Plant Cell Physiol. 38(11): 1177-1186 (1997)
JSPP © 1997
Quantitative Evaluation of the Rate of 3-Phosphoglycerate Reduction in
Chloroplasts
Leonid E. Fridlyand1, Jan £ . Backhausen2, Simone Holtgrefe2, Camillo Kitzmann3 and Renate
Scheibe2-4
1
2
3
Institute of Experimental Botany, Academy of Sciences of the Belarus, Skorina 27, Minsk, 220072 Belarus
Pflanzenphysiologie, Fachbereich Biologie/Chemie, Universitat Osnabruck, D-49069 Osnabriick, Germany
Lehrstuhl fur Pflanzenphysiologie, Humboldt-Universitdt, D-10099 Berlin, Germany
The 3-phosphoglycerate reduction has often been considered as a rate-limiting step in photosynthesis. To investigate this, a kinetic equation for 3-phosphoglycerate
reduction is developed. The reaction catalyzed by 3-phosphoglycerate kinase was considered as close to the thermodynamic equilibrium and that of NADP-linked glyceraldehyde 3-phosphate dehydrogenase as Michaelis-Menten
type. Isolated intact spinach chloroplasts were used to obtain the data that are required to apply the equation for a
description of photosynthesis in vivo. The apparent Km for
1,3-bisphosphoglycerate is evaluated to be 0.95 fM. in isolated chloroplasts. The temperature dependence of the activity of NADP-linked glyceraldehyde 3-phosphate dehydrogenase is determined; the QI0 is 1.8 between 15° and
25°C. Numerous examples are presented where the developed kinetic equation is used to describe the reaction rate in
the isolated chloroplast as well as in the leaf under steadystate and induction conditions. It is shown that within the
physiological range, the rate of 3-phosphoglycerate reduction can be estimated by measuring the activity of NADPlinked glyceraldehyde 3-phosphate dehydrogenase, the
[ATP]/[ADP] ratio and the 3-phosphoglycerate concentration. It is shown that the assumption of a thermodynamic
equilibrium at the 3-phosphoglycerate reduction cannot be
reconciled with existing experimental data. The possible
limiting role of NADP-linked glyceraldehyde 3-phosphate
dehydrogenase in the Calvin cycle is discussed.
Key words: ATP/ADP ratio — Chloroplast — CO2 assimilation — Kinetic equation — NADP-linked glyceraldehyde
3-phosphate dehydrogenase.
In many situations, the operation of the Calvin cycle
in chloroplasts of C3 plants is restricted by the availability
Abbreviations: DHAP, dihydroxyacetone-phosphate; BPGA,
1,3-bisphosphoglycerate; GAPDH, NADP-linked glyceraldehyde
3-phosphate dehydrogenase; GAP, glyceraldehyde 3-phosphate;
PGA, 3-phosphoglycerate; PGK, 3-phosphoglycerate kinase; Pj,
inorganic phosphate; r, correlation coefficient; Rubisco, ribulose
1,5-bisphosphate carboxylase/oxygenase; RuBP, ribulose 1,5-bisphosphate; TPI, triosephosphate isomerase.
4
Corresponding author.
of CO2. At low substomatal CO2 concentrations, the carboxylation of RuBP, catalyzed by Rubisco, causes the major
limitation in the photosynthetic production of carbohydrates (Farquhar et al. 1980). With increasing CO2 concentrations, the Rubisco limitation of photosynthesis is eased,
and the regeneration of RuBP may become limiting (Stitt
1991, Woodrow 1994).
A potential bottle neck within the regeneration of
RuBP in the Calvin cycle is the reduction of 3-phosphoglycerate (3PGA) to triose phosphate, since it consumes the
largest part of the energy provided by the photosynthetic
light reactions (in the form of ATP and NADPH), while
the acceptors ADP, NADP + and Pj are regenerated in this
step. For these reasons many researchers have proposed
to use the rate of PGA reduction as an important index
of photosynthesis (Robinson and Walker 1979, Dietz and
Heber 1984). However, a substantiation of such possibility
requires a detailed analysis.
The following three reactions are involved:
PGA+ATP -* BPGA+ADP
BPGA + NADPH + H + -> GAP + NADP + + Pj
GAP ->• DHAP
(A)
(B)
(C)
The first reaction is catalyzed by PGK, the second one
by GAPDH and the third one by TPI. The activity of the
GAPDH is regulated by an interplay between reduction/
oxidation of the enzyme and activation/inactivation by
specific metabolites, with a specific change in the molecular weight being the underlying mechanism (Scheibe 1990,
Baalmann et al. 1995). For the reactions catalyzed by PGK
and TPI, no regulation of enzyme activities is known. The
inhibition of the PGK by ADP as reported for the purified
enzyme (Pacold and Anderson 1975) does not seem to play
a role in vivo (Robinson and Walker 1979).
It has been assumed that the reaction sequence from
PGA to triose-P is close to the equilibrium (Dietz and
Heber 1984), but a critical examination of the published
data shows a considerable displacement from equilibrium
(see Discussion). For this reason, the attempt to describe
this reaction as a kinetic equation is made.
It should also be noted that numerous attempts of the
quantitative description of CO2 assimilation on the basis of
the measured RuBP concentration and Rubisco activity are
1177
1178
3-Phosphoglycerate reduction in chloroplasts
known (Farquhar and von Caemmerer 1982, Quick et al.
1991). It is evident also that at steady-state all reactions in
the cycle must operate at equal rates, and can be described
as kinetic approach at this stage. We are not aware of attempts to perform such work for PGA reduction, although
it should be considered as an approach necessary for the
study of the Calvin cycle. For this reason, in this work the
attempt was made to explain all available data on PGA
reduction, as obtained earlier by us and by various other
groups on the basis of the obtained equations, and evaluate
the role of PGA reduction as possible rate-limiting step in
CO 2 assimilation.
Kinetic equations—The full kinetic equations to determine the true rate of PGA reduction were obtained for the
reactions (A-C) by Fridlyand (1992).
*.^2.[H + ]AT 3e F A [PGA]/[DHAP]-l
[DHAPll
Klmu[ATP]
(1)
where
F A =[ATP][NADPH][H + ]/[ADP][PJ[NADP + ]
D, =KA(l + [ A T P ] / ^ ™ + [PGA]/.K£GA
+ [ADP]/.K£DP + [ATP] [PGA]/ATA
(2)
+ [PGA][ADP]/ATB + [ATP][ADP]/J<: C )
D 3 = A^AP(1 + [DHAP]/A£ HAP )
The actual rates are denoted by v, maximum rates for
each enzyme by Vima, equilibrium constants by KK, apparent Michaelis constants by Km, and dissociation constants by Ks. Kh, KB and Kc are complex constants. The
reaction components are indicated by the corresponding
superscript letters and the reaction by subscript numbers (1
is corresponding to A, 2 to B and 3 to C). Corresponding
values for coefficients are as in Fridlyand (1992).
In the analysis that was made by Fridlyand (1992) it
was noted that the value of [PJ should be considered as
very small in vivo. Using Eq. (1) for a low Ps concentration
it can be concluded that a low NADPH/NADP + ratio
is sufficient to saturate PGA reduction (Fridlyand 1992).
This assumption is reasonable, because the Km value for
NADPH of GAPDH is as low as about 20/iM (Baalmann
et al. 1995).
However, Eq. (1) is very complex and its analysis is
restricted. Here we further analyze the obtained Eq. (1) to
simplify it, and conclude that at metabolite concentrations
in the physiological range nearly the same results as reported by Fridlyand (1992) can be received, if the following is assumed: (i) reactions A and C are close to thermody-
namic equilibrium, and (ii) reaction B is considered as simple Michaelis-Menten reaction with BPGA as one substrate. This means that PGK and TPI activities are reasonably high under physiological conditions.
If the first reaction is close to the thermodynamic equilibrium, then
[BPGA] =A-le[PGA][ATP]/[ADP],
(3)
where Kle is the equilibrium constant for reaction A.
Then the steady-state rate of PGA reduction (v) can be determined by the equation
v=
+ [BPGA]),
(4)
where Km is the apparent Michaelis constant of GAPDH
for BPGA, Kgmaj, is the maximum actual activity of
GAPDH, [BPGA] is determined from Eq. (3).
The difference in the calculations made by Eqs. (1) and
(4), respectively, was no more than a several per cent in all
analyzed cases. It is necessary to point out that Eq. (4)
agrees well with the data obtained by Robinson and Walker
(1979) for the reconstituted chloroplast system, where it
was found that the dependence of O2 evolution on the
[PGA][ATP]/[ADP] ratio is described by a curve close to
the Michaelis-Menten relationship.
Instead of Eq. (4) an even simpler equation may be
used to study the relative rate changes (see also Fridlyand
1992), if in leaves the true PGA concentration in the chloroplast stroma cannot be determined and only the total PGA
concentration is available
(5)
where S is a proportionality coefficient, and [PGA]t is the
total concentration on a chlorophyll or area basis.
Calculated according to Eq. (4) and Eq. (5) the relative
rates of PGA reduction change in the same direction, but
the quantitative solutions can be overestimated by Eq. (5).
However, the full Eq. (1) should be used, if [NADPH] or
the activities of PGK or TPI are limiting.
In order to use Eqs. (4) and (5) to study the photosynthetic rate, it is necessary to connect the rate of PGA reduction with CO 2 assimilation. The known dependencies were
used for this purpose. According to Farquhar and von
Caemmerer (1982) the net rate of CO2 assimilation (A) can
be calculated as
A=K C (1-O.5<4)-Rd,
(6)
where 0 = KomMO
Vc is the rate of carboxylation of RuBP in the presence
of O 2 , Rd is the rate of CO2 evolution in the processes that
differ from photorespiration, 0 is the ratio of the activities
3-Phosphoglycerate reduction in chloroplasts
of oxygenase and carboxylase. C and O are the partial
pressures of CO2 and O2, respectively, Ke and Ka are the
Michaelis-Menten constants for CO2 and O2) Vcma and
^omax are the maximum velocities for carboxylation and oxygenation of RuBP, respectively.
Two NADPH molecules are needed for the reduction
of one CO2 molecule. For this reason and taking into account the influence of photorespiration, the rate of PGA
production is given according to Farquhar and von Caemmerer (1982) by
hausen et al. (1994) was used. Full activation of the enzyme
and activity assay was done by the method of Baalmann et al.
(1994) at 25°C. For the determination of the temperature dependence, GAPDH purified from spinach leaves was activated as
described in Baalmann et al. (1995). Since the activity of the
GAPDH is routinely assayed at 50|iM BPGA, the V!pax used
in Eq. (4) was calculated from the Michaelis-Menten equation.
The apparent Km for the isolated enzyme was taken as 20 /iM
(Baalmann et al. 1995). For this reason, full enzyme activity was
obtained by multiplying the measured enzyme activity by 1.4. The
full enzyme activity at different temperatures was obtained by
multiplying it by the thermal coefficient that was obtained as described below.
Results and Discussion
Then Eq. (6) can be rewritten as
A = v(l-O.50)/(2 + 1.5<4)-Rd
1179
(7)
and Eq. (7) as
(8)
According to Farquhar and von Caemmerer (1982):
^cm«^o/^omax^c=80. In Eq. (3) Klc=3Axl0-*
(Bergmeyer et al. 1985) and the coefficient Km (Eq. 4) will be accounted for below.
Materials and Methods
Chloroplast isolation, CO3 fixation and measurements of metabolites— Culture of the spinach plants (Spinacia oleracea L.,
var. US hybrid 424), isolation of chloroplasts, determination of
intactness, incubation conditions, O2-production measurements
and determination of [MC]CO2-fixation rate were done as described previously (Backhausen et al. 1994). Samples for the measurement of PGA were obtained by silicone-oil centrifugation according to Heldt (1980). PGA in both phases was determined in an
enzymatic assay (Stitt et al. 1989) to obtain stromal PGA concentration and the rate of PGA export. The rate of PGA reduction
was determined from the rate of [14C]CO2 assimilation, multiplied
by two, minus the rate of PGA export. The samples for the determination of ATP and ADP were obtained by silicone-oil centrifugation to concentrate the samples. For each determination, six
samples were pooled. The concentrations of ATP and ADP were
measured in a Iuminometric assay by a modified method of
Hampp (1985). The stroma volume of the chloroplasts was determined to be 27 /A (mg Chi)" 1 , using the method of Heldt (1980).
The chloroplasts were illuminated as previously described
(Backhausen et al. 1994) Samples were taken at the indicated time
points between 4 and 8 min of illumination and assayed for the activity of GAPDH, ['"ClCOz fixation, ATP, ADP, stromal PGA
and for PGA content in the medium. For the experiments shown
in Fig. 1, the data obtained under control conditions, and upon addition of 1 mM NH4C1, 0.2 mM OAA and/or 0.2 mM nitrite were
used.
GAPDH-activation state in isolated chloroplasts and full activation of purifed enzyme—For the determination of the activation state of the GAPDH in isolated chloroplasts, the extraction
method described for NADP-malate dehydrogenase in Back-
Temperature dependence of activity of isolated
GAPDH— Since it was required for the following consideration, the temperature dependence of GAPDH activity for the fully activated isolated enzyme was determined
(Fig. 1). The thermal coefficient (Q10) was determined to be
1.8, when the temperature was increased from 15 to 25°C.
Determination of the apparent Michaelis-Menten constant for BPGA in isolated chloroplasts—As an initial step
it was necessary to determine the real Michaelis-Menten
constant for BPGA reduction by GAPDH in vivo, which is
a very complex problem. The data that were received with
the isolated enzyme varied from 4-7 ^M (Trost et al. 1993)
to 20 /iM (Baalmann et al. 1995). Besides, there is some information about the possible existence of a specific multienzyme complex (Suss et al. 1993, Anderson et al. 1995) that
might change the apparent value of Km. Furthermore, the
protein concentration and the presence of salts may influence the properties of the enzyme (J.E. Backhausen, C.
Rak and R. Scheibe, unpublished results). For this reason,
the measured values for the ATP/ADP ratio, the stromal
PGA concentration and the corresponding activities of
GAPDH were plotted against the rate of PGA reduction
(Fig. 2B) and were used to obtain a Km value for BPGA
reflecting the situation in isolated chloroplasts.
15
20
25
30
Temperature (*C)
Fig. 1 Temperature dependence of GADPH activity of the purified spinach enzyme. The result of linear regression analysis is represented by a solid line (Kgmax=5.38 t ° - 17.4).
3-Phosphoglycerate reduction in chloroplasts
1180
1
JUU
.
—
250
o
200
I
'
A
°
o
•
o
0
;
•
3
O
3 _
O
1
150
Q.
1
•
.ATP
1
1
1
B
-
a
<
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•
2
•
i
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200
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220
•
•
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*
•
1
240
•
900
800
2. 2
700
Si
600
1
3
500
260
Measured PGA reduction
(umol nig-1 Chi h1)
Fig. 2 PGA reduction in isolated intact spinach chloroplasts at
15°C. A. Correlation between the rate of PGA reduction calculated by Eq. (4) at the estimated mean value of Km (o), and this rate
as measured in chloroplasts (X-axis). B. PGA concentration (A),
ATP/ADP ratio (•) and GAPDH activity (•) in isolated chloroplasts (for conditions see Material and Methods). To obtain the
full enzyme activity at 15°C the calculated one was multiplied by
0.54. This corresponds to Q 10 =1.8 as obtained from the data in
Fig. 1.
The equation required to determine the apparent
Michaelis-Menten constant for BPGA in vivo can be obtained from Eq. (4)
= Kgmaj[[BPGA]/v= [BPGA],
(9)
where [BPGA] can be found from Eq. (3).
In Fig. 2B, every measured PGA reduction rate (v)
corresponds to the measured PGA concentration, ATP/
ADP ratio and GAPDH activity, respectively. To introduce
these four measured values into Eq. (9), we had obtained
some value of Km for every value of measured PGA-reduction rate. The mean Km value for all data represented in
Fig. 2A is 0.95±0.04 fM.. Using this mean Km, the rate of
PGA reduction (Eq. 4) was calculated on the basis of measured PGA concentration, ATP/ADP ratio and GAPDH activity. These data are represented in Fig. 2A in dependence
on the measured PGA reduction.
It should be noted that the data (Fig. 2B) were not especially generated in order to check the Eqs. (1) and (4), but
we used data from our earlier studies (Backhausen et al.
1994), and some unpublished results were added. For this
reason, the range of ATP/ADP ratios in Fig. 2B is rather
small. Initially, it was only intended to obtain theKm value.
However, a linear relationship can be observed between the
rates calculated on the basis of Eq. (4) using the mean value
for the Km and the rate of PGA reduction measured in
the chloroplast preparation (Fig. 2A). A good correlation
(r = 0.755) exists despite considerable deviations of PGA
concentration, ATP/ADP ratio and GAPDH activities
(Fig. 2B). It should be noted that the use of measured rates
of PGA reduction for the calculation of the mean Km leads
to the coincidence only of the mean values of calculated
and measured rates of PGA reduction (Fig. 2A). The correlation of measured and calculated rates of PGA reduction proves the existence of some real dependence that can
be described by the obtained equations.
In the article by Fridlyand (1992) the coefficients obtained for isolated enzyme were used in Eq. (1). However,
the results of our measurements show that in vivo this
coefficient can be different. To compare the solutions of the
kinetic Eq. (1) with Eq. (4), the corresponding change of
the coefficient should be done in Eq. (1). The Km in Eq. (4)
corresponds to the constant K^°A in Eq. (1). For this reason, it was calculated that the value K%?GA in Eq. (1) should
be changed from 0.0075 mM as used by Fridlyand (1992) to
0.0028 mM. This permits to receive the same numerical solutions from Eq. (1) as in Eq. (4) under the conditions represented in Fig. 2.
Induction processes in isolated chloroplasts—The obtained equations permit the attempt to explain the change
of PGA-reduction rate in the induction processes in chloroplasts. This is a very complex problem, and we do not
know of any attempt to solve this problem on a quantitative basis. Figure 3 shows the changes in [PGA], ATP/
ADP, GAPDH activity, and CO2 assimilation during the induction period. As it can be seen after the isolation of the
chloroplasts, the endogenous metabolite pools are very
small in the dark. In the first minutes of illumination, the
concentration of Calvin-cycle intermediates such as PGA
increases.
However, when the measured values for PGA concentration, ATP/ADP ratio and GADPH activity are substituted in Eq. (4), the calculated rate of PGA reduction in
the first two minutes was considerably higher than the measured one. However, some peculiarities of the initial period
of the induction process permit to explain this deviation. It
is known that in this period the rate of CO2 assimilation is
very low, since the concentration of RuBP is also low (see
Prinsley and Leegood 1986, Furbank et al. 1987). However, the concentration of estimated Rubisco catalytic sites
is high and ranges from 1 to 4 mM (Jensen and Bahr 1977,
Servaites and Geiger 1995). It is evident that at a low RuBP
concentration and a concentration of Rubisco catalytic
sites that is several times higher than the PGA concentration, the majority of measured PGA molecules is bound to
Rubisco catalytic sites, since PGA can effectively compete
with RuBP for binding sites of Rubisco (Foyer et al. 1987).
3-Phosphoglycerate reduction in chloroplasts
4
3
!
2
I
1
0
1
0.8
0.6
0.4
3
<
o
a
m
200
0.2
I
I
I
I
I
I
I
I
I
0
15
I
10
IP
£f
(9
o o
a.
3E
4
6
8
10
Time (min)
Fig. 3 Photosynthesis in isolated intact spinach chloroplasts. A.
Time course of the measured rate of PGA reduction ( + ) on the
basis of [I4COJ assimilation (see Material and Methods) and as calculated by Eq. (4) (O), and ATP/ADP ratio (•). B. GAPDH activity (•) and calculated BPGA concentration (v). C. Measured PGA
concentration (A) and the rate of PGA export (•).
Therefore, an attempt was made to calculate the free
PGA concentration by using the PGA-export rate (see
Fig. 3C). It was assumed that the rate of PGA export depends linearly upon the concentration of free PGA in the
stroma and that, at a high rate of CO2 assimilation, the majority of the PGA molecules is free. As a result of such approach the free PGA concentration after one minute of illumination was evaluated to be as low as 0.166 mM instead
of the measured 0.658 mM. It can be seen in Fig. 3C that
after 3 min the evaluated PGA concentrations can be considered as due to free PGA, since in all these cases the
relative rate of export and the PGA concentration coincide.
The sequential activation of the GAPDH which occurs
during the dark-light transition should be taken into account, too. Our earlier results obtained with isolated chloroplasts and with the purified enzyme (Baalmann et al.
1994, 1995) show that this process involves the change of
the redox state and of the molecular mass of the enzyme,
1181
the latter being accompanied by a strong change of the affinity for the substrate BPGA. The dark form of the GAPDH
is the oxidized 600-kDa hexadecamer, exhibiting a low affinity towards the substrate BPGA (Km> 100//M for the purified enzyme). Upon illumination of the chloroplasts, the
photosynthetic electron flow via ferredoxin generates reduced thioredoxin which in turn reduces the enzyme.
The reduced 600-kDa hexadecamer shows only a slightly
increased apparent activity, since its affinity for BPGA
remains relatively low (Km about 90 //M). However, this reduced enzyme form is sensitive towards activation by
BPGA (Ka=l-2nM, as opposed to 20/iM for the oxidized
enzyme). Therefore, dissociation of the enzyme into the
150-kDa tetramer can only occur, when some BPGA has
been formed in the stroma. Only the reduced 150-kDa
tetrameric enzyme form exhibits a high affinity towards its
substrate BPGA.
As it can be seen in Fig. 3B, during the first minutes
of illumination the calculated value of [BPGA] is considerably lower than the activation constant (KJ. Therefore, only a small portion of the enzyme has been transferred into the high-affinity form. This means, that only
part of the measured enzyme activity can actually take part
in PGA reduction. In order to estimate the activity of this
part of the enzyme during the first three minutes, the maximum measured enzyme activity (after 4 min of illumination) was multiplied by the ratio of [BPGA] in the first
minute to [BPGA] after the fourth minute, and the obtained values of actual GAPDH activity were used to calculate
the rate of PGA reduction in the first minutes of illumination.
After such evident refinements the results of the calculations (Fig. 3A) show a good agreement with the measured
values. The transient rise or fall in [PGA], ATP/ADP and
GAPDH activity are in agreement with the ongoing PGA
reduction. This quantitative description will allow an understanding of the role of GAPDH activation and of the
concentration of free PGA in the induction process.
Steady-state photosynthesis in leaves—In the work of
Fridlyand (1992) on the basis of data from Dietz and Heber
(1984, 1986), it was shown that Eq. (1), and consequently
Eq. (4), upon substitution of [PGA] and ATP/ADP ratio
measured in chloroplasts subsequently isolated from these
leaves, yields results which are in agreement with the experimental data showing the relative change of steady-state
photosynthesis in the whole leaf. The dependence of photosynthesis in leaves on light intensity, CO2 concentration
and temperature was analyzed by Fridlyand (1992).
A more detailed consideration of the temperature dependence was made to analyze the data from Dietz and
Heber (1989). In their work CO2 fixation and, in addition,
ATP/ADP and [PGA] were measured, but not the activity
of GAPDH. For this reason the temperature dependence
of CO2 assimilation in leaves is only comparable with the
1182
3-Phosphoglycerate reduction in chloroplasts
I
250
o
o
-
-
A
200
150
100
50
250
>^a-
-
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^
^
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- %y^^
-
-
200
2-
150
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100 Z o
50
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200. I
300
12
2,0
10
8
<
C9
100
6
4
0,5
2
0
0,0
10
20
30
Temperature (°C)
Fig. 4 Photosynthesis in spinach leaves. A. Comparison of
model calculations with respect to temperature dependence of the
relative rate of CO 2 assimilation, calculated on the basis of PGA
reduction (Eq. 7) (o) with the CO2-absorption rate ( + ) . B. ATP/
ADP ratio (•) and PGA concentration (A) for non-aqueously isolated chloroplasts taken from Dietz and Heber (1989: Table 2,
where CO 2 concentration was 2,000fi\ liter"'). The arrow shows
the experimental point used for the equalization of calculated and
measured rate of CO 2 assimilation.
calculated relative rate of PGA reduction (Fig. 4). Since
these data were obtained at COt saturation, Eq. (7) with
(4 = 0 was used. In this case, the value [PGA][ATP]/[ADPJ
does not change considerably upon a change of temperature (Fig. 4B). This means that according to Eq. (3), the
concentration of BPGA is similar under all temperature
conditions. Since due to the fact that this metabolite is not
only the substrate of GAPDH, but its activator as well, it
can be concluded that the enzyme-activation state is similar
under all temperature conditions. However, a close agreement of the relative change of calculated photosynthesis
rate with the experimental data can be obtained (Fig. 4A).
This agreement is caused by the apparent increase of
GAPDH activity with temperature. This example shows
the necessity to take into account the change of GAPDH activity, when PGA reduction is considered.
PGA-reduction rate in leaves during a period of
sinusoidal light—A set of data that fulfiles the requirements for our calculations can be taken from the work of
Servaites et al. (1991), who analyzed photosynthesis of
sugarbeet leaves. However, the distribution of the metabolites between the compartments of the cell is unknown. For
2
4
S
8
10
12
14
Time in the light (hours)
Fig. 5 Photosynthesis parameters in sugarbeet leaves measured
under sinusoidal light regime. The data are taken from Servaites et
al. (1991), and only the light period is shown. A. Net carbon assimilation rate (photosynthesis rate plus respiration in darkness) ( + )
and data for air calculated on the basis of Eq. (7) at 0=0.27 (o).
B. PGA concentration (a) and ATP/ADP ratio (•). C. GAPDH
activity (•).
this reason, the stromal PGA concentration for comparison was obtained by the following method. The PGA
concentration during maximum photosynthesis (7 hours
after the start of irradiation) was calculated using Eq. (8) to
obtain the rate of PGA reduction (v), and then Eqs. (3, 4)
were used to calculate the concentration of BPGA on the
basis of the known leaf-PGA concentration and the ATP/
ADP ratio. As a result, a concentration of BPGA of
1.8 /iM was obtained. All other BPGA concentrations were
obtained by multiplying [BPGA] at the maximum of photosynthesis with the ratio of [PGA] at a denned time point to
[PGA] after 7 hours of illumination. Then Eq. (7) was used
to calculate the rates of photosynthesis at other times.
In Fig. 5, the comparison between the data measured
by Servaites et al. (1991) and the calculated values is
shown. It is evident that a good correlation exists. A deviation between the experimental and the calculated data is
only evident at the end of the light period. This can be ex-
3-Phosphoglycerate reduction in chloroplasts
1183
plained by the sharp decrease of the PGA content in the should be noted that upon addition of oxaloacetate NADPH
dark in chloroplasts relative to the cytoplasm (see Gerhardt is used for its reduction to malate, thus the NADPH/
et al. 1987). This cannot be taken into account when meas- NADP + ratio is slightly decreased and the rate of oxygen
uring the PGA concentration in whole leaves. Although evolution is increased (Backhausen et al. 1994). For this reathere are the known restrictions of metabolite measure- son it is likely that NADPH limitation does not exist in
ments in whole leaves, the results can be considered as a leaves in the physiological range except under low light
close approximation.
near the compensation point.
Effects of plant nutrition on the rate of PGA reducThe concept of thermodynamic equilibrium—The astion and photosynthesis in intact leaves—The parameters sumption has been made that the reaction chain involved
necessary for calculations according to Eq. (4) were also in reduction of PGA is close to the thermodynamic equilibmeasured in leaves of sugarbeet (Rao and Terry 1989, Rao rium, i.e. that the mass action ratio (R) is not displaced conet al. 1989) and soybean (Fredeen et al. 1990) grown under siderably from equilibrium (Dietz and Heber 1984), where
various levels of phosphate. However, no data are available on the compartmentation of PGA. For this reason, R = [H + ] [PGA] [ATP] [NADPH]/
these data are difficult to use for a precise quantitative ap[DHAP] [ADP] [Pd [NADP+]
(10).
proach, since according to Dietz and Heilos (1990) there
are considerable differences in chloroplast volume in phosIn order to prove this suggestion, it was necessary to
phate-starved leaves of spinach in comparison with the con- determine the metabolite concentrations. At first sight, this
trol.
requirement was fulfilled (Dietz and Heber 1984). HowHowever, the evaluation of these data can be done on ever, these measurements are rather critical, in particular,
a relative basis using Eq. (5). In sugarbeet, the leaf-PGA the true concentration of inorganic phosphate in chlorolevel and the activity of GAPDH were increased and the plasts cannot be easily determined (Siebke et al. 1990). For
ATP/ADP ratio remained constant while increasing the this reason the concentration of Pj obtained by Siebke et al.
phosphate level during growth (Rao and Terry 1989, Rao et (1990) is the result of subtracting the measured concentraal. 1989). In this case, the substitution of the measured tion of organic phosphates from the assumed total phosPGA concentrations and of GAPDH activity into Eq. (5) phate concentration. The resulting concentration for Pj
leads to an increase of the calculated photosynthesis rate was 1.2 mM under strong light. It should be remembered
upon increasing the phosphate level during growth, which that under the same conditions the measured P; concentrais in coincidence with the experimental data. The leaf-PGA tion was 22.1 mM in the original article of Dietz and Heber
level increased about 5 fold, the activity of GAPDH in- (1984; Table 5 at CO 2 = 1,100//I liter" 1 ). Evidently, if we
creased by 16%, and the ATP/ADP ratio decreased by substitute the P, concentration assumed by Siebke et al.
60% upon increasing the phosphate level under growth in (1990) in Eq. (10) and use the other data from Dietz and
soybean (Fredeen et al. 1990). Analogous calculations on Heber (1984), we can receive a value of R that is conEq. (5) also lead to sufficiently reliable results, i.e. to an in- siderably higher than at thermodynamic equilibrium.
crease of the calculated photosynthesis rate with increasing
The same problems of the determination of P( are apthe phosphate level during growth, again in coincidence parent in the work of Usuda (1988), where the thermodywith the experimental data.
namic equilibrium has been deduced from measurements
Analysis of the data of Dietz and Heilos (1990) shows of metabolite concentrations for maize leaves. In addition,
also a good correlation between the calculated changes of in this study, a pH value was assumed in such a manner
the PGA-reduction rate and photosynthesis. However, in (pH = 8.1) to receive the mass action ratio that is necessary
this work the measured GADPH activity was lower than for equilibrium.
the photosynthesis rate, a fact that hampers the possibility
When a constant value of R (near the thermodynamic
for quantitative analysis.
equilibrium) was assumed, and the more likely value of
The influence of the intrachloroplast NADPH/
1.2 mM for [PJ was used, the NADPH/NADP + ratio was
NADP* ratio—The NADPH/NADP + ratio remains large- calculated to be no more than 0.2 in the light (Siebke et al.
ly constant over a broad range of light intensities (Wigge et
1990). Such low calculated NADPH/NADP"1" ratio, howal. 1993, Gerst et al. 1994). This is in agreement with the un- ever, contradicts the higher value for this ratio that was
changed activation state of NADP-malate dehydrogenase received by direct measurements (see Heber et al. 1986,
in leaves under various conditions (Scheibe and Stitt 1988). Backhausen et al. 1994).
Furthermore our data support also the supposition that a
A considerable deviation from equilibrium was also
change of NADPH/NADP + does not influence the rate of found recently for the chloroplast stroma in the light,
PGA reduction. According to Backhausen et al. (1994) no where the measured value of R was 8 times higher than at
change can be seen in the rate of CO2 fixation by isolat- equilibrium (Heineke et al. 1991). From these observations
ed chloroplasts after addition of 0.2 mM oxaloacetate. It it can be deduced that the thermodynamic equilibrium at
1184
3-Phosphoglycerate reduction in chloroplasts
this step of the Calvin cycle might not be a fact. In reality,
the mass action ratio (R) in a leaf might be considerably
higher than at thermodynamic equilibrium. Therefore, a
kinetic equation to describe the flux through this step can
be valid.
Assimilatory force—Assuming that the reaction chain
involved in reduction of PGA is close to the thermodynamic equilibrium, the value FA has been obtained from Eq.
(10).
= R[DHAP]/[PGA]
= [ATP][NADPH][H + ]/[ADP][PJ[NADP + ]
(11)
has been denoted as the assimilatory force and was used as
a motive force of the photosynthetic reaction (Dietz and
Heber 1984, 1986, 1989, Heber et al. 1986). However, such
assumption is only valid if this step is at its thermodynamic
equilibrium. Also the calculation of F A from measurements
of the ratio between [DHAP] and [PGA] is questionable,
since this method was based on the primary assumption of
a thermodynamic equilibrium at this step at constant R. If
according to Heineke at al. (1991) the value of R can
change up to 8 times, then F A can change within the same
limits without any change of the [DHAP]/[PGA] ratio (see
Eq. 11). For this reason, the numerous measurements of F A
through the [DHAP]/[PGA] ratio should thus be considered only as the measurements of this ratio, and cannot
be characteristic of the energy status of the chloroplast.
GAPDH as limiting enzyme—The assumption of a
freely reversible conversion of PGA to triose phosphates
has led to the conclusion that the activities of PGK
and GAPDH are not limiting for photosynthesis at all
(Buchanan 1992, Price et al. 1995). However, the kinetic investigation developed in this article brings theory and experiment into better agreement. It should be noted that recently there was agreement that kinetic Eq. (5) can be used, if
only the rate of carbon flux is of interest (Gerst et al. 1994).
Since the kinetic equation is applicable to PGA reduction,
it is hkely that the reduction of PGA to triose phosphates is
a potential site of metabolic regulation.
Especially the results obtained with transgenic plants
indicate that GAPDH can be a limiting enzyme, because
pertubations of RuBP regeneration were observed even
after the smallest reductions in GAPDH activity (Price et
al. 1995). However, since in this work there is no information about the ATP/ADP ratio, a quantitative analysis was
impossible.
It should be noted that the mass-action ratio of PGA
reduction can be only about 8 times higher than at equilibrium (Heineke et al. 1991), and a change in the free energy
for this reaction can be evaluated as — 1.2kcal, i.e. this
reaction is not fully irreversible. For this reason the suggestion of a limiting role of GAPDH activity seems contradictory to the assumption that only irreversible reactions have
the potential to limit the rate of a biochemical process (see
Dietz and Heber 1989, Buchanan 1992). However, numerous examples that were obtained with transgenic plants
show also that a 2 to 4 fold decrease in the amount of enzyme at "freely reversible steps" leads to a decrease of the
flux through these steps (see Stitt 1995). It is obvious that
GAPDH is the same type of enzyme being strongly limiting
despite of little deviation of the reaction from the thermodynamic equilibrium. Finally, the GAPDH activity is also
regulated directly by light (Scheibe 1990, Baalmann et al.
1995), a fact that is hard to be accepted if this enzyme were
not of any significance for regulation of the Calvin cycle.
It should be noted that some limitation at the step of
PGA reduction is possible only when the process of RuBP
regeneration is limiting. When the rate of CO2 assimilation
is strongly restricted by the activity of Rubisco or by the
availability of CO2, the rate of PGA reduction is determined by the rate of RuBP carboxylation.
The mathematical modelling of PGA reduction—A
number of detailed mathematical models for Calvin-cycle
processes and their regulation has been developed. The
similar approach as presented here, i.e. reactions A and C
considered as freely reversible and reaction B as catalyzed
by GADPH on a kinetic basis, was only used by Laisk et al.
(1989). However, no detailed analysis was made for PGA
reduction. In the majority of the other recent studies, PGA
reduction is considered as freely reversible according to the
concept of thermodynamic equilibrium (Pettersson and
Ryde-Pettersson 1988, Giersch et al. 1990, Woodrow and
Mott 1993). The rate-limiting role of PGA reduction was
not regarded in the attempts to apply the theory of control
analysis on these systems of mathematical equations describing the Calvin cycle (Giersch et al. 1990, Woodrow
and Mott 1993). However, it is obvious that control analysis of mathematical models cannot detect any influence of
an enzyme that was not included in the primary model.
This consideration shows the necessity to include the step
of PGA reduction as an essential factor in such models. It
is also evident from this article that kinetic constants received with a purified enzyme might be different from the real
situation inside a cell, and a detailed analysis is needed in
every case.
Conclusion
In our work we have made an attempt to use available data from other studies as well as from our own investigations to analyze the possibility to use the obtained
equations of PGA reduction for the evaluation of photosynthesis rates. Unfortunately, for an estimation it was
impossible to use data from studies where one or more parameters were not measured. For this reason the set of used
data was restricted. In all considered cases, however, the
kinetic approach allowed us to obtain favourable results,
3-Phosphoglycerate reduction in chloroplasts
i.e. the predicted change of the rate of PGA reduction,
made on the basis of metabolite and enzyme-activity measurements, corresponds to the direction of the change of the
rate of photosynthesis. In no case we obtain contradictory
results. It can be expected that the coincidence of experimental data and theoretical estimations will increase with
an increased precision of the measurements. For this reason the obtained equations can be recommended to be used
in kinetic investigations of PGA reduction.
L. Fridlyand received a fellowship from the DAAD for his
stay at the University of Osnabriick. The work of C. Kitzmann
was supported by the Deutsche Forschungsgemeinschaft (Pe 486/
1). The technical assistance of Susanne Vetter is gratefully
acknowledged.
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(Received October 21, 1996; Accepted July 22, 1997)