Planta 149, 78-90 (1980) Planta
9 by Springer-Verlag 1980
A Biochemical Model of Photosynthetic
CO 2
Assimilation
in Leaves of C 3 Species
G.D. Farquhar
1,
S. von Caemmerer
1,
and J.A. Berry 2
1 Department of Environmental Biology, Research School of Biological Sciences, Australian National University, P.O. Box 475, Canberra
City ACT 2601, Australia and
2 Carnegie Institution of Washington, Department of Plant Biology, Stanford, Cal. 94305, USA
Abstract.
Various aspects of the biochemistry of
photosynthetic carbon assimilation in C3 plants are
integrated into a form compatible with studies of gas
exchange in leaves. These aspects include the kinetic
properties of ribulose bisphosphate carboxylase-
oxygenase; the requirements of the photosynthetic
carbon reduction and photorespiratory carbon oxida-
tion cycles for reduced pyridine nucleotides; the de-
pendence of electron transport on photon flux and
the presence of a temperature dependent upper limit
to electron transport. The measurements of gas ex-
change with which the model outputs may be com-
pared include those of the temperature and partial
pressure of
CO2(p(CO2) )
dependencies of quantum
yield, the variation of compensation point with tem-
perature and partial pressure of O2(p(O2)), the de-
pendence of net CO 2 assimilation rate
on p(CO2)
and
irradiance, and the influence of p(CO2) and ir-
radiance on the temperature dependence of assimi-
lation rate.
Key words:
Electron transport - Leaf model - Light
and CO2 assimilation - Ribulose bisphosphate carb-
oxylase-oxygenase - Temperature - Photosynthesis
(C3).
Introduction
The present study aims to integrate current knowl-
edge of the functioning of the biochemical com-
ponents of photosynthetic carbon assimilation in C 3
plants. It results in a model, a further development of
those described by Hall and BjOrkman (1975), Peisker
(1976) and Berry and Farquhar (1978), which SUC-
Abbreviations: RuP2 = ribulose bisphosphate; PGA=3-
phosphoglycerate; C = p (CO2) = partial pressure of CO2 ; O = p (O z)
=partial pressure of 02; PCR=photosynthetic carbon reduc-
tion; PCO=photorespiratory carbon oxidation
ceeds in relating studies of enzyme kinetics and whole
chain electron transport to those of gas exchange of
whole leaves.
We first describe overall processes in the leaf, then
analyse the partial processes at the organelle level,
and finally attempt to describe the overall system in
terms of its component parts.
Model Development
1. Limitations to the Rate of Assimilation of
CO 2
1.1. Dark Reactions. The photosynthetic carbon re-
duction (PCR) and photorespiratory carbon oxida-
tion (PCO) cycles are linked by an enzyme common
to both, viz. ribulose bispho@hate (RuP2) carboxy-
lase-oxygenase (Fig. 1). In the PCO cycle, when the
enzyme catalyses the reaction of RuP 2 with one mol
of O2, 0.5 mol of CO 2 is released. Thus the net rate of
CO 2 assimilation is
A = Vc- 0.5 Vo-R ? (1)
where V c is the rate of carboxylation, and V o the rate
of oxygenation. The symbol R e represents CO 2 evolu-
tion from mitochondria in the light, other than that
associated with the PCO cycle. Mitochondrial oxy-
gen uptake and electron transport associated with
normal dark respiration are likely to be inhibited by
illumination but CO 2 release may continue (Graham
1979). For want of a better term we call this "dark
respiration".
Graham (1979) has reviewed the conflicting evidence
on the effects of light on "dark respiration", and
concluded himself that dark respiration in the light is
a significant part of the carbon lost by the plant. We
assume no effect of light on the CO 2 flux, Re, but
recognise that this is an oversimplification.
1 Symbols and units are listed at the end of this article
0032-0935/80/0149/0078/$02.60
G.D. Farquhar et al.: CO2 Assimilation in C3 Species 79
I
".
electron
"',,
transport
0.Sflb PGA ,,
Ru P2 r :ri;:Ynla *PGA " ~ f 2~-2,~-~
9 i 3 ~
. ,, )
(
I I,-0.5,11c.~o~ [
Fig. 1. Simplified photosynthetic carbon reduction
(PCR) and photorespiratory carbon oxidation
(PCO) cycles, with cycle for regeneration of
NADPH linked to light driven electron transport.
For each carboxylation, ~b oxygenations occur. Gly
denotes glycine, Fd- denotes reduced ferredoxin
(assumed equivalent to 1/2 NADPH), PGA denotes
3-phosphoglycerate, PGIA phosphoglycolate. At
the compensation point q~ = 2
If the enzyme reaction is ordered with RuP 2
binding first, carboxylation and oxygenation velo-
cities are given by (Farquhar 1979)
C R
c +/q(1 + o//;o)R+K;
C/K~ R/K' r
~-
gcmax 1 +
C/K c + O/K o" 1 + R/K'y
(2)
and
O R
V~ V~ O-nt- Ko(l q- C/Kc) R + K;
O/K o R/K'•
= V~ 1 + C/Kc+O/K o "1 +R/K;
(3)
where V~m,, and
Vomax
are the maximum velocities of
the carboxylase and oxygenase, respectively, C and O
are the partial pressures of CO2 and 02,
p(CO2)
and
p(O2) respectively, in equilibrium with their dissolved
concentrations in the chloroplast stroma; K C and
K o
are the Michaelis-Menten constants for CO 2 and 02;
R is the concentration of free (unbound) RuP 2 and
K'~ is the effective Michaelis-Menten constant for
RuP 2.
Dividing (3) by (2) we obtain ~b, the ratio of
oxygenation to carboxylation.
~=~cC=romax O/Ko
Vcma x
"C/Kc
(4)
For each carboxylation, q5 oxygenations occur.
We see that several factors may limit the rate of
carboxylation in vivo. Firstly the relative partial pres-
sures of CO2 and 02 determine the partitioning be-
tween carboxylation and oxygenation. Secondly, the
amount of activated enzyme present determines the
maximum velocity, V~r~, x (and, therefore
Vom,x ).
Third-
ly, the rate of regeneration of acceptor, RuP 2,
determines the concentration of free RuP 2. The re-
generation rate itself is usually limited by the supply
of NADPH and ATP.
1.2. NADPH and ATP Requirements.
Each carbocy-
lation produces two molecules of 3-phosphoglycerate
(PGA); each PGA is first phosphorylated and then
reduced, requiring one ATP and one NADPH mo-
lecule. Each oxygenation produces one molecule of
PGA and one of phosphoglycolate. In turn one mole
of phosphoglycolate produces 0.5 tool of PGA. Thus:
rate of PGA production =2 V~+ 1.5
V o
(5)
The events that follow oxygenation of 1 tool
RuP 2 include release and refixation of 0.5 mol am-
monia (Woo et al. 1978; Keys et al. 1978), a sequence
which requires the use of 2Fd- (reduced ferredoxin)
per NH +. The PCO cycle therefore appears to have
an additional cost of 0.5 NADPH for each 0.5 NH~-
refixed. Thus:
rate of NADPH consumption=rate of PGA pro-
duction
+ rate of NH~ refixation
=(2 V~+ 1.5 Vo) +0.5
Vo
Using (4)
= (2 + 2 ~b) V~. (6)
It has similarly been shown (Berry and Farquhar
1978), that
rate of consumption of ATP =(3 + 3.5q~) ~ (7)
1.3. Photosynthetic Electron Transport.
The rates of
production of NADPH and ATP depend on the rate
of photosynthetic electron transport. Two electrons
are required for the generation of one NADPH. Thus
from Eq. (6) an electron transport rate of (4 + 4~b) V~ is
required to meet the rate of NADPH consumption.
ATP is produced by photophosphorylation of ADP,
and controversy exists over linkage with electron
80 G.D. Farquhar et al. : CO2 Assimilation in Ca Species
transport; the number of ATP produced per electron
pair (ATP/2e) is variously estimated as 1, 1.33 or 2
and may be flexible (Heber 1976). Using Eq. (7) the
rate of electron transport required to sustain the
necessary ATP use is (6 + 7 q~) V~ + (ATP/2e).
A limitation to electron transport occurs when
insufficient quanta are absorbed. If one quantum
must be absorbed by each of the two photosystems to
move an electron from the level of
HzO to
the level
of NADP +, the potential rate of electron transport,
J, will be related to the absorbed photon flux, I, by
J =0.5(1 -J)I (8)
where f is the fraction of light lost as absorption by
other than the chloroplast lamellae. The fractionfmay
increase with leaf thickness. There is an upper limit
to photosynthetic electron transport which may limit
photosynthesis in vivo (Armand et al. 1978). Intrinsic
properties of the thylakoid membranes, such as the
pool sizes of intersystem intermediates place one
limitation,
"/max, on the maximum rate of electron
transport. Ymax is lower in shade leaves than in sun
leaves (Bj6rkman et al. 1972). Equation (8) can only
hold when d <Jmax" The incorporation of this upper
bound is discussed in an appendix. We later discuss
further limitations on electron transport, imposed by
insuffcient concentrations of ADP and NADP +.
Following Berry and Farquhar (1978), we could
write that the velocity of carboxylation is either at
the RuP 2 saturated rate, Wc, where
C
W~= V~ma~ C+K~(1
+O/Ko)
(9)
or, limited by RuP 2, at the rate, J'.
J' is the maximum rate of carboxylation allowed
by the electron transport. It is determined by the
potential rate of electron transfer, J, at the particular
irradiance and temperature and is derived from Eq.
(6) as
J
S' =. . (10)
2(2+2~b)
(The additional 2 in the denominator arises from the
requirement of two electrons per NADPH.)
Thus
Vc = min { W~, d'} (11)
where rain { } denotes 'minimum of'.
However, the actual rate will be less than min
{W~,J'}. Specifically, the availability of ADP and
NADP +, which is dependent on the dark reactions of
carbon assimilation, also influences the rates of ATP
and NADPH production. West and Wiskich (1968)
coined the term 'photosynthetic control' for the ADP
dependence of electron transport and associated oxy-
gen production.
2. Integrating the Rate-Limiting Processes
at the Chloroplast Level
We will now follow Hall and BjSrkman (1975) and
Peisker (1976) and treat the system as three interact-
ing cycles - the PCR and PCO cycles and one for the
input of chemical energy by the photosystems. Eq.
(11) will emerge as a limiting case of perfect coupling
of the photochemical cycle with the other two. In
order to do this we first consider the fluxes at the
level of the individual organelles. We use lower case
letters for fluxes expressed on this basis.
2.1. RuP 2 Carboxylase-Oxygenase.
In Appendix 2, it
is shown that at the high enzyme concentrations
found in vivo, the rate of carboxylation, vc, is related
to the total concentration (free plus bound) of RuP2,
R t,
by
v c = k' c R t (12)
where
kr C (13)
k'c - c + Kc(1 + O/Ko)
kc is the turnover number of the carboxylase site,
which is 1.7 s -1 in purified enzyme from
Atriplex
glabriuscula
at 25 C (Badger and Collatz 1977), and
3.4-3.9 at 30C in freshly prepared crude extracts
from spinach chloroplasts (Badger, pers. comm.). The
disparity is less when the temperature dependence is
taken into account. The present model (see Table 1)
assumes 2.5 s-1 at 25 C (equivalent to 2.2 gmol CO 2
mg carboxylase -1 rain-l). When
Rt>E t,
(the total
concentration of enzyme sites) then
v c = k'~ E,
Thus
G = rain {k'~ Rt, k'r
Et}
(14)
and at saturating partial pressures of CO 2
v .... = rain {k~
R t, k~ Et}.
(15)
The concentration,
Et,
is here taken as 87 gmol
(gcht) -1. Since there are 8 catalytic sites per mo-
lecule, and the carboxylase has a molecular weight of
550,000 (Jensen and Bahr 1977), this corresponds to
6 g carboxylase/gChl. Further, since we use a value
G.D. Farquhar et al.: CO2 Assimilation in C3 Species
Table 1. Kinetic parameters for the activity of RuP z carboxylase-oxygenase. The underlined values are those
used in the present model
81
k c K~ Reference
At 25 C Activation At 25 C Activation
energy energy
(s 1) (J mot 1) (gbar) (J mol 1)
13.7+8" 58,520 810 59,356
750
525
2.5 460
Badger and Collatz (1977)
Laing et al. (1974)
Badger and Andrews (1974)
Freshly ruptured spinach chloroplasts
(Badger, persona/communication)
k o K o
mbar
0.18 k c 58,520 265 35,948 Badger and Collatz (1977)
640 Laing et al. (1974)
0.22 k c 158 Badger and Andrews (1974)
0.21 k c 330
Division by 8 is necessary since sites rather than molecules form the basis of the present treatment
for k C of 2.5 s- 1 at 25 C this corresponds to a maxi-
mum rate,
kcE,,
of 218 gmol (g Chl)-~ s
From Appendix 2,
(16)
where
k o,
the turnover number for the oxygenase, is
0.21 times that of the carboxylase at 25 C (cf 0.22 at
25C determined by Badger and Andrews (1974)).
Thus Eq. (4) may be rewritten as
= k~ O/K~
(17)
k~ c/K/
Using the values in Table l, 4) is 0.27 at 25 C and
partial pressures of CO 2 and
0 2
of 230~tbar and
210mbar respectively, values typical of those inside
leaves of C 3 plants (Wong 1979). The rate of oxy-
genation,
vo,
is given by
G=~vc
(18)
2.2. Pool Sizes.
There is evidence (Heldt 1976) that
the total concentration of phosphate in the chloro-
plast is conserved. Assuming that the total pool of
phosphate in forms other than PGA or RuP 2 is
constant, the sum of [PGA] plus
2R t
(RuP z contains
two phosphates) is constant, at 2Rp, say.
[PGA] +2R t =2Rp. (19)
Rp is the potential concentration of RuP 2 which
would occur if the carboxylase-oxygenase velocity
were zero in the light, i.e. in the absence of CO 2 and
0 2. Collatz (1978) found in
Chlamydomonas rhein-
hardtii
that the concentration of RuP 2 at low partial
pressures of CO 2 and 0 2 was 325 ~tmol (gChl)-1 In
spinach protoplasts he measured a concentration of
100 ~tmol (gChl) -I. In the present model a potential
concentration, Rp, of 300 lamol (g Chl)- 1 is assumed.
The total concentration of pyridine nucleotides in
the chloroplast is assumed constant, at
Nt,
although
it emerges that N t does not appear, even implicitly, in
the general solution (Eq. (33)). Thus
[NADPH] + [NADP+J = N,.
(2o)
2.3. Electron Transport and the Production and Con-
sumption of NADPH.
The potential rate of electron
transport, j, (expressed on a chlorophyll basis as ~tEq
(gChl) -1 s-l), depends only on temperature and
quantum flux. The chosen upper limit, Jmax, placed on
electron transport of 467btEq (gChl)-i s-1
(=l,680gEq (mgChl)-lh -1) at 25C, derives from
the measurements of Nolan and Smillie (1976) on
chloroplasts of
Hordeum vulgate
(see Fig. 2).
Two electrons plus two protons are required to
convert NADP + to NADPH+H +. The potential
rate of NADPH production is thus
j/2.
In practice,
electron flow and NADPH production will be some-
what limited by the supply of ADP and NADP +.
The present model assumes first order dependence on
82 G.D. Farquhar et al. : CO2 Assimilation in C3 Species
"7
U
400
._.E
-c"
300
"6
200
7~
o
e~
100
o
o
o
?
o
&
A
A
A
A A
o
A
I I I I
0 10 20 30 ~,0
T(C)
Fig. 2. Temperature dependence of the light saturated potential
rate of electron transport, Jm,x, The data are the rates of DCIP
reduction (here doubled to obtain rates of electron transport)
obtained by Nolan and Smillie (1976) in two batches of chloro-
plasts from
Hordeum vulgare.
The smooth curve is given by Eq. (36)
[NADP+], which will be approximately true if the
working concentration of NADP § is similar to the
Michaelis constant for its reduction. Thus:
rate of production of NADPH
= 1/2
(actual
rate of electron transport)
[NADP +3
= 1/2j.
Nt
(21)
As before,
rate of consumption of NADPH =(2+2q~)vc. (22)
Equating the rates of consumption and produc-
tion (Eqs. (21) and (22))
[NADP +] j
(2+ 2qb)v c -
N, 2
and using (20)
Nt-[NADPH] j
N, 2"
Rearranging
[NADPH]
- 1 -(4 + 44)
vJj.
(23)
N
An equivalent argument may be made for ATP:
[ATP3 =1 (6+7qS)v
[ATP] + [-ASP]
(ATP/2e)j"
2.4. Production and Consumption of PGA.
As before,
rate of production of PGA = (2 + 1.54)) v~. (24)
Following Hall and Bj6rkman (1975) and Peisker
(1976) we now assume a simplified model of the
Calvin cyle in which PGA is "reduced" to RuP 2, and
that the reduction of PGA is first order in [PGA]
and in [NADPH]. The maximum rate of reduction,
m, occurs when [PGA] and [NADPH] equal
2Rp
and N~, respectively. Thus
rate of reduction of PGA =[-PGA] [-NADPH]
9 -m.
2 Rp N t
(25)
The parameter, m, a fictional composite from many
reactions, determines the degree of coupling between
the photochemical cycle on the one hand, and PCR
and PCO cycles on the other. In the present outputs,
m is made equal to
2k~E t
(=436 gmol PGA reduced
(gChl) -1 s -1 at 25C). This is sufficiently large to
ensure a reasonable coupling and only minimal limi-
tation to photosynthetic rate9 Once m is large, its
value becomes unimportant, as is true with analogous
parameters in the models of Hall and Bj6rkman
(1975) and Peisker (1976).
Equating the rate of production of PGA with its
rate of reduction (Eqs. (24) and (25))
(2 + 1.5 qS) v c - [-PGA] [NADPH]. m
2R v Nt
and using (19)
=(I_R_~
[-NADPH] m. (26)
\ Rvl
N~
2.5. Calculation of RuP 2 Concentration.
The concen-
tration of total (free plus bound) RuP 2,
R t,
is found
by substituting Eq. (23) in (26) and rearranging
R~= 1 (2+ 1.5q~) v~ 1
R~ 1-(4+44))vc/j m
i.e.
R~ = 1 v c .1 (27)
Rp 1 - vJj' m'