of the free enzyme are thus independent. The kinetic behaviour of the active site becomes different if ribulose bisphosphate carboxylase-oxygenase is inserted ...
Eur. J. Biochem. 226, 999-1006 (1994) 0 FEBS 1994
The modulation of enzyme reaction rates within multi-enzyme complexes 2. Information transfer within a chloroplast multi-enzyme complex containing ribulose bisphosphate carboxylase-oxygenase Brigitte GONTERO, Marie-Thtrkse GIUDICI-ORTICONI and Jacques RICARD Institut Jacques Monod, CNRS, Universitt Paris VII, France (Received July 20/September 29, 1994) - EJB 94 108714
Octameric ribulose bisphosphate carboxylase-oxygenase binds in an independent manner its substrate (ribulose bisphosphate) and a substrate analog (6-phosphogluconate). The eight active sites of the free enzyme are thus independent. The kinetic behaviour of the active site becomes different if ribulose bisphosphate carboxylase-oxygenase is inserted in the five-enzyme complex previously isolated from chloroplasts. Ribulose bisphosphate carboxylase-oxygenase then becomes more active than the corresponding free enzyme form. By comparing the behaviour of the same enzyme in the free state and in the associated state it then becomes possible to study how the thermodynamics of protein -protein interactions alters the kinetic behaviour of ribulose bisphosphate carboxylaseoxygenase. This alteration may be expressed in terms of stabilization-destabilization energies exerted upon the various intermediate states of the enzyme reaction, within the multi-protein complex. Heterologous interactions within this complex exert a constant stabilization energy on the enzyme ground states along the reaction co-ordinate of - 1.68 kJ/mol and a constant stabilization energy of -3.79 kJ/mol on the enzyme transition states. These stabilization energies express how information propagates within the multi-enzyme complex as to increase the apparent affinity of the substrate for the active sites of ribulose bisphosphate carboxylase-oxygenase, as well as to increase the catalytic rate constant. The binding of the substrate analog 6-phosphogluconate to free ribulose bisphosphate carboxylase-oxygenase is non-co-operative. It becomes positively co-operative if this enzyme is inserted in the multi-protein complex. Under these conditions, only one type of enzyme-inhibitor complex is detected experimentally. Here again heterologous interactions stabilize this enzyme-inhibitor complex relative to that expected if ribulose bisphosphate carboxylase oxygenase is free. The extent of stabilization is - 1.03 kJ/mol. Neither free nor associated ribulose bisphosphate carboxylase-oxygenase display any co-operativity relative to substrate binding. However, in the presence of the substrate analog 6-phosphogluconate, this enzyme displays positive co-operativity relative to substrate, although not if it is naked. These results can be explained theoretically and show that the maximum value of the Hill coefficient is < 2 . As 6-phosphogluconate and other substrate analogs are present in chloroplasts under normal conditions, this co-operativity might be of functional importance in vivo.
Statistical mechanical theories developed in the preceding paper offer the physical basis for understanding why, owing to heterologous interactions, an enzyme may behave differently depending on whether it is free or inserted in a multienzyme complex [l]. If this enzyme naturally occurs in the free state or is inserted in a multi-enzyme complex, it is then possible to estimate the kinetic parameters of this enzyme in these two states. According to the theories developed in the preceding paper, it should then be possible to determine the numerical values of the thermodynamic parameters defined previously [ 11. These parameters, as already outlined, allow .___
Correspondence to J. Ricard, Institut Jacques Monod, C. N. R. S., Universitt Paris VII, Tour 43, 2 place Jussieu, F-75251 Paris Cedex 05, France Enzymes. Ribose-5-phosphate isomerase (EC 5.3.1.6) ; phosphoribulokinase (EC 2.7.1.19); ribulose 1,5-bisphosphate carboxylase-oxygenase (EC 4.1.1.39) ; glyceraldehyde-3-phosphatedehydrogenase (EC 1.2.1.13); phosphoglycerate kinase (EC 2.7.2.3).
one to express quantitatively how heterologous interactions and conformational constraints in a multi-enzyme complex affect the enzyme reaction rate [l]. It is probably worth pointing out that the use of classical kinetic methods allow one to describe in quantitative terms how the behaviour of the same enzyme may be different depending on whether it is in the naked state or inserted in a complex. These methods, however, do not provide a physical explanation for this difference. For that reason, it is absolutely mandatory to use the concepts of statistical thennodynamics developed in the preceding paper [I]. One may expect that the conditions required to allow the experimental evaluation of these thermodynamic parameters are feasible with the enzyme ribulose bisphosphate carboxylase-oxygenase. As already outlined, this enzyme may be isolated either in the free state or associated with four other enzymes, namely phosphoribulokinase, phosphoribose isomerase, phosphoglycerate kinase, glyceraldehyde phosphate
1000 dehydrogenase [2-61. In these two states the enzyme displays Michaelis-Menten kinetics but the parameters V, and K,,, assume different values depending on whether the enzyme is naked or inserted in the complex [3]. Moreover this enzyme is made up of eight large (L) and eight small (S) subunits in the free state [7-91 but contains only two large (L) and four small (S) subunits in the five-enzyme complex [5]. This biochemical system is thus, potentially, a good one to study how the thermodynamics of polypeptide chain interactions may modulate the kinetics of enzyme activity. Moreover, as outlined previously, free and complexed ribulose bisphosphate carboxylase-oxygenase do not display any kinetic co-operativity [3]. However, owing to the biological importance of this enzyme, one may wonder whether some sort of kinetic co-operativity may not occur in vivo under specific experimental conditions. The aim of this paper is to answer these unsolved questions.
2
"0
6
4
2
8
10
dimensionless substrate concentrahon
Z" x [S] MATERIALS AND METHODS Free ribulose bisphosphate carboxylase-oxygenase and the five-enzyme complex were isolated from spinach chloroplasts and purified to homogeneity as described previously [2, 10, 111. The carboxylase activity of free ribulose bisphosphate carboxylase-oxygenase and of the complex were determined spectrophotometrically [2, 121. Ribulose bisphosphate carboxylase-oxygenase was activated with assay buffer (50 mM glycylglycine, 50 mM KC1, 0.5 mM EDTA, 5 mM dithiothreitol) containing 20 mM bicarbonate and 10 mM magnesium at 30°C for 15 min. The various kinetic equations were fitted to the data using the Marquardt algorithm [13]. Programs were run with a VAX computer. The V,, and the K,,, values of the free ribulose bisphosphate carboxylase-oxygenase and of the complex were estimated by non-linear least-square fitting using the Michaelis-Menten equation. Chemicals of reagent grade were from Boehringer Mannheim. Ribulose-l,5-phosphate and 6-phosphogluconate were from Sigma.
RESULTS Ribulose bisphosphate carboxylase-oxygenase displays Michaelis-Menten kinetics whether free or inserted in the five-enzyme complex. As shown in the preceding paper [l], this implies that the difference of stabilization- destabilization energies for all the reaction steps along the reaction coordinate is either null or constant. In the first case, this means that there is no information transfer between active sites during the various steps of substrate binding and catalysis. In the second case, this implies that there is an information transfer, but that the extent of this transfer does not depend upon the degree of advancement of the reaction. As will be shown below, the use of 6-phosphogluconate as a competitive inhibitor of the reaction may lead to the conclusion that the active subunits of ribulose bisphosphate carboxylase-oxygenase behave in an independent manner and therefore that no information is transferred to the rest of the protein molecule when a subunit binds a substrate molecule or performs catalysis. As the active sites of free ribulose bisphosphate carboxylase-oxygenase are located at the interface between two large subunits and as their number is equal to eight, the relevant rate equation assumes the form
Fig. 1. Variation of the dimensionless rate u/nk*[El, as a function of the dimensionless substrate concentration K*[S]. (0, 0) The activity measurements of ribulose bisphosphate carbuxylaseoxygenase inserted in (0)the multi-enzyme complex (L&I or (0) free in solution (L8S8).Solid lines are fitted to Eqn (1) for the isolated enzyme and to Eqn (3) for the enzyme inserted in the multienzyme complex. The numerical values @fit these equations are U& = -5.47 kJ/mol, /1 = -1.68 kJ/mol, K* = 7.19mM- .
~_
V
-
K* [S] 1 + K* [S]
8 k* [Elo where k* is the catalytic constant for the independent active sites and K* the apparent substrate binding constant to these sites. Both of these kinetic parameters may be determined experimentally and therefore the left-hand side of Eqn (1) above represents the dimensionless, or normalized, rate for one active site only. This dimensionless rate may be plotted as a function of the dimensionless substrate concentration K* [S] (Fig. 1). The resulting curve thus represents the \ariation of the dimensionless rate of an active site as a function of the dimensionless substrate concentration when no information is transferred within the free enzyme. The ribulose bisphosphate carboxylase-oxygenase inserted in the complex has a L,S, structure and contains only two active sites for the substrate or for a competitive inhibitor, thus the corresponding dimensionless rate for an active site is d3k* [El,. If this rate is plotted as a function of K* [S], the curve thus obtained is not superimposed on the previous one (Fig. 1). This means that an information transfer occurs due to heterologous interactions between the active ribulose bisphosphate carboxylase-oxygenase and the other silent enzymes of the multi-protein complex. Moreover the extent of this information transfer, as expressed by the difference of stabilization-destabilization energies,
uy.-=, - up; = il (i = 1, 2) (2) is the same for the two substrate-binding steps and equal to A. Then the corresponding rate equation is V
-
z*
exp (- U;;,/RT) [S] 1 + exp (- AIR73 K* [S]
(3) ' 2 k* [Elo As the values of k* and K* are known from the lunetic behaviour of the naked ribulose bisphosphate carboxylase-oxy-
1001
y
Bib
+E S A
Fig. 2. Kinetic model of the reaction catalyzed by free octameric ribulose bisphosphate carboxylase-oxygenase.The enzyme is assumed to react with bothjts substrate and an inhibitor. The eight active sites behave independently and bind either the substrate with an apparent binding constant K*, or the inhibitor with a binding constant K?. k* is the catalytic rate constant.
genase. the values of thermodynamic parameters U& and can be determined. One finds
A
U:.? = VYj = - 5.47 +0.24 W/mol ( i = 1 , 2 ) . (4) - K.,P = -1.68 2 0.32 kJ/mol The results of Fig. 1 provide thermodynamic significance for the results already described showing that ribulose bisphosphate carboxylase-oxygenase in the complex has a higher V,,, (per active site) and a lower K,, than the corresponding free enzyme [3]. In order to be fulfilled, this condition implies that 2 u:? l>->(i = 0 , 1 , 2 ) . (5) RT RT The numerical results of expressions (4) show this is precisely the case. Results previously obtained show that if the rate for the free enzyme is measured either in the presence (ui) or in the
2=
vT1, ~
absence (11,) of 6-phosphogluconate, the expression ( u,/u,) -1 plotted as a function of the inhibitor concentration yields a family of straight lines passing through the origin [S]. This is compatible only with the view that, for naked ribulose bisphosphate carboxylase-oxygenase, the eight active sites behave independently. Therefore an active enzyme may well have bound substrate and inhibitor molecules on different sites. The relevant kinetic model is shown in Fig. 2 and the corresponding rate equation assumes the form _s - I = L' I
KP [I1
1
+ K* [S]
(6)
where K* is still the apparent substrate binding constant and K,* the inhibitor binding constant to these sites. If ribulose bisphosphate carboxylase-oxygenase is now inserted in the five-enzyme complex, the inhibitory effect of 6-phosphogluconate is completely different. A plot of ( v d v , ) - 1 versus [I] is now parabolic and a plot of
1002 k
2k
r r
Fig. 4. General model of a dimeric enzyme that may bind a substrate and an inhibitor following two different modes. The substrate is assumed to bind in a non-co-operative manner whereas the inhibitor binds following a co-operative mode.
Fig. 3. Exclusive binding of inhibitor and substrate to the multienzyme complex. The ribulose bisphosphate carboxylase-oxygenase
inserted in the five-enzyme complex binds either the substrate or the substrate analog, but not both. K is the apparent substrate binding constant, Kl and K2 the two inhibitor binding constants, k’ is the catalytic constant. The various U;. represent the stabilization-destabilization energies of all the enzyme states.
-4
as a function of this inhibitor concentration, [I], yields a family of straight lines passing through the origin [5]. These results have two interesting implications. First, they show that ribulose bisphosphate carboxylase-oxygenase can bind either the substrate or the inhibitor but not both. On the other hand, they show that the binding of the inhibitor is strongly co-operative whereas that of the substrate is not. The kinetic scheme of Fig. 3 offers a formal description of these results. The corresponding expression of (v,/v,) - 1 assumes the form Ki [I1 (2 + Kz [I]> V, _ 1= (7) 0, (1 + E [S]),
where K , and K2 are the two b&ding constants of the inhibitor on the two active sites and K the apparent substrate-binding constant. As d m is a linear function of [I], the relative concentration of the complex EI, (Fig. 3) is certainly negligible for it cannot be detected experimentally. This means that K2 [I] B 2 . (8) Therefore, Eqn (7) reduces to
and As is thus identical to A used previously. Eqn (9) above then assumes the form
Since E*, KT and A, have been determined from previous experimental results, the value of 1,may also be estimated by using Eqn (12). At this stage of the present reasoning it is of interest to note that the kinetic scheme of Fig. 3 is a particular case of the more general and realistic model shown in Fig. 1.One may thus wonder about the conditions that result in a 4implification of this model to that of Fig. 3. The relevant rate equation pertaining to this model is
u, 2 k’ [El, -
-
K [Sl (1 + E [Sl + K l [I]) (1 + K [S])’ + 2 Kl [S] [I] + K j [I] (2
Kz [I1 + 2 K, [SI -
K [S] B 2 K , [I]
where
K
and of the product
(14)
K, [I] B 2 then the rate equation (13) reduces to
2 k’ [El, The thermodynamic formulation of K,K, is
(13)
If there is a strong positive co-operativity in the binding of the inhibitor to the enzyme such that Kl is very small and Kz very large, it may be expected that
0,
(9)
+ K2 [I]).
E [S] (1 + E [S])
-
(1
+
[S])’
+ K , K2 [II2
(15) ’
Thus the ternary complex ESI is not formed to any significant extent during the enzyme reaction. The relevant kinetic model is that of Fig. 3. As the difference between the binding constants K, and K, increases, the plots (v.lu,)- 1 versus the inhibitor concentration become more and more concave upwards. This is illustrated in Fig. 5. Simple inspection of Eqns (13) and (15) predict that, at fixed concentration of inhibitor, co-operativity relative to substrate should exist. This co-opcrativity may be expressed by the extreme Hill coefficient, h,,,. For Eqn (13) this extreme Hill coefficient may be shown to be
1003 10
1.0 I
8
-
i
.
6
h
>-
5
4
2
0
0.0
0.2
0.6
0.4
0.8
[inhibitor] (mM) Fig. 5. Effect of the difference between the two inhibitor binding constants on the curvature of the ( v J v i ) - l versus the inhibitor concentration. The straight line pertains to a dimeric enzyme that does not display any co-operativity relative to the binding of the substrate and of the inhibitor (Eqn 6). The fixed concentration of the substrate is [S] = 0.Ql mM and the two relevant parameters are KP = 10 mM-' and K* = 10 mM-'. The other parabolic plots are representative of Eqn (7) and pertain to a dimeric enzyme that binds the substrate non-co-operatively, but binds theinhibitor in a co-operative mode-The respective values of [S], K and Kl are: [S] = 0.01 mM, K = 10 mM-I, Kl = 1 mM-'. As the value of K, increases, the concavity of the plots increases as well. The values of K2 are 5 mM-' (curve l), 20 mM-' (curve 2), 50 mM-' (curve 3), 100 mM-' (curve 4), 500 mM-' (curve 5).
"."
0
1
2
3
[substrate] (mM) Fig. 6. Effect of an inhibitor binding on the apparent co-operativity of a dimeric enzyme. The dimeric enzyme, whether free or inserted in a multi-enzyme complex, does not per se display any cooperativity in substrate binding. The corresponding apparent binding constant is K = 7 mM-' and the relevant dimensionless rate curve is hyperbolic (---). If an inhibitor binds co-operatively to the enzyme (reaction scheme of Fig. 4) a co-operativity relative to substrate appears. This co-operativity is positive (. . . .) if K, < K, ( K , = 1 mM-', K, = 100 mM-I), or negative (---) if Kz < K, ( K , = 100 mM-', K, = 1 mM-I). For the dotted line, the extreme Hill coefficient is equal to 1.67 and for the full line it is equal to 0.29.
41 + 2 K, [I] + Kl K2 [I]* and may assume values greater or smaller than unity depending on the values of K , and K,. If K2 > K,, i.e. there is positive co-operativity in inhibitor binding A,,, > 1, and there is a positive co-operativity with respect to substrate. If, alternatively, Kl > K,, there is a negative co-operativity in inhibitor binding and 0 < he,, < 1, therefore a negative co-operativity relative to substrate. These results are illustrated in Fig. 6. Similarly for Eqn (15) the extreme Hill coefficient is 2
I
hex,= 1+
1
(17)
41 + Kl K, [I]'
and the kinetic co-operativity can only be positive. For both Eqns (13) and (15) the extent of co-operativity should vary with the inhibitor concentration (Fig. 7) but the value of the Hill coefficient cannot exceed two. Free ribulose bisphosphate carboxylase-oxygenase does not display any co-operativity in the presence of 6-phosphogluconate but the multi-enzyme complex does (Figs 8 and 9). This kinetic co-operativity is positive and the corresponding Hill coefficient is equal to 1.2. The experimental rate data obtained under these conditions may be perfectly fitted to Eqn (1 3). It is however impossible to perform a kinetic study of the evolution of this co-operativity as a function of inhibi-
I 0
1
2
3
[inhibitor] (mM) Fig. 7. Effect of the inhibitor concentration on the extreme Hill coefficient for different values of inhibitor binding constants. The relevant reaction scheme is that of Fig. 4. The parameter values used for simulations of Eqn(16) are K, = 10mM-' and K,= 1 mM-' (curve 1); Kl = 1 mM-' and K, = 1 mM-' (curve 2); K , = 1 mM-' and K2 = 10 mM-' (curve 3).
tor concentration, as suggested by Eqn (17). This experimental difficulty arises from the decrease of the enzyme reaction rate in the presence of inhibitor. As the inhibitor concentration increases, the reaction rate decreases as well, and therefore the relative magnitude of the error becomes larger and larger in such a way that this kind of analysis looses any significance.
1004 1
1.6
/ o
/
0
l
I
h
>
-> I
-1
\
-2 5
-2
0.0
-3
0
1
2
3
-3
-2
-1
0
log ([Sl)
[RuBP] mM 8
B
-4
T
t
[RuBP] mM
Fig. 8. Kinetic behaviour of free and associated ribulose bisphosphate carboxylase-oxygenasein the absence and in the presence of 6-phosphogluconate. (A) Kinetic behaviour of isolated ribulose bisphosphate carboxylase-oxygenase (Rubisco). The activity of the enzyme was measured as previously described (0) at pH7.7 and 30°C. Competitive inhibitor was added (0.6mM) in the reaction The enzyme concentramixture and the assay was performed (0). tion was 5.9 nM. The apparent concentration of sites in the medium was 47.2 nM. In both cases, curves are hyperbolic and the value K, = 2.37 20.18 mM-' was obtained. (B) Kinetic behaviour of ribulose bisphosphate carboxylase-oxygenase inserted in a multi-enzyme complex. The activity of ribulose bisphosphate carboxylase-oxygenase was measured in the absence (0)or in the presence (0) of 0.6 mM 6-phosphogluconate. In the presence of the inhibitor, the curve becomes sigmoid. The enzyme concentration was 11.2 nM. The apparent concentration of sites in the medium was 22.4 nM. The sigmoid curve was fitted to Eqn(l5) and the value K,K,= 15.73 2 1.8 mM-* was obtained.
DISCUSSION The theoretical developments described in the preceding paper [l] allow one to study how heterologous interactions between polypeptide chains pertaining to different enzyme molecules may alter the behaviour of an enzyme within a multi-molecular complex. There are probably no quaternary constraints within free ribulose bisphosphate carboxylase-oxygenase and the active sites behave in an independent manner. They display no co-operativity in the binding of sub-
Fig.9. Hill plot pertaining to the region of maximum slope of ribulose bisphosphate carboxylase-oxygenaseactivity inserted in the complex. The experimental conditions are those used for the sigmoid curve of Fig. 8 B. The corresponding Hill coefficient is 1.2.
strate and of the inhibitor 6-phosphogluconate. This is by no means a surprising or novel result for several authors have shown that ribulose bisphosphate carboxylase-oxygenase follows Michaelis-Menten kinetics relative to ribulose bisphosphate concentration [ 14- 181. Moreover, equilibrium binding studies have shown that this ligand binds to the decarhamoylated enzyme in an anti-co-operative manner [19]. These results, however, are not in conflict since decarbamoyldted ribulose bisphosphate carboxylase-oxygenase is devoid of any catalytic activity and has therefore properties that are different from those of the active, carbamoylated enzyme. The inhibitory effect of 6-phosphogluconate on the enzyme reaction described above is also consistent with previous binding studies showing that this ligand binds in a non-co-operative manner to free ribulose bisphosphate carboxylase-oxygenase and that eight binding sites are available on this enzyme 1201. The situation is completely different if ribulose bisphosphate carboxylase-oxygenase is inserted into the five-enzyme complex. Heterologous interactions exist between the 'silent' enzymes and ribulose bisphosphate carboxylase-oxygenase that do not induce any co-operativity but result in an increase of both the V , and the apparent substrate binding constant. Heterologous interactions within the multi-enzyme complex do not induce any kinetic co-operativity of ribulose bisphosphate carboxylase-oxygenase since the strength of these interactions does not vary significantly along the reaction coordinate as the enzyme binds its two substrate molecules. However, these constant heterologous interactions generate a positive co-operativity in the binding of the substrate analog 6-phosphogluconate. This binding process has the peculiarity of being exclusive. In contrast to the free ribulose bisphosphate carboxylase-oxygenase that can bind both the wbstrate and the inhibitor molecules on different active sites, the multi-enzyme complex can bind either the substrate or the inhibitor but not both. Moreover, the binding of the wbstrate and of the inhibitor on the enzyme, whether free or associated with other proteins, is an exergonic process. The analysis of rate data allows one to determine the values of thermodynamic parameters that control the activity of the enzyme complex as well as of the free ribulose
1005 Table 1. Thermodynamic parameters associated with catalytic activity of ribulose bisphosphate carboxylase-oxygenase in the f r e e a t e ancwithin the multi-enzyme complex. The expressions of AG* and AG correspond to the apparent free energy of substrate binding to the free or to the associated ribulose bisphosphate carboxylase-oxymase, respectively. These v a l u e m e obtained from the values of K* and K through the relations AG* = -RT In K* and AG = -RT In K. Similarly the sum AG, + AG, and AG?: may be AG,= -RT In K, K2 obtained from the relations AG, and AG,Y = -RT In K?. The values of A,, A, and U;,+express how heterologous interactions between ‘silent’ enzymes and ribulose bisphosphate carboxylase-oxygenase alter the kinetic behaviour of this enzyme in the multi-protein complex.
+
Parameter
B
=A
A AGI + AG2
a 5kJ/mol
Value C
W/mol
__
&*
-22.23 L 0.41 -23.91 20.51 -20.03 2 0.134 -41.09 t 0.3 - 1.68L0.32 - 1.03L0.15 - 5.4720.24
AG AG,* AG, + AG,
A, 2,
G , Y
bisphosphate carboxylase-oxygenase. These numerical values are reported in Table 1. Of particular interest are the values of 2 = ”U“,“ - “PYO t-1.Y
,Ii
U;;; U& = su;g
=
(i
=
1, 2)
that are reported in this table. It is worth pointing out that the values of As and A,are negative, which means that heterologous interactions within the five-enzyme complex increase the apparent affinity of the substrate and the real affinity of the inhibitor for the ribulose bisphosphate carboxylaseoxygenase inserted in the complex. The thermodynamic significance of this enhancement is illustrated in Fig. 10. Moreover, the large value of the thermodynamic parameter Uz,y emphasizes the magnitude of the strength of heterologous interactions within the five-enzyme complex. Last, as the relation that associates the catalytic rate constant icto the intrinsic rate constant k* [l]is
Lc = k*
Fig. 10. Effect of heterologous interactions between ribulose bisphosphate carboxylase-oxygenase activity and the other enzymes of the multi-protein complex, on the thermodynamic parameters of the reaction. (A) Heterologous interactions decrease the exergonic character of substrate binding to the active site. (B) Heterologous interactions decrease the exergonic character of inhibitor binding to the active site. (C) Heterologous interactions stabilize the transition states during the catalytic process.
is inserted in the multi-enzyme complex, then this enzyme is more active than in a free state and, in the presence of 6phosphogluconate, displays positive kinetic co-operativity. Although this kinetic co-operativity is moderate, it is nevertheless significant and one may speculate that it represents an interesting aspect of ribulose bisphosphate carboxylaseoxygenase functioning in vivo.
exp { - (U:, - IJRT}
one may estimate how heterologous interactions increase the value of this catalytic constant kc. This is again illustrated in Fig. 10. Whereas the five-enzyme complex does not display any kinetic co-operativity in the absence of the inhibitor, it does do so in the presence of the inhibitor. The theory predicts that, if the binding of the inhibitor to the complex is positively co-operative, the kinetic co-operativity with respect to substrate is positive as well and the maximum value of the extreme Hill coefficient cannot exceed two. This is a prediction which is experimentally found to occur with the fiveenzyme complex and the inhibitor 6-phosphogluconate. Alternatively, if the binding of the inhibitor to the multi-enzyme complex is negatively co-operative, then the kinetic co-operativity relative to substrate should be negative as well. These results are of potential biological interest since substrate analogues are present in chloroplasts [21]. If a significant part of ribulose bisphosphate carboxylase-oxygenase
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2. 3.
4.
5.
modulation of enzyme rates within multi-enzyme complexes. I. Statistical thermodynamics of information transfer through multi-enzyme complexes, Eur. J. Biochem. 226, 993-998. Gontero, B., Cirdenas, M. L. & Ricard, J. (1988) A functional five-enzyme complex of chloroplasts involved in the Calvin cycle, Eur: J. Biochem. 173, 437-443. Gontero, B., Mulliert, G., Rault, M., Giudici-Orticoni, M. T. & Ricard, J. (1993) Structural and functional properties of a multi-enzyme complex of spinach chloroplasts. 2. Modulation of the kinetic properties of enzymes in the aggregated state, Eur: J. Biochem. 217, 1075-1082. Rault, M., Gontero, B. & Ricard, J. (1991) Thioredoxin activation of phosphoribulokinase in a chloroplast multi-enzyme system, Eur. J. Biochem. 197,791-797. Rault, M., Giudici-Orticoni, M. T., Gontero, B. & Ricard, J. (1993) Structural and functional properties of a multi-enzyme complex of spinach chloroplasts. 1. Stoichiometry of the polypeptide chains, Eul: J. Biochem. 217, 1065-1073.
1006 6. Giudici-Orticoni, M. T., Gontero, B., Rault, M. & Ricard, J. (1992) Organisation structurale et fonctionnelle d'enzymes du cycle de Benson-Calvin a la surface de thylacoydes de chloroplastes d'Epinard, C. R. Acad. Sci. Paris 314, Se'r. III, 477483. 7. Andersson, I., Knight, S., Schneider, G., Lindqvist, Y., Lundqvist, T., BrandCn, C. I. & Lorimer, G. H. (1989) Crystal structure of the active site of ribulose-1,s-bisphosphate carboxylase, Nature 337, 229-234. 8. Knight, S., Andersson, I. & BrandCn, C. I. (1990) Crystallographic analysis of b-ibulose-1,5-bisphosphate carboxylase from spinach at 2.4 A resolution. Subunit interactions and active site, J. Mol. Biol. 215, 113-160. 9. Schneider, G., Knight, S. G., Andersson, I., BrandCn, C. I., Lindqvist, Y. & Lundqvist, T. (1990) Comparison of the structures of L, and L,S, Rubisco suggests a functional role for the small subunit, EMBO J. 9, 2045-2050. 10. Miziorko, H. M. & Lorimer, G. H. (1983) Ribulose-l,5-bisphosphate carboxylase/oxygenase, Annu. Rev. Biochem. 52, 507 535 11. Keys, A. J. & Parry, M. A. J. (1990) Ribulose-1,5-bisphosphate carboxylase/oxygenase and carbonic anhydrase, Methods Plant Biochem. 3, 1-14. 22. Pierce, J., Lorimer, G. H. & Reddy, G. S. (1986) Kinetic mechanism of ribulose bisphosphate carboxylase: evidence for an ordered, sequential reaction, Biochemistry 25, 1636- 1644. 13. Marquardt, D. W. (1963) An algorithm for least-squares estimation of non-linear parameters, J. SOC.Indust. Appl. Muth. 11, 431-441.
14. Paulsen, J. M. & Lane, M. D. (1966) Spinach ribulose diphosphate carboxylase. I. Purification and properties of the enzyme, Biochemistry 5, 2350-2357. 15. Lorimer, G. H., Badger, M. R. & Andrews, T. J. (19761 The activation of ribulose-l,5-bisphosphatecarboxylase by carbon dioxide and magnesium ions. Equilibria, kinetics, a suggestive mechanism, and physiological implications, Biochemistry 15, 529-536. 16. Paech, C. & Tolbert, N. E. (1978) Active site studies of ribulose1,s-bisphosphate carboxylase/oxygenase with pyridoxal 5'phosphate, J. Biol. Chem. 253, 7864-7873. 17. Pierce, J., Tolbert, N. E. & Barker, R. (1980) Interaction of ribulosebisphosphate carboxylase/oxygenase with transitionstate analogues, Biochemistry 19, 934-942. 18. Khan, M. A., Dixit, A. & Upadhyaya, K. C. (1994) Puirification and characterization of ribulose-l,5-bisphosphatecarbovylase from triticale, Indian. J. Biochem. Biophys. 31, 121- 126. 19. Jensen, R. G. & Zhu, G. (1992) Rubisco fallover and negative cooperativity of substrate binding, in Research in photosynthesis, vol. 111 (Murata, N., ed.) pp. 617-620, Kluwer Academic Publishers, Dordrecht. 20. Badger, M. R. & Lorimer, G. H. (1981) Interaction of sugar phosphates with the catalytic site of ribulose-1,5-bisphosphate carboxylase, Biochemistry 20, 2219-2225. 21. Gardemann, A., Stitt, M. & Heldt, H. W. (1983) Control of CO, fixation. Regulation of spinach ribulose-5-phosphate kinase by stromal metabolite levels, Biochim. Biuphys. Acra 722, 51 -60.
