Structural and functional properties of a multienzyme complex from spinach chloroplasts. 2. Modulation of the kinetic properties of enzymes in the aggregated state.
ABSTRACT The carboxylase activity of free ribulose 1,5bisphosphate carboxylaseoxygenase has been compared to that of the fiveenzyme complex present in chloroplasts. Kinetic results have shown that the V/active site is lower for the free enzyme than for the complex. Conversely the Km is smaller for the complex than for the free enzyme. This implies that the catalytic activity of the enzyme is enhanced when it is embedded in the complex. Under reducing conditions and in the presence of reduced thioredoxin, inactive oxidized phosphoribulokinase, free in solution or inserted in the multienzyme complex, becomes active. The kinetics of this activation process has been studied and shown to be exponential. The time constant of this exponential decreases, for the free enzyme, as thioredoxin concentration is increased. Alternatively, for the enzyme embedded in the complex, this time constant increases with thioredoxin concentration almost in a linear fashion. This implies that the complex is much more rapidly activated by reduced thioredoxin than is the free phosphoribulokinase. The variation of the amplitude of this activation process as a function of thioredoxin concentration is a hyperbola. The concentration of thioredoxin which results in half the asymptotic value of this hyperbola is smaller for the complex than for the free enzyme. A kinetic model has been proposed and the dynamic equations resulting from this model have been derived. They fit the experimental results exactly. From the variation of the amplitude of the activation process one may derive the binding constants of thioredoxin on either the oxidized enzyme or on a partly dithiothreitolreduced enzyme (both of them free or inserted in the complex). In either case, the affinity of reduced thioredoxin is larger for the complex than for the free enzyme. The individual values of some of the rate constants have also been estimated from the variation of the time constants as a function of thioredoxin concentration. Taken together, these results show that at least two enzymes, ribulose 1,5bisphosphate carboxylaseoxygenase and phosphoribulokinase, have quite different kinetic properties depending on whether they are in free solution or embedded in the multienzyme complex.
 Malika Mekhalfi, Carine Puppo, Luisana Avilan, Régine Lebrun, Pascal Mansuelle, Stephen C. Maberly, Brigitte Gontero[Show abstract] [Hide abstract]
ABSTRACT: Diatoms are a widespread and ecologically important group of heterokont algae that contribute c. 20% to global productivity. Previous work has shown that regulation of their key Calvin cycle enzymes differs from that of the Plantae, and that in crude extracts, glyceraldehyde3phosphate dehydrogenase (GAPDH) can be inhibited by nicotinamide adenine dinucleotide phosphate reduced (NADPH) under oxidizing conditions.The freshwater diatom, Asterionella formosa, was studied using enzyme kinetics, chromatography, surface plasmon resonance, mass spectrometry and sequence analysis to determine the mechanism behind this GAPDH inhibition.GAPDH interacted with ferredoxin–nicotinamide adenine dinucleotide phosphate (NADP) reductase (FNR) from the primary phase of photosynthesis, and the small chloroplast protein, CP12. Sequences of copurified GAPDH and FNR were highly homologous with published sequences. However, the widespread ternary complex among GAPDH, phosphoribulokinase and CP12 was absent. Activity measurements under oxidizing conditions showed that NADPH can inhibit GAPDHCP12 in the presence of FNR, explaining the earlier observed inhibition within crude extracts.Diatom plastids have a distinctive metabolism, including the lack of the oxidative pentose phosphate pathway, and so cannot produce NADPH in the dark. The observed downregulation of GAPDH in the dark may allow NADPH to be rerouted towards other reductive processes contributing to their ecological success.New Phytologist 05/2014; · 6.37 Impact Factor  SourceAvailable from: Valerie Jerome
 [Show abstract] [Hide abstract]
ABSTRACT: Significance: The posttranslational modification of thiol groups stands out as a key strategy cells employ for metabolic regulation and adaptation to changing environmental conditions. Nowhere is this more evident than in chloroplaststhe O2evolving photosynthetic organelles of plant cells that are fitted with multiple redox systems, including the thioredoxin (Trx) family of oxidoreductases functional in the reversible modification of regulatory thiols of proteins in all types of cells. The best understood member of this family in chloroplasts is the ferredoxinlinked thioredoxin system (FTS) by which proteins are modified via lightdependent disulfide/dithiol (SS/2SH) transitions. Recent Advances: Discovered in the reductive activation of enzymes of the CalvinBenson cycle in illuminated chloroplast preparations, recent studies have extended the role of the FTS far beyond its original boundaries to include a spectrum of cellular processes. Together with the NADPlinked thioredoxin reductase (NTRC) and glutathione/glutaredoxin systems, the FTS also plays a central role in the response of chloroplasts to different types of stress. Critical Issues: The comparisons of redox regulatory networks functional in chloroplasts of land plants with those of cyanobacteriaprokaryotes considered to be the ancestors of chloroplastsand different types of algae summarized in this review have provided new insight into the evolutionary development of redox regulation, starting with the simplest O2evolving organisms. Future Directions: The evolutionary appearance, mode of action and specificity of the redox regulatory systems functional in chloroplasts, as well as the types of redox modification operating under diverse environmental conditions stand out as areas for future study.Antioxidants & Redox Signaling 02/2014; · 8.20 Impact Factor
Page 1
Eur. J. Biochem. 217, 10751082 (1993)
0
FEBS 1993
Structural and functional properties of a multienzyme complex
from spinach chloroplasts
2. Modulation of the kinetic properties of enzymes in the aggregated state
Brigitte GONTERO, Guillermo MULLIERT, Magali RAULT, MarieThtrkse GIUDICIORTICONI and Jacques RICARD
Institut Jacques Monod, CNRS  UniversitC Paris VII, Paris, France
(Received July 20, 1993)  EJB 931074/3
The carboxylase activity of free ribulose 1,5bisphosphate carboxylaseoxygenase has been com
pared to that of the fiveenzyme complex present in chloroplasts. Kinetic results have shown that
the V/active site is lower for the free enzyme than for the complex. Conversely the K,,, is smaller
for the complex than for the free enzyme. This implies that the catalytic activity of the enzyme is
enhanced when it is embedded in the complex.
Under reducing conditions and in the presence of reduced thioredoxin, inactive oxidized phos
phoribulokinase, free in solution or inserted in the multienzyme complex, becomes active. The
kinetics of this activation process has been studied and shown to be exponential. The time constant
of this exponential decreases, for the free enzyme, as thioredoxin concentration is increased. Alterna
tively, for the enzyme embedded in the complex, this time constant increases with thioredoxin
concentration almost in a linear fashion. This implies that the complex is much more rapidly acti
vated by reduced thioredoxin than is the free phosphoribulokinase.
The variation of the amplitude of this activation process as a function of thioredoxin concentra
tion is a hyperbola. The concentration of thioredoxin which results in half the asymptotic value of
this hyperbola is smaller for the complex than for the free enzyme.
A kinetic model has been proposed and the dynamic equations resulting from this model have
been derived. They fit the experimental results exactly. From the variation of the amplitude of the
activation process one may derive the binding constants of thioredoxin on either the oxidized en
zyme or on a partly dithiothreitolreduced enzyme (both of them free or inserted in the complex).
In either case, the affinity of reduced thioredoxin is larger for the complex than for the free enzyme.
The individual values of some of the rate constants have also been estimated from the variation of
the time constants as a function of thioredoxin concentration.
Taken together, these results show that at least two enzymes, ribulose 1,5bisphosphate carboxyl
aseoxygenase and phosphoribulokinase, have quite different kinetic properties depending on
whether they are in free solution or embedded in the multienzyme complex.
The interactions that may exist between different or iden
tical polypeptide chains within a multienzyme complex may
alter the catalytic efficiency of the enzymes embedded in this
complex. One may thus wonder whether the specific activity
of an enzyme inserted in a multienzyme complex is different
from that it would have if it were in free solution. Referring
to the fiveenzyme complex of chloroplasts studied pre
viously [l], the specific activity and kinetics of some of the
enzymes present in this complex may be considered. There
are at least two enzymes that are worth studying: ribulose
1,5bisphosphate carboxylaseoxygenase and phosphoribu
lokinase. Ribulose 1,5bisphosphate carboxylaseoxygenase
in this complex has a structure which is completely different
from that of the free enzyme. In particular, the stoichiometry
of large and small polypeptide chains is completely different
within the complex relative to that prevailing in the free en
Correspondence to J. Ricard, lnstitut Jacques Monod, CNRS 
UniversitC Paris VII, Tour 43, 2 place Jussieu, F7.5251 Paris Cedex
05, France
Fax: +33 1 44 27 59 94.
Enzymes. Phosphoribulokinase (EC 2.7.1.19); ribulose 1,sbis
phosphate carboxylaseoxygenase (EC 4.1.1.39).
zyme. As the catalytic efficiency of this enzyme is usually
considered as being related to the interactions between large
and small subunits, one may expect the carboxylase activity
of ribulose 1 ,Sbisphosphate carboxylaseoxygenase in the
complex to be different from that of the free enzyme. The
other enzyme, phosphoribulokinase, is believed to be one of
the key enzymes of the BensonCalvin cycle since it may be
activated by light through the thioredoxin system [2, 31. As
preliminary experiments have shown that the activation of
phosphoribulokinase by thioredoxin is different depending
on whether the enzyme is embedded in the complex or free
in solution [4], it appears of interest to study the kinetics of
this activation.
The aim of this paper is thus to compare the kinetic be
haviour of ribulose 1 ,Sbisphosphate carboxylaseoxygenase
and phosphoribulokinase depending on whether they are in
serted in the fiveenzyme complex or isolated in solution.
MATERIALS AND METHODS
Ribulose 1,5bisphosphate carboxylaseoxygenase, phos
phoribulokinase and the fiveenzyme complex were isolated
Page 2
1076
Table 1. Total and free thioredoxin concentrations. Free thiore
doxin concentrations were calculated from the dissociation constant
estimated for the isolated phosphoribulokinase.
[Thioredoxin]
Total
free
0.1
0.2
0.3
0.4
1
2
4
6
8
10
0.086
0.175
0.265
0.358
0.93
1.92
3.90
5.90
7.90
9.9
from chloroplasts and purified as described previously [ 11.
The carboxylase activity of ribulose 1,5bisphosphate car
boxylaseoxygenase and of the complex was determined
spectrophotometrically [ 1, 51. Free ribulose 1,5bisphosphate
carboxylaseoxygenase contained eight active sites or eight
large subunits. Each active site is located at the interface
between two large subunits [6]. The results described in the
previous paper showed the complex to possess only two large
subunits and thus, most probably, two active sites only. In
order to compare carboxylase activity of the free enzyme and
of the complex, this activity was expressed per active site.
Thioredoxin was isolated from chloroplast, and purified with
minor modifications as previously described [7].
Determination of the amplitude and of the time constant
of phosphoribulokinase activity were performed by adding to
an incubation medium (50 mM glycylglycine, 10 mM
MgCI2, 0.5 mM EDTA, 50 mM KC1 at pH 7.7) containing
either phosphoribulokinase or the complex, a mixture of a
fixed dithiothreitol concentration and different thioredoxin
concentrations. The final concentration of dithiothreitol in
the reaction mixture was 2 mM. At different times of incuba
tion an aliquot was withdrawn and its activity was measured
in the assay medium as previously described [4]. Free (un
bound) concentration of thioredoxin was determined through
an estimation of the apparent dissociation constant of thiore
doxin from either the free phosphoribulokinase or from the
multienzyme complex, under conditions where the thiore
doxin is in large excess relative to the enzyme (or to the
multienzyme complex). From the estimation of this apparent
dissociation constant, one may estimate the free concentra
tion of thioredoxin that prevailed when the two reaction part
ners were at similar concentrations. As an example of the
results obtained, the concentrations of total and free thiore
doxin are given in Table 1.
The equations generated by kinetic models were fitted to
the data using the Marquardt algorithm [SJ. Programs were
run with a VAX computer. The V and K, of ribulose 1,5
bisphosphate carboxylaseoxygenase were determined by
nonlinear leastsquare fitting of a MichaelisMenten equation
to the rate data. The equilibrium constant of the spontaneous
reduction of phosphoribulokinase (free or embedded in the
complex), as well as the equilibrium constants for the bind
ing of thioredoxin to this enzyme, were estimated from the
variation of the amplitude of the activation of phosphoribu
(cd
Fig. 1. A simple model of phosphoribulokinase (free or inserted
in the complex) activation induced by thioredoxin reduction. In
this model, E,, Ex and E, stand for oxidized, thioredoxinreduced
and dithiothreitolreduced enzyme respectively.
lokinase as a function of the free concentration of thiore
doxin. The rate constants of thioredoxin binding or release
to, or from, phosphoribulokinase were obtained (as described
below) from the variation of the time constant of the activa
tion process plotted against the free concentration of thiore
doxin.
Chemicals of reagent grade were bought from Boehringer
Mannheim. Ribulose5phosphate and ribulose 1,5bisphos
phate were from Sigma.
THEORY
The simplest model that allows expression of the varia
tion of the time constant and the amplitude of the activation
of free phosphoribulokinase and of phosphoribulokinase
within the complex is shown in Fig. 1. This model postulates
that the enzyme (free or inserted in the complex) may be
directly reduced by reduced thioredoxin or may be partly
reduced by dithiothreitol and then reduced by thioredoxin.
In this model c,, c2 and c3 represent the concentrations of
the three enzyme forms, namely that of E, (oxidized en
zyme), ED (dithiothreitolreduced enzyme) and Ex (thiored
oxinreduced enzyme). Qualitatively, the same model is used
to fit the data obtained with the free enzyme or with the
complex. x represents the concentration of free (unbound)
thioredoxin and e, that of the initial (or total) enzyme, or
complex, concentration. Then
eT = c, + c2 + c3 .
(1)
This conservation equation allows one to describe the
temporal evolution of the system with only two differential
equations, for instance
= k,, eT  (k+] + k, + k+2 X) CZ + (k2  k + ~ )
dt
dc2

C3
dt
If thioredoxin concentration x is in excess with respect to
that of phosphoribulokinase, these equations are linear and
may be integrated using, for instance, the LaplaceCarson
transform. One thus finds
c2 = yo + y, e'!' + t , v 2 eA2t
c1 = yh + wi e+' + y: e+,
(3)
Page 3
1077
In these equations w and iy’ are the amplitudes of the various
terms and the 1 values their time constants. As the time t
increases the system evolves towards its equilibrium and one
has
G = yo
C? = w;.
(4)
The expressions of yo and w:, thus represent the equilibrium
concentrations of c2 and c , . Their sum is proportional to the
amplitude of the activation process.
As shown in the Appendix, the expressions of t y , ,
are equal to
and t y ;
From Eqn (9) one may obtain the apparent dissociation
constant ($) as the sum of individual dissociation constants
of the enzymethioredoxin complex 1/K, + l/K3.
Setting for simplicity
a = k+,  k+,
p = k,  k,,
y 1
k,  k,
a’ = k,, + k+,
/3’ = k, + k+,
y‘ = k, + k,
(11)
However, owing to the occurrence of microscopic reversibil
ity in the model of Fig. 1, one must have
k+, k,, k, = k, k, k,,
and this allows factorization and simplification of Eqns (5).
One thus has
or
K, Kz = K,
(6)
Under these forms it becomes obvious that the expressions
are equivalent to the expression of the equilibrium concentra
tion of c2 and c?. One has
1 1
Therefore, for the overall process of the model shown in
Fig. 1, the amplitude which may be determined experimen
tally is
In the absence of thioredoxin, the observed amplitude re
duces to
the time constants A, and & are expressed through the equa
tion (see Appendix)
a’x + p’ + y‘ t ,/<a x + j~
A,,* =
+ y>’  4 p y . (12)
2
If ,Il + A,, the activation process will appear monoexponen
tial and its time constant is A2, namely
afx + p’ + y’  J<a x + B + y>’  4 B y
A, =
. (13)
2
This is the experimental situation which has been encoun
tered in Figs 5 and 7. In order to find out whether this time
constant may increase or decrease with the thioredoxin con
centration, or may vary linearly with this concentration, one
has to determine first the expressions of a/z,/dx and a2?J
ax2. The first derivative of the time constant may be written
as
which reduces to
Thus it appears that the sign of dA,lax relies in part upon
whether the ratio
is larger or smaller than unity. By talung into account the
definition of a and a’, Eqn (15) may be reexpressed as
It is thus evident that a necessary, but by no means sufficient,
condition for aA,/ax < 0 is that R > 1. This, in turn, would
imply that
Page 4
1078
/ a
I
"." 0
2 4
[XI (106~.M)
6 8 10
Fig. 2. Simulations of some possible types of kinetic behaviour
of the reaction model of Fig. 1. The numerical values (in SP) of
the rate constants used for simulation are (a) k,, = 2.5 X lo', k,, =
4X104, k+,=4X104, k,=2.5X102,
1 X lo' (b) k+, = 1 X lo', k,, = 1 X lo', k, = 2 X lo4, k, =
IxlO',
k,= 1, k,= 2X10',
lX1O6, k+,= 1X102, k,= lSXlO', k,=
kz=1X103, k,=
(c) k , , = 1.5X10',
1, k,= 1X104.
k+,=
The necessary and sufficient condition for aA,lax < 0 is
R(k+2  k+3) > k+, + k+,
which requires expression (1 8). Alternatively, a necessary
and sufficient condition for A, to be an increasing function
of thioredoxin concentration is
k+2 + k+, > R (k+z  k44 .
The condition for linearity of the plot of A, versus thio
redoxin concentration is
1
~   (k+3  k+,) 
ax,
2
Thus this condition is fulfilled if k+,= k+, or (and) if aRl
ax = 0. Setting again for simplicity
u = (a x + p + 7)'  4 B y
one has
(19)
(20)
a z n ,
dR
ax
:= 0 .
(22)
d X
U
which may be reexpressed as
In order for this expression to be identical to zero, one must
have
(ax + B + y)' = u
and this in turn implies that p y = 0. Thus there are three
conditions that result in a linear plot when plotting A2 versus
thioredoxin concentration, namely
,
I
T   I
. 
2r
1.6
1.2
0.8
0.4
0
0
0.6
[Ribulose 1,sbisphosphate] mM
1.2
1.8
2.4
Fig. 3. Kinetic behaviour of free ribulose 1,5bisphosphate car
boxylaseoxygenase as a function of ribulose 1,5bisphosphate
concentration. Enzyme activity was determined at pH7.7 as de
scribed in Materials and methods. Free ribulose 1,5bisphosphate
carboxylaseoxygenase was preincubated with 20 mM bicarbonate
in reaction buffer containing 10 mM magnesium at 30°C. The en
zyme concentration in the assay was 5.9 nM. The apparent 'concen
tration' of sites in the medium was 47.2 nM.
Fig. 2 illustrates by simulation some possible types of
variation of A, as a function of free thioredoxin concentra
tion. In the absence of thioredoxin the time constant of the
slow relaxation Az, becomes either
A2= k,, + k,
or
A, = k, + k, .
From a purely mathematical point of view, it is not possible
to screen among these two possibilities. However, one may
notice that, in absence of thioredoxin, the reaction scheme of
Fig. 1 reduces to the spontaneous reduction of E, into ED and
therefore it is only expression (26) which may have a physi
cal meaning.
The analysis of the relaxation amplitudes allows to esti
mate the three equilibrium constants Kl, Kz, K3. As Eqn (26)
may be rewritten as
A,= k, (1 + K,)
it allows estimation of k, and then of k,, from rate data.
The other rate constants may be estimated by leastsquare
fitting.
(26)
(27)
(28)
RESULTS
The steadystate rate of the carboxylase activity of either
free ribulose 1,5bisphosphate carboxylaseoxygenase or of
the multienzyme complex follows MichaelisMenten kine
tics (Figs 3 and 4). From these data one may estimate the V
and the K,. One may notice that the K,, for the complex is
about half that of the free enzyme (Table 2) whereas the V
of that complex is about five times that of isolated ribulose
1,5bisphosphate carboxylaseoxygenase (Table 2). This im
plies that the ratio VIK,, is about tenfold higher for the com
plex than for the free enzyme (Table 2).
Taken together, these results unambiguously show that,
in the absence of its activase, ribulose 1,5bisphosphate car
boxylaseoxygenase displays a much higher activity when
embedded in the complex.
Page 5
1079
,
ded in the complex, whereas the asymptotic value is the same
for these two types of phosphoribulokinase. The values of
the equilibrium constants for this process were calculated as
described in Materials and Methods (Table 3). The apparent
dissociation constant is about eightfold smaller for the com
plex than for free phosphoribulokinase (Table 3). Thus re
duced thioredoxin appears to have a greater affinity for the
complex than for the free enzyme.
For free phosphoribulokinase, and in the range of the thi
oredoxin concentrations explored experimentally, the time
constant decreases as this concentration is increased
[Ribulose 1,5bisphosphate] mM
Fig. 4. Kinetic behaviour of ribulose 1,5bisphosphate carboxyl
aseoxygenase in the complex as a function of ribulose 1,5bis
phosphate concentration. Enzyme activity was determined as de
scribed in Fig. 3. The complex concentration in the assay was
11.2 nM. The apparent 'concentration' of sites in the medium was
22.4 nM.
Table 2. Comparison of kinetic constants of free ribulose 1,5
bisphosphate carboxylaseoxygenase and ribulose 1,5bisphos
phate carboxylaseoxygenase inserted in the fiveenzyme com
plex. The errors of K,, and V are those given by the leastsquare
method; and for VIK, was obtained as described by Cleland [9].
State of ribulose K,
1,5bisphosphate
carboxylase
oxygenase
V
VIK,,,
mM
0.14 ? 0.03
0.07 5 0.006 7.13 ? 0.20
site' s'
1.57 ? 0.10
mM' site' s'
11.21 ? 1.70
101.86 ? 7.14
Isolated
Embedded
When a mixture of dithiothreitol and thioredoxin is added
to either free phosphoribulokinase, or to the complex, one
may observe an increase of activity whether the enzyme is
free or embedded in the complex [4]. This enhancement of
activity may be detected by taking aliquots of the mixture at
different times, mixing these aliquots with the substrates of
phosphoribulokinase and measuring the resulting reaction
rates. These rates increase exponentially with time and reach
a plateau value (Fig. 5). It is possible to determine a time
constant and an amplitude of this activation process. As the
steadystate rate which may be measured experimentally is
proportional to the concentration of the reduced enzyme (or
of the reduced complex), the ratio of the actual enzyme activ
ity over the maximum activity that may be obtained is a
measure of the proportion of active enzyme present in the
assay medium.
The time constant and the amplitude of this activation
process may be studied as a function of free thioredoxin pre
sent in the assay medium (Fig. 6). This free concentration
may be estimated as described in Materials and Methods.
The amplitude of the activation process may be plotted, for
either free phosphoribulokinase or for the complex, against
the concentration of free thioredoxin. In either case, the vari
ation of this amplitude versus the free thioredoxin concentra
tion is a hyperbola whose intercept with the y axis is positive.
Moreover this hyperbola reaches a plateau value at high thio
~U
complex, the time constant decreases at low thioredoxin con
centrations and then increases linearly (Fig. 7B). These re
sults are consistent with the kinetic model of the previous
section. It is possible to estimate the rate constants involved
in the model of Fig. 1. When thioredoxin concentration ap
proaches zero, the time constant of the activation process
becomes equal to k,, + k,. As the equilibrium constant K,
is known, both k,, and k, may be determined. These values
may be used as a starting point to fit the Eqn (13) to the data.
It is thus, in theory, possible to estimate the numerical values
of all the rate constants involved in this model (Table 4).
However, only lower and upper bounds of k,, and k2, k,,
and k, may be determined. Above and below these limits
the sum of squares of the residuals are in practice unchanged
when the values of the constants are altered. Thus although
the numerical values of these rate constants perfectly fit the
rate data, the set of these values is not unique.
The interesting conclusion of these results is that for cer
tain thioredoxin concentrations (about 8 pM in Fig. 7) the
time constant of the activation process is about 12 times
faster with the complex than with free phosphoribulokinase.
A time constant of about 0.35 min' is quite compatible with
the induction time of the BensonCalvin cycle upon dark
light transition.
DISCUSSION
It is usually implicitly, or explicitly, considered that the
main, or even the only, functional advantage that may origi
nate from the packing of different enzymes which catalyse
consecutive reactions is to avoid dilution of the reaction in
termediates in the cellular medium through channelling of
these intermediates from one active site to another one [lo
151. But the interaction of different polypeptide chains within
a complex may also alter qualitatively or quantitatively the
kinetic behaviour of the enzymes that are associated in this
complex.
In the case of the fiveenzyme complex purified from
chloroplasts there are two enzymes that are worth con
sidering from this point of view, namely ribulose 1,5
bisphosphate carboxylaseoxygenase and phosphoribuloki
nase. Ribulose 1,5bisphosphate carboxylaseoxygenase ap
pears interesting to study from this point of view because the
stoichiometry of the large and small subunits is different in
the free enzyme and in the complex [16] and one may there
fore suspect that this difference of structure affects the kinetic
properties of the enzyme. The second enzyme which is worth
studying is phosphoribulokinase because its activity may be
regulated by thioredoxin and it is possible that the activation
is basically different when the enzyme is in free solution
rather than inserted in the complex.
Page 6
1080
100
h
5
Q
;;j 50
p:
0 
100
h
5
Q ; ; i 50
c 4
0


0
B 
d
A
~~ ~
0
25
50
75
100
0
25
50
75
100
Time (min)
Time (min)
Fig. 5. Activation of phosphoribulokinase by thioredoxin. (A) 0.12 pM of isolated (free) phosphoribulokinase. (B) 0.14 pM of phosphori
bulokinase embedded in the complex. In both cases the enzyme was incubated at pH 7.7 for the time given on the abscissa with a mixture
of 2 mM dithiothreitol and either no thioredoxin (M), 1 pM thioredoxin (A) or 10 pM thioredoxin (0). The initial reaction rate was
measured on aliquots of these mixtures as described under Materials and methods. The curves are exponentials fitted to experimental data.
100
 75
E
8
P
d
2
3 50
25
n
v
100
 15
e
m
'CI a
E
4
50
25
n
v
B
0
2
4
6
8
10
0
2
4
6
8
10
[Thoredoxin]
M)
[Thioredoxin]
M)
Fig. 6. Variation of the amplitudes of the exponential of the activation process as a function of thioredoxin concentration. (A) Isolated
phosphoribulokinase, (B) phosphoribulokinase in the complex. The solid lines represent the best fits of Eqii (9) to experimental data. The
corresponding numerical values are given in Table 3.
Table 3. Comparison of different constants for model in Fig. 1 for free phosphoribulokinase and phosphoribulokinase inserted in
the fiveenzyme complex.
The errors of K, and K2 are given by the leastsquare method; and those of K3 and Kd were obtained as described by Cleland [9].
State of
phosphori
bulokinase
K,
k
K3
R d
M' M
Isolated
Embedded
0.49 2 0.05
0.66 ? 0.07
3.71X10h + 0.67X10'
22.8 X 10' 2 3.79 X 10'
1.82X106 2 0.18X10'
15.1X10'2 1.42X106
8.19~107 + 1.02~107
i.10~107 + 0.13~107
The results presented in this study, and their kinetic
analysis, show that the catalytic efficiency of ribulose 1,s
bisphosphate carboxylaseoxygenase is increased by a factor
close to ten when this enzyme is embedded in the complex.
This increase of catalytic efficiency is achieved through an
increase of the V and a decrease of the K,, values.
These changes of the catalytic properties of ribulose 1,s
bisphosphate carboxylaseoxygenase
whether this enzyme is free or inserted in a multienzyme
complex are to be related to the difference of susceptibility
depending upon
of this enzyme to the inhibitor 6phosphogluconate (see pre
ceding paper in this journal [16]).
The activation of phosphoribulokinase by reduced thiore
doxin is also markedly dependent upon whether the enzyme
is free in solution or inserted in the complex. The amplitude
of this activation reaches about the same plateau value for
the free enzyme and for the complex but the concentration
of free thioredoxin required to reach this plateau is lower for
the complex than for the free enzyme. This means that the
affinity of thioredoxin for phosphoribulokinase is higher if
Page 7
1081
I'
c
1
4
0.15
0.1
h

I
3
v
4
0.05
0.0
3
2
4
6
8
10
[Thioredoxin]
M)
0.45
 0.30
v .3
4
0.15
0.00
0
2
4
6
8 10
[Thioredoxin]
M)
Fig.7. Variation of the time constants of the exponential of the activation process as a function of thioredoxin concentration. (A)
Isolated phosphoribulokinase, (B) phosphoribulokinase inserted in the complex. The solid lines represent the best fits of Eqn (1 3) to
experimental data. The corresponding numerical values are given in Table 4.
Table 4. Comparison of different rate constants for model in Fig. 1 for free phosphoribulokinase and phosphoribulokinase inserted
in the fiveenzyme complex.
State of
phosphori
bulokinase
k+ 1
k 1
k+2 k2
k+3
k ,
S'
MI 51
S'
MI sl
sl
Isolated
Embedded
3.80x
1.51 x lo'
7.77 x
2.29 X
4.35 x 105
20.84 X lo6
1.16x 10I
20.25
51.00x lo'
4.08 X 10'
%5.49XlO'
2.70 x 1 0  3
the enzyme is embedded in the complex than if it is free in
solution. Moreover the time constant of the activation pro
cess of the free enzyme decreases as the concentration of
free thioredoxin is increased, whereas that of the complex
increases with the concentration of thioredoxin. This results
in a time constant for the activation of the complex higher
than that of the free enzyme. A time constant of about
0.35 min' is quite compatible with the time required for the
activation by light of the BensonCalvin cycle [17].
Although it is difficult, at the moment, to know what part
is played by the complex in the reduction of carbon dioxide,
there is little doubt that this complex exists and that its struc
ture modifies the intrinsic properties of at least two of the
enzymes that are associated in the multimolecular entity.
A = s'(s2 + 0s + <)
(2')
where (T is the sum of the Encke's roots of the quadratic and
< their product. One finds
0 = (k+, + k+,) x + k,, + k, + k, + k ,
t = k+, k+, x2 + [k+, (k1 + kz)
+ k+, (k+i + k,)l x + (k+i + k1) (k2 + k3).
It thus appears that plotting the sum of the two roots, 0, as a
function of the thioredoxin concentration, x, should yield a
straight line, whereas plotting the product of these two roots
should give a parabola. Solving the system (1') for z(c2]
and 2{ c,) yields
k,, s + k,, (k* + k,) + k, k,, x
2(c,} =
s (s* + 0s + ()
and
k+, s + ki k+, + k+, k+, + k+z k+, x
s (72 + 0 s + ()
Expansion in partial fractions yields
(3')
el
(4')
APPENDIX
The system of linear differential Eqns (2) of the main
text may be rewritten, by using the Laplace transforms of c2
and c,, 2{cz} and z{c,), as
s (s + k,, + k, + k+*)x
s (k+?  k+J x
2{c,l =
xeT. (5')
2{c2) =  +
~
s + I',
+
~
s + &
s
w o
w1
w 2
(1')
1
s (k+
i  h2)
s (s + k + k, + k+, x)
and
w:
+
w:,
s
wl
where s is the usual complex operator. The principal determi
nant of this Cramer system is thus
s + A ,
s+A,
2?{c3) =  +
~
Page 8
1082
Moreover, one may determine by the usual methods the ex
pression of the iy and y ~ ' involved in these expressions. One
finds thus:
k,, (kz + kJ + k, k,, x
w o =
A1 1 2
k1 k+3 + k+i k+z + k+2k+3 x
w:, =
x eT
A1 A2
A1 ( 1 2  A11
 ki k+,  k+i k+z  k+2 k+, x
w: =
XeT
2 1 (12  A,)
A2 (A2  1,)
 k+3 12 + k, k+, + k+, k+2 + k+zk++
w: =
A 2 ( 2 2  11)
One may also notice that
yo + w1+w2= 0
w:,+ w: + w:=o.
From the expressions of Laplace transforms of the con
centrations c, and c1 one may thus derive the time evolution
of these concentrations. One has
c2 = yo + cy,e'I' + y2e'Zr
+ y:e'Il' + y:e*zf .
It is thus obvious that when t + 0
XeT.

e T
k+, A,  k,, (k2
+ k,)  k, k,, x
w 1 =
e T
(8')
k+3
 k,, A2 + k+, (k, + k3)
w 2 =
+ k, k+, x
eT
(9')
ci =
(10')
and from Eqns (9') above these concentrations should obvi
ously be equal to zero. As it is only the sum c2 + cl, which
may be evaluated experimentally, it may be derived using
expressions (10')
c2 + c, = iyo + I , V : + (lyl + w:) e'lc + (w2 + w:) eQ. (12')
The expression of these two time constants is thus
(13')
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2.
3.
4.
5.
6.
7.
8.
9.
10.
and this expression is equivalent to Eqn (12) of the main
text.