8], while the linked nature of the polymerization pattern provides a means, effected by dilution, of forming insulin monomer, even in the presence of Zn(II): it is thought that it is the monomeric form that binds to insulin-receptors on membranes [4, 19].
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