The effects of COz and O, on nonsteady-state photosynthesis following an .... In this study, we examined the effects of O2 and CO2 on ..... substrate for the carbamylation reaction of Rubisco activation .... (a) the conversion of ER to E by activase and (b) the carba- ... imbalances in Calvin-cycle intermediates during nonsteady-.
Plant Physiol. (1993) 102: 859-866
Effects of O2and C 0 2 on Nonsteady-State Photosynthesis' Further Evidence for Ribulose-l,5-Bisphosphate Carboxylase/Oxygenase Limitation Keith A. Mott* and lan E. Woodrow Biology Department, Utah State University, Logan, Utah 84322-5303 (K.A.M.); and Botany Department, James Cook University of North Queensland, Townsville, Qld 481 1, Australia (I.E.W.)
The time course for photosynthesis following an increase in PPFD can be divided into at least three phases (Pearcy, 1990). The first of these phases occurs within approximately the initial 1 min of the increase in PPFD and reflects the buildup of R and other substrates in the photosynthetic carbon reduction cycle (Walker, 1976; Sassenrath-Cole and Pearcy, 1992). The second phase is slower, occumng over approximately 10 min, and is primarily limited by the rate at which Rubisco is converted from an inactive to an active
form (Seemann et al., 1988; Woodrow and Mott, 1989,1992). The third and slowest phase reflects an increase in ci caused by light-dependent stomatal opening (Kirschbaum and Pearcy, 1988). The second of these phases, the Rubisco phase, has been shown to approximate a first-order process (Woodrow and Mott, 1989). It can be mathematically separated from the first and third phases by normalizing the photosynthetic rate to a constant ci value and analyzing the approach of normalized photosynthesis to a steady state on a semilogarithmic plot (Woodrow and Mott, 1989). On this semilogarithmic plot, the Rubisco phase appears as a linear portion of the time course that begins approximately 1 min after the increase in PPFD and has a T of a few minutes. Evidence that this phase is limited primarily by Rubisco activation has been discussed previously (Woodrow and Mott, 1992). The characterization of the second phase has allowed researchers to use it to probe the kinetics of Rubisco activation in whole leaves. Jackson et al. (1991), for example, showed that Rubisco activation is slower in leaves starting in darkness than in leaves starting in low PPFD. This phenomenon has been attributed to the existence of two, sequential, lightdependent processes in the activation of Rubisco (Woodrow and Mott, 1992). The first of these processes saturates at low PPFD values (approximately 200 Fmol m-' s-'); the second saturates in parallel with the rate of photosynthesis. Analyses of Rubisco and Rubisco activase activities in crude extracts from freeze-clamped leaves (Lan et al., 1992) suggest that the first of these two processes is light-dependent activation of Rubisco activase and that the second process is the activation of Rubisco, some portion of which is presumably catalyzed by activase (Portis, 1990; Wang and Portis, 1992). Although severa1 other studies have suggested an effect of light on the rate of Rubisco activation (Campbell and Ogren, 1990a, 1990b), the role of changes in activase activity in this effect is controversial (Campbell and Ogren, 1992). The two-step process proposed by Woodrow and Mott (1992) is diagrammed below; the asterisk denotes the active
' This work supported by grant No. 91-37306-6326 from the U.S. Department of Agriculture, Cooperative State Research Service, by the Utah Agricultura1 Experiment Station, and by an Australian Research Council grant and Senior Research Fellowship to I.E.W. * Corresponding author; fax 1-801-750-1575.
Abbreviations: A, photosynthesis rate; A*, normalized photosynthesis rate; A;, steady-state normalized photosynthesisrate; ci, intercellular COZconcentration; E, inactive Rubsico; ECM, carbamylated (activated) Rubisco; ER, inactive-Rubisco:Rcomplex; R, ribulose-1,5bisphosphate; T, relaxation time.
The effects of COz and O , on nonsteady-state photosynthesis following an increase in photosynthetic photon flux density (PPFD) were examined in Spinacia oleracea to investigate the hypotheses that (a) a slow exponential phase (the ribulose-1,5-bisphosphate carboxylase/oxygenase [Rubisco] phase) of nonsteady-state photosynthesis is primarily limited by Rubisco activity and (b) Rubisco activation involves two sequential, light-dependent processes as described in a previous study (I.E. Woodrow, K.A. Mott 119921 Plant Physiol 99: 298-303). Photosynthesis was found to be sensitive to 0,during the Rubisco phase in the approach of photosynthesisto steady state. Analyses of this sensitivity to O, showed that the control coefficient for Rubisco was approximately equal to 1 during this phase, suggesting that Rubisco was the primary limitation to photosynthesis. O2had almost no effect on the kinetics (described using a relaxation time, T ) of the Rubisco phase for leaves starting in darkness or for leaves starting in low PPFD, but T was substantially higher in the former case. COZ was found to affect both the rate of photosynthesis and the magnitude of T for the Rubisco phase. The T value for the Rubisco phase was found to be negatively correlated with intercellular CO, concentration (c,), and leaves starting in darkness had higher values of T at any c, than leaves starting in low PPFD. The effects of CO, and Oz on the Rubisco phase are consistent with the existence of two sequential, lightdependent processes in the activation of Rubisco if neither process i s sensitive to 0,and only the second process i s sensitive to COz. The implications of the data for the mechanism of Rubisco activation and for the effects of stomatal condudance on nonsteadystate photosynthesisare discussed.
859
860
Plant Physiol. Vol. 102, 1993
Mott and Woodrow
form of activase, and ER and ECMR are inactive and active forms of Rubisco, respectively. activase + activase* (saturates at low PPFD)
C 0 2 + Mg2++ ER S ECMR (saturates at high PPFD) ectiuase*
According to this mechanism, light-dependent Rubisco activation in leaves starting from darkness proceeds slowly because both processes must occur sequentially to form ECMR. Light-dependent activation of Rubisco in leaves starting at low PPFD, however, is more rapid because activase is substantially in the active form, and Rubisco activation involves only the second process. The mechanism proposed above allows the formulation of severa1 testable hypotheses conceming the effects of O2 and C 0 2 on the kinetics of the slow, exponential phase (the Rubisco phase) of nonsteady-state photosynthesis. First, if photosynthesis rate is indeed limited primarily by Rubisco during the exponential phase, it should be sensitive to 0 2 and C 0 2 during this phase. Furthermore, because the kinetic constants for O2 and COZfor Rubisco are known, the degree of Rubisco limitation can be calculated from the sensitivity of photosynthesis rate to changes in the concentration of these gases (Woodrow and Mott, 1988). Second, because COZ is a substrate for the second process in Rubisco activation (diagrammed above), the rate of Rubisco activation should be sensitive to C 0 2 , and this should be detectable as an effect on the kinetics of the Rubisco phase: Because O2 is not involved in the activation process, the rate of activation should be relatively insensitive to changes in 0 2 concentration. Finally, the relative difference in activation rate between leaves starting from darkness and those starting in low PPFD should be unaffected by C 0 2 or 02, because, according to our hypothesis, the first process (activase activation) involves neither of these gases. In this study, we examined the effects of O2 and CO2 on nonsteady-state photosynthesis to investigate the hypotheses that (a) Rubisco activity substantially limits the rate of photosynthesis during the slow exponential phase of nonsteadystate photosynthesis and (b) Rubisco activation in leaves involves two, sequential, light-dependent processes as proposed in previous studies (Woodrow and Mott, 1992; Lan et al., 1992).
MATERIALS A N D METHODS Plant Material and Cas Exchange
Spinach (Spinacia oleracea L.) plants were grown hydroponically in aerated, half-strength Hoagland solution. The PPFD was approximately 350 pmol m-' s-' with 10 h of light daily. Day and night temperatures were 25 and 2OoC, respectively. Gas-exchange measurements were made with a singlepass system that was described previously (Mott, 1988). In a11 experiments the leaf temperature was 25 & 0.3OC, and the difference in water mo1 fraction between the leaf and the air at the leaf surface was 15.5 k 1.0 mbar bar-'. For each timecourse experiment the leaf was kept at the initial conditions
(i.e. darkness ar 180 pmol m-'s-') for at least 1 h before the PPFD was increased to 1200 pmol m-' s-l in a single step. Gas-exchange data were then recorded at 5-s intervals for approximately 10 min. The leaf was kept at 1200 pmol m-' s-' for at least 1 h to allow determination of steady-state values; it was then retumed to 180 pmol m-' s-l or darkness for 1 h before ihe next experiment. Photosynthesis was normalized to a c1 of 250 pL L-' by assuming a linear relationship between A and c, that passed through the C 0 2 compensation point (Woodrow and Mott, 1989). This normalization procedure removed the effect of c, on photosynthesis and allowed quantification of the approach of the A versus c, curve to steady state despite changes in c, during the time course. The selection of 250 fiL L-' for normalization was arbitrary and did not affect the kinetics of the approach to steady state.
Data Analysis
The T for the Rubisco phase was determined by pbtting normalized photosynthesis (A*) versus time. These graphs showed a distinct linear region beginning approximatdy 2 min after the increase in PPFD, and the slope of this portion was determined by linear regression of the data between 2 and 6 min. The value of T was calculated as:
The c, value for each time course was determined by averaging the c, values between 2 and 6 min; the value of c, typically varied less than 20 pL L-' during this period. A flux control coefficient (Kacser and Bums, 1973), C$ was used to describe the degree to which Rubisco limited photosynthesis rate during the slow (Rubisco) phase. This cofefficient is defined as: A
cR
-
dA (m)
- d[E] A
where A is the assimilation rate and [E] is the concentra tion of Rubisco active sites. C$ is approximately the percentage change in A that would result from a 1% increase in [E]. Values of about 0.8 have been measured during steady-state photosynthesis (at a saturating PPFD (Woodrow and Mott, 1988). The control coefficient was calculated from the sensitivity of the assimilation rate during the slow phase to [O2].This sensitivity was expressed as a response coefficient, R& as:
In this equation AA/A [O21 is the slope of an A versus [O*] plot at 21% 02,and A is the assimilation rate also at 21% 0 2 .
Effects of O2 and C 0 2 on Nonsteady-State Photosynthesis
86 1
The slope of A versus [O2]was calculated from assimilation rates measured at 18, 21, and 24% 02. The following equations were then used to calculate Cg from RG,:
where
I
I
I
I
1
O
I
4
8
time (min)
Y = K,Ko
+ K0ci + K.4021,
and K, (270 pbar), K, (400 mbar), and S,I (2360 bar bar-’) are the Rubisco Michaelis constants for C 0 2 , 02,and the relative specificity, respectively. The values in parentheses are those that were used in calculating C .; The validity of these equations, which have been discussed in detail elsewhere (Woodrow and Mott, 1988), depends on the assumption that (a) R is largely saturating during the slow phase (Seemann et al., 1988; Woodrow and Mott, 1989) and (b) changes in the amount of active Rubisco or the concentrations of Rubisco effectors do not alter the Rubisco Michaelis constants for CO2 and O2 (Farquhar, 1989). RESULTS Sensitivity of Nonsteady-State Photosynthesis to O2
The effect of O2 on the kinetics of the Rubisco phase was assessed by determining photosynthesis time courses following a rapid PPFD transition from 180 to 1200 pmol m-’ s-’ at a ci of 175 f 20 pL L-’ and at O2 concentrations between 5 and 24%. Two representative time courses are shown in Figure la. The results of these experiments show that the rate of CO, assimilation was sensitive to O2 during the entire time course. A similar pattern was observed when leaves were held in darkness for 1 h before exposure to a photon flux density of 1200 pmol m-’ s-’, but the approach to a steady state was slower than for leaves that started from 180 pmol m-’ s-’ (see below). Semilogarithmic plots of normalized assimilation versus time showed that the increase in assimilation rate became
Figure 1. Time courses for photosynthesis at at 5 and 21% O2 and a c, of 175 +20 pL L-’ following an increase in PPFD from 180 to 1200 pmol m-’ s-’. a, CO, assimilation rate (A) as a function of time. b, A.semilogarithmic plot of the difference between the A* and maximum A; as a function of time. The linear portion of the
semilogarithmic plot reflects an exponential phase in the time come that is believed to be limited primarily by Rubisco, and the slope of this linear portion is equal to the negative reciproca1 of the 7 for Rubisco activation. approximately exponential after 1 to 2 min at the higher PPFD under a11 O2regimens (Fig. lb). The 7 for the exponential phase, which was calculated from the slope of the linear portion of the semilogarithmic plot (see “Materialsand Methods“), was relatively constant at a value of approximately 3.5 min over the range of O2 concentrations tested (Figs. l b and 2). Similar experiments for dark-to-high PPFD time courses showed r to be approximately constant at a value of about 5 min over the same range of O2 concentrations (Fig. 2). Low-to-high PPFD time courses at 18, 21, and 24% 0 2 were then used to calculate the sensitivity of the assimilation rate to O2 (expressed here as a response coefficient; see “Materials and Methods”) at each time point during the approach to steady state. From this, the degree to which Rubisco activity limits the rate of CO, assimilation was calculated (expressed as a control coefficient; see “Materialsand Methods“). The control coefficientfor Rubisco was more than 1 during the first 1 to 2 min of the time course but had a value of approximately unity throughout the slow, exponential increase in assimilation rate (Fig. 3). There is some indication that the control coefficient declined somewhat as the steady state was approached. The calculated control coefficients during approximately the first minute following the increase in PPFD were found to be highly inaccurate because of division by the low assimilation rate terms.
I
Plant Physiol. Vol. 102, 1993
Mott and Woodrow
862
n
7ul 12 N I
E
c-(
o
3
6
v
4
O
darkness
O
I
I
I
I
10
O
I
20 2
%02 n
Figure 2. The 7 for Rubisco activation as a function of O2 concentration. O, Data for leaves exposed to an increase in PPFD from 180 to 1200 j " l m-* s-'; O, data for leaves exposed to an increase in PPFD from darkness to 1200 pmol m-'s-'. The 7 was determined as described in the text and in the legend to Figure 1 . The lines show linear regressions of the data.
4
*-I
4
v
d
-
0
O
The effect of C 0 2 on the Rubisco phase was determined from time courses of photosynthesis following an increase in PPFD at 21% O2 and ci values between 70 and 300 p L L-'; data from two representative experiments are shown in Figure 4a. These experiments showed that at different COZ concentrations, assimilation rates were different at a11 times during the approach to steady state (Fig. 4a). This difference, however, was not simply due to the effect of C 0 2 on the catalytic velocity of Rubisco; it was also due to an effect of C 0 2 on the T for the Rubisco phase. This is evident from the semilogarithmic plots of normalized photosynthesis versus time (Fig. 4b), which show that the approach to steady state was substantially slower for a ci of 120 p L L-' than for a ci
..
Figure 4. Time courses for photosynthesis at two C 0 2 concentrations and at 21% Oz. a, C 0 2 assimilation rate ( A ) as a function of time; b, a semilogarithmic plot of the difference between the A* and maximum Ar as a function of time. The 7 for Rubisco activation was determined as described in the text and in the legend to Figure 1.
of 270 pL L-'. Experiments in which a wide range of ci values were used showed that the T for the Rubisco phase was negatively correlated with ci, but at any given ci, the value of T was higher for the dark-to-1200 rmol m-' s-' experinnents than for the 180-to-1200pmol m-'s-' experiments (Fig. 5a). A plot of 1 / ~ versus ci revealed an approximately linear relationship between these two parameters for both transients, but the slope of the relationship was higher for the 180-to-1200pmol m-' s-' experiments than for the dark-to1200 pmol m-'s-' experiments (Fig. 5b). DISCUSSION
2 -
0 I O
4
time (min)
Sensitivity of Nonsteady-State Photosynthesis to COz
4 t
2
I
I
4
I
I
8
time (min) Figure 3. Time course for the control coefficient for Rubisco as calculated from data similar to that in Figure 1 but at 18, 21, and 24% O*. The meaning and derivation of the control coefficient are discussed in the text.
The effect of O2on assimilation rate in C3 plants has been attributed primarily to the role of O2as a competitive inhibitor of CO2 on Rubisco (Farquhar, 1989). If this is the case, the approach of assimilation to steady state following an incyease in PPFD should be sensitive to O2 during the period of time that the flux rate is limited by Rubisco activity, and it should be less sensitive to O2 when other processes are limiting. If it is assumed that (a) variations in Oz concentration oveir the range used in these experiments affect the assimilation rate through effects on the carboxylase and oxygenase actiirities of Rubisco and (b) the T of the slow phase does not vary with O2 concentration (see below), then the measured sensitivity of assimilation to O2 (Fig. la) can be compared to the smsitivity predicted from the Rubisco kinetic equation to provide a measure of the degree to which Rubisco activity detemines
Effects of O2and COz on Nonsteady-State Photosynthesis
a
8 8
o O
4
=. . . .
0
0
- -
darkness
O
/ I
I
I
b
O 0
0.4
.O
oo
.
0.0
O
1O0
200
300
ci (p11-1) Figure 5. The T for Rubisco activation and its reciprocal as a function of the average c, during the Rubisco phase. O, Data for leaves subjected to an increase in PPFD from 180 to 1200 pmol m-2 s-'; O, data for leaves subjected to an increase in PPFD from darkness to 1200 pmol m-'s-'. T h e T was determined as described in the text and in the legend to Figure 1. The lines show linear regressions of the data.
the assimilation rate. We have expressed this degree of nonsteady-state flux limitation as a control coefficient, which is defined as:
where A is the C 0 2assimilation rate and [E] is the concentration of Rubisco active sites. The control coefficient gives the sensitivity of the C 0 2 assimilation rate (expressed as a proportion) to an infinitesimal change in the concentration of Rubisco active sites (also expressed as a proportion). Thus, a control coefficient of unity indicates that the assimilation rate is directly proportional to the concentration of active sites, whereas a coefficient of zero indicates that a change in the concentration of active sites would have no effect on the flux. With this interpretation, the data presented in Figure 3 suggest that assimilation rate is limited primarily by Rubisco during the slow exponential phase that occurs 1 to 2 min after an increase in PPFD. This conclusion supports the hypothesis of Seemann et al. (1988) that Rubisco can substantially limit nonsteady-state photosynthesis following an increase in PPFD, and it specifically supports the analyses of Woodrow and Mott (1989), indicating that the slow exponentia1 phase of nonsteady-state photosynthesis is limited primarily by the rate of Rubisco activation. The fact that T for the Rubisco phase is insensitive to O2
863
(Figs. l b and 3) is consistent with the fact that the carbamylation reaction for activation of Rubisco does not involve 02. Although previous studies have shown effects of O2on the steady-state activation state of Rubisco, our data suggest that the kinetics of the approach to steady state are not affected by 02. The insensitivity of T to O2 for both dark-to-high PPFD and low-to-high PPFD transitions (Fig. 2) is consistent with the two sequential processes in the activation of Rubisco that have been proposed by Woodrow and Mott (1992), because neither process should depend on 0 2 . The difference in T between dark-to-high PPFD experiments and low-tohigh PPFD experiments agrees well with previously published data (Jackson et al., 1991; Woodrow and Mott, 1992). The data for the sensitivity of nonsteady-state photosynthesis to COz are more complex than those for O2 because both the rate of photosynthesis and the kinetics of its approach to steady state were affected by CO2 (Fig. 4, a and b). Therefore, the sensitivity of photosynthesis rate to C 0 2 could not be used to determine quantitatively the degree of Rubisco limitation during the nonsteady state, as was done with O2 (see above). On a simple, qualitative basis, the decrease in T with increasing ci (Fig. 5a) is consistent with the fact that C 0 2 is a substrate for the carbamylation reaction of Rubisco activation (Miziorko and Lorimer, 1983). Quantitatively, the reciprocal of T can be taken as an approximate estimate of the C 0 2 rate constant for the carbamylation (activation) reaction. A plot of these values against ci for low-to-high PPFD transitions reveals an approximately linear relationship that passes close to the origin (Fig. 5b). Because 300 pL L-' C 0 2 in the gas phase is approximately equivalent to 10 PM C 0 2 in aqueous solution, a11 of the C 0 2 concentrations used in this study were well below the apparent K , (C02) for activase-catalyzed Rubisco activation of 53 p~ reported by Lan and Mott (1991). Therefore, the linear relationship between C 0 2 and 1 / ~ shown in Figure 5b is consistent with the results of that study. Experiments at higher ci values would have provided more information in this regard. However, models of steadystate photosynthesis (Farquhar, 1989) suggest that at ci values greater than about 300 pL L-', it is likely that other processes (such as R regeneration or Suc synthesis) would begin to limit the rate of photosynthesis before steady state was reached. It was, therefore, not possible to obtain an accurate estimate of T from photosynthesis time courses at these higher cl values. Values of 1 / ~ for dark-to-high PPFD experiments also yielded an approximately linear relationship when plotted versus ci, but, for any ci value, activation rate was slower starting from darkness than starting from low PPFD. These data are consistent with the existence of two sequential processes in Rubisco activation of which the first is not C 0 2 dependent and second is CO2 dependent (Woodrow and Mott, 1992). To interpret mechanistically the effect of ci on the T for the Rubisco phase, consider the two models for Rubisco activation shown in Figure 6 . In model I, activase directly catalyzes the carbamylation of the ER, and C 0 2 is a substrate for activase. This model is consistent with apparent MichaelisMenten kinetics for C 0 2and activase that have been reported previously. If C 0 2 is a true substrate of activase (model I),
Plant Physiol. Vol. 102, 1993
Mott and Woodrow
864
1
ATP
' ADP
\
M+C+ER
I
MODELI
+ Pi
>ECMR
activase
'b/
LC
'on
M+C+E,
+
\
R
R
I
MODELII
I
24p
.ikm
ER
ATP
ECMR
activase
ADP
+ Pi
M+C+E
+ R
ECM
+
'i
,
'k
'i
\
ECM
+ R
Figure 6. Two possible mechanisms for activase-catalyzed Rubisco activation. In the first model, activase directly catalyzes the addition of COz and Mg2+to the ER form of Rubisco. In t h e second model, activase catalyzes the removal of R from E, which is subsequently carbamylated in a noncatalyzed reaction. 60th models predict that Rubisco activation rate should be linearly dependent o n COz concentration at low C 0 2 concentrations (see "Discussion" and "A p pend ix").
then the r for the Rubisco phase in leaves subjected to a lowto-high PPFD transition would directly reflect the K,(C02) for activase. Results of recent studies, however, suggest that activase catalyzes only the remova1 of R from the ER and that activation proceeds through the uncatalyzed carbamylation reaction (Wang and Portis, 1992). This is shown in model I1 (Fig. 6). At first glance, model I1 does not appear consistent with apparent Michaelis-Menten kinetics for COz, but in the 'Appendix" of this paper we derive the apparent kinetic equation for activase if it simply removes R from ER. This analysis reveals that CO2 could appear to obey MichaelisMenten kinetics despite the fact that it was not a true substrate of the activase-catalyzed reaction. Thus, the linear relationship between 1 / and ~ ciis consistent with the reported value for the apparent K,(CO,) and with either model described here for activase action. It should be noted, however, that for model 11, the apparent K,(CO,) would be a function of the R concentration, the rate constant for recombination of E and R, and the overall rate constant for carbamylation of E (see 'Appendix" and Portis, 1990). In model I1 there are two slow processes that could determine the value of 7:
(a) the conversion of ER to E by activase and (b) the carbamylation of E to form ECM. Therefore, at low COz concentrations and high activase activities, it is possible that r could reflect primariby the k& reaction. The dependence of Rubisco activation rate on COz has physiological as well as mechanistic implications. From a physiological s tandpoint, this finding indicates that Rubisco activation will be slower in leaves with low stomatal conductance than in leaves with open stomata. Thus, a leaf that can maintain a relatively high stomatal conductance during a prolonged "darkfleck" (long enough for Rubisco to substantially deactivate) can respond more rapidly to a subsequent sunfleck than c'an a leaf with closed stomata. On one hand, this effect should allow the leaf with more open stomata to gain substantially more COz during sunflecks; on the other hand, the effect may serve to coordinate Rubisco activation with stomatal opening during sunflecks, thus preventing imbalances in Calvin-cycle intermediates during nonsteadystate photosynthesis. In summary, the results reported from this study support the hypothesis that Rubisco is the primary limitation to photosynthesis during the slow exponential phase of nonsteady-state photosynthesis following an increase in PPFD. Furthermore, the data are consistent with the two sequential, light-dependent processes in Rubisco activation that were proposed in previous studies. Finally, the data show that the kinetics of the Rubisco phase are CO, dependent, suggesting a second role for stomata in determining the approach of photosynthesis to steady state following an increase in PPFD. APPENDIX Kinetics of Mechanism I
Two models describing the interconversion of catalyti!cally active and inactive forms of Rubisco are presented in Figure 6. According to model I, Rubisco activase can catalytically carbamylate the inactive (ER) form of Rubisco using .ATE', COz, and Mg2+.If we assume that throughout the activation process the concentration of R is high enough such that [ER] >> [E] (Woodrow and Mott, 1989), then activation will proceed predominantly according to the reaction: C02
+ Mg2++ nATP + ER
.lCtlVaSe
+ ECMR
+ nADP + nP,
At constant concentrations of COz, Mg2+, and ATP, the activation velocity can be described as follows (Lan and Mott, 1989):
where v is the rate of Rubisco activation and V",ppand K X are the apparent maximum catalytic velocity and Michaelis constant for ER, respectively. If the rate of the reaction decreases with time because of depletion of the substrate ER alone, then an expression for [ECMR] as a function of time can be derived by integrating Equation 1 and then expressing the logarithmic term in the solution as a power series in [ECMR]/[ER], (the subscript o indicates the initial [ER]). The resulting polynomial function of Rubisco activation over time may, under certain circumstances, be approximated
Effects of O2and CO, o n Nonsteady-State Photosynthesis by an exponential function of the form used here to analyze the gas-exchange transients. However, because Ka,sP
